Lecture_07_DefConcept

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14_Lecture_Presentation

– Temporal isolation
– Habitat isolation
– Behavioral isolation – Mechanical isolation
– Gametic isolation
© 2010 Pearson Education, Inc.
PREZYGOTIC BARRIERS Temporal Isolation Habitat Isolation
Sterile next-generation rice hybrid
Figure 14.5c
Mechanisms of Speciation
• A key event in the potential origin of a species occurs when a population is severed from other populations of the parent species.
• Macroevolution:
– Encompasses the major biological changes evident in the fossil record
– Includes the formation of new species
© 2010 Pearson Education, Inc.
© 2010 Pearson Education, Inc.
Allopatric speciation
Simpatric speciation
Figure 14.6
Allopatric Speciation
• Geologic processes can:
– Fragment a population into two or more isolated populations

Lecture 7

3. Four types of market structure
i) Perfect competition: Firms produce identical products with price set by the impersonal forces of supply and demand. ii) Monopolistic competition: Firms produce differentiated products. As each firm enjoys some brand loyalty and is able to set its own price. But: The availability of substitute good limits the degree of discretion in price-setting; The lack of entry barrier means no limit of new comers into the market, leading to the elimination of economic profit in the long run.
• HHI (Hirschman-Herfindhal Index) is sensitive to the problem of size and competition. It is the sum of the squared market share for all firms in the industry (usually expressed as %). Maximum value of HHI = 100 x 100 = 10,000 Minimum value of HHI 0 0.5 x 0.5 + 0.3 x 0.3 + …+ 0.01 x 0.01 Expressed in % = HHI value/10,000 x 100% We must know the market share of every firm, not just the top 4 or 8 firms.

Lecture 07

5
Examples and Definition
Example. Let
S {( x1 , x2 , x3 )T | x1 x2 } .
S
is
nonempty
since
x (1,1,0)T S . To show S is a subspace of R 3 , we need to verify that the
(a, a, b)T (c, c, d )T (a c, a c, b d )T S
Since S is nonempty and satisfies the two closure conditions, it follows that S is a subspace of R 3 .
is called the span of v1 , v 2 ,
Span(v1 , v 2 ,
, vn ) . , v n are elements of a vector space V , then Span(v1 , v 2 , , vn )
Theorem. If v1 , v 2 , is a subspace of V mp; Linear Independent
1
Examples and Definition
Given a vector space, it is often possible to form another vector space by taking a subset S of V and using the operations of V . Since V is a vector space, the operations of addition and scalar multiplication always produce another vector in

Lecture 7 DB

CONTAINS
PART
• part number • part description • unit cost
Generalisation
NAME ADDRESS EMPLOYEE NO. EMPLOYEE DATE HIRED
ISA
ISA
ISA
HOURLY EMPLOYEE
SALARIED EMPLOYEE
CONSULTANT
• EMPLOYEE NO •HOURLY RATE
•EMPLOYEE NO •ANNUAL SALARY •STOCK OPTION
•EMPLOYEE NO •CONTACT NO. •DAILY RATE
Data Modelling Exercise
University Student Recreation Centre Database Students can only use the centre if they have paid their recreation fees in full. The centre will also allow a faculty to purchase a membership as well. Members are allowed to check out sports equipment such as basketballs, softball bats and balls, tennis rackets, badminton rackets and table tennis rackets that can be used at the facility. When the members check out equipment, an equipment-issue form is completed listing the membership number and equipment being used. This form must list at least one piece of equipment in order to be retained in the file. Otherwise it is discarded. A member of staff is employed to monitor the checkout and the use of the sporting equipment. Every employee is assigned to one of two departments: maintenance or general staff. The centre has 10 tennis courts. These courts may be reserved up to one week in advance. Reservations can be made via the equipment checkout window. The centre also operates a small accessory shop where some sporting equipment and clothing is sold. The sporting goods include tennis balls, table tennis balls, bandages, etc. Sportswear bearing the university emblem and mascot as well as a limited assortment of some name-brand sportswear are sold. Finally, the centre sponsors a limited number of classes in officiating various sports . A general rule is that instructors often teach in more than one sport but there is never more than one class offered in a particular sport.

2024年1月浙江省首考普通高等学校招生全国统一考试英语试题

2024年1月浙江省首考普通高等学校招生全国统一考试英语试题一、阅读理解Tom Sawyer Play Is an AdventureA 35-minute hand-clapping, foot-stomping musical version of a Mark Twain favorite returns with this Tall Stacks festival.“Tom Sawyer: A River Adventure” has all the good stuff, including the fence painting, the graveyard, the island and the cave. It is adapted by Joe McDonough, with music by David Kisor. That’s the local stage writing team that creates many of the Children’s Theatre of Cincinnati’s original musicals, along with the holiday family musicals at Ensemble Theatre.This year Nathan Turner of Burlington is Tom Sawyer, and Robbie McMath of Fort Mitchell is Huck Finn.Tumer, a 10th-grader at School for Creative and Performing Arts, is a familiar presence on Cincinnati’s stages. He is a star act or of Children’s Theatre, having played leading roles in “The Legend of Sleepy Hollow” and “The Wizard of Oz,” and is fresh from Jersey Production “Ragtime”.McMath is a junior at Beechwood High School. He was in the cast of “Tom Sawyer” when it was first performed and is a Children’s Theatre regular, with five shows to his credit. This summer he attended Kentucky’s Governor’s School for the Arts in Musical Theatre.Note to teachers: Children’s Theatre has a study guide demonstrating how math and science can be taught through “Tom Sawyer.” For downloadable lessons, visit the official website of Children’s Theatre.1．Who wrote the music for “Tom Sawyer: A River Adventure”?A．David Kisor.B．Joe McDonough.C．Nathan Turner.D．Robbie McMath.2．What can we learn about the two actors?A．They study in the same school.B．They worked together in ”Ragtime“.C．They are experienced on stage.D．They became friends ten years ago.3．What does Children’s Theatre provide for teachers?A．Research funding.B．Training opportunities.C．Technical support.D．Educational resources.【答案】1．A 2．C 3．D【解析】1．根据第二段中的“It is adapted by Joe McDonough, with music by David Kisor.(本剧由乔·麦克多诺改编，大卫·基索作曲。

Lecture 7 -- Definitions (corrected)

Lecture 8:
Definitions
Howard Barrell
Introduction
We have seen how the same word can have more than one meaning, depending on its use. The meaning of language depends upon its use and context. It not easy to say exactly what a particular word means without looking at the context in which it is used. For this reason, I recommended to you the Meaning-as-Use theory. But sometimes this approach to establishing the meanings of words is inadequate. Sometimes it is necessary to establish the exact meaning of a particular word. If, for example, you as a journalist or a lawyer talk about someone who has not met their ‘fiduciary duties’, it is necessary to know the exact meaning of ‘fiduciary’ is. If we do not, we may well misunderstand what is being said. Let us find a similar example in Albanian and BHS. At other times, we may come across a word we are unfamiliar with, or when a word we know is being used in a way that is unfamiliar to us. In this case we want to avoid not understanding what is being said at all. In these two cases, we may call for the word or the way it is being used to be explained or ‘defined’ to us. For this we ask for, or look for, a definition of the word.

lecture_notes_ch1-4

1IntroductionThis chapter introduces the concept of a game and encourages the reader to begin thinking about the formal analysis of strategic situations.The chapter contains a short history of game theory,followed by a description of“non-cooperative theory”(which the book emphasizes),a discussion of the notion of contract and the related use of“cooperative theory,”and comments on the science and art of applied theoretical work.The chapter explains that the word“game”should be associated with any well-deﬁned strategic situation,not just adversarial contests.Finally,the format and style of the book are described.Lecture NotesThe non-administrative segment of aﬁrst lecture in game theory may run as follows.•Deﬁnition of a strategic situation.•Examples(have students suggest some):chess,poker,and other parlor games;tennis,football,and other sports;ﬁrm competition,international trade,inter-national relations,ﬁrm/employee relations,and other standard economic exam-ples;biological competition;elections;and so on.•Competition and cooperation are both strategic topics.Game theory is a generalmethodology for studying strategic settings(which may have elements of bothcompetition and cooperation).•The elements of a formal game representation.•A few simple examples of the extensive form representation(point out the basiccomponents).Examples and Experiments1.Clap game.Ask the students to stand and then,if they comply,ask them toclap.(This is a silly game.)Show them how to diagram the strategic situationas an extensive form tree.The game starts with your decision about whether toask them to stand.If you ask them to stand,then they(modeled as one player)have to choose between standing and staying in their seats.If they stand,thenyou decide between saying nothing and asking them to clap.If you ask them toclap,then they have to decided whether to clap.Write the outcomes at terminalnodes in descriptive terms such as“professor happy,students confused.”Thenshow how these outcomes can be converted into payoﬀnumbers.13Instructors' Manual for Strategy:Copyright 2002, 2008 by Joel Watson1INTRODUCTION142.Auction the textbook.Many students will probably not have purchased thetextbook by theﬁrst class meeting.These students may be interested in pur-chasing the book from you,especially if they can get a good deal.However,quite a few students will not know the price of the book.Without announcingthe bookstore’s price,hold a sealed-bid,ﬁrst-price auction(using real money).This is a common-value auction with incomplete information.The winning bidmay exceed the bookstore’s price,giving you an opportunity to talk about the“winner’s curse”and to establish a fund to pay students in future classroomexperiments.Instructors' Manual for Strategy:Copyright 2002, 2008 by Joel Watson2The Extensive FormThis chapter introduces the basic components of the extensive form in a non-technical way.Students who learn about the extensive form at the beginning of a course are much better able to grasp the concept of a strategy than are students who are taught the normal formﬁrst.Since strategy is perhaps the most important concept in game theory,a good understanding of this concept makes a dramatic diﬀerence in each student’s ability to progress.The chapter avoids the technical details of the extensive form representation in favor of emphasizing the basic components of games.The technical details are covered in Chapter14.Lecture NotesThe following may serve as an outline for a lecture.•Basic components of the extensive form:nodes,branches.Nodes are wherethings happen.Branches are individual actions taken by the players.•Example of a game tree.•Types of nodes:initial,terminal,decision.•Build trees by expanding,never converging back on themselves.At any placein a tree,you should always know exactly how you got there.Thus,the treesummarizes the strategic possibilities.•Player and action labels.Try not to use the same label for diﬀerent places wheredecisions are made.•Information sets.Start by describing the tree as a diagram that an externalobserver creates to map out the possible sequences of decisions.Assume theexternal observer sees all of the players’actions.Then describe what it meansfor a player to not know what another player did.This is captured by dashedlines indicating that a player cannot distinguish between two or more nodes.•We assume that the players know the game tree,but that a given player maynot know where he is in the game when he must make any particular decision.•An information set is a place where a decision is made.•How to describe simultaneous moves.•Outcomes and how payoﬀnumbers represent preferences.15Instructors' Manual for Strategy:Copyright 2002, 2008 by Joel Watson2THE EXTENSIVE FORM16Examples and ExperimentsSeveral examples should be used to explain the components of an extensive form.In addition to some standard economic examples(such asﬁrm entry into an industry and entrant/incumbent competition),here are a few I routinely use:1.Three-card poker.In this game,there is a dealer(player1)and two potentialbetters(players2and3).There are three cards in the deck:a high card,amiddle card,and a low card.At the beginning of the game,the dealer looks atthe cards and gives one to each of the other players.Note that the dealer candecide which of the cards goes to player2and which of the cards goes to player3.(There is no move by Nature in this game.The book does not deal with movesof Nature until Part IV.You can discuss moves of Nature at this point,but itis not necessary.)Player2does not observe the card dealt to player3,nor doesplayer3observe the card dealt to player2.After the dealer’s move,player2observes his card and then decides whether to bet or to fold.After player2’sdecision,player3observes his own card and also whether player2folded orbet.Then player3must decide whether to fold or bet.After player3’s move,the game ends.Payoﬀs indicate that each player prefers winning to folding andfolding to losing.Assume the dealer is indiﬀerent between all of the outcomes(or specify some other preference ordering).2.Let’s Make a Deal game.This is the three-door guessing game that was madefamous by Monty Hall and the television game show Let’s Make a Deal.Thegame is played by Monty(player1)and a contestant(player2),and it runs asfollows.First,Monty secretly places a prize(say,$1000)behind one of threedoors.Call the doors a,b,and c.(You might write Monty’s actionsas a ,b ,and c ,to diﬀerentiate them from those of the contestant.)Then,without observing Monty’s choice,the contestant selects oneof the doors(by saying“a,”“b,”or“c”).After this,Monty must open one of the doors,but he is not allowedto open the door that is in front of the prize,nor is he allowed to openthe door that the contestant selected.Note that Monty does not havea choice if the contestant chooses a diﬀerent door than Monty chosefor the prize.The contestant observes which door Monty opens.Notethat she will see no prize behind this door.The contestant then has the option of switching to the other unopeneddoor(S for“switch”)or staying with the door she originally selected(D for“don’t switch”).Finally,the remaining doors are opened and the contestant wins theprize if it is behind the door she chose.The contestant obtains a Instructors' Manual for Strategy:Copyright 2002, 2008 by Joel Watson2THE EXTENSIVE FORM17 payoﬀ1if she wins,zero otherwise.Monty is indiﬀerent between allof the outcomes.For a bonus question,you can challenge the students to draw the extensive formrepresentation of the Let’s Make a Deal game or the Three-Card Poker game.Students who submit a correct extensive form can be given points for the classcompetition.The Let’s Make a Deal extensive form is pictured on the nextpage.Instructors' Manual for Strategy:Copyright 2002, 2008 by Joel Watson2THE EXTENSIVE FORM18Instructors' Manual for Strategy:Copyright 2002, 2008 by Joel Watson3Strategies and the Normal FormAs noted already,introducing the extensive form representation at the beginning ofa course helps the students appreciate the notion of a strategy.A student that doesnot understand the concept of a“complete contingent plan”will fail to grasp the sophisticated logic of dynamic rationality that is so critical to much of game theory.Chapter3starts with the formal deﬁnition of strategy,illustrated with some examples.The critical point is that strategies are more than just“plans.”A strategy prescribes an action at every information set,even those that would not be reached because of actions taken at other information sets.Chapter3proceeds to the construction of the normal-form representation,starting with the observation that each strategy proﬁle leads to a single terminal node(an outcome)via a path through the tree.This leads to the deﬁnition of a payoﬀfunction.The chapter then deﬁnes the normal form representation as comprising a set of players, strategy spaces for the players,and payoﬀfunctions.The matrix form,for two-player,ﬁnite games,is illustrated.The chapter then brieﬂy describes seven classic normal form games.The chapter concludes with a few comments on the comparison between the normal and extensive forms.Lecture NotesThe following may serve as an outline for a lecture.•Formal deﬁnition of strategy.•Examples of strategies.•Notation:strategy space S i,individual strategy s i∈S i.Example:S i={H,L}and s i=H.•Refer to Appendix A for more on sets.•Strategy proﬁle:s∈S,where S=S1×S2×···×S n(product set).•Notation:i and−i,s=(s i,s−i).•Discuss howﬁnite and inﬁnite strategy spaces can be described.•Why we need to keep track of a complete contingent plan:(1)It allows theanalysis of games from any information set,(2)it facilitates exploring how aplayer responds to his belief about what the other players will do,and(3)itprescribes a contingency plan if a player makes a mistake.•Describe how a strategy implies a path through the tree,leading to a terminalnode and payoﬀvector.•Examples of strategies and implied payoﬀs.19Instructors' Manual for Strategy:Copyright 2002, 2008 by Joel Watson3STRATEGIES AND THE NORMAL FORM20•Deﬁnition of payoﬀfunction,u i:S→R,u i(s).Refer to Appendix A for moreon functions.•Example:a matrix representation of players,strategies,and payoﬀs.(Use anyabstract game,such as the centipede game.)•Formal deﬁnition of the normal form.•Note:The matrix representation is possible only for two-player,ﬁnite games.Otherwise,the game must be described by sets and equations.•The classic normal form games and some stories.Note the diﬀerent strategicissues represented:conﬂict,competition,coordination,cooperation.•Comparing the normal and extensive forms(translating one to the other).Examples and Experiments1.Ultimatum-oﬀer bargaining game.Have students give instructions to others asto how to play the game.Those who play the role of“responder”will have tospecify under what conditions to accept and under what conditions to reject theother player’s oﬀer.This helps solidify that a strategy is a complete contingentplan.2.The centipede game(like the one in Figure3.1(b)if the textbook).As with thebargaining game,have some students write their strategies on paper and givethe strategies to other students,who will then play the game as their agents.Discuss mistakes as a reason for specifying a complete contingent plan.Thendiscuss how strategy speciﬁcations helps us develop a theory about why playersmake particular decisions(looking ahead to what they would do at variousinformation sets).3.Any of the classic normal forms.4.The Princess Bride poison scene.Show the“poison”scene(and the few minutesleading to it)from the Rob Reiner movie The Princess Bride.In this scene,protagonist Wesley matches wits with the evil Vizzini.There are two gobletsﬁlled with wine.Away from Vizzini’s view,Wesley puts poison into one ofthe goblets.Then Wesley sets the goblets on a table,one goblet near himselfand the other near Vizzini.Vizzini must choose from which goblet to drink.Wesley must drink from the other goblet.Several variations of this game can bediagrammed for the students,ﬁrst in the extensive form and then in the normalform.Instructors' Manual for Strategy:Copyright 2002, 2008 by Joel Watson3STRATEGIES AND THE NORMAL FORM215.A3×3dominance-solvable game,such as the following.The payoﬀs are in dollars.It is very useful to have the students play a gamesuch as this before you lecture on dominance and best response.This will helpthem to begin thinking about rationality,and their behavior will serve as areference point for formal analysis.Have the students write their strategiesand their names on slips of paper.Collect the slips and randomly select aplayer1and a player2.Pay these two students according to their strategyproﬁle.Calculate the class distribution over the strategies,which you can lateruse when introducing dominance and iterated dominance.6.Repeated Prisoners’Dilemma.Describe the k-period,repeated prisoners’dilemma.For a bonus question,ask the students to compute the number of strategies forplayer1when k=3.Challenge the students toﬁnd a mathematical expressionfor the number of strategies as a function of k.Instructors' Manual for Strategy:Copyright 2002, 2008 by Joel Watson4Beliefs,Mixed Strategies,and Expected PayoﬀsThis chapter describes how a belief that a player has about another player’s behavior is represented as a probability distribution.It then covers the idea of a mixed strat-egy,which is a similar probability distribution.The appropriate notation is deﬁned.The chapter deﬁnes expected payoﬀand gives some examples of how to compute it.At the end of the chapter,there are a few comments about cardinal versus ordinal utility(although it is not put in this language)and about how payoﬀnumbers reﬂect preferences over uncertain outcomes.Risk preferences are discussed in Chapter25.Lecture NotesThe following may serve as an outline for a lecture.•Example of belief in words:“Player1might say‘I think player2is very likelyto play strategy L.’”•Translate into probability numbers.•Other examples of probabilities.•Notation:µj∈∆S j,µj(s j)∈[0,1], s j∈S jµj(s j)=1.•Examples and alternative ways of denoting a probability distribution:for S j={L,R}andµj∈∆{L,R}deﬁned byµj(L)=1/3andµj(R)=2/3,we canwriteµj=(1/3,2/3).•Mixed strategy.Notation:σi∈∆S i.•Refer to Appendix A for more on probability distributions.•Deﬁnition of expected value.Deﬁnition of expected payoﬀ.•Examples:computing expected payoﬀs.•Brieﬂy discuss how payoﬀnumbers represent preferences over random outcomes,risk.Defer elaboration until later.22Instructors' Manual for Strategy:Copyright 2002, 2008 by Joel WatsonBELIEFS AND EXPECTED PAYOFFS23 Examples and Experiments1.Let’s Make a Deal game again.For the class competition,you can ask thefollowing two bonus questions:(a)Suppose that,at each of his information sets,Monty randomizes by choosing his actions with equal probability.Is it optimal for the contestant to select“switch”or“don’t switch”when she has this choice?Why?(b)Are there conditions(a strategy for Monty)under which it is optimal for the contestant to make the other choice?2.Randomization in sports.Many sports provide good examples of randomizedstrategies.Baseball pitchers may desire to randomize over their pitches,and batters may have probabilistic beliefs about which pitch will be thrown to them.Tennis serve and return play is another good example.11See Walker,M.,and Wooders J.“Minimax Play at Wimbledon,”American Economic Review 91(2001):1521-1538.Instructors' Manual for Strategy: An Introduction to Game Theory Copyright 2002, 2008 by Joel Watson For instructors only; do not distribute.。

examples7

Mathematical Tripos Part IA Michaelmas term2011 Mechanics(non-examinable)Exercises for lectures7and8Dr S.T.C.Siklos Comments and corrections:e-mail to stcs@cam.All examples sheets and solutions are avail-able on /user/stcs/mechanics.htmlOn these sheets,no attempt is made to‘model’real-life situations:no trains,cars,cyclists, lifts,governors of steam engines,etc.It is assumed that there are no‘real’forces,such as air-resistance unless they are speciﬁcally mentioned.Most questions,but not all,avoid numbers and units,prefering general algebraic formulae with consistent dimensions.1A particle is released from rest and falls under the action of gravity.By calculating its speed after falling a distance h,verify that the principle of conservation of energy holds in this situation.2A particle of mass m is projected with initial speed u up a line of maximum slope of a rough plane inclined atαto the horizontal.The coeﬃcient of friction isµ(assume the frictional force isµ×normalreaction).Show that the acceleration down the plane is g(sinα+µcosα) and hence calculate the distance s up the plane at which the particle comes to e the conservation of energy to show that the amount of work done against the frictional force is1 2mu2µcosαsinα+µcosα.Verify this result using work done against frictional force=frictional force×distance moved.3Use the principle of conservation of energy carefully!toﬁnd the maximum height of a particle projected with speed V at an angle ofαto the horizontal,noting that the horizontal velocity is constant.4A light inelastic string passes over two small smooth pulleys A and B at the same horizontal level a distance2a apart.Particles of mass m are attached to either end and a particle of mass M(where M<2m)is attached to the midpoint.The system is released from rest with the particle of mass M at the midpoint of ing conservation of energy,show that the system next comes to rest when the particle of mass M has fallen a distance4amM4m2−M2.5Water is pumped to the surface of the Earth from a depth d and issues from a pipe of cross-sectional area A at a speed of v.The density of the water isρ.Using energy considerations,ﬁnd the power of the pump.1。

Partie3c

●
B
En effet, soient deux points A et B d’une boucle C : On peut écrire le travail de A à B de deux façons : (puisque le trajet n’importe pas)
A●
C2
(le long de C1) (le long de C2)
3/ Exemples de forces conservatives a – Force constante (en norme, direction et sens) A
•
C
P α
α
•
B
angle ne dépend que des positions de A et de B ⇒ force conservative
1. CIRCULATION D’UN VECTEUR – NOTION DE TRAVAIL 1/ Définitions a – Champ vectoriel. Champ scalaire Champ vectoriel : ensemble de grandeurs vectorielles attachées à chaque point de l’espace (ou portion d’espace) Champ scalaire : ensemble de grandeurs scalaires attachées à chaque point de l’espace (ou portion d’espace) Exemples : Champ de vitesse de vent : champ de vecteurs Champ de pression : champ scalaire Un champ vectoriel peut être uniforme ou non b – Circulation Champ de vecteurs Quantité scalaire du champ de vecteurs L’intégrale notée dépendant des coordonnées d’espace (coordonnées de P) : circulation élémentaire A lors du déplacement est la circulation du vecteur

Concept培训的资料03_Product_Portfolio

CT-Concept Technologie AG - Switzerland Page 8
SCALE Plug-and-Play Driver
2SB315A/ 2SB315B Dual channel driver for 130mmx140mm IGBT dual modules IGBTs from 1200V to 1700V Fuji, ABB, Mitsubishi, Infineon, Dynex DIC-20 (A) or Fiber-optic (B) interface ±15A gate current, ±15V 3W per channel Active clamping Short-circuit protection Under-voltage lockout Up to 20kHz Delay time 400ns 100kV/us -40°C…+85°C
CT-Concept Technologie AG - Switzverview
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convexity_lecture

(ii) c = ATλ, λ ≥ 0. Indeed, (i) is not solvable if and only if c ∈ K ◦ , which is equivalent to (ii). Example 2.7 Suppose we have n securities with present prices c1 , . . . , cn . The securities
2
Lemma 2.3 Assume that X is a convex set. Then the set cone(X ) = {γx : x ∈ X, γ ≥ 0} is a convex cone. The set cone(X ) is called the cone generated by the set X . For a convex set X and a point x ∈ X the set KX (x) = cone(X − x) is called the cone of feasible directions of X at x (or the radial cone). It follows directly from the deﬁnition that it is a convex cone. Deﬁnition 2.4 Let K be a cone in Rn . The set K ◦ = {y ∈ Rn : y, x ≤ 0 for all x ∈ K } is called the polar cone of K . For example, the set K = {x ∈ Rn : xi ≥ 0, i = 1, . . . , n} is a convex closed cone. Its polar is −K , as can be veriﬁed directly. The negative of the polar cone, K ∗ = −K ◦ , is called the dual cone. We use the notation K ◦◦ for the polar cone of the polar cone of K . The following result is known as the Bipolar Theorem. Theorem 2.5 If K ⊂ Rn is a closed convex cone, then K ◦◦ = K. Polar cones to pre-images of cones under linear transformations can be calculated in an explicit form. Theorem 2.6 Assume that A is an m × n matrix. Let K = {x ∈ Rn : Ax ≤ 0}. Then K is a closed convex cone and K ◦ = {ATλ : λ ≥ 0}. This result is known as Farkas Lemma). It islternative: exactly one of the following two systems has a solution, either (i) Ax ≤ 0 and c, x > 0; or 3

Concept and Practical Considerations of Non-orthogonal Multiple Access for Future Radio Access

Concept and Practical Considerations of Non-orthogonal Multiple Access (NOMA) for Future Radio AccessAnass Benjebbour† Yuya Saito† Yoshihisa Kishiyama† Anxin Li‡ Atsushi Harada‡ Takehiro Nakamura††Radio Access Network Development Department, NTT DOCOMO, INC.‡DOCOMO Beijing Communications Laboratories Co., Ltdanass@nttdocomo.co.jpAbstract—As a promising downlink multiple access scheme for future radio access (FRA), this paper discusses the concept and practical considerations of non-orthogonal multiple access (NOMA) with a successive interference canceller (SIC) at the receiver side. The goal is to clarify the benefits of NOMA over orthogonal multiple access (OMA) such as OFDMA adopted by Long-Term Evolution (LTE). Practical considerations of NOMA, such as multi-user power allocation, signalling overhead, SIC error propagation, performance in high mobility scenarios, and combination with multiple input multiple output (MIMO) are discussed. Using computer simulations, we provide system-level performance of NOMA taking into account practical aspects of the cellular system and some of the key parameters and functionalities of the LTE radio interface such as adaptive modulation and coding (AMC) and frequency-domain scheduling. We show under multiple configurations that the system-level performance achieved by NOMA is higher by more than 30% compared to OMA.Keywords − non-orthogonal multiple access, future radio access, power-domain, successive interference cancellerI.INTRODUCTIONIn order to continue to ensure the sustainability of mobile communication services over the coming decade, new technology solutions that can respond to future challenges must be identified and developed [1]. For future radio access (FRA) in the 2020s-era, significant gains in capacity and quality of user experience (QoE) are required in view of the anticipated exponential increase in the volume of mobile traffic, e.g., beyond a 500 fold increase in the next decade. In cellular mobile communications, the design of radio access technology (RAT) is one important aspect in improving system capacity in a cost-effective manner. Radio access technologies are typically characterized by multiple access schemes, e.g., frequency division multiple access (FDMA), time division multiple access (TDMA), code division multiple access (CDMA), and OFDMA, which provide the means for multiple users to access and share the system resources simultaneously. In the 3.9 and 4th generation (4G) mobile communication systems such as Long-Term Evolution (LTE) [2] and LTE-Advanced [3], standardized by the 3rd Generation Partnership Project (3GPP), orthogonal multiple access (OMA) based on OFDMA or single carrier (SC)-FDMA is adopted. Orthogonal multiple access is a reasonable choice for achieving good system-level throughput performance in packet-domain services with a simplified receiver design. However, in order to boost further the spectrum efficiency in the future, more advanced receiver designs are required in order to mitigate intra-cell and/or inter-cell interference. As a candidate multiple access scheme for FRA, we proposed a downlink non-orthogonal multiple access (NOMA) scheme where multiple users are multiplexed in the power-domain on the transmitter side and multi-user signal separation on the receiver side is conducted based on successive interference cancellation (SIC) [4-12]. From an information-theoretic perspective, it is well-known that non-orthogonal user multiplexing using superposition coding at the transmitter and SIC at the receiver not only outperforms orthogonal multiplexing, but also is optimal in the sense of achieving the capacity region of the downlink broadcast channel [4]. Note that NOMA can also be applied to uplink (multiple access channel) with SIC applied at the BS side [4,6]. In previous works [6-12], system-level gains of NOMA were investigated in both downlink and uplink. In this paper, our focus is on downlink NOMA (broadcast channel). Our goal is two-fold: The first is to clarify the basic concept, the benefits, and motivations behind downlink NOMA as a potential candidate multiple access for FRA; and the second is to discuss practical aspects of NOMA, such as multi-user power allocation, signalling overhead, SIC error propagation, performance in high mobility scenarios, and combination with multiple input multiple output (MIMO). Using computer simulations and taking into account practical aspects of the cellular system and some of the key parameters and functionalities of the LTE radio interface such as adaptive modulation and coding (AMC) and frequency-domain scheduling, we provide the system-level performance of downlink NOMA and discuss its related practical considerations. We show under multiple configurations that the cell throughput achieved by NOMA is higher by more than 30% compared to OMA. The remainder of this paper is organized as follows. Section II describes the concept and benefits of NOMA. Section III, discusses practical considerations of NOMA based on the simulation results of its system-level performance. Finally, Section IV concludes the paper.II.NOMA C ONCEPTIn this section, we explain the concept and benefits of NOMA as a potential downlink multiple access for FRA.A.PrincipleFig. 1 illustrates downlink NOMA for the case of one BS and two-UE.Fig. 1. Downlink NOMA with SIC applied at UE receiver.For simplicity, we assume in this section the case of single transmit and receive antennas. The overall system transmission bandwidth is assumed to be 1 Hz. The base station transmits a signal for UE-i (i = 1, 2), x i, where E[|x i|2] = 1, with transmit power P i and the sum of P i is equal to P. In NOMA, x1 and x2 are superposed as follows:Freq.UE 1UE 2SIC of UE 2signalUE 1 signaldecodingUE 2 signaldecodingReceived SINRHigh Low PowerBS12x . (1) Thus, the received signal at UE-i is represented asi i i y h x w =+, (2)where h i is the complex channel coefficient between UE-i and the BS. Term w i denotes additive white Gaussian noise (AWGN) including inter-cell interference. The power spectral density of w i is N 0,i .In downlink NOMA, the SIC process is implemented at the UE receiver. The optimal order for decoding is in the order of decreasing channel gain normalized by noise and inter-cell interference power, |h i |2/N 0,i (called simply channel gain in the remaining). Based on this order, we assume that any user can correctly decode the signals of other users whose decoding order comes before the corresponding user. Thus, UE-i can remove the inter-user interference from the j -th user whose |h j |2/N 0,j is lower than |h i |2/N 0,i . In a 2-UE case, assuming that |h 1|2/N 0,1 > |h 2|2/N 0,2, UE-2 does not perform interference cancellation since it comes first in the decoding order. UE-1 first decodes x 2 and subtracts its component from received signal y 1, then next, it decodes x 1 without interference from x 2. Assuming successful decoding and no error propagation, the throughput of UE-i , R i , is represented as221122122220,1120,2||||log 1,log 1||P h P h R R N P h N ⎛⎞⎛⎞=+=+⎜⎟⎜⎟⎜⎟⎜⎟+⎝⎠⎝⎠. (3) From (3), it can be seen that power allocation for each UE greatlyaffects the user throughput performance and thus the modulation and coding scheme (MCS) used for data transmission of each UE. By adjusting the power allocation ratio, P 1/P 2, the BS can flexibly control the throughput of each UE. Clearly, the overall cell throughput, cell-edge throughput, and user fairness are closely related to the power allocation scheme adopted.Fig. 2. Simple comparison example of NOMA and OMA (OFDMA).B. Comparison with OMAFor OMA as orthogonal user multiplexing, the bandwidth of α (0 < α < 1) Hz is assigned to UE 1 and the remaining bandwidth, 1−α Hz, is assigned to UE 2. The throughput of UE-i , R i , is represented as22112212220,10,2||||log 1,(1)log 1(1)P h P h R R N N αααα⎛⎞⎛⎞=+=−+⎜⎟⎜⎟⎜⎟⎜⎟−⎝⎠⎝⎠. (4)In NOMA, the performance gain compared to OMA increases whenthe difference in channel gains, e.g., path loss between UEs, is large. For example, as shown in Fig. 2, we assume a 2-UE case with a cell-interior UE and a cell-edge UE, where |h 1|2/N 0,1 and |h 2|2/N 0,2 are set to 20 and 0 dB, respectively. For OMA with equal bandwidth and equal transmission power are allocated to each UE (α = 0.5, P 1 = P 2 = 1/2P ), the user rates are calculated according to (4) as R 1 = 3.33 and R 2 = 0.50 bps, respectively. On the other hand, in NOMA, when the power allocation is conducted as P 1 = 1/5P and P 2 = 4/5P , the user rates are calculated according to (3) as R 1 = 4.39 and R 2 = 0.74 bps, respectively. The corresponding gains of NOMA over OMA are 32% and 48% for UE 1 and UE 2, respectively. According to the above simple example of 2-UE, NOMA provides higher sum rate than OMA. As later shown in the simulation results, this can indeed be generalized to the case of multiple users with sophisticated multi-user proportional fairness scheduling being used.C. Motivations and benefits of NOMAWe envisage NOMA as a promising candidate multiple accessscheme in the future for the following motivations and benefits. Exploitation of channel gain difference among usersUnlike OMA (OFDMA) where channel gain difference is translated into multi-user diversity gains via frequency-domain scheduling, in NOMA the channel gain difference is translated into multiplexing gains by superposing in the power-domain the transmit signals of multiple users of different channel gains. As shown in Fig. 2, exploiting the channel gain difference in NOMA, both UEs of high and low channel gains are in a win-win setup. Indeed, UEs with high channel gain (bandwidth-limited UEs) lose a little by being allocated less power, but gain much more by being allocated more bandwidth, while UEs with low channel gain (power-limited UEs) also lose only a little by being allocated little less power and “effective” bandwidth (because of being interfered by the signal designated to the other UEs with high channel gain) but gain much more by being allocated more bandwidth. This win-win situation is also the main reason why NOMA gains over OMA increase when the difference in channel gains between NOMA paired UEs become larger [11].Intentional non-orthogonality via power-domain user multiplexing and advanced receiver processingNOMA is a mutliplexing scheme that utilizes an additional new domain, i.e., the power domain, which is not sufficiently utilized in previous systems. Non-orthogonality is intentionally introduced via power-domain user multiplexing; however, interestingly, quasi-orthogonality still can be achieved. In fact, user demultiplexing is ensured via the allocation of large power difference between paired UEs and the application of SIC in power-domain. The UE with high channel gain (e.g., UE1 in Figs. 1, 2) is allocated less power and the UE with low channel gain (e.g., UE2 in Figs. 1, 2) is allocated more power. Such large power difference facilitates the successful decoding (with high probability) and thus the successful cancellation of the signal designated to UE2 (being allocated high power) at UE1 receiver. In addition, at UE2 receiver, the signal designated to UE2 is decoded directly by treating the interference from the signal designated to UE1 (being allocated low power) as noise.On another hand, NOMA captures well the evolution of device processing capabilities, generally following Moore’s law, by relying on more advanced receiver processing such as SIC. In this same spirit, but for the purpose of inter-cell interference mitigation, network-assisted interference cancellation and suppression (NAICS), including SIC, is being discussed in LTE Release 12 [13]. Thus, NOMA can be one good direction to extend the work in 3GPP on NAICS in LTE Release 13 and beyond, as it should be much easier to apply SIC to deal with intra-cell interference than inter-cell interference. The issue of the increased downlink overhead (common to both intra-cell and inter-cell SIC) owing to the signalling of the information related to the demodulation and decoding of other UEs in addition to those for its own UE is discussed in Section III.Robust performance gain in practical wide area deployments NOMA user multiplexing does not rely that much on the knowledge of the transmitter of the instantaneous frequency-selective fading channels such as the frequency-selective channel quality indicator (CQI) or channel state information (CSI), which require fine feedback signalling from the UE side. In NOMA, CSI is used at the receiver for user demultiplexing and at the transmitter mainly to decide on user pairing and multi-user power allocation. Thus, a robust performance gain in practical wide area deployments can be expected irrespective of UE mobility or CSI feedback latency.III. P RACTICAL C ONSIDERATIONSWe discuss some practical considerations regarding NOMA, such as multi-user power allocation, signalling overhead, SIC errorBW x1/2BW x1/2P o w e rR 1= 3.33 bps/Hz R 2= 0.50 bps/Hz UE 1UE 2OFDMAP x1/5P x4/5UE 1UE 2P o w e rNOMAR 1= 4.39 bps/Hz (+32%)R 2= 0.74 bps/Hz (+48%)propagation, performance in high mobility scenarios, and combination with MIMO. Evaluation results of the performance of NOMA in a multi-cell system-level simulation [14] are also presented. The major simulation parameters assumed are based on existing LTE/LTE-Advanced specifications [15]. We employed a 19-hexagonal macrocell model with 3 sectors per cell. The system bandwidth is 10MHz (48RBs) and the cell radius is set to 289 meters (inter-site distance of 500 meters). The locations of the UEs are assigned randomly with a uniform distribution. In the propagation model, we take into account distance-dependent path loss with the decay factor of 3.76, lognormal shadowing with the standard deviation of 8 dB and instantaneous multipath fading. The shadowing correlation between the cells (sectors) is set to 0.5 (1.0). The 6-ray typical urban (TU) channel model is assumed. The baseline maximum Doppler frequency, f D, is set to 5.55 Hz, which corresponds to 3 km/h at the carrier frequency of 2 GHz. The transmission power of the macrocells is 46 dBm. The antenna gain at the macrocell and UE is 14 dBi and 0 dBi, respectively. One-antenna transmission and two-antenna reception (1x2 SIMO) and maximal ratio combining (MRC) at the UE side are assumed as baseline antenna configuration and receiver. Full buffer traffic model is used and the feedback delay is modeled such that the CQI is not available for scheduling until 4 subframes after the periodic report with a 2-ms interval. Hybrid Automatic Repeat reQuest (HARQ) is not assumed. In NOMA, the multi-user scheduler maximizes multi-user proportional fairness metric [16,17] and selects the best UE set among all possible UE sets. Full search power allocation and exhaustive user pairing described in [12] are assumed as baseline. Also, for NOMA, dynamic switching to OMA is assumed with the maximum number of simultaneously paired UEs, m, is set to 2 (m=2).A.NOMA signalling overheadWideband vs. Subband schedulingWe explore NOMA performance gains with subband scheduling and subband MCS and compare it to NOMA with wideband scheduling and wideband MCS selection. For the case of subband (wideband) scheduling, the system bandwidth is divided into 8 (1) subbands with 6RBs (48RBs) per subband. In Fig. 3, the cell throughput and cell-edge throughput gains for NOMA over OMA are approximately 40% and 39% for wideband scheduling, and 37% and 32% for subband scheduling, respectively. Thus, similar gains can be maintained for NOMA even with larger number of subbands and thus larger frequency-domain scheduling gains. Also note that the performance of all cases is increased according to the number of UEs per cell (10UEs, 20UEs) because of the multi-user diversity gain.Fig. 3. CDF of user throughput for OMA (m = 1) and NOMA (m = 2)with subband and wideband scheduling (w/o error propagation).In the case of NOMA with subband scheduling, signalling overhead increases linearly with the number of subbands. To reduce signalling overhead, joint encoding of modulation, coding and power set (MCPS) would be beneficial or some signallings could be widedbandor long-term while others can remain subband or short-term. In LTEfor example, even when subband scheduling is applied, the same channel coding rate (including rate matching) and data modulation scheme are assumed over all the subbands allocated to each single user, as the average SINR over all the subbands is used for MCS selection. However, for NOMA, such a mismatch between MCS adaptation granularity (e.g., wideband) and power allocation granularity (e.g., subband) might not allow the full exploitation of NOMA gains with subband scheduling [11]. Thus, considerations from this aspect need to be also taken into account.Multi-user power allocationBecause of the power-domain user multiplexing of NOMA, the transmit power allocation (TPA) to one user affects the achievable throughput of not only that user but also the throughput of other users. The best performance of NOMA can obviously be achieved by exhaustive full search of user pairs and dynamic transmit power allocations. In case of full search power allocation (FSPA), all possible combinations of power allocations are considered for each candidate user set. FSPA remains, however, computationally complex. Also, with such dynamic TPA, the signalling overhead associated with SIC decoding order and power assignment ratios increases significantly.In order to reduce the signalling overhead associated with multi-user transmit power allocation of NOMA and clarify the degree of impact of user pairing on the performance of NOMA, both exhaustive and simplified user pairing and power allocation schemesare explored [12]. In NOMA, users with large channel gain difference (e.g., large path-loss difference) are paired with high probability; thus, considering practical implementations, user pairing and TPA, could be simplified by using pre-defined user grouping and fixed per-group power allocation(FPA),where users are divided into multiple user groups according to the magnitude of their channel gains using pre-defined thresholds [12].Fig. 4. CDF of user throughput for OMA (m = 1) and NOMA (m = 2) with various power allocation and user grouping schemes(subband scheduling, 20UEs, w/o error propagation).Figure 4 shows the performance comparison between OMA and NOMA with different power allocation schemes, with and without user grouping. Here, three power allocation schemes are simulated: FSPA, fractional transmit power allocation (FTPA) similar to LTE uplink power control (αFTPA=0.4) [9], and FPA. With grouping, two user groups were assumed where the threshold for user grouping is 8dB and power allocations in FPA are fixed to (0.2P, 0.8P). Theperformance gains in the overall cell throughput for NOMA are, FSPA w/o grouping: 37%; FTPA w/o grouping: 31%; FPA w/o grouping: 30%; FSPA w/ grouping: 30%; and FPA w/ grouping: 28%. Thus, even with simplified TPA schemes such as FPA and pre-defined user grouping, a large portion of NOMA gains can be maintained. Taking into account the potential saving in signalling overhead, pre-defined user grouping and fixed TPA can be promising in practical usage. For example, the order of successive interference cancellation (SIC) and information on power assignment do not need to be transmitted in every subframe but rather on a longer time scale.B. Impact of SIC error propagationIn practice, the impact of SIC error propagation on NOMA performance remains as one concern. To emulate this effect in the system-level simulations of NOMA, we adopt a worst-case model [12]. The worst-case model assumes that at the receiver of UE1, where SIC is applied, the decoding of UE2 is performed first at stage 1. Based on the knowledge of the MCS assigned to UE2 and its received SINR at UE1, the BLER of the user decoded first (UE2) is obtained and decoding is attempted. Then, its replica signal is generated and subtracted from the received signal before the decoding of UE1 at stage 2. Depending on the decoding result of UE2 (successful or not) at stage 1, the signal used for the decoding of UE1 at stage 2 differs, which make the link-to-system mapping difficult. In the worst-case model we assume that the decoding of UE1 at stage 2 is always unsuccessful whenever the decoding of UE2 at stage 1 of the UE1 receiver is unsuccessful. Such a worst-case model is simple but provides us with a simple tool to evaluate the impact of error propagation on NOMA performance without the need for NOMA specific link-to-system mapping.Fig. 5. CDF of user throughput for OMA (m = 1) and NOMA (m = 2) with and without error propagation (subband scheduling, 20UEs).Figure 5 shows the impact of error propagation on performance of NOMA using the explained worst-case model. It can be seen that error propagation has almost no impact on NOMA performance. The reason is that in most cases NOMA scheduler pairs a UE with bad channel gain with a UE with good channel gain. Because MCS for the UE with bad channel gain is selected with a targeted BLER<=0.1, the decoding failure of a data packet designated to the UE with bad channel gain at the receiver of the UE with good channel is very small, i.e. the BLER is usually much less than 0.01. This again confirms the quasi-orthogonality of NOMA achieved by multi-user power allocation and SIC as mentioned earlier in Section II.C. Performance in low and high mobility scenariosNext, we investigate NOMA gain with various UE speeds. Figure 6 shows the cell throughput gain and cell-edge throughput gain of NOMA over OMA for wideband and subband scheduling withdifferent user velocities. The number of users per cell is 10 and FTPA with αFTPA =0.5 is used for NOMA power allocation. It can be seen that the cell throughput gains of NOMA over OMA are observed over a wide range of UE speeds for both wideband and subband scheduling and with and without error propagation. Specifically, NOMA is shown to maintain good gains compared to OMA in particular with wideband scheduling. Thus, NOMA can be a promising multiple access to provide a good robustness to mobility as it relies mainly on receiver side CSI and signal processing.Fig. 6. NOMA cell throughput gains with various UE speeds (wideband and subband scheduling, with and without error propagation, 10UEs).D. Combination of NOMA and MIMOFigure 7 shows one form of combining downlink NOMA with MIMO using random (opportunistic) beamforming [17, 18]. In this form, the BS transmitter generates multiple beams similarly to multi-user (MU)-MIMO, and superposes multiple UEs within each beam [8]. In the UE receiver side, two interference cancellation approaches, non-linear SIC and linear interference suppression by interference rejection combining (IRC) [19], are jointly used as follows.9 SIC is used for intra-beam user demultiplexing, i.e.,interference cancellation among the UEs belonging to a group with the same precoding weights applied. The multiple access scheme within each beam (group) is the same as NOMA.9 IRC is used for inter-beam interference suppression, i.e.,interference suppression among UE groups with different precoding weights applied. Interference from other beams is simply suppressed by combining the signals received at the receive antennas of the UE. A key benefit of IRC is that it does not require the decoding of other UE groups in other beams.Fig. 7. NOMA/MIMO scheme applying with IRC-SIC receivers.BSBeam-level SINRHighLowBeam 1Beam 2Freq.Freq.UE 1UE 2UE 3UE 4PowerPowerUE 2 signal decodingIRCSIC of UE 2 signal UE 1 signal decoding IRCSIC of UE 4 signalUE 3 signal decodingIRCUE 4 signal decodingIRCFigure 8 shows the CDF of the user throughput for NOMA andOMA for 1x2 SIMO (as in previous evaluations), and for 2x2 MIMOusing random beamforming at the BS transmitter side and IRC-SIC receiver at the UE side. Differently from previous evaluations in Section III, we apply a 19-hexagonal macrocell model without sectorization. For the case of OMA with 2x2 MIMO, a single-stream transmission is applied per transmit beam. Figure 8 shows that NOMA gains can be maintained almost at the same level irrespectiveof the antenna configuration, i.e., 1x2 SIMO or 2x2 MIMO with random beamforming. One interesting thing observed here is that the performance of NOMA with 1x2 SIMO is very similar to that ofOMA with 2x2 MIMO using opportunistic beamforming (OBF). This implies that the NOMA with SIC has a similar effect to spatial multiplexing using random beamforming, and NOMA can achieve a competitive level of performance to random beamforming with a smaller number of transmit antennas at the BS. However, the proposed NOMA/MIMO scheme requires a relatively large numberof UEs to obtain a sufficient throughput gain for random (opportunistic) beamforming [17, 18]. When the number of UEs percell is small, it may be better to apply a closed-loop precoding orsingle-user (SU)-MIMO approach rather than the random beamforming approach. Therefore, the support for multiple MIMO modes, e.g., closed-loop and open-loop, SU-MIMO and MU-MIMOand so on, needs to be investigated for NOMA.Fig. 8. System-level evaluation of downlink NOMA combined with MIMO using random beamforming (20UEs).IV.C ONCLUSIONThis paper presented our NOMA concept for FRA toward the2020s-era. Different from the current LTE radio access scheme, NOMA superposes mutliple users in the power-domain, exploits the channel gain difference between multiplexed UEs. Although NOMA adopts an SIC receiver as a baseline receiver, we believe this is becoming more and more viable with the expected evolution of device processing capabilities in the future. In addition, we discussedthe practical considerations and the gains of NOMA under practical considerations, such as, multi-user power allocation, signalling overhead, SIC error propagation, and performance in high mobility scenarios. Furthermore, we discussed the combination of NOMAwith MIMO by applying random beamforming to transform the MIMO channel to a SIMO channel where SIC receiver is used forintra-beam interference mitigation and IRC for inter-beam interference mitigation. Under multiple configurations and setups, the achievable gains are shown promising, in the order of 30%, evenwhen practical considerations were taken into account. R EFERENCES[1]Y. Kishiyama, A. Benjebbour, H. Ishii, and T. Nakamura,“Evolution concept and candidate technologies for future stepsof LTE-A,” IEEE ICCS 2012, Nov. 2012.[2]3GPP TS36.300, Evolved Universal Terrestrial Radio Access(E-UTRA) and Evolved Universal Terrestrial Radio Access Network (E-UTRAN); Overall description.[3]3GPP TR36.814 (V9.0.0), “Further advancements for E-UTRAphysical layer aspects,” Mar. 2010.[4] D. Tse and P. Viswanath, Fundamentals of WirelessCommunication, Cambridge University Press, 2005.[5]G. Caire and S. Shamai, “On the achievable throughput of amulti-antenna Gaussian broadcast channel,” IEEE Trans. Inf.Theory, vol. 49, no. 7, pp. 1692-1706, July 2003.[6]T. Takeda and K. Higuchi, “Enhanced user fairness using non-orthogonal access with SIC in cellular uplink,” IEEE VTC Fall2011, Sept. 2011.[7]K. Higuchi and Y. Kishiyama, “Non-orthogonal access withsuccessive interference cancellation for future radio access,”APWCS 2012, Aug. 2012.[8]K. Higuchi and Y. Kishiyama, "Non-orthogonal access withrandom beamforming and intra-beam SIC for cellular MIMO downlink," IEEE VTC Fall 2013, Sept. 2013.[9]N. Otao, Y. Kishiyama, and K. Higuchi, “Performance of non-orthogonal access with SIC in cellular downlink using proportional fair-based resource allocation,” ISWCS 2012, pp.476-480, Aug. 2012.[10]Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li,and K. Higuchi, “Non-orthogonal multiple access (NOMA) forfuture radio access,” IEEE VTC spring 2013, June 2013.[11]Y. Saito, A. Benjebbour, Y. Kishiyama, and T. Nakamura,“System-level performance evaluation of downlink non-orthogonal multiple access (NOMA),” IEEE PIMRC 2013,Sept. 2013.[12] A. Benjebbour, A. Li, Y. Saito, Y. Kishiyama, A. Harada, andT. Nakamura, “System-level performance of downlink NOMAfor future LTE enhancements,” IEEE Globecom, Dec. 2013. [13]3GPP, RP-130404,“Study on network-assisted interferencecancellation and suppression for LTE,” Feb. 2013.[14]K. Brueninghaus et al., “Link performance models for systemlevel simulations of broadband radio access systems,” IEEEPIMRC 2005, Sept. 2005.[15]3GPP, “Physical layer aspects for Evolved UTRA,” TR25.814,V7.1.0, Oct. 2006.[16] F. P. Kelly et al., “Rate control for communication networks:shadow prices, proportional fairness and stability,” Journal of the Operational Research Society, vol. 49, Sept. 1998.[17]M. Kountouris and D. Gesbert, “Memory-based opportunisticmulti-user beamforming,” Proc. IEEE Int. Symp. Information Theory (ISIT), Sept. 2005.[18]P. Viswanath, D.N.C. Tse, and R. Laroia, “Opportunisticbeamforming using dumb antennas,” IEEE Trans. Inf. Theory,vol. 48, no. 6, pp. 1277-1294, June 2002.[19]Y. Ohwatari, N. Miki, T. Asai, T. Abe, and H. Taoka,“Performance of interference rejection combining receiver to suppress inter-cell interference in LTE-Advanced downlink,”IEICE Trans. Commun., vol. E94-B, no. 12, Dec. 2011.ACKNOWLEDGMENTPart of this work has been performed in the framework of the FP7 project ICT-317669 METIS, which is partly funded by the European Union. The authors would like to acknowledge the contributions of their colleagues in METIS, although the views expressed are those of the authors and do notnecessarily represent the project.。

2024版New Concept English Volume 3 Lesson 1 Coursew

Courseware•Course Introduction and Background •Vocabulary and Phrase Analysis•Intensive Reading and Understanding of Texts•Grammar knowledge sorting andapplication•Listening training and improvement •Oral expression and communication ability cultivation目录01 Course Introduction and BackgroundSystematicApproachThe textbooks are designed to follow a logical and sequential structure, gradually introducing new concepts and building on previously learned materials CommunicationBasedThe series emphasizescommunication skills,encoding students toactively participate inconversations anddiscussionsCulturalAwarenessIt involves cultural elements,allowing students to gaininsights into differentcultures and improve theircross cultural communicationabilitiesIntegrated SkillsThe textbooks promote theintegration of listening,speaking, reading, andwriting skills through a varietyof activities and exercises01020304Characteristics of the New Concept English Series TextbooksThe Structure and Content of the Textbook in Volume•Units and Lessons: Volume 3 is divided into several units, with eachunit focusing on a specific topic Each unit consistency of multiplelessons that explores the topic in depth•Vocabulary and Grammar: Each lesson introduces new vocabulary andgrammar points, providing examples and context for betterunderstanding•Listening and Speaking Activities: The textbook includes listeningexercises and speaking tasks to help students improve their listeningcomprehension and oral communication skills•Reading and Writing Practices: Students are provided with readingtexts and writing assignments to enhance their readingcomprehension and written expressionTopic: Lesson 1 focuses on the topic of "Travel and Tourism," exploring various aspects of traveling and visiting new places Learning Objectives: By the end of Lesson 1, students should be able to+Understand and use vocabulary related to travel and tourism +Communicate effectively about their travel experiences and plans+Read and compare texts related to travel destinations and activities +Write about their own travel experiences or imaging tripsTopic and Learning Objectives of Lesson02 Vocabulary and Phrase AnalysisKey vocabulary explanation and example sentencesVocabulary 1* Definition 1 * -* ExampleSentence 1*Vocabulary 2* Definition 2 * -* ExampleSentence 2*Vocabulary 3* Definition 3 * -* Example Sentence 3** Explanation 1 * -* ExampleSentence with Phrase 1*Phrase 1* Explanation 2 * -* Example Sentence with Phrase 2*Phrase 2* Explanation 3 * -* Example Sentence with Phrase 3*Phrase 3Common Phrase Matching and ApplicationUse mnemonic devices such as rhymes or acronyms to help remember new wordsTip 1Tip 2Tip 3Practice using new vocabulary in context by writing intentions or participating in conversationsReview and repeat new words regularly to commit them to long term memory030201Vocabulary Memory Skills Sharing03 Intensive Reading and Understanding ofTextsIntroduction to the background and overview of the main idea of the textThe background of the textThe lesson is set in a contemporary social context,discussing issues related to technology, environment,and social changeOverview of the main ideaThe text explores the impact of technology on our livesand the environment, and resources readers to thinkcritically about the role of technology in societyKey presence structure analysis and translationKey presence structuresThe text uses a variety of presence structures, including complexpresence, passive voice, and normalization to confirm informationeffectivelyTranslation of key sensesSome key senses in the text may be difficult to understand due to theircomplex syntax or vocabulary Providing translations can help readersbetter grasp the meaning of these sensesIn depth exploration of article content•Analysis of themes and topics: The text touches on themes such astechnology, environment, social change, and ethics Analyzing thesethemes and topics can help readers gain a deeper understanding ofthe issues discussed•Critical thinking questions: Encouraging readers to think criticallyabout the content of the text can help them form their own opinionsand views on the issues raised Questions such as "What are thepotential risks of releasing too health on technology?" or "How can webalance the benefits of technology with its negative impacts on theenvironment?" can stimulate critical thinking and discussion•Connection to real world examples: Relating the content of the text toreal world examples can make it more reliable and easier tounderstand For instance, discussing how cancer technologies havechanged the way we communicate or how they have contributed toenvironmental problems can help readers see the relevance of the textto their own lives04 Grammar knowledge sorting andapplicationReview of Key Grammar Projects in This Lesson"Past particle as objectiverevised the concept of using past particle forms as objectives to describe nouns,e.g.," a broken window, "" a painted house. ""Reported speech with 'said' and 'told'reviewed the rules for converting direct speech to reported speech using 'said'and 'told,' including changes in tense, pronouns, and question structureModal verbs for production and specificationpracticed using modal verbs such as' must, '' can, '' could, '' may, 'and' right 'toexpress production and specification in different contextsPast particle as objectiveDiscussed how past particle forms can be used as objectives to modify nounsAnalyzed examples such as "a fried child" and "a well trained dog" to illustrate how the past particle form changes mean based on contextReported speech with 'said' and 'told'Provided a detailed explanation of the rules for converting direct speech toreported speech Discussed changes in tense, pronunciations, and question structure, and analyzed example sentences to clarify the conceptsModal verbs for production and specificationExplained the use of modal verbs to express production and specification indifferent contexts Discussed the nuances of each modal verb and provided example sentences to illustrate their usageDetailed explanation and example analysis of relevant grammar rulesExercise questions on modal verbs for production and specification: Presented a range of exercise questions on using modal verbs for production and specification Analyzed the answers to assess understanding and offered additional practicematerials for furtherreinforcementExercise questions on pastparticle as objective: Provided aset of exercise questions on using past particle forms as objectivesAnalyzed the answers to identifycommon errors and discussed strategies for improvement Exercise questions on reported speech with 'said' and 'told': Offered a series of exercise questions on converting direct speech to reported speech Reviewed the answers to highlight common misses and providedguidance on how to avoid them Grammar exercise questions and answer analysis05 Listening training and improvementSelect authentic and varied listening materials: Choose materials that are representative of real life situations and cover a range of topics, accounts, and speeds to expose students to different listening challenges Teaching listening skills explicitly:Provide students with strategiesand techniques to improve theirlistening, such as predictingcontent, recognizing key wordsand phrases, and inferringmeaning from contextGuide students in active listening:Encourage students to engageactively with the listening materialby taking notes, summarizing, ordiscussing what they hear to deeptheir understanding010203 Listening material selection and skill guidanceListening practice questions and answer analysis Design targeted practice questionsCreate questions that test students' understanding of specific details, main ideas, and implied meanings inthe listening materialProvide answer analysisAfter students complete the practice questions, go through the answers with them, discussing why eachanswer is correct or incorrect and how they can improve their listening comprehensionEncourage self reflectionPrompt students to reflect on their performance and identify areas where they need toimprove their listening skillsSelf testing and assessment of listening expertiseOffer guidance and feedback on students' self-assessment to help themidentify areas of strength and weakness and set goals for further improvementProvide feedback on self-assessmentProvide students with resources to create their own listening tests, such asaudio recordings and accompanying questions, to allow them to practiceindependentlyDevelop self testing materials Advise students to regularly assess their own listening expertise by taking selftests and reflecting on their progressEncourage regular self-assessment06Oral expression and communication abilitycultivationDesigning various speaking activities: including individual presentations, group discussions, debites, and role plays to enhance active participation and improve students' oral Providing constructive feedback on students'performance, highlighting areas forimprovement, and providing tips and strategiesfor effective communicationImplementing authentic materials:incorporating authentic materials such as newsarticles, podcasts, and videos to provide real life context and stimulate discussionDesign and implementation of oral practice activitiesRole playing and situational dialogue examplesPreparing role play scenarios01Creating scenarios that simulate real life situations, allowingstudents to practice language use in a controlled environmentModeling dialogues02demonstrating example dialogues to illustrate appropriatelanguage use, promotion, and introductionEncouraging improvement03encoding students to improve within the role-play scenarios todevelop their spontaneity and creativityReflecting on performance encoding students to reflect on their own performance, identify strengths and weaknesses, and set goals for improvement Using fabrics forself-assessmentimproving fabrics or checklists tohelp students objectively evaluatetheir own oral expression skillsSeeking peerfeedbackencoding students to seekfeedback from peers, which canprovide val010203 Self evaluation of oral expression capabilityTHANKS。

2024年度Deform培训教程

结果分析
通过对比模拟结果和实际加工结果，可以验证材料属性和边界条件设置的准确性。如果存在差异，需要对设置进行调整，并重新运行模拟。
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模拟计算与结果分析
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模拟计算参数设置
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材料参数
包括弹性模量、泊松比、密度等，用于描述材料的力学性质
。
边界条件
定义模型在特定方向或位置的位移、速度、加速度等限制条
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软件功能和特点
强大的有限元分析能力
丰富的材料数据库
DEFORM软件提供了全面的有限元分析功能，可以对金属成形过程中的应力、应变、温度等物理量进行准确计算。
软件内置了多种材料的数据库，用户可以根据需要选择合适的材料模型进行模拟。
直观的图形界面
多种求解器选择
DEFORM软件采用了直观的图形界面设计，使得用户可以更加方便地进行模型建立、结果查看等操作。
件。
载荷条件
施加在模型上的外力或内力，如集中力、均布载荷、热载荷
等。
求解设置
选择适当的求解器、迭代方法、收敛准则等，以确保计算结
果的准确性和效率。
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结果文件类型及查看方法
结果文件类型
Deform软件支持多种结果文件输出格式，如.odb、.h3d、.vtk等，方便用户进行后处理和可视化分析。
鼓励学员们将Deform软件应用于更多领域，如塑料成形、复合材料加工等，探索新的应用场景和解决方案。
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交流与合作
建议学员们之间保持联系，定期交流学习心得和应用经验，共同提高。同时，可以与相关领域的专家和企业合作，共同推动Deform软件的发展和应用。

Lecture7

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Yu Ren
Mathematical Economics: Lecture 7
Chapter 12: Limits and Open Sets
Sequence in R m
Deﬁnition: {xi }, xi ∈ R m Euclidean metric in R m : d(xi , xj ) = ||xi − xj || = (xi1 − xj1 )2 + · · · + (xim − xjm )2
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Yu Ren
Mathematical Economics: Lecture 7
Chapter 12: Limits and Open Sets
Sequences of Real Numbers
Subsequence: {yj } is a subsequence of {xi } if ∃ an inﬁnite increasing set of natural number {nj } s.t. y1 = xn1 , y2 = xn2 ,y3 = xn3 , for example {1, −1, 1, −1, · · · } has two subsequences: {1, 1, · · · } {−1, −1, · · · } and so on.
logo
Yu Ren
Mathematical Economics: Lecture 7
Chapter 12: Limits and Open Sets
Sequences of Real Numbers
Properties of Limits Theorem 12.1: A sequence can have at most one limit Theorem 12.2 If xn → x and yn → y, then xn + yn → x + y Theorem 12.3 If xn → x and yn → y, then xn × yn → xy

高等数学中定义定理的英文表达

高等数学中定义定理的英文表达Value of function ：函数值Variable ：变数Vector ：向量Velocity ：速度Vertical asymptote ：垂直渐近线Volume ：体积X-axis ：x轴x-coordinate ：x坐标x-intercept ：x截距Zero vector ：函数的零点Zeros of a polynomial ：多项式的零点TTangent function ：正切函数Tangent line ：切线Tangent plane ：切平面Tangent vector ：切向量Total differential ：全微分Trigonometric function ：三角函数Trigonometric integrals ：三角积分Trigonometric substitutions ：三角代换法Tripe integrals ：三重积分SSaddle point ：鞍点Scalar ：纯量Secant line ：割线Second derivative ：二阶导数Second Derivative Test ：二阶导数试验法Second partial derivative ：二阶偏导数Sector ：扇形Sequence ：数列Series ：级数Set ：集合Shell method ：剥壳法Sine function ：正弦函数Singularity ：奇点Slant asymptote ：斜渐近线Slope ：斜率Slope-intercept equation of a line ：直线的斜截式Smooth curve ：平滑曲线Smooth surface ：平滑曲面Solid of revolution ：旋转体Space ：空间Speed ：速率Spherical coordinates ：球面坐标Squeeze Theorem ：夹挤定理Step function ：阶梯函数Strictly decreasing ：严格递减Strictly increasing ：严格递增Sum ：和Surface ：曲面Surface integral ：面积分Surface of revolution ：旋转曲面Symmetry ：对称RRadius of convergence ：收敛半径Range of a function ：函数的值域Rate of change ：变化率Rational function ：有理函数Rationalizing substitution ：有理代换法Rational number ：有理数Real number ：实数Rectangular coordinates ：直角坐标Rectangular coordinate system ：直角坐标系Relative maximum and minimum ：相对极大值与极小值Revenue function ：收入函数Revolution , solid of ：旋转体Revolution , surface of ：旋转曲面Riemann Sum ：黎曼和Riemannian geometry ：黎曼几何Right-hand derivative ：右导数Right-hand limit ：右极限Root ：根P、QParabola ：拋物线Parabolic cylinder ：抛物柱面Paraboloid ：抛物面Parallelepiped ：平行六面体Parallel lines ：并行线Parameter ：参数Partial derivative ：偏导数Partial differential equation ：偏微分方程Partial fractions ：部分分式Partial integration ：部分积分Partiton ：分割Period ：周期Periodic function ：周期函数Perpendicular lines ：垂直线Piecewise defined function ：分段定义函数Plane ：平面Point of inflection ：反曲点Polar axis ：极轴Polar coordinate ：极坐标Polar equation ：极方程式Pole ：极点Polynomial ：多项式Positive angle ：正角Point-slope form ：点斜式Power function ：幂函数Product ：积Quadrant ：象限Quotient Law of limit ：极限的商定律Quotient Rule ：商定律M、N、OMaximum and minimum values ：极大与极小值Mean Value Theorem ：均值定理Multiple integrals ：重积分Multiplier ：乘子Natural exponential function ：自然指数函数Natural logarithm function ：自然对数函数Natural number ：自然数Normal line ：法线Normal vector ：法向量Number ：数Octant ：卦限Odd function ：奇函数One-sided limit ：单边极限Open interval ：开区间Optimization problems ：最佳化问题Order ：阶Ordinary differential equation ：常微分方程Origin ：原点Orthogonal ：正交的LLaplace transform ：Leplace 变换Law of Cosines ：余弦定理Least upper bound ：最小上界Left-hand derivative ：左导数Left-hand limit ：左极限Lemniscate ：双钮线Length ：长度Level curve ：等高线L'Hospital's rule ：洛必达法则Limacon ：蚶线Limit ：极限Linear approximation：线性近似Linear equation ：线性方程式Linear function ：线性函数Linearity ：线性Linearization ：线性化Line in the plane ：平面上之直线Line in space ：空间之直线Lobachevski geometry ：罗巴切夫斯基几何Local extremum ：局部极值Local maximum and minimum ：局部极大值与极小值Logarithm ：对数Logarithmic function ：对数函数IImplicit differentiation ：隐求导法Implicit function ：隐函数Improper integral ：瑕积分Increasing/Decreasing Test ：递增或递减试验法Increment ：增量Increasing Function ：增函数Indefinite integral ：不定积分Independent variable ：自变数Indeterminate from ：不定型Inequality ：不等式Infinite point ：无穷极限Infinite series ：无穷级数Inflection point ：反曲点Instantaneous velocity ：瞬时速度Integer ：整数Integral ：积分Integrand ：被积分式Integration ：积分Integration by part ：分部积分法Intercepts ：截距Intermediate value of Theorem ：中间值定理Interval ：区间Inverse function ：反函数Inverse trigonometric function ：反三角函数Iterated integral ：逐次积分HHigher mathematics 高等数学/高数E、F、G、HEllipse ：椭圆Ellipsoid ：椭圆体Epicycloid ：外摆线Equation ：方程式Even function ：偶函数Expected Valued ：期望值Exponential Function ：指数函数Exponents , laws of ：指数率Extreme value ：极值Extreme Value Theorem ：极值定理Factorial ：阶乘First Derivative Test ：一阶导数试验法First octant ：第一卦限Focus ：焦点Fractions ：分式Function ：函数Fundamental Theorem of Calculus ：微积分基本定理Geometric series ：几何级数Gradient ：梯度Graph ：图形Green Formula ：格林公式Half-angle formulas ：半角公式Harmonic series ：调和级数Helix ：螺旋线Higher Derivative ：高阶导数Horizontal asymptote ：水平渐近线Horizontal line ：水平线Hyperbola ：双曲线Hyper boloid ：双曲面DDecreasing function ：递减函数Decreasing sequence ：递减数列Definite integral ：定积分Degree of a polynomial ：多项式之次数Density ：密度Derivative ：导数of a composite function ：复合函数之导数of a constant function ：常数函数之导数directional ：方向导数domain of ：导数之定义域of exponential function ：指数函数之导数higher ：高阶导数partial ：偏导数of a power function ：幂函数之导数of a power series ：羃级数之导数of a product ：积之导数of a quotient ：商之导数as a rate of change ：导数当作变率right-hand ：右导数second ：二阶导数as the slope of a tangent ：导数看成切线之斜率Determinant ：行列式Differentiable function ：可导函数Differential ：微分Differential equation ：微分方程partial ：偏微分方程Differentiation ：求导法implicit ：隐求导法partial ：偏微分法term by term ：逐项求导法Directional derivatives ：方向导数Discontinuity ：不连续性Disk method ：圆盘法Distance ：距离Divergence ：发散Domain ：定义域Dot product ：点积Double integral ：二重积分change of variable in ：二重积分之变数变换in polar coordinates ：极坐标二重积分CCalculus ：微积分differential ：微分学integral ：积分学Cartesian coordinates ：笛卡儿坐标图片一般指直角坐标Cartesian coordinates system ：笛卡儿坐标系Cauch’s Mean Value Theorem ：柯西均值定理Chain Rule ：连锁律Change of variables ：变数变换Circle ：圆Circular cylinder ：圆柱Closed interval ：封闭区间Coefficient ：系数Composition of function ：函数之合成Compound interest ：复利Concavity ：凹性Conchoid ：蚌线Cone ：圆锥Constant function ：常数函数Constant of integration ：积分常数Continuity ：连续性at a point ：在一点处之连续性of a function ：函数之连续性on an interval ：在区间之连续性from the left ：左连续from the right ：右连续Continuous function ：连续函数Convergence ：收敛interval of ：收敛区间radius of ：收敛半径Convergent sequence ：收敛数列series ：收敛级数Coordinate：s：坐标Cartesian ：笛卡儿坐标cylindrical ：柱面坐标polar ：极坐标rectangular ：直角坐标spherical ：球面坐标Coordinate axes ：坐标轴Coordinate planes ：坐标平面Cosine function ：余弦函数Critical point ：临界点Cubic function ：三次函数Curve ：曲线Cylinder：圆柱Cylindrical Coordinates ：圆柱坐标A、BAbsolute convergence ：绝对收敛Absolute extreme values ：绝对极值Absolute maximum and minimum ：绝对极大与极小Absolute value ：绝对值Absolute value function ：绝对值函数Acceleration ：加速度Antiderivative ：反导数Approximate integration ：近似积分Approximation ：逼近法by differentials ：用微分逼近linear ：线性逼近法by Simpson’s Rule ：Simpson法则逼近法by the Trapezoidal Rule ：梯形法则逼近法Arbitrary constant ：任意常数Arc length ：弧长Area ：面积under a curve ：曲线下方之面积between curves ：曲线间之面积in polar coordinates ：极坐标表示之面积of a sector of a circle ：扇形之面积of a surface of a revolution ：旋转曲面之面积Asymptote ：渐近线horizontal ：水平渐近线slant ：斜渐近线vertical ：垂直渐近线Average speed ：平均速率Average velocity ：平均速度Axes, coordinate ：坐标轴Axes of ellipse ：椭圆之轴Binomial series ：二项级数。

1-2007_-_Y_F_Han_-_PreparationofnanosizedMn3O4SBA15catalystforcomplet[retrieved-2016-11-15]

Preparation of nanosized Mn 3O 4/SBA-15catalyst for complete oxidation of low concentration EtOH in aqueous solution with H 2O 2Yi-Fan Han *,Fengxi Chen,Kanaparthi Ramesh,Ziyi Zhong,Effendi Widjaja,Luwei ChenInstitute of Chemical and Engineering Sciences,1Pesek Road,Jurong Island 627833,Singapore Received 11May 2006;received in revised form 18December 2006;accepted 29May 2007Available online 2June 2007AbstractA new heterogeneous Fenton-like system consisting of nano-composite Mn 3O 4/SBA-15catalyst has been developed for the complete oxidation of low concentration ethanol (100ppm)by H 2O 2in aqueous solution.A novel preparation method has been developed to synthesize nanoparticles of Mn 3O 4by thermolysis of manganese (II)acetylacetonate on SBA-15.Mn 3O 4/SBA-15was characterized by various techniques like TEM,XRD,Raman spectroscopy and N 2adsorption isotherms.TEM images demonstrate that Mn 3O 4nanocrystals located mainly inside the SBA-15pores.The reaction rate for ethanol oxidation can be strongly affected by several factors,including reaction temperature,pH value,catalyst/solution ratio and concentration of ethanol.A plausible reaction mechanism has been proposed in order to explain the kinetic data.The rate for the reaction is supposed to associate with the concentration of intermediates (radicals: OH,O 2Àand HO 2)that are derived from the decomposition of H 2O 2during reaction.The complete oxidation of ethanol can be remarkably improved only under the circumstances:(i)the intermediates are stabilized,such as stronger acidic conditions and high temperature or (ii)scavenging those radicals is reduced,such as less amount of catalyst and high concentration of reactant.Nevertheless,the reactivity of the presented catalytic system is still lower comparing to the conventional homogenous Fenton process,Fe 2+/H 2O 2.A possible reason is that the concentration of intermediates in the latter is relatively high.#2007Elsevier B.V .All rights reserved.Keywords:Hydrogen peroxide;Fenton catalyst;Complete oxidation of ethanol;Mn 3O 4/SBA-151.IntroductionRemediation of wastewater containing organic constitutes is of great importance because organic substances,such as benzene,phenol and other alcohols may impose toxic effects on human and animal anic efﬂuents from pharmaceu-tical,chemical and petrochemical industry usually contaminate water system by dissolving into groundwater.Up to date,several processes have been developed for treating wastewater that contains toxic organic compounds,such as wet oxidation with or without solid catalysts [1–4],biological oxidation,supercritical oxidation and adsorption [5,6],etc.Among them,catalytic oxidation is a promising alternative,since it avoids the problem of the adsorbent regeneration in the adsorption process,decreases signiﬁcantly the temperature and pressure in non-catalytic oxidation techniques [7].Generally,the disposalof wastewater containing low concentration organic pollutants (e.g.<100ppm)can be more costly through all aforementioned processes.Thus,catalytic oxidation found to be the most economical way for this purpose with considering its low cost and high efﬁciency.Currently,a Fenton reagent that consists of homogenous iron ions (Fe 2+)and hydrogen peroxide (H 2O 2)is an effective oxidant and widely applied for treating industrial efﬂuents,especially at low concentrations in the range of 10À2to 10À3M organic compounds [8].However,several problems raised by the homogenous Fenton system are still unsolved,e.g.disposing the iron-containing waste sludge,limiting the pH range (2.0–5.0)of the aqueous solution,and importantly irreversible loss of activity of the reagent.To overcome these drawbacks raised from the homogenous Fenton system,since 1995,a heterogeneous Fenton reagent using metal ions exchanged zeolites,i.e.Fe/ZSM-5has proved to be an interesting alternative catalytic system for treating wastewater,and showed a comparable activity with the homogenous Fenton system [9].However,most reported heterogeneous Fenton reagents still need UV radiation during/locate/apcatbApplied Catalysis B:Environmental 76(2007)227–234*Corresponding author.Tel.:+6567963806.E-mail address:han_yi_fan@.sg (Y .-F.Han).0926-3373/$–see front matter #2007Elsevier B.V .All rights reserved.doi:10.1016/j.apcatb.2007.05.031oxidation of organic compounds.This might limit the application of homogeneous Fenton system.Exploring other heterogeneous catalytic system considering the above disadvantages,is still desirable for this purpose.Here,we present an alternative catalytic system for the complete oxidation of organic com-pounds in aqueous solution using supported manganese oxide as catalyst under mild conditions,which has rarely been addressed.Mn-containing oxide catalysts have been found to be very active for the catalytic wet oxidation of organic efﬂuents (CWO)[10–14],which is operated at high air pressures(1–22MPa)and at high temperatures(423–643K)[15].On the other hand,manganese oxide,e.g.MnO2[16],is well known to be active for the decomposition of H2O2in aqueous solution to produce hydroxyl radical( OH),which is considered to be the most robust oxidant so far.The organic constitutes can be deeply oxidized by those radicals rapidly[17].The only by-product is H2O from decomposing H2O2.Therefore,H2O2is a suitable oxidant for treating the wastewater containing organic compounds.Due to the recent progress in the synthesis of H2O2 directly from H2and O2[18,19],H2O2is believed to be produced through more economical process in the coming future.So,the heterogeneous Fenton system is economically acceptable.In this study,nano-crystalline Mn3O4highly dispersed inside the mesoporous silica,SBA-15,has been prepared by thermolysis of organic manganese(II)acetylacetonate in air. We expect the unique mesoporous structure may provide add-itional function(conﬁnement effect)to the catalytic reaction, i.e.occluding/entrapping large organic molecules inside pores. The catalyst as prepared has been examined for the complete oxidation of ethanol in aqueous solution with H2O2,or to say, wet peroxide oxidation.Ethanol was selected as a model organic compound because(i)it is one of the simplest organic compounds and can be easily analyzed,(ii)it has high solu-bility in water due to its strong hydrogen bond with water molecule and(iii)the structure of ethanol is quite stable and only changed through catalytic reaction.Presently,for theﬁrst time by using the Mn3O4/SBA-15catalyst,we investigated the peroxide ethanol oxidation affected by factors such as temperature,pH value,ratio of catalyst(g)and volume of solution(L),and concentration of ethanol in aqueous solution. In addition,plausible reaction mechanisms are established to explain the peroxidation of ethanol determined by the H2O2 decomposition.2.Experimental2.1.Preparation and characterization of Mn3O4/SBA-15 catalystSynthesis of SBA-15is similar to the previous reported method[20]by using Pluronic P123(BASF)surfactant as template and tetraethyl orthosilicate(TEOS,98%)as silica source.Manganese(II)acetylacetonate([CH3COCH C(O)CH3]2Mn,Aldrich)by a ratio of2.5mmol/gram(SBA-15)wereﬁrst dissolved in acetone(C.P.)at room temperature, corresponding to ca.13wt.%of Mn3O4with respect to SBA-15.The preparation method in detail can be seen in our recent publications[21,22].X-ray diffraction proﬁles were obtained with a Bruker D8 diffractometer using Cu K a radiation(l=1.540589A˚).The diffraction pattern was taken in the Bragg angle(2u)range at low angles from0.68to58and at high angles from308to608at room temperature.The XRD patterns were obtained by scanning overnight with a step size:0.028per step,8s per step.The dispersive Raman microscope employed in this study was a JY Horiba LabRAM HR equipped with three laser sources(UV,visible and NIR),a confocal microscope,and a liquid nitrogen cooled charge-coupled device(CCD)multi-channel detector(256pixelsÂ1024pixels).The visible 514.5nm argon ion laser was selected to excite the Raman scattering.The laser power from the source is around20MW, but when it reached the samples,the laser output was reduced to around6–7MW after passing throughﬁltering optics and microscope objective.A100Âobjective lens was used and the acquisition time for each Raman spectrum was approximately 60–120s depending on the sample.The Raman shift range acquired was in the range of50–1200cmÀ1with spectral resolution1.7–2cmÀ1.Adsorption and desorption isotherms were collected on Autosorb-6at77K.Prior to the measurement,all samples were degassed at573K until a stable vacuum of ca.5m Torr was reached.The pore size distribution curves were calculated from the adsorption branch using Barrett–Joyner–Halenda(BJH) method.The speciﬁc surface area was assessed using the BET method from adsorption data in a relative pressure range from 0.06to0.10.The total pore volume,V t,was assessed from the adsorbed amount of nitrogen at a relative pressure of0.99by converting it to the corresponding volume of liquid adsorbate. The conversion factor between the volume of gas and liquid adsorbate is0.0,015,468for N2at77K when they are expressed in cm3/g and cm3STP/g,respectively.The measurements of transmission electron microscopy (TEM)were performed at Tecnai TF20S-twin with Lorentz Lens.The samples were ultrasonically dispersed in ethanol solvent,and then dried over a carbon grid.2.2.Kinetic measurement and analysisThe experiment for the wet peroxide oxidation of ethanol was carried out in a glass batch reactor connected to a condenser with continuous stirring(400rpm).Typically,20ml of aqueous ethanol solution(initial concentration of ethanol: 100ppm)wasﬁrst taken in the round bottomﬂask(reactor) together with5mg of catalyst,corresponding to ca.1(g Mn)/30 (L)ratio of catalyst/solution.Then,1ml of30%H2O2solution was introduced into the reactor at different time intervals (0.5ml at$0min,0.25ml at32min and0.25ml at62min). The total molar ratio of H2O2/ethanol is about400/1. Hydrochloric acid(HCl,0.01M)was used to acidify the solution if necessary.NH4OH(0.1M)solution was used to adjust pH to9.0when investigating the effect of pH.The pH for the deionized water is ca.7.0(Oakton pH meter)and decreased to 6.7after adding ethanol.All the measurements wereY.-F.Han et al./Applied Catalysis B:Environmental76(2007)227–234 228performed under the similar conditions described above if without any special mention.For comparison,the reaction was also carried out with a typical homogenous Fenton reagent[17], FeSO4(5ppm)–H2O2,under the similar reaction conditions.The conversion of ethanol during reaction was detected using gas chromatography(GC:Agilent Technologies,6890N), equipped with HP-5capillary column connecting to a thermal conductive detector(TCD).There is no other species but ethanol determined in the reaction system as evidenced by the GC–MS. Ethanol is supposed to be completely oxidized into CO2and H2O.The variation of H2O2concentration during reaction was analyzed colorimetrically using a UV–vis spectrophotometer (Epp2000,StellarNet Inc.)after complexation with a TiOSO4/ H2SO4reagent[18].Note that there was almost no measurable leaching of Mn ion during reaction analyzed by ICP(Vista-Mpx, Varian).3.Results and discussion3.1.Characterization of Mn3O4/SBA-15catalystThe structure of as-synthesized Mn3O4inside SBA-15has beenﬁrst investigated with powder XRD(PXRD),and the proﬁles are shown in Fig.1.The proﬁle at low angles(Fig.1a) suggests that SBA-15still has a high degree of hexagonal mesoscopic organization even after forming Mn3O4nanocrys-tals[23].Several peaks at high angles of XRD(Fig.1b)indicate the formation of a well-crystallized Mn3O4.All the major diffraction peaks can be assigned to hausmannite Mn3O4 structure(JCPDS80-0382).By N2adsorption measurements shown in Fig.2,the pore volume and speciﬁc surface areas(S BET)decrease from 1.27cm3/g and937m2/g for bare SBA-15to0.49cm3/g and 299m2/g for the Mn3O4/SBA-15,respectively.About7.7nm of mesoporous diameter for SBA-15decreases to ca.6.3nm for Mn3O4/SBA-15.The decrease of the mesopore dimension suggests the uniform coating of Mn3O4on the inner walls of SBA-15.This nano-composite was further characterized by TEM. Obviously,the SBA-15employed has typical p6mm hex-agonal morphology with the well-ordered1D array(Fig.3a). The average pore size of SBA-15is ca.8.0nm,which is very close to the value(ca.7.7nm)determined by N2adsorption. Along[001]orientation,Fig.3b shows that the some pores areﬁlled with Mn3O4nanocrystals.From the pore A to D marked in Fig.3b correspond to the pores from empty to partially and fullyﬁlled;while the features for the SBA-15 nanostructure remains even after forming Mn3O4nanocrys-tals.Nevertheless,further evidences for the location of Mn3O4inside the SBA-15channels are still undergoing in our group.Raman spectra obtained for Mn3O4/SBA-15is presented in Fig.4a.For comparison the Raman spectrum was also recorded for the bulk Mn3O4(97.0%,Aldrich)under the similar conditions(Fig.4b).For the bulk Mn3O4,the bands at310,365, 472and655cmÀ1correspond to the bending modes of Mn3O4, asymmetric stretch of Mn–O–Mn,symmetric stretch of Mn3O4Fig.1.XRD patterns of the bare SBA-15and the Mn3O4/SBA-15nano-composite catalyst.(a)At low angles:(A)Mn3O4/SBA-15,(B)SBA-15;and (b)at high angles of Mn3O4/SBA-15.Fig.2.N2adsorption–desorption isotherms:(!)SBA-15,(~)Mn3O4/SBA-15.Y.-F.Han et al./Applied Catalysis B:Environmental76(2007)227–234229groups,respectively [24–26].However,a downward shift ($D n 7cm À1)of the peaks accompanying with a broadening of the bands was observed for Mn 3O 4/SBA-15.For instance,the distinct feature at 655cm À1for the bulk Mn 3O 4shifted to 648cm À1for the nanocrystals.The Raman bands broadened and shifted were observed for the nanocrystals due to the effect of phonon conﬁnement as suggested previously in the literature [27,28].Furthermore,a weak band at 940cm À1,which should associate with the stretch of terminal Mn O,is an indicative of the existence of the isolated Mn 3O 4group [26].The assignment of this unique band has been discussed in our previous publication [22].3.2.Kinetic study3.2.1.Blank testsUnder a typical reaction conditions,that is,20ml of 100ppm ethanol aqueous solution (pH 6.7)mixed with 1ml of 30%H 2O 2,at 343K,there is no conversion of ethanol was observed after running for 120min in the absence of catalyst or in the presence of bare SBA-15(5mg).Also,under the similar conditions in H 2O 2-free solution,ethanol was not converted for all blank tests even with Mn 3O 4/SBA-15catalyst (5mg)in the reactor.It suggests that a trace amount of oxygen dissolved in water or potential dissociation of adsorbed ethanol does not have any contribution to the conversion of ethanol under reaction conditions.To study the effect of low temperature evaporation of ethanol during reaction,we further examined the concentration of ethanol (100ppm)versus time at different temperatures in the absence of catalyst and H 2O 2.Loss of ca.5%ethanol was observed only at 363K after running for 120min.Hence,to avoid the loss of ethanol through evaporation at high temperatures,which may lead to a higher conversion of ethanol than the real value,the kinetic experiments in this study were performed at or below 343K.The results from blank tests conﬁrm clearly that ethanol can be transformed only by catalytic oxidation during reaction.3.2.2.Effect of amount of catalystThe effect of amount of catalyst on ethanol oxidation is presented in Fig.5.Different amounts of catalyst ranging from 2to 10mg were taken for the same concentration of ethanol (100ppm)in aqueous solution under the standard conditions.It can be observed that the conversion of ethanol increases monotonically within 120min,reaching 15,20and 12%for 2,5and 10mg catalysts,respectively.On the other hand,Fig.5shows that the relative reaction rates (30min)decreased from 0.7to ca 0.1mmol/g Mn min with the rise of catalyst amount from 2to 10mg.Apparently,more catalyst in the system may decrease the rate for ethanol peroxidation,and a proper ratio of catalyst (g)/solution (L)is required for acquiring a balance between the overall conversion of ethanol and reaction rate.In order to investigate the effects from other factors,5mg (catalyst)/20ml (solution),corresponding to 1(g Mn )/30(L)ratio of catalyst/solution,has been selected for the followedexperiments.Fig.4.Raman spectroscopy of the Mn 3O 4/SBA-15(a)and bulk Mn 3O 4(b).Fig.3.TEM images recorded along the [001]of SBA-15(a),Mn 3O 4/SBA-15(b):pore A unﬁlled with hexagonal structure,pores B and C partially ﬁlled and pore D completely ﬁlled.Y.-F .Han et al./Applied Catalysis B:Environmental 76(2007)227–2342303.2.3.Effect of temperatureAs shown in Fig.6,the reaction rate increases with increasing the reaction temperature.After 120min,the conversion of ethanol increases from 12.5to 20%when varying the temp-erature from 298to 343K.Further increasing the temperature was not performed in order to avoid the loss of ethanol by evaporation.Interestingly,the relative reaction rate increased with time within initial 60min at 298and 313K,but upward tendency was observed above 333K.3.2.4.Effect of pHIn the pH range from 2.0to 9.0,as illustrated in Fig.7,the reaction rate drops down with the rise of pH.It indicates that acidic environment,or to say,proton concentration ([H +])in the solution is essential for this reaction.With considering our target for this study:purifying water,pH approaching to 7.0in the reaction system is preferred.Because acidifying the solution with organic/inorganic acids may potentially causea second time pollution and result in surplus cost.Actually,there is almost no effect on ethanol conversion with changing pH from 5.5to 6.7in this system.It is really a merit comparing with the conventional homogenous Fenton system,by which the catalyst works only in the pH range of 2.0–5.0.3.2.5.Effect of ethanol concentrationThe investigation of the effect of ethanol concentration on the reaction rate was carried out in the ethanol ranging from 50to 500ppm.The results in Fig.8show that the relative reaction rate increased from 0.07to 2.37mmol/g Mn min after 120min with increasing the concentration of ethanol from 50to 500ppm.It is worth to note that the pH value of the solution slightly decreased from 6.7to 6.5when raising the ethanol concentration from 100to 500ppm.paring to a typical homogenous Fenton reagent For comparison,under the similar reaction conditions ethanol oxidation was performed using aconventionalFig.5.The ethanol oxidation as a function of time with different amount of catalyst.Conversion of ethanol vs.time (solid line)on 2mg (&),5mg (*)and 10mg (~)Mn 3O 4/SBA-15catalyst,the relative reaction rate vs.time (dash line)on 2mg (&),5mg (*)and 10mg (~)Mn 3O 4/SBA-15catalyst.Rest conditions:20ml of ethanol (100ppm),1ml of 30%H 2O 2,708C and pH of6.7.Fig.6.The ethanol oxidation as a function of temperature.Conversion of ethanol vs.time (solid line)at 258C (&),408C (*),608C (~)and 708C (!),the relative reaction rate vs.time (dash line)at 258C (&),408C (*),608C (~)and 708C (5).Rest conditions:20ml of ethanol (100ppm),1ml of 30%H 2O 2,pH of 6.7,5mg ofcatalyst.Fig.7.The ethanol oxidation as a function of pH value.Conversion of ethanol vs.time (solid line)at pH value of 2.0(&),3.5(*),4.5(~),5.5(!),6.7(^)and 9.0("),the relative reaction rate vs.time (dash line)at pH value of 2.0(&),3.5(*),4.5(~),5.5(5),6.7(^)and 9.0(").Rest conditions:20ml of ethanol (100ppm),1ml of 30%H 2O 2,708C,5mg ofcatalyst.Fig.8.The ethanol oxidation as a function of ethanol concentration.Conver-sion of ethanol vs.time (solid line)for ethanol concentration (ppm)of 50(&),100(*),300(~),500(!),the relative reaction rate vs.time (dash line)for ethanol concentration (ppm)of 50(&),100(*),300(~),500(5).Condi-tions:20ml of ethanol,pH of 6.7,1ml of 30%H 2O 2,708C,5mg of catalyst.Y.-F .Han et al./Applied Catalysis B:Environmental 76(2007)227–234231homogenous reagent,Fe 2+(5ppm)–H 2O 2(1ml)at pH of 5.0.It has been reported to be an optimum condition for this system [17].As shown in Fig.9,the reaction in both catalytic systems exhibits a similar behavior,that is,the conversion of ethanol increases with extending the reaction time.Varying reaction temperature from 298to 343K seems not to impact the conversion of ethanol when using the homogenous Fenton reagent.Furthermore,the conversion of ethanol (deﬁning at 120min)in the system of Mn 3O 4/SBA-15–H 2O 2is about 60%of that obtained from the conventional Fenton reagent.There are no other organic compounds observed in the reaction mixture other than ethanol suggesting that ethanol directly decomposing to CO 2and H 2O.3.2.7.Decomposition of H 2O 2In the aqueous solution,the capability of metal ions such as Fe 2+and Mn 2+has long been evidenced to be effective on the decomposition of H 2O 2to produce the hydroxyl radical ( OH),which is oxidant for the complete oxidation/degrading of organic compounds [9,17].Therefore,ethanol oxidation is supposed to be associated with H 2O 2decomposition.The investigation of H 2O 2decomposition has been performed under the reaction conditions (in an ethanol-free solution)with different amounts of catalyst.H 2O 2was introduced into the reaction system by three steps,initially 0.5ml followed by twice 0.25ml at 32and 62min,the pH of 6.7is set for all experiments except pH of 5.0for Fe 2+.As shown in Fig.10,H 2O 2was not converted in the absence of catalyst or presence of bare SBA-15(5mg);in contrast,by using the Mn 3O 4/SBA-15catalyst we observed that ca.Ninety percent of total H 2O 2was decomposed in the whole experiment.It can be concluded that that dissociation of H 2O 2is mainly caused by Mn 3O paratively,the rate of H 2O 2decomposition is relatively low with the homogenous Fenton reagent,total conversion of H 2O 2,was ca.50%after runningfor 120min.Considering the fact that H 2O 2decomposition can be signiﬁcantly enhanced with the rise of Fe 2+concentration,however,it seems not to have the inﬂuence on the reaction rate for ethanol oxidation simultaneously.The similar behavior of H 2O 2decomposition was also observed during ethanol oxidation.The rate for ethanol oxidation is lower for Mn 3O 4/SBA-15comparing to the conventional Fenton reagent.The possible reasons will be discussed in the proceeding section.3.3.Plausible reaction mechanism for ethanol oxidation with H 2O 2In general,the wet peroxide oxidation of organic constitutes has been suggested to proceed via four steps [15]:activation of H 2O 2to produce OH,oxidation of organic compounds withOH,recombination of OH to form O 2and wet oxidation of organic compounds with O 2.It can be further described by Eqs.(1)–(4):H 2O 2À!Catalyst =temperture 2OH(1)OH þorganic compoundsÀ!Temperatureproduct(2)2 OHÀ!Temperature 12O 2þH 2O(3)O 2þorganic compoundsÀ!Temperature =pressureproduct(4)The reactive intermediates produced from step 1(Eq.(1))participate in the oxidation through step 2(Eq.(2)).In fact,several kinds of radical including OH,perhydroxyl radicals ( HO 2)and superoxide anions (O 2À)may be created during reaction.Previous studies [29–33]suggested that the process for producing radicals could be expressed by Eqs.(5)–(7)when H 2O 2was catalytically decomposed by metal ions,such asFeparison of ethanol oxidation in systems of typical homogenous Fenton catalyst (5ppm of Fe 2+,20ml of ethanol (100ppm),1ml of 30%H 2O 2,pH of 5.0acidiﬁed with HCl)at room temperature (~)and 708C (!),and Mn 3O 4/SBA-15catalyst (&)under conditions of 20ml of ethanol (100ppm),pH of 6.7,1ml of 30%H 2O 2,708C,5mg ofcatalyst.Fig.10.An investigation of H 2O 2decomposition under different conditions.One milliliter of 30%H 2O 2was dropped into the 20ml deionized water by three intervals,initial 0.5ml followed by twice 0.25ml at 32and 62min.H 2O 2concentration vs.time:by calculation (&),without catalyst (*),SBA-15(~),5ppm of Fe 2+(!)and Mn 3O 4/SBA-15(^).Rest conditions:5mg of solid catalyst,pH of 7.0(5.0for Fe 2+),708C.Y.-F .Han et al./Applied Catalysis B:Environmental 76(2007)227–234232and Mn,S þH 2O 2!S þþOH Àþ OH (5)S þþH 2O 2!S þ HO 2þH þ(6)H 2O $H þþO 2À(7)where S and S +represent reduced and oxidized metal ions,both the HO 2and O 2Àare not stable and react further with H 2O 2to form OH through Eqs.(8)and (9):HO 2þH 2O 2! OH þH 2O þO 2(8)O 2ÀþH 2O 2! OH þOH ÀþO 2(9)Presently, OH radical has been suggested to be the main intermediate responsible for oxidation/degradation of organic compounds.Therefore,the rate for ethanol oxidation in the studied system is supposed to be dependent on the concentra-tion of OH.Note that the oxidation may proceed via step four (Eq.(4))in the presence of high pressure O 2,which is so-called ‘‘wet oxidation’’and usually occurs at air pressures (1–22MPa)and at high temperatures (423–643K)[15].However,it is unlikely to happen in the present reaction conditions.According to Wolfenden’s study [34],we envisaged that the complete oxidation of ethanol may proceed through a route like Eq.(10):C 2H 5OH þ OH À!ÀH 2OC 2H 4O À! OHCO 2þH 2O(10)Whereby,it is believed that organic radicals containing hydroxy-groups a and b to carbon radicals centre can eliminate water to form oxidizing species.With the degrading of organic intermediates step by step as the way described in Eq.(10),the ﬁnal products should be CO 2and H 2O.However,no other species but ethanol was detected by GC and GC–MS in the present study possibly due to the rapid of the reaction that leads to unstable intermediate.Fig.5indicates that a proper ratio of catalyst/solution is a necessary factor to attain the high conversion of ethanol.It can be understood that over exposure of H 2O 2to catalyst will increase the rate of H 2O 2decomposition;but on the other hand,more OH radical produced may be scavenged by catalyst with increasing the amount of catalyst and transformed into O 2and H 2O as expressed in Eq.(3),instead of participating the oxidation reaction.In terms of Eq.(10),stoichiometric ethanol/H 2O 2should be 1/6for the complete oxidation of ethanol;however,in the present system the total molar ratio is 1/400.In other words,most intermediates were extinguished through scavenging during reaction.This may explain well that the decrease of reaction rate with the rise of ratio of catalyst/solution in the system.The same reason may also explain the decrease of reaction rate with prolonging the time.Actually,H 2O 2decomposition (ca.90%)may be completed within a few minutes over the Mn 3O 4/SBA-15catalyst as illustrated in Fig.10,irrespective of amount of catalyst (not shown for the sake of brevity);in contrast,the rate for H 2O 2decomposition became dawdling for Fe 2+catalyst.As a result,presumably,the homogenous system has relatively high concentration ofradicals.It may explain the superior reactivity of the conventional Fenton reagent to the presented system as depicted in Fig.9.Therefore,how to reduce scavenging,especially in the heterogeneous Fenton system [29],is crucial for enhancing the reaction rate.C 2H 5OH þ6H 2O 2!2CO 2þ9H 2O(11)On the other hand,as illustrated by Eqs.(1)–(4),all steps in the oxidation process are affected by the reaction temperature.Fig.6demonstrates that increasing temperature remarkably boosts the reactivity of ethanol oxidation in the system of Mn 3O 4/SBA-15–H 2O 2possibly,due to the improvement of the reactions in Eqs.(2)and (4)at elevated temperatures.In terms of Eqs.(6)and (7),acidic conditions may delay the H 2O 2decomposition but enhance the formation of OH (Eqs.(5),(8)and (9)).This ‘‘delay’’is supposed to reduce the chance of the scavenging of radicals and improve the efﬁciency of H 2O 2in the reaction.The protons are believed to have capability for stabilizing H 2O 2,which has been elucidated well previously [18,19].Consequently,it is understandable that the reaction is favored in the strong acidic environment.Fig.7shows a maximum reactivity at pH of 2.0and the lowest at pH of 9.0.As depicted in Fig.8,the reaction rate for ethanol oxidation is proportional to the concentration of ethanol in the range of 50–500ppm.It suggests that at low concentration of ethanol (100ppm)most of the radicals might not take part in the reaction before scavenged by catalyst.With increasing the ethanol concentration,the possibility of the collision between ethanol and radicals can be increased signiﬁcantly.As a result,the rate of scavenging radicals is reduced relatively.Thus,it is reasonable for the faster rate observed at higher concentration of ethanol.Finally,it is noteworthy that as compared to the bulk Mn 3O 4(Aldrich,98.0%of purity),the reactivity of the nano-crystalline Mn 3O 4on SBA-15is increased by factor of 20under the same typical reaction conditions.Obviously,Mn 3O 4nanocrystal is an effective alternative for this catalytic system.The present study has evidenced that the unique structure of SBA-15can act as a special ‘‘nanoreactor’’for synthesizing Mn 3O 4nanocrystals.Interestingly,a latest study has revealed that iron oxide nanoparticles could be immobilized on alumina coated SBA-15,which also showed excellent performance as a Fenton catalyst [35].However,the role of the pore structure of SBA-15in this reaction is still unclear.We do expect that during reaction SBA-15may have additional function to trap larger organic molecules by adsorption.Thus,it may broaden its application in this ﬁeld.So,relevant study on the structure of nano-composites of various MnO x and its role in the Fenton-like reaction for remediation of organic compounds in aqueous solution is undergoing in our group.4.ConclusionsIn the present study,we have addressed a new catalytic system suitable for remediation of trivial organic compound from contaminated water through a Fenton-like reaction withY.-F .Han et al./Applied Catalysis B:Environmental 76(2007)227–234233。

大一微积分知识点英文

大一微积分知识点英文Calculus Knowledge Points for FreshmenCalculus, a fundamental branch of mathematics, is essential for students majoring in science, engineering, and mathematics. Mastering the core concepts and principles of calculus is crucial for a successful academic journey in these fields. In this article, we will explore some key calculus knowledge points for freshmen.1. Limits:Limits are fundamental to the study of calculus. A limit represents the value that a function or sequence approaches as its input or index approaches a certain point. Limits are extensively used to define derivatives and integrals.2. Derivatives:Derivatives measure the rate at which a function changes. It represents the slope of the tangent line to a curve at a particular point. Derivatives allow us to analyze the behavior of functions, determine critical points, and solve optimization problems. Notation for derivatives includes the prime symbol (') and the differential operator d/dx.3. Differentiation Rules:Differentiation rules provide shortcuts for computing derivatives. Some of the important rules include the power rule, product rule, quotient rule, chain rule, and trigonometric derivatives. Understanding these rules simplifies the process of finding derivatives of functions.4. Applications of Derivatives:Derivatives have various applications in real-life scenarios. They can be used to determine velocity and acceleration, solve related rates problems, find maximum and minimum values, and analyze the behavior of functions. Application areas include physics, economics, engineering, and biology.5. Integrals:Integrals, also known as antiderivatives, are the reverse process of derivatives. They represent the accumulation of quantities over an interval. Integrals are used to find areas, volumes, average values, and solve differential equations. Notation for integrals includes the integral symbol (∫) and the differential operator dx.6. Integration Techniques:Integration techniques provide methods for computing integrals. These techniques include u-substitution, integration by parts, trigonometric substitutions, and partial fractions. Mastery of these techniques enables students to evaluate a wide range of integrals efficiently.7. Applications of Integrals:Integrals have numerous applications, particularly in calculating areas and volumes. They can be used to find the area between curves, volumes of solids of revolution, work done by a force, and average values of functions. Integration is a powerful tool in physics, engineering, and economics.8. Fundamental Theorem of Calculus:The Fundamental Theorem of Calculus establishes the relationship between differentiation and integration. It states that the derivative of an integral of a function is equal to the original function. This theorem allows for the evaluation of definite integrals using antiderivatives.9. Sequences and Series:Sequences and series involve the summation of infinite terms. Convergence and divergence of sequences and series are crucialconcepts in calculus. Tests such as the ratio test, comparison test, and integral test can determine the convergence or divergence of a series.10. Multivariable Calculus:Multivariable calculus extends the concepts of calculus to functions of multiple variables. It involves partial derivatives, gradient vectors, multiple integrals, line integrals, and surface integrals. Multivariable calculus is essential for fields such as physics, computer science, and engineering.In summary, these calculus knowledge points provide a foundation for freshmen to embark on their study in calculus. Understanding and applying these concepts will enable students to solve complex problems and analyze real-world phenomena. By building a solid understanding of calculus, students can pave the way for success in their academic and professional pursuits.。

英语构词法讲座英语作文

英语构词法讲座英语作文Title: Lecture on English Word Formation。

English Word Formation: An Insightful Lecture。

English word formation is a fascinating aspect of linguistics that delves into the creation and evolution of words in the English language. In this lecture, we will explore the various processes involved in forming words in English, ranging from affixation to compounding and conversion.Affixation is one of the most common methods of word formation in English. It involves adding prefixes, suffixes, or infixes to existing words to create new ones. For example, the addition of the prefix "un-" to the word "happy" forms "unhappy," while the suffix "-ness" added to "kind" creates "kindness." Affixation allows for the expansion of vocabulary by altering the meaning or grammatical function of words.Another significant process in English word formation is compounding, which involves combining two or more words to form a new one. For instance, "blackboard" is formed by combining "black" and "board," and "sunflower" results from merging "sun" and "flower." Compounding enables speakers to express complex ideas succinctly and efficiently.Conversion, also known as zero derivation, is a process whereby words change their grammatical category without any overt affixation. For example, the noun "hammer" can be converted into a verb as in "to hammer," and the adjective "green" can become a noun in "the color green." Conversion demonstrates the flexibility and adaptability of the English language.Additionally, blending involves merging parts of two words to create a new one, often through contraction or abbreviation. For instance, "brunch" combines "breakfast" and "lunch," and "smog" blends "smoke" and "fog." Blending reflects the dynamic nature of language as it evolves to meet the needs of its speakers.Furthermore, derivation involves creating new words by adding prefixes or suffixes to existing ones, thereby altering their meaning or grammatical function. For example, the addition of "-able" to "predict" forms "predictable," and "-ment" added to "develop" results in "development." Derivation enriches the lexicon of English by generating a wide array of related words.Moreover, backformation is a process whereby a word is created by removing what is mistakenly perceived as anaffix from an existing word. For instance, "edit" isderived from "editor," and "televise" from "television." Backformation illustrates how language can evolve through speakers' reinterpretation of word structures.In conclusion, English word formation encompasses a variety of processes, including affixation, compounding, conversion, blending, derivation, and backformation. These processes contribute to the richness and versatility of the English language, allowing for the creation of new wordsand the expression of nuanced meanings. By understandingthese mechanisms, we gain insight into the dynamic nature of language and its continual evolution.。

复变函数英语

复变函数英语1. IntroductionComplex analysis, also known as the theory of complex variables, is a branch of mathematics that is concerned with the study of functions that have complex variables. A complex variable can be thought of as a number that has a real part and an imaginary part. Complex numbers are used extensively in physics, engineering, and many other fields, and complex analysis provides a powerful tool for analyzing these numbers and the functions that use them. In this article, we will provide an overview of complex analysis and explore some of the key topics in this field.2. Complex FunctionsA complex function is a function that takes complex numbers as inputs and outputs complex numbers. Complex functions can be represented using complex variables, which are usually denoted by the symbol z. The real part of a complex function is denoted by Re(z), and the imaginary part is denoted by Im(z).One of the most important properties of complex functions is that they are holomorphic, which means that they aredifferentiable at every point in their domain. The derivative of a complex function is denoted by a symbol that is similar to the derivative of a real function, but with an i added to the denominator to indicate that the derivative is with respect to a complex variable.3. Analytic FunctionsAnalytic functions are a special type of holomorphic function that are infinitely differentiable. These functions are also known as entire functions, and they play an important role in complex analysis. One of the most famous entire functions is the exponential function, which is given by the formula e^z = exp(z) = ∑n=0^∞ (z^n/n!).Analytic functions have many interesting properties, such as the Cauchy-Riemann equations, which provide a relationship between the real and imaginary parts of a complex function. These equations state that if f(z) = u(x,y) + iv(x,y) , where z = x+iy, then ∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x.4. Conformal MappingConformal mapping is a powerful tool in complex analysis that is used to transform one complex function into another. In essence, it is a transformation that preserves angles andshapes. This property has many practical applications infields such as physics and engineering.One of the most famous examples of conformal mapping isthe mapping of the complex plane onto a sphere, which isknown as the Riemann sphere. This mapping is used to extendthe concept of infinity to complex numbers, and it has many important applications in mathematics and physics.5. Applications of Complex AnalysisComplex analysis has many practical applications in awide variety of fields. In physics, complex analysis is usedto study many phenomena, such as electric and magnetic fields, waves and vibrations, and quantum mechanics. In engineering, complex analysis is used to solve problems in areas such as fluid dynamics, solid mechanics, and control systems.In addition to its practical applications, complexanalysis has also inspired many beautiful and interesting mathematical concepts, such as the Mandelbrot set, Julia sets, and fractals. These concepts have captured the imagination of mathematicians and scientists for decades, and they continueto be an important area of research today.6. ConclusionIn conclusion, complex analysis is a fascinating field of mathematics that has many practical applications and has inspired many interesting and beautiful mathematical concepts. Its applications are broad, ranging from physics and engineering to pure mathematics, and it continues to be an important area of research today. Whether you are interestedin practical applications or purely theoretical concepts, complex analysis is a fascinating subject that is well worth exploring in more detail.。

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