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New heuristics for packing unequal circles into circular container

New Heuristics for Packing Unequal Circles into a CircularContainer∗WenQi HUANG1,Yu LI2,ChuMin LI2,RuChu XU1(1)College of Computer Science,HuaZhong Univ.of Science and Technology,Wuhan430074,China,email:wqhuang@(2)LaRIA,Universitéde Picardie Jules Verne,33Rue Saint Leu,80039Amiens cedex1,France,email:{yli,cli}@laria.u-picardie.frAbstractWe propose two new heuristics to pack unequal circles into a two dimensional circular con-tainer.Theﬁrst one,denoted by A1.0,is a basic heurisitc which selects the next circle to placeaccording to the maximal hole degree rule.The second one,denoted by A1.5,uses a self look-ahead strategy to improve A1.0.We evaluate A1.0and A1.5on a series of instances up to100cir-cles from the literature and compare them with existing approaches.We also study the behaviourof our approach for packing equal circles comparing with a speciﬁed approach in the literature.Experimental results show that our approach has a good performance in terms of solution qualityand computational time for packing unequal circles.Keywords:circle packing problem;combinatorial optimization;heuristic1IntroductionThe two dimensional(2D)circle packing problem is a famous packing problem[14],encountered in some industries(textile,glass,wood,paper,etc).It consists in placing a set of circles in a container without overlap.The usual objective is to maximize the material utilization and hence to minimize the wasted area.There are various options in the problem,e.g.the container can be circle,rectangle or polygon,the radii of circles to be placed can be equal or unequal.In this paper,we investigate the problem of packing unequal circles into a circular container.The problem is known to be NP-hard[7].Most published research on circle packing focused on packing equal circles into a container[2,3, 5,15].The proposed approaches were heavily inﬂuenced by the congruence of the circles.Several authors addressed the problem of packing unequal circles into a rectangular or a strip container.George et al.[4]proposed a set of heuristic rules and different combinations of these rules to pack unequal circles into a rectangle and the best ones were a quasi-random algorithm and a genetic algorithm.Stoyan and Yaskov[16,17]proposed a mathematical model and a solution method basedon a combination of the branch-and-bound algorithm and the reduced gradient method to pack unequal circles into a strip.Hiﬁand M’Hallah[6]presented a Bottom-Left(BL)based genetic algorithm to solve a dual of circle packing problem:cutting unequal circles on a rectangular plate.But to our knowledge,no signiﬁcant published research addresses the problem of packing unequal circles into a circular container,except a simulation approach based on an elasticity physics model, proposed by Huang et al.[9,10]and Wang et al.[18].This approach can obtain good enough solutions for packing unequal circles and very good solutions for packing equal circles,but the computational time greatly increases for large instances.In this paper,we propose two new heuristics to solve the problem.A preliminary version of this work appeared in[12,13],and then extended to solve the problem of packing unequal circles into a rectangular container[11].The basic idea of our approach is a quantiﬁed measure,called hole degree, to evaluate the beneﬁt of placing a circle in the container,which gives theﬁrst algorithm,denoted by A1.0.Another feature of our approach is the use of a self look-ahead strategy to improve A1.0and gives the second algorithm,denoted by A1.5.We evaluate our approach on a series of instances up to100circles from the literature[10,12,13,16,17,18,20]and compare it with existing approaches. We also study the behaviour of our approach when it is applied to pack equal circles.Experimental results show that our approach has a good performance in terms of solution quality and computational time for packing unequal circles.The paper is organized as follows.In Section2,we give a formal deﬁnition of the circle packing problem.In Section3,we present the two heuristics A1.0and A1.5.In Section4,we present and analyze the experimental results.Section5concludes the paper.2Circle Packing ProblemWe consider the following circle packing optimization problem:given a set of unequal circles,ﬁnd the minimal radius of a circular container so that all the circles can be packed into the container without overlap.The associated decision problem is formally stated as follows.Given a circular container of radius r0and a set of n circles c1,...,c n of radii r1,...,r n.There may be several circles with the same radius.Let(0,0)be the coordinate of the container center,and (x i,y i)the coordinate of the center of the circle c i,the problem is to determine if there exist2n real numbers x1,y1,...,x n,y n such thatr0−r i−(x i−x j)2+(y i−y j)2−r i−r j≥0,i=j∈{1,...,n}(2)Constraint(1)states that circle c i placed in the container should not extend outside the container, i.e.,the distance from c i to the container,denoted by d i0,should not be negative:d i0=r0−r i−Figure1:Circle packing problemProcedure DichotomousSearch(I, ,A)Beginr0= r i;while(A(I,r0/2)return“success”)dor0=r0/2;r 0=r0/2;repeatif(A(I,(r0+r 0)/2)return“success”)then r0=(r0+r 0)/2;else r 0=(r0+r 0)/2;until r0−r 0< ;r min=r0;End.Figure2:Dichotomous searchConstraint(2)requires that circles placed in the container cannot overlap each other.For such two circles c i et c j,the distance between them,denoted by d ij,should not be negative:d ij=3Algorithms A1.0and A1.5Inspired from human experiences in packing,we propose a quantiﬁed measure,called hole degree, to evaluate the beneﬁt of placing a circle in the container.The selection of the next circle to pack is guided by the Maximal Hole Degree(MHD)rule,which gives our basic packing algorithm A1.0.Following the same line,we propose a self look-ahead strategy to improve A1.0,which consists in using A1.0itself to evaluate the beneﬁt of placing a circle in the container,which gives our second packing algorithm A1.5.First,we explain the basic notions,corner placement and hole degree.Then,we present the MHD rule and A1.0,and the self look-ahead strategy and A1.5.3.1Corner placement and hole degreeWe give some preliminaries before presenting the corner placement and the hole degree.Deﬁnition(Conﬁguration)A conﬁguration C is a partial pattern(layout)where m≥2circles have been already placed inside the container without overlap,and n−m circles remain to be packed into the container.A conﬁguration is said to be successful if m=n,i.e.,all circles have been placed inside the container without overlap.A conﬁguration is said to be failure if m<n and none of the circles outside the container can be placed into the container to satisfy constraints(1)and(2).Let M be the set of circles already placed in the container.Assume in addition that the container is itself in M.3.1.1Corner placementHuman experiences in packing show that the placements of a circle at some particular positions, like corner regions formed by the container and circles already placed,are worth to be examined to generate a successful conﬁguration[11].The notion corner placement in our approach is inspired from these experiences,which refers to placing a circle at a corner region formed by the container and circles already placed,so that the circle touches at least two circles.Deﬁnition(corner placement)Given a conﬁguration C,a corner placement is the placement of a circle c i inside the container,so that c i does not overlap any other circle in M and is tangent at least with two circles in M(note that the two circles are not necessarily tangent each other, and one of them may be the container itself).A corner placement is represented by a triplet p(c i,x,y),meaning that c i is to be placed at position(x,y).Figure3illustrates an instance of7circles,c1,c2,c3,c4,c5,c6and c7,to be placed into a circular container with radius r0,where c2and c4are of the same size,i.e.r2=r4.Note that,(a)Corner placements to put circle c5(b)A successful conﬁguration obtained by A1.0Figure3:An instance of7circles1.Let p(c i,x,y)be a corner placement,the two circles tangent with c i if c i is placed at(x,y)areuniquely determined.Reciprocally,if c i is placed in the container and tangent with two circlesc u and c v,then the center of c i is also uniquely determined.So a corner placement might alsobe denoted by p(c i,c u,c v).2.There may be several corner placements to put a circle in the container.Figure3(a)illustratesfour possible corner placements to put circle c5:p1,p2,p3and p4,where circles c1,c2,c3and c4are already placed in the container(in this order),p1places c5at the position tangent with c1 and the container,p2places c5at the position tangent with c1and c2,p3places c5at the position tangent with c2and c4,p4places c5at the position tangent with c4and the container.3.For circles of the same radius,the corresponding corner placements are identical.For example,the placements to put circles c2and c4are the same.3.1.2Hole degreeHuman experiences also tell us that a good placement may be a region of a good“hole”form so that the wasted area after placing the circle is as small as possible.To evaluate the beneﬁt of a corner placement,we propose a quantiﬁed measureλ,called hole degree,to describe how the circle to be placed at a corner placement is close to the nearest circle already inside the container.Deﬁnition(Hole degree)Let p(c i,x,y)be a corner placement,c u and c v be the two circles in M and tangent with circle c i if c i is placed at(x,y).The degreeλof the corner placement p(c i,x,y) is deﬁned asd minλ=(1−occupies a complete“hole”,and the wasted area after placing this circle is the minimal.For example, the degreeλof the corner placement putting c3at the position tangent with c1,c2and the container in Figure3(a)is equal to1,since the corresponding d min=0.Figure3(a)also indicates the minimal distance d min of the four corner placements to put circle c5.3.2Maximal Hole Degree(MHD)rule and Algorithm A1.0We use the hole degreeλas the beneﬁt of a corner placement.Intuitively,since one should place a circle as close as possible to the circles already inside the container,a packing procedure should select a corner placement having the maximal hole degree to put the next circle into the container.Deﬁnition(MHD rule)By the MHD rule,the corner placement p(c i,x,y)having the maximal hole degreeλis selected to place c i at position(x,y).The MHD rule directly results in our basic packing algorithm A1.0.Given a circle packing instance I,A1.0proceeds as follows.It starts by placing a pair of un-equal circles into the empty container,so that the two circles are tangent each other and also to the container,generating an initial conﬁguration.Under the current conﬁguration,for each circle outside the container,A1.0examines every corner placement by calculating its degree.Among all possible placements,A1.0selects the placement p(c i,x,y)with the maximal degreeλ,and places c i at(x,y).If all circles are placed in the container so that constraints(1)and(2)are satisﬁed,A1.0stops with success.If a failure conﬁguration is reached,A1.0tries the next pair of circles.If all pairs of circles have been tried but no successful conﬁguration is found,A1.0stops with failure.Figure3(b)illustrates a successful conﬁguration obtained by A1.0to pack seven circles into the container,where circles c1and c2areﬁrst placed in the container to generate an initial conﬁguration, then c3,c4,c5,c6and c7are successively placed according to the MHD rule.Figure4(a)shows a successful conﬁguration obtained by A1.0for packing26circles into a container(instance NR26-1in Table1).Algorithm A1.0is described in Figure5.Given a conﬁguration C,we always associate to C the list L of all possible corner placements. Note that L is empty for a successful conﬁguration or a failure conﬁguration.After placing circle c i, the list L of corner placements is modiﬁed as follows.•Remove all invalid corner placements.A corner placement becomes invalid because the in-volved circle would overlap c i if it was placed;•Re-calculate the degreeλof the remaining corner placements;•If a circle outside the container can be placed inside the container without overlap so that it is tangent with c i and another circle inside the container(including the container),create a new corner placement and put it into L,and compute its degree.Algorithm A1.0was tested on the instances presented in Section4.Experimental results show that A1.0is effective enough to solve some instances.(a)Solution by A1.0,r 0=249.93(b)Solution by A1.5,r 0=249.93Figure 4:Two successful conﬁgurations for instances NR26-1obtained by A1.0and A1.5,where the number of each circle is the order to place.The same conﬁgurations with the order of circles in Table 1are shown in Figure 8(a),(b).Procedure A1.0(I )Beginfor k :=1to n −1dofor l :=k +1to n dogenerate an initial configuration C using circles k and l ;generate the corner placement list L ;if (A1.0Core(C,L )returns a successful configuration)then stop with success;stop with failure;End.Procedure A1.0Core(C,L )Beginwhile (there are corner placements in L )dofor every corner placement p (c i ,x,y )dobenefit(p (c i ,x,y )):=λ;select the corner placement p (c i ,x,y )with the maximum benefit;modify C by placing c i at (x,y );modify L ;return C ;End.Figure 5:Algorithm A1.0Procedure A1.5(I)Beginfor k:=1to n−1dofor l:=k+1to n dogenerate an initial configuration C using circles k and l;generate the corner placement list L;if(A1.5Core(C,L)returns a successful configuration)then stop with success;stop with failure;End.Procedure A1.5Core(C,L)Beginwhile(there are corner placements in L)dofor(every corner placement p(c i,x,y)dolet C and L be copies of C and L;modify C by placing circle c i at(x,y);modify L ;C =A1.0Core(C ,L );if(C is successful)then return C ;else benefit(p(c i,x,y)):=density(C );select the corner placement p(c i,x,y)with the maximum benefit;modify C by placing circle c i at(x,y);modify L;return C;End.Figure6:Algorithm A1.53.3Self look-ahead strategy and Algorithm A1.5Given a conﬁguration,A1.0only looks at the relation between the circles already inside the container and the circle to be packed.It doesn’t examine the relation between the circles outside the container.In order to more globally evaluate the beneﬁt of a corner placement and to improve A1.0,we propose a self look-ahead strategy which consists in using the result obtained by A1.0(A1.0Core more precisely)to measure the beneﬁt of a corner placement,which gives our second packing algorithmA1.5which is presented below.Given a conﬁguration C,A1.5examines every corner placement using procedure A1.0Core on a copy of C.It places the circle of the examined placement in the container and then applies A1.0Coreto reach aﬁnal conﬁguration.If theﬁnal conﬁguration is successful,A1.5stops;otherwise,the density of theﬁnal conﬁguration is used to deﬁne the beneﬁt of the examined placement,where theconﬁguration density is the ratio of the total surfaces of the circles inside the container to the surfaceof the container.After examining all placements,A1.5takes the corner placement with the maximal beneﬁt to really change the conﬁguration C.Like A1.0,A1.5tries all pairs of unequal circles before stopping with failure.A1.5is described in Figure6.Obviously,A1.5looks further forward and evaluates the beneﬁt of a corner placement by examin-ing the relation between all circles(inside and outside the container).Figure4(b)shows a successful conﬁguration obtained by A1.5to solve NR26-1in Table1.3.4Complexity of A1.0and A1.5The analysis of the real computational time of A1.0and A1.5is difﬁcult,because it not only depends on the number of circles and the container radius,but also the diversity of circle radii,as well as the implementation.Here,we analyze the upper bound of the complexity of A1.0and A1.5in the worse case,i.e.,when they do notﬁnd a successful conﬁguration,and discuss the real computational time to ﬁnd a successful conﬁguration.3.4.1Upper bound of A1.0’s complexityGiven a conﬁguration C where m circles are already placed in the container and it remains n−m circles outside the container.Let|L|be the number of corner placements in the list L of corner place-ments.After placing a new circle c i into the container,the modiﬁcation of L is done by removing all invalid corner placements,re-calculating the degreeλfor remaining ones and computing new corner placements.To remove invalid placements,we must check each placement in L to verify if it over-laps the new placed circle c i,which is done in O(|L|).To re-calculate the degreeλfor remaining placements,we must compute the distance between c i and the circles involved in the remaining place-ments,which is done in O(|L|).New corner placements for n−m circles outside the container are generated by using c i and m circles in the current conﬁguration,which is done in O(m(n−m)).So the complexity for placing a circle is O(|L|+m(n−m)).Then the complexity for placing n circles, i.e.,the complexity of A1.0Core,is O(n(|L|+m(n−m)))=O(n|L|+n3).A1.0calls A1.0Core for every pair of circles,its complexity is bounded by O(n3|L|+n5).3.4.2Upper bound of A1.5’s complexityA1.5Core uses a powerful self look-ahead strategy in which the consequences of each possible place-ment in L is evaluated by applying A1.0Core in full,which allows to examine the relation between all circles(inside and outside the container).So,the complexity of A1.5Core for placing a circle is O(|L|(n|L|+n3))=O(n|L|2+n3|L|).The complexity of A1.5Core for placing n circles is bounded by O(n(n|L|2+n3|L|))=O(n2|L|2+n4|L|).A1.5calls A1.5Core for every pair of circles,its com-plexity is bounded by O(n4|L|2+n6|L|).In theory,since every pair(there are m(m−1)/2pairs)of circles(including the container)can give two possible corner placements for n−m circles outside the container,|L|is bounded by O(n3). But in practice,most corner placements are infeasible and the real number of corner placements in L is much smaller than the theoretical upper bound O(n3).In Tables4and5,the rows max(|L|)record the maximal number of placements to be examined for placing a circle by A1.0and A1.5to solve an instance.These numbers vary from32to360for A1.0,and from52to571for A1.5,for solving24 instances of up to60circles in Table4;and from70to750for A1.0,and from135to792for A1.5, for solving6instances of up to100circles in Table5.The real computational time of A1.0and A1.5toﬁnd a successful conﬁguration is still much smaller than the above upper bounds.When a successful conﬁguration is found,A1.0does not con-tinue to try other pairs of circles,nor A1.5to exhaust the search space.In fact,every call to A1.0Corein A1.5Core may lead to a successful conﬁguration and stop the execution.Then,the real computa-tional cost of A1.0and A1.5essentially depends on the real number of corner placements in L and the distribution of successful conﬁgurations.4Experimental results and analysisIn this section,we evaluate our approach on a series of instances up to100circles from the literature [10,12,13,16,17,18,20],and compare our approach with the simulation approach proposed by Huang et al.and Wang et al.[9,10,18]in terms of solution quality and running time.We also study the behaviours of our approach when it is applied to pack equal circles.The simulation approach in[9,10,18]is practically a Local Search based on an elasticity physics model,denoted by LS.We brieﬂy present it below:the n circles are considered as elastic disks and squeezed inside the container.Due to elastic forces between the disks,the n disks will move to restore their original shapes.The objective function to minimize is thus deﬁned as the sum of the potential energies of the disks in the system.Such movements continue until the potential energy of the system reaches a local minimum.Then a strategy inspired from human behaviour is used to make the system escape from local minima.A more detailed description of the approach can be found in[10,18,20]. Though LS can obtain enough good solutions for packing unequal circles and very good solutions for packing equal circles,the computational time greatly increases for large instances,as shown by the following experimental results.A1.0,A1.5and LS were all implemented in C language,and executed on a PC with an Athlon XP2000+processor and256Mo of RAM.4.1Test instancesUnequal circle packing instances can be classﬁed into two categories:irregular instances and regular instances.For an irregular instance,the successful conﬁgurations have an irregular form(see Figures 7and8)and the optimal container radius is unknown;while for a regular instance,the successful conﬁgurations are of regular form and the optimal container radius can be obtained by geometrical calculation.Regular instances are in general easier to solve than irregular ones[12].We concentrate thus the following discussion on irregular instances.We evaluate our approach on two groups of irregular instances which are intended to represent a large spectrum of the difference between the radii of circles to be placed.Theﬁrst group includes24 irregular instances from10to60circles listed in Table1.The radii of the circles to be packed are of discrete values and some of them are identical.The column Inst gives the identiﬁer of an instance, the columns n and r i respectively provide the number and the radii of the circles to be placed,and the column r∗0gives the minimal container radii obtained by A1.5.The5instances marked by“*”were used to test LS:NR10-1*,NR11-1*,NR14-1*and NR17-1*used in[10];NR15-2*in[18];NR15-2* and NR17-1*also in[20].The19other instances are taken from a preliminary version of the present work in[12,13].We also use the6irregular instances of20to100circles proposed by Stoyan and Yaskov[16,17], in such a way that we place the cirlces into a circular container instead of a rectangular one.The6instances,denoted by SY1,...,SY6,constitute the second group.The radii of the circles to be packed are random real numbers and all different,available from[19].In addition,we made these instances and their solutions publicly available from[19],including the successful conﬁgurations and the corresponding circle center coordinates,hoping to help further study on this problem.4.2Results and analysisWe apply A1.0and A1.5to solve the above instances and analyze the obtained results in terms of solution quality and running time,i.e.the obtained minimal container radius and the running time to get a successful conﬁguration with this minimal container radius.We also evaluate LS in the same way for the comparison purpose.The results obtained by A1.0,A1.5and LS for theﬁrst group of the instances are reported in Table2and Table4,and for the second group in Table3and Table5.Table2and Table3provide the solution quality results of A1.0,A1.5and LS.The columns r0 give the obtained minimal container radii.The columns density(%)are the corresponding successful conﬁguration densities.We summerize,in the columns gain(%),the density gains made by A1.5over A1.0,A1.5over LS,and A1.0over LS respectively,which are calculated as100×density1−density2Inst r i1099.89 1160.71 1265.30 14113.84 1538.97 1538.85 16143.44 16128.29 1849.25 18197.40 20125.53 20122.21 21148.82 23175.47 24138.38 25190.4726246.7526303.3827222.5830178.6630173.7040357.0050380.00 60522.93 Table1:24irregular instances of theﬁrst groupInst A1.5r0density(%)r0density(%)gain(%)gain(%)gain(%)NR10-1*99.8981.27961.5879.55560.7981.636 2.810.26-2.62NR12-165.3079.970114.8380.396114.3981.016 1.720.96-0.77NR15-138.9783.13239.1580.90239.0681.275 1.53 1.07-0.46NR16-1143.4484.530129.2679.817129.3579.706 1.50 1.630.14NR17-1*49.2583.486198.8882.512199.6781.860 1.48 2.260.79NR20-1125.5384.022123.5582.708123.6782.547 2.16 2.350.19NR21-1148.8283.694176.6583.092177.8581.974 1.33 2.66 1.35NR24-1138.3886.234192.6881.327192.3381.623 2.28 1.92-0.36NR26-1246.7583.207306.2580.906306.0081.038 1.87 1.71-0.16NR27-1222.5883.961178.9085.217180.9083.3440.27 2.46 2.20NR30-2173.7085.627360.7582.480361.7582.025 2.07 2.610.55NR50-1380.0085.648525.5783.602528.9782.531 1.00 2.27 1.2881.97781.961 1.83 1.830.02Table2:Solution quality results obtained by A1.0,A1.5and LS for theﬁrst group of instances.For each algorithm,r0indicates the obtained minimal container radius,density(%)the density of the corresponding successful conﬁguration,gain(%)the density gain obtained by one algorithm over another one.Inst n A1.0LS A1.5/A1.0r0density(%)gain(%)gain(%)density(%) SY1307.3082.5647.3282.114 2.456.2783.689 2.200.0081.638SY325 6.4584.242 6.4983.2070.939.0585.106 3.65 1.3081.738SY510013.2085.72213.3883.4310.4514.9486.123 3.39 3.2682.24385.117 2.91 1.5082.161 Table3:Solution quality results obtained by A1.0,A1.5and LS for the second group of instances.For eachalgorithm,r0indicates the obtained minimal container radius,density(%)the density of the corresponding successful conﬁguration,gain(%)is the density gain obtained by one algorithm over another one.Column S.Y.gives the density of a successful conﬁguration obtained by Stoyan and Yaskov’s approach[17,16]to pack these circles into a rectangular container.Inst A1.5r0time(s)time(s)r0time(s)time(s)max(|L|)max(|L|) NR10-1*99.89<161.58<1<160.7948<12836NR12-165.306114.83<13114.39115034050 NR15-138.972539.15<1<139.0652737375NR16-1143.4471129.26<110129.35121385284 NR17-1*49.2530198.88<16199.671080378112 NR20-1125.5339123.55<1<1123.673029280118 NR21-1148.82683176.65<15177.853******** NR24-1138.382339192.68336192.33107761395158 NR26-1246.751019306.255185306.009981557108193 NR27-1222.584436178.906200180.9026219154229 NR30-2173.701078360.751058361.754152314192324 NR50-1380.009717525.571031219528.9774574272360571 Table4:Running time results of A1.0,A1.5and LS for theﬁrst group of instances.For each algorithm,r0indicates the obtained minimal container radius;time(s)is the running time(in second)toﬁnd a successfulconﬁguration under r0.The last two columns max(|L|)give the maximum number of corner placements to be examined for placing a circle by A1.0and A1.5for an instance.Inst n A1.0A1.5LS A1.5A1.0A1.5r0time(s)time(s)r0time(s)time(s)max(|L|)max(|L|) SY1307.30157.3297332126183SY220 6.34<1<1 6.344671<170135SY325 6.45319 6.4916119<1112222SY4359.16429.224749<1156323SY510013.20364261613.38327563710741SY610014.958445601415.20415133750792Table5:Running time results of A1.0,A1.5and LS for the second group of instances.For each algorithm,r0indicates the obtained minimal container radius;time(s)is the running time(in second)toﬁnd a successfulconﬁguration under r0.The last two columns max(|L|)give the maximum number of corner placements to be examined for placing a circle by A1.0and A1.5for an instance.(a)Solution for NR50-1,r 0=380.00(b)Solution for NR60-1,r 0=522.93(c)Solution for SY5,r 0=13.17Figure 7:Three successful conﬁgurations obtained by A1.5,where the number of circles for NR50-1and NR60-1is theorder in Table 1,and for SY5the order in Stoyan and Yaskov’s ﬁles [19]•The running time of A1.0to get a successful conﬁguration under its minimal container radius for an instance is reasonable,but that of A1.5is considerable for large instances.On the one hand,this fact can be explained by the computational complexity analysis in the sub-section 3.4,and on the other hand we can also give some practical analyses as follows:•The real computational time of A1.0and A1.5essentially depends on the number |L|of corner placements for placing a circle and the distribution of successful conﬁgurations.|L|is related to the size of the instance and the structure of the instance (radii of the circles).In general,the larger the instance,the more the number of corner placements (see the column max(|L|)in Table 4and 5).Concerning the distribution of successful conﬁgurations,when the container radius is not close to the optimal one,there exist many successful conﬁgurations,A1.0and A1.5can quickly ﬁnd such one (see Table 4and 5).However,when the container radius is very close to the optimal one,few successful conﬁgurations exist in the search space,A1.0and A1.5may need more time to ﬁnd a successful conﬁguration in this case.The minimal container radii found by A1.5are guessed to be very close to the optimal values,even though the optimal ones are not known.•Our main objective in this paper is to study the behaviours of the proposed algorithms A1.0and A1.5,so we did not make a big effort to optimize our implementation.The further improvement to the implementation might considerably reduce the real run time of A1.0and A1.5.Figure 7gives three successful conﬁgurations for NR50-1,NR60-1and SY5obtained by A1.5with its minimal container radius r 0.Figure 8(a)and (b)give two successful conﬁgurations for NR26-1obtained by A1.0and A1.5with r 0=249.93.The corresponding circle center coordiantes for these conﬁgurations are available from [19].4.2.2Comparison of A1.0and A1.5with LS We observe that:。

asia uncensored section

Asia Uncensored SectionIntroductionThe Asia Uncensored Section is a platform that aims to promote and share uncensored content from various countries in Asia. With the rapid growth of internet usage and the increasing demand for diverse perspectives and uncensored information, this platform serves as a valuable resource for individuals seeking a deeper understanding and alternative viewpoints on Asian cultures, politics, and social issues.ContentThe Asia Uncensored Section provides a wide range of content, including articles, opinion pieces, and interviews with individuals from different walks of life. The platform covers a diverse range of topics, such as government policies, human rights issues, cultural traditions, environmental challenges, and economic developments. By featuring uncensored content, the platform seeks to provide a fresh and unfiltered perspective on these topics, allowing readers to form their own opinions based on facts and alternative viewpoints.ObjectiveThe main objective of the Asia Uncensored Section is to empower individuals with reliable and uncensored information about Asian countries and their cultures. By providing a platform for voices that are often unheard or suppressed due to political and cultural constraints, the platform promotes freedom of speech and democratizes access to information. It allows readers to gain a more comprehensive understanding of Asian countries beyond the mainstream narratives often presented by media outlets.FeaturesUncensored ArticlesThe Asia Uncensored Section publishes articles written by independent journalists and experts who have firsthand experience and knowledge of the topics they cover. These articles are meticulously researched, ensuring accuracy and reliability. By avoiding censorship and self-censorship, the authors can express their opinions and present alternative perspectives without fear of reprisal or suppression.Opinion PiecesOpinion pieces are a distinctive feature of the Asia Uncensored Section. The platform encourages individuals from various backgrounds to share their thoughts and opinions on various subjects. These pieces provide a platform for constructive discussions and debates, encouraging readers to think critically and form their own perspectives.InterviewsThe Asia Uncensored Section conducts interviews with notable individuals, including activists, artists, academics, and community leaders. These interviews provide readers with unique insights into the personal experiences, struggles, and aspirations of these individuals. By amplifying their voices, the platform aims to inspire and empower readers to take action and make positive changes in their own communities.User-generated ContentThe Asia Uncensored Section also welcomes user-generated content, allowing individuals to share their experiences, stories, and opinions. By providing a space for users to contribute, the platform creates a community where diverse voices are heard and valued.ConclusionThe Asia Uncensored Section is a valuable platform for individuals seeking uncensored information, alternative perspectives, and an understanding of Asian cultures beyond mainstream narratives. Through its uncensored articles, opinion pieces, interviews, and user-generated content, the platform promotes freedom of speech and empowers individuals to form their own informed opinions. By bridging the gap between different cultures and promoting dialogue, the Asia Uncensored Section plays a crucial role in fostering a more inclusive and democratic society.。

美国陪审团的一致裁决原则

美国陪审团的一致裁决原则：历史与当下关键词: 美国，陪审团，一致裁决原则内容提要: 陪审团的一致裁决原则起源于14世纪的英国，作为一项普通法的传统，它在美国确立后经历了一个联邦强制适用与各州选择适用并存这一局面被明确和强化的过程。

虽然饱受质疑，但是从一致裁决原则对陪审团司法工具价值和政治民主价值的发挥及对审判成本控制的影响这三个角度出发综合考虑，其在一定时间内还将继续存在下去。

“你为什么会认为他无罪？”“虽然你们11个都认为他有罪，但我想先和你们好好谈谈，否则我很难说服自己举手认同你们的观点，送这个男孩去死。

”[1]作为美国司法体系的核心组成部分，陪审团制度曾为其赢得了广泛的赞[2]。

陪审团审理案件时，在就相关情况进行充分的“秘密评议”[3]后，无论要做出有罪还是无罪裁决，均需首先在其内部达成一致意见，否则会导致无效审判（mistrial）的出现（此时陪审团相应地被称作“悬置陪审团”（hung ju-ry）—这就是美国陪审团的一致裁决原则[4]。

这项原则起源于英国，作为普通法的传统为美国所接受后，长期以来被视为一项“神圣不可侵犯的”[5]、“统治性的规则”[6]，并作为陪审团制度的“基石”[7]、裁决规则的“底线”[8]在美国联邦法院系统和州法院系统被严格遵行。

然而，随着一系列具有争议的陪审团裁决的出现[9]，美国民众对陪审团审判“不准确、不公正”的印象日益滋生，对其进行根本性改革的呼声也越来越高[10]。

在这种整体性的不满之中，指向一致裁决原则的自然也占有相当大的比重。

有学者认为这是一个“过时的传统”[11]，甚至认为它所带来的危害正是现在陪审团面临的“最严重的问题之一”[12]。

与民众的呼声和学界的议论相伴，在司法实践中，这一原则也已有所松动。

虽然在联邦层面，依然继续严格要求使用一致裁决，但是在各州，情况则发生了变化。

就刑事案件而言，路易斯安那州和俄勒冈州已经在州宪法中明确规定，除死刑案件外，其他案件允许非一致裁决。

不通存不通兑范英文术语

不通存不通兑范英文术语The term "notional" in English financial terminology refers to a fictitious or theoretical amount of money. It is commonly used in derivatives contracts, such as options and swaps, to determine the value of the contract and to calculate payments between parties.In simple terms, the notional amount is the face value or principal of the contract, which determines the size of the financial obligation or exposure. It does not represent the actual amount of money that is exchanged between the parties but is used as a reference point for pricing and settlement.For example, in an interest rate swap, the notional amount is the principal balance on which the interest payments are calculated. If two parties agree to exchange fixed and floating interest rate payments on a notional amount of $1 million, they are not actually exchanging $1 million, but the contractual payments are based on this theoretical amount.The notional amount is important because it affects the cash flows and risks associated with the contract. For instance, in a currency swap, the notional amount determines the size of the foreign currency payments exchanged between the parties. A larger notional amount would result in larger cash flows and potentially higher risks.It's worth noting that the notional amount is not the same as the market value or the actual exposure of the contract. The market value represents the current worth of the contract, which can fluctuate with changes in market conditions. The notional amount, on the other hand, remains constant throughout the life of the contract, unless there is a specific agreement to change it.The concept of notional amounts is also used in other financial contexts. For example, in insurance contracts, the notional amount is the maximum potential payout or coverage amount. In this case, it represents the hypothetical value of the insured property or the potential liability of the insurer.In conclusion, the term "notional" in English financial terminology refers to a theoretical or fictitious amount of money used as a reference point in derivatives contracts and other financial agreements. It is an important factor in determining the size of financial obligations and exposures. However, it should be distinguished from the actual market value or exposure, which can vary over time.。

不方便鉴合同英语

不方便鉴合同英语In the realm of contract law, the intricacies of language play a pivotal role. The ability to comprehend and interpret the legal jargon in contracts is paramount, especially when dealing with international agreements where English is the lingua franca. The challenge arises when parties to a contract are not equally proficient in English, leading to potential misunderstandings and disputes.Contracts are the backbone of commercial transactions, providing a framework for the rights and obligations of the parties involved. They are legally binding and enforceable by law, which is why clarity and precision in language are essential. When one party is not comfortable with English, it becomes crucial to ensure that the contract is still accessible and understandable to them.The use of plain language in contracts can significantly reduce the risk of misinterpretation. Legal documents traditionally filled with archaic terms and lengthy sentences can be transformed into clear and concise agreements. This approach not only benefits those who are not native English speakers but also streamlines the contract review process for all parties.Moreover, the translation of contracts into other languages is a common practice to accommodate the needs of all signatories. However, translation must be done meticulously to preserve the original intent and meaning of the contract terms. Any discrepancy between the English version and its translation can lead to legal complications.In addition to language barriers, cultural differences can also impact contract negotiations and execution. Legal concepts that are standard in one jurisdiction may be foreign in another. Therefore, it is crucial to have a cross-cultural understanding and to seek legal advice when drafting contracts that cross international borders.Furthermore, the rise of technology has introduced new tools to assist in contract drafting and review. Software solutions can help identify potential issues in contractlanguage and suggest improvements. These tools are particularly beneficial for those who may not have a strong command of English, as they provide an additional layer of scrutiny.In conclusion, the importance of language in contracts cannot be overstated. It is the medium through which legal rights and duties are communicated and understood. For parties not comfortable with English, it is essential to employ strategies such as using plain language, accurate translation, and leveraging technology to ensure that contracts are clear, fair, and enforceable. By doing so, we can foster trust and cooperation in international commerce, paving the way for successful business relationships.This article has explored the significance of language in contracts, particularly for those who are not at ease with English. It has highlighted the need for clarity, the role of translation, the influence of cultural differences, and the support of technology in making contracts accessible to all parties involved. Through these measures, we can achieve a balance between legal formality and practical understanding, ensuring that contracts serve their intended purpose without excluding those who are less familiar with the English language. 。

地域歧视英文介绍作文

地域歧视英文介绍作文Title: Combating Regional Discrimination: Understanding and Addressing a Global Issue。

Regional discrimination is a pervasive societal problem that manifests in various forms across the globe. Definedas prejudice or bias against individuals based on their geographical origin, it undermines social cohesion, perpetuates inequality, and stifles progress. In this essay, we delve into the complexities of regional discrimination, examining its root causes, consequences, and strategies for mitigation.At its core, regional discrimination stems from deep-seated stereotypes, misconceptions, and historical animosities towards specific geographic regions or communities. Whether it manifests as xenophobia towards immigrants from certain countries, prejudice against individuals with regional accents, or unequal treatment based on residential address, its effects are profoundlydamaging. Not only does it hinder individuals'opportunities for advancement and social inclusion, but it also fosters divisiveness and undermines efforts to build diverse and inclusive societies.One of the primary challenges in addressing regional discrimination lies in its subtle and often implicit nature. Unlike overt forms of discrimination, such as racial slursor hate crimes, regional discrimination can be more insidious, manifesting through subtle biases in hiring practices, educational opportunities, or access toessential services. These systemic inequalities perpetuate cycles of disadvantage, trapping individuals in socio-economic marginalization based on their geographic origin.Moreover, regional discrimination intersects with other forms of prejudice, exacerbating its impact on marginalized communities. For example, individuals from historically marginalized regions may face compounded discrimination based on their race, ethnicity, or socio-economic status, further limiting their opportunities for advancement. This intersectionality underscores the need for comprehensiveapproaches to address the root causes of discrimination and promote equity and inclusion for all.To combat regional discrimination effectively, it is essential to adopt a multi-faceted approach that encompasses legislative measures, educational initiatives, and community engagement efforts. Firstly, governments and policymakers must enact laws and policies that explicitly prohibit discrimination based on geographic origin and enforce strict penalties for offenders. Additionally, educational institutions should implement curriculum reforms that promote cultural sensitivity, diversity appreciation, and empathy towards individuals fromdifferent regions.Furthermore, fostering dialogue and understanding between communities is crucial in dismantling stereotypes and fostering mutual respect and solidarity. Initiatives such as intercultural exchanges, community forums, and awareness campaigns can facilitate constructive conversations about the impact of regional discrimination and promote empathy and understanding across diversepopulations. By engaging individuals from all walks of life in these efforts, we can cultivate a culture of inclusivity and respect that transcends geographical boundaries.In conclusion, regional discrimination poses a significant barrier to social cohesion, equality, and human dignity. Addressing this complex issue requires a concerted effort from all sectors of society, including governments, civil society organizations, educational institutions, and individuals. By acknowledging the harmful effects of regional discrimination, challenging stereotypes, and promoting inclusive policies and practices, we can work towards a more just and equitable world where everyone, regardless of their geographic origin, can thrive and contribute to society.。

涉外合同英语争议点

涉外合同英语争议点Dispute Points in International Contracts.International contracts, by their nature, are complex and often fraught with potential disputes. These disputes can arise from a wide range of issues, including but not limited to language barriers, differences in legal systems, cultural misunderstandings, and varying interpretations of contract terms. In this article, we will explore some of the key dispute points that commonly arise in international contracts.1. Language Barriers.One of the most significant dispute points in international contracts is language barriers. When parties to a contract come from different countries, they may use different languages as their primary mode of communication. This can lead to misunderstandings and misinterpretations of contract terms, which can, in turn, lead to disputes.To address this issue, it is crucial for parties to ensure that the contract is drafted in a language that is mutually understood by all parties. If necessary, they should consider using a neutral language such as English, which is widely spoken and understood internationally. Additionally, parties should ensure that any translations of the contract are accurate and complete, to avoid any potential misunderstandings.2. Differences in Legal Systems.Another common dispute point in international contracts arises from differences in legal systems. Each country has its own unique legal system, with its own rules, regulations, and interpretations of the law. This can lead to differences in how contract terms are interpreted and enforced by the courts of different countries.To mitigate this risk, parties should conduct thorough research on the legal systems of the countries involved in the contract. They should also consider including disputeresolution clauses in the contract, such as arbitration clauses or choice of law clauses, which can help to resolve disputes in a more efficient and cost-effective manner.3. Cultural Misunderstandings.Cultural misunderstandings can also be a significant dispute point in international contracts. Differences in culture, values, and business practices can lead to misunderstandings and conflicts between parties. For example, certain cultural norms may consider certain business practices acceptable, while others may consider them unethical or illegal.To avoid these misunderstandings, parties should make an effort to understand the cultures and business practices of the other party involved in the contract. They should also ensure that the contract is drafted in a way that is culturally sensitive and respectful of the other party's values and norms.4. Varying Interpretations of Contract Terms.Finally, varying interpretations of contract terms can also lead to disputes. Different parties may interpret the same contract term differently, depending on their own understanding and interpretation of the law and business practices. This can lead to conflict and disputes over the meaning and intent of the contract.To address this issue, parties should ensure that the contract is drafted in a clear and unambiguous manner. They should also consider including definitions andclarifications of key terms to help avoid any potential misunderstandings. Additionally, parties should strive to negotiate and agree on a common interpretation of the contract terms before signing the contract.In conclusion, international contracts can be complex and fraught with potential disputes. To avoid these disputes, parties should take the necessary steps to ensure that the contract is drafted in a clear, unambiguous, and culturally sensitive manner. They should also conduct thorough research on the legal systems and cultures of thecountries involved in the contract, and strive to negotiate and agree on a common interpretation of the contract terms. By doing so, they can help to minimize the risk of disputes and ensure a successful and beneficial outcome for all parties involved.。

法律英语翻译：涉外公正书

法律英语翻译：涉外公正书和其他法律文书一样，涉外公证书的结构也是有首部、正文和尾部三个部分组成。

第一、公证书首部(标题)的翻译。

( Heading ) 公证书可译作“ Notarization ”或“ NotarialCertificate ”，一般不应做改动。

具体的，比如‘ 毕业公证书’ 、‘ 收养公证书’ 等可以译成‘Notarization of Diploma’ 和‘Notarization of Adoption’ ，也可以就直接译成“ Notarization ”或“ Notarial Certificate ”标题翻译过程中应特别注意以下四个问题：1. 标题字母必须全部大写( Capitalize All Letters ) 或大写标题中每个单词的第一个字母( Capitalize the VeryFirst Letter of Each Word )；但2. 标题中的冠词( Articles )及少于5个字母的连词( Conjunctions )、介词( Prepositions )不应大写，除非位于句首；3. 标题中不用引号( Quotation Marks )及句号( Periods )；4. 标题要在公证书上方中央位置( Center Top )；受公证书类型限制，在公证书标题中一般不会出现象“ Between”这样长的连词或介词。

二、公证书正文的翻译( Body)1. “兹证明”的翻译：我国公证书公证词多以“兹证明…… ”开头，其英文翻译( English Equivalent )应该是：“ This is to certify that… ”2. 公证词翻译应忠实于原文( Conformity )。

没收合同保证金英语

没收合同保证金英语Enforcement and Forfeiture of Contract Deposits.Introduction.In commercial transactions, a contract deposit is typically required as a means of securing the performance of contractual obligations. These deposits, often referred to as earnest money or security deposits, serve as a form of financial commitment that incentivizes parties tofulfill their contractual duties. However, in the event of a breach of contract, the question of enforcement and forfeiture of such deposits arises.Legal Basis for Forfeiture.The authority to enforce and forfeit contract deposits is primarily derived from the principles of equity and common law. Courts have consistently recognized the equitable principle that a party who breaches a contractmay be required to forfeit any deposits made as securityfor performance. This forfeiture operates as a form of liquidated damages, compensating the non-breaching partyfor the breach and deterring future breaches.Statutory Provisions.In addition to common law principles, statutory provisions in various jurisdictions may also govern the enforcement and forfeiture of contract deposits. These statutes often provide specific guidelines and procedures for handling such situations, including the circumstances under which forfeiture may be appropriate and the rights of the parties involved.Conditions for Forfeiture.The enforceability of a contract deposit forfeiture is generally subject to certain conditions. These conditions typically include:Material Breach: The breach of contract must bematerial, meaning it significantly impairs the performance of the contract or goes to the heart of the parties' obligations. Minor or immaterial breaches may not justify forfeiture.Non-Performance by the Breaching Party: The party seeking to enforce the forfeiture must have substantially performed their contractual obligations while the breaching party has failed to fulfill their duties.Clarity of Contract Terms: The contract should clearly state the consequences of a breach, including thepossibility of deposit forfeiture. Vague or ambiguous contract language may weaken the enforceability offorfeiture provisions.Proportionality: The amount of the deposit forfeited should be proportionate to the actual damages caused by the breach. Excessive or unreasonable forfeitures may be deemed unconscionable and unenforceable.Procedural Requirements.In many jurisdictions, specific procedural requirements must be followed before a contract deposit can be forfeited. These requirements may include:Notice of Breach: The non-breaching party must provide the breaching party with written notice of the breach andan opportunity to cure the default within a reasonable time.Demand for Payment: If the breach is not cured within the specified time frame, the non-breaching party may issue a formal demand for payment of the deposit.Legal Action: If the breaching party fails to satisfy the demand, the non-breaching party may initiate legalaction to enforce the forfeiture.Equitable Considerations.While the law generally supports the enforcement of contract deposits, courts may consider equitable factors in determining whether forfeiture is appropriate. Thesefactors can include:Good Faith Efforts: The courts may inquire whether the breaching party made reasonable attempts to cure thedefault or mitigate damages.Hardship: The courts may consider the potential hardship that a forfeiture would impose on the breaching party, particularly in cases where extenuating circumstances contributed to the breach.Public Policy: In certain cases, public policy considerations may outweigh the right to forfeiture, such as when the breaching party is a consumer or small business that would be unfairly burdened by the loss of the deposit.Conclusion.The enforcement and forfeiture of contract deposits is a complex legal issue that involves a delicate balance between protecting the rights of non-breaching parties and ensuring that forfeitures are fair and proportionate. Byunderstanding the legal principles and procedural requirements governing deposit forfeiture, parties can effectively navigate these situations and minimize the potential for disputes.。

入子分割线英语

入子分割线英语The English language has become a global phenomenon over the past century as it has spread across the world and become the primary language of communication in numerous fields such as business, science, technology, and education. As the world has become increasingly interconnected through the rise of globalization and advancements in communication technologies, the importance of English as a universal language has only grown stronger.One of the key reasons for the widespread adoption of English is its utility as a lingua franca, allowing individuals from diverse linguistic backgrounds to communicate effectively with one another. This has been particularly beneficial in the realms of international trade, diplomacy, and academic collaboration, where the ability to converse in a common language is essential. The dominance of English in these areas has further reinforced its status as a language of power and prestige, making it an attractive skill for individuals to acquire in order to enhance their career prospects and social mobility.Moreover, the prevalence of English in popular culture, includingmusic, film, and literature, has also contributed to its global appeal. The widespread consumption of English-language media has exposed people around the world to the language, sparking an interest in learning and mastering it. This cultural influence has been amplified by the rise of the internet and social media, which have facilitated the rapid dissemination of English-language content and enabled cross-cultural exchanges on a unprecedented scale.However, the global dominance of English has also raised concerns about its potential impact on linguistic diversity and the preservation of local languages and cultural identities. Critics argue that the hegemony of English can lead to the marginalization and even extinction of minority languages, as individuals and communities feel compelled to prioritize the learning and use of English over their native tongues. This can have far-reaching consequences, as the loss of linguistic diversity can erode cultural traditions, traditional knowledge, and modes of self-expression.To address these concerns, efforts have been made to promote multilingualism and to ensure that the spread of English does not come at the expense of other languages. Many educational systems around the world have implemented policies that encourage the learning of multiple languages, including both local and global languages, in an effort to maintain linguistic diversity and to equip students with the skills necessary to navigate an increasinglyinterconnected world.Additionally, there have been calls for a more nuanced and contextual approach to the teaching and use of English, one that acknowledges the diverse cultural and linguistic backgrounds of its learners and users. This involves recognizing the existence of multiple "Englishes," each with its own unique characteristics and norms, and embracing the idea that English can be adapted and appropriated to serve the needs and identities of different communities.Furthermore, the rise of digital technologies has opened up new avenues for the preservation and promotion of endangered languages. Online platforms and social media have provided opportunities for speakers of minority languages to connect with one another, share content, and advocate for the recognition and revitalization of their linguistic heritage. This grassroots effort, coupled with the efforts of policymakers and language activists, has the potential to counterbalance the homogenizing effects of English and to ensure that linguistic diversity remains a vital aspect of the global landscape.In conclusion, the global dominance of the English language is a complex and multifaceted phenomenon that has both benefits and drawbacks. While the utility of English as a lingua franca hasundoubtedly facilitated cross-cultural communication and collaboration, the potential erosion of linguistic diversity is a legitimate concern that requires thoughtful and proactive measures to address. By embracing a pluralistic approach to language education and language use, and by empowering speakers of minority languages to maintain and revitalize their linguistic heritage, it is possible to strike a balance between the practical advantages of English and the preservation of the rich tapestry of human languages that have shaped and continue to shape our world.。

争议项目英语作文初一

争议项目英语作文初一Title: Controversial Issues: A First-Year English Essay。

Controversial issues are a constant presence in our lives, shaping our perspectives and sparking debates. Inthis essay, we will delve into some of these contentious topics, analyzing their significance and exploring diverse viewpoints.One highly debated issue is climate change. Many argue that human activities, such as burning fossil fuels and deforestation, contribute significantly to global warming. The scientific consensus supports this claim, pointing to rising temperatures, melting ice caps, and extreme weather events as evidence. However, some skeptics question the extent of human influence on climate change, citing natural fluctuations in the Earth's temperature over millennia.Another contentious topic is animal testing. Proponents argue that it is necessary for medical research, enablingthe development of life-saving treatments and vaccines. They emphasize the importance of ensuring the safety and efficacy of pharmaceutical products before they are used on humans. On the other hand, opponents of animal testing raise ethical concerns about the treatment of animals in laboratories, advocating for alternative methods such as computer simulations and tissue engineering.The issue of gun control is also highly divisive, particularly in the United States. Advocates for stricter gun laws argue that they are essential for reducing gun violence and preventing mass shootings. They point to countries with stringent gun regulations, such as Australia and Japan, where firearm-related deaths are significantly lower. Conversely, proponents of gun rights emphasize the Second Amendment and argue that restricting access to firearms infringes upon individual liberties. They contend that responsible gun ownership is a fundamental right enshrined in the Constitution.Gender equality is another topic that elicits passionate debate. While progress has been made in recentyears, disparities persist in areas such as pay, representation, and access to opportunities. Advocates for gender equality call for systemic changes to address these inequalities, including policies that promote equal pay for equal work and initiatives to increase women'sparticipation in male-dominated fields such as STEM. However, some critics argue that the push for gender equality has gone too far, leading to reversediscrimination against men and undermining traditional family values.Finally, the issue of censorship in the age of the internet raises complex questions about freedom of speech and expression. While censorship may be justified incertain cases to protect public safety or prevent the spread of harmful content, it can also be used as a tool to suppress dissent and control information. The challengelies in striking a balance between safeguarding against hate speech and misinformation while upholding the principles of free speech and open debate.In conclusion, controversial issues permeate oursociety, challenging us to critically examine our beliefs and engage in meaningful dialogue with others. By fostering open-mindedness and empathy, we can navigate these debates constructively and work towards solutions that benefit us all. As we continue to confront these complex issues, let us remember the importance of listening to diverse perspectives and seeking common ground. Only through respectful discourse and collaboration can we hope to address the pressing challenges of our time.。

英语硬币具有两面性英语作文

英语硬币具有两面性英语作文English:On one hand, English coins are a symbol of economic stability and security. They are tangible representations of a country's currency and are widely accepted as a form of payment in daily transactions. Coins are durable and can withstand wear and tear, making them a reliable means of exchange. Additionally, coins often feature historical figures, national symbols, or iconic landmarks, serving as a reflection of a country's culture and heritage. On the other hand, English coins can also be seen as a source of inconvenience and clutter. Due to their small size and weight, coins can easily accumulate in pockets or wallets, making them cumbersome to carry around. Counting out coins for purchases can be time-consuming and inefficient, leading to frustration for both customers and cashiers. Furthermore, the presence of coins can complicate transactions and result in the need for exact change, adding an unnecessary layer of complexity to everyday transactions.中文翻译:一方面，英国硬币象征着经济稳定和安全。

关于鸡头的英语作文初一

Chicken heads,though not a popular choice among many diners,have a unique place in culinary traditions around the world.Heres a detailed composition on the topic suitable for a firstyear middle school student.The Curious Case of Chicken HeadsIn many cultures,the chicken head is considered a delicacy,a culinary delight that is both nutritious and flavorful.This essay aims to explore the reasons why chicken heads are cherished in certain regions and the cultural significance they hold.Cultural SignificanceIn some Asian countries,particularly in China,chicken heads are a symbol of respect and hospitality.When a host offers a chicken head to a guest,it is a gesture of the highest honor.This tradition dates back to ancient times when the head of the chicken was reserved for the most esteemed guests or elders in the family.Nutritional ValueDespite being a small part of the chicken,the head is packed with nutrients.It contains a good amount of protein,vitamins,and minerals.The brain,in particular,is rich in omega3fatty acids,which are beneficial for brain health and development.Preparation and Cooking MethodsThe preparation of chicken heads varies greatly depending on the region.In some parts of Southeast Asia,they are boiled and served with a spicy sauce.In other areas,they might be deepfried or grilled to achieve a crispy texture.The cooking process not only enhances the flavor but also makes the meat tender and easy to eat.Challenges and PerceptionsDespite their nutritional benefits and cultural importance,chicken heads are not universally accepted.In Western cultures,they are often considered offputting due to unfamiliarity and misconceptions about their taste and texture.However,for those who dare to try,chicken heads can be a surprisingly delicious and satisfying culinary experience.ConclusionThe chicken head,though not a mainstream food item in every culture,offers a unique insight into the diversity of culinary practices around the world.It challenges our perceptions and invites us to explore the flavors and traditions that make up the rich tapestry of global cuisine.This composition provides a balanced view of the topic,covering cultural,nutritional, and culinary aspects while acknowledging the challenges and perceptions associated with consuming chicken heads.It is written in a style that is informative and engaging, suitable for a firstyear middle school students understanding and vocabulary.。

JOINT INVESTIGATION MODE OF INTERNATIONAL POLICE C

JOINT INVESTIGATION MODE OF INTERNATIONALPOLICE COOPERATION IN CROSS-BORDER PURSUITEVASION AND RETURN OF STOLEN MONEY ORGOODSZhai Yue*Joint investigation is one of the significant international criminaljudicial assistance modes, which has positive effects on pursuing cross-border evasion and returning stolen money or goods. This papergeneralizes the theories, evaluates practical phenomenon, and providessuggestions to perfect the joint investigation mode of international policecooperation.I NTRODUCTION (733)I.G ENERAL T HEORIES ON J OINT I NVESTIGATION (734)A. Concept of Joint Investigation (734)B. Special Techniques and Procedures of Joint Investigation (734)II.Q UESTIONS ON J OINT I NVESTIGATION IN O UR D OMESTIC L AW (734)A. The Lack of Domestic Legislation on Joint Investigations (734)B. The International Treaties on Joint Investigations that ChinaAll Rights Reserved.Participated are not Operational Enough (735)C. Imperfect Censorship (735)III.P ERFECTION OF THE J OINT I NVESTIGATION S YSTEM (735)A. To Perfect Our Domestic Legislation (735)B. To Enhance the Operability of the Treaties (736)C. To Coordinate Evidence Conflicts (736)C ONCLUSION (737)I NTRODUCTIONJoint investigation is no doubt the most effective way in striking transnational crime, since it deals with the suspects, victims, and insidersface to face, and it ensures that the national investigation organizations startthe investigation directly in the counter-part country and examine the crimescene directly to collect solid evidence and then solve the cases efficiently.* PhD student of Dalian Maritime University, Lecturer of Basic Courses Department of ChinaCriminal Police University. Research field: International Criminal Law & International Policing.Fund project: This paper is the staged result of Liaoning Social Science Planning Fund Project(L13DFX027).733734 US-CHINA LAW REVIEW Vol. 11: 733Therefore, the investigation organizations are capable to adjust the criminalinvestigation measures and direction and shorten the time to seize thesuspects.I.G ENERAL T HEORIES ON J OINT I NVESTIGATIONA.Concept of Joint InvestigationInternational police cooperation joint investigation on cross-border pursuit evasion and return of stolen money is a national investigativeassistant method which deals with specific transnational criminal cases, inwhich police in two or more than two countries join together to collectevidences and to capture suspects or criminals. It is a mutual activity basedon the International Police Cooperation in international criminalinvestigation field.1B.Special Techniques and Procedures of Joint InvestigationSpecial investigative techniques such as controlled delivery, electronic eavesdropping, the temptation investigation, undercover and undercoveroperations belong to the scope of the joint investigation, but due to the All Rights Reserved.special conditions of its application, under normal circumstances, inaddition to the relevant legal provisions of different nations, relevantinternational conventions will specifically make provisions. Jointinvestigations should be based on each country’s cooperation will and needs,and the procedures are relatively complex, usually divided into request,examine, negotiation and implementation phases, etc.II.Q UESTIONS ON J OINT I NVESTIGATION IN O UR D OMESTIC L AWA.The Lack of Domestic Legislation on Joint InvestigationsInternational Police Cooperation needs to transfer international treaties into national law, to ensure that international treaties can be effectivelyimplemented. Domestic law is the base of the domestic police activities, soimperfect domestic legislation, to a certain extent, restricts in internationalpolice joint activities to combat transnational crime investigation results.Article 17 of “China Criminal Procedure Law” provides China mutual legalassistance with foreign judicial authorities based on international treaties1Wei Jingchao (魏敬朝), Lun Woguo Lianhe Zhencha Zhidu de Falv Wanshan—Yi MeigongheChanan Weili (论我国联合侦查制度的法律完善—以湄公河惨案为例) (Sichuan 2012), at 35.2014 JOINT INVESTIGATION MODE 735and China’s foreign and mutual benefit principles, no other relevantdomestic law gives the joint investigation any legal support. Furthermore,our domestic law is lack of specific norms related to the joint investigation,such as implementation procedures, communication channels, cooperationscopes, etc.B.The International Treaties on Joint Investigations that ChinaParticipated are not Operational EnoughIn recent years, China has strengthened its cooperation with neighboring countries and signs some relevant international treaties.However, in the case of a joint investigation in the course of the MekongRiver, it is easy to see that it is quite a lack of relevant international treatiesfor international joint investigations. Meanwhile, these treaties are moreprincipled provisions, which are less satisfactory when encountered specificcases. The only way is to negotiate to resolve the detailed issue of jointinvestigation.C.Imperfect CensorshipAll Rights Reserved.Currently, from the legal assistance treaties signed by China with other countries, it is obvious to see that the authorities in charge of contact are thefollowing four departments: first, the central authority; second, the Ministryof Justice; the third, the Supreme People’s Procuratorate; and the fourth, theSupreme Court. All the request and judicial assistance should be contactedwith their representative central authorities, and the central authorities are tobe clearly specified through diplomatic channels. Due to the lack of contactwith foreign authorities, China faces not enough consistency or coherence incoping with joint investigation issues and other judicial cooperation, andthus it impacts international criminal judicial cooperation.2III.P ERFECTION OF THE J OINT I NVESTIGATION S YSTEMA.To Perfect Our Domestic LegislationChina should increase specific provisions of joint investigation requests, examination, establishment, relationships among membership onthe base of existing legislation, to ensure the joint investigation activitiesprecede smoothly, and to reduce unnecessary obstacles, meanwhile, to2 Xiang Dang (向党), Lun Guoji Zhencha Xiezuo (论国际侦查协作) (1988), at 68.736 US-CHINA LAW REVIEW Vol. 11: 733coordinate domestic laws with international treaties. Besides, the China’sadministrative organizations in charge of cooperation are complex and haveno united commanding department. China should provide specificorganizations to take the responsibility of joint investigation and constructspecial teams to coordinate with foreign countries. Therefore, differentdepartments will have clear divisions in joint investigation activities withother countries more effectively and more efficiently.B.To Enhance the Operability of the TreatiesChina should add more detailed implementation regulations to enhance the operability of the joint investigation cooperation international treatiessigned with other parties. By doing so, countries will clearly acknowledgetheir rights and obligations when signing the treaties, and they can adjusttheir domestic laws according to the international treaties, to ensure that thetreaties are practicable in domestic laws. Detailed implementationregulations help relevant countries carry out joint investigation activitiesefficiently according to international treaties signed by them, rather thannegotiating on each specific case. Due to the lack of detailedimplementation regulations on the joint investigation cooperation of theAll Rights Reserved.Mekong River case, countries have to send personnel to attend the lawenforcement security cooperation conference on the details of the event.C.To Coordinate Evidence ConflictsWhen requesting for joint investigation to another country, China should thoroughly understand the provisions of evidence regulations of therequested country and prepare necessary evidence documents to avoid beingconsidered illegal document collecting by requested country. Thus, it canensure the time of case investigation and evidence collection to promote thejoint investigation efficiency. In the process of implementing jointinvestigation, investigating and evidence collecting activities have to takethe attitude of the court to the evidence into consideration. Since evidencecollected in any other countries can be used in the trials of the parties,criminal investigation department should obey the provisions ofinvestigation, including the illegal evidence exclusion regulations. It isforbidden to use illegal measure to collect evidence due to the evidence maynot be used in domestic trials.33 Zhao Yongchen (赵永琛), Shewai Xingshi Anjian zhong de Jige Wenti (涉外刑事案件侦查中的几个问题) (1994), at 47.2014 JOINT INVESTIGATION MODE 737C ONCLUSIONTo strike cross-border crimes effectively, China should increase specific provisions of joint investigation requests, examination,establishment, relationships among membership on the base of existinglegislation. Meanwhile, it is of great importance to coordinate domestic lawswith international treaties and to improve the operability of certain treatiesto ensure the joint investigation activities precede smoothly.All Rights Reserved.。

(耳鼻咽喉头颈外科学)4.2(参考翻译)asom宣讲培训

Anatomy of the Nose
Explore the complex anatomy of the nose, including the nasal cavity and paranasal sinuses. Learn about the functions of these structures and their role in olfaction and
History and Development of ASOM
Pioneers in the Field
Delve into the notable figures who shaped ASOM, such as William Harvey, Anton von Troeltsch, and Chevalier Jackson. Discover their groundbreaking contributions to the field.
Common ENT Diseases and Disorders
1
Upper Respiratory Infections
Explore the common viral and bacterial infections affecting the ENT system, including the common cold, sinusitis, and tonsillitis. Understand their etiology, symptoms, and treatment options.
(耳鼻咽喉头颈外科学)4.2(参考翻译)ASOM宣讲培训
Welcome to the ASOM training session, where we will explore the fascinating world of Otolaryngology - Head and Neck Surgery. Get ready to dive into the anatomy, diseases, diagnostic techniques, and advancements in this field.

Do Elections Always Motivate Incumbents

DO ELECTIONS ALWAYS MOTIVATE INCUMBENTS?Eric le BorgneAndBen LockwoodNo 580WARWICK ECONOMIC RESEARCH PAPERSDEPARTMENT OF ECONOMICSDo Elections Always Motivate Incumbents?Eric Le Borgne and Ben Lockwood¤University of WarwickFirst version:y April2000This version:November2000AbstractThis paper studies a principal-agent model of the relationship between o¢ce-holders and the electorate,where the o¢ce-holder is initially uninformed about herability(following Holmström,1999).If o¢ce-holder e¤ort and ability interact in the“production function”that determines performance in o¢ce,then an o¢ce-holderhas an incentive to experiment,i.e.raise e¤ort so that performance becomes a moreaccurate signal of her ability.Elections reduce the experimentation e¤ect,and thereduction in this e¤ect may more than o¤set the positive“career concerns”e¤ectof elections on e¤ort.Moreover,when this occurs,appointment of o¢cials(randomselection from the citizenry and tenure)may Pareto-dominate elections.Keywords:Career Concerns,Elections,Citizen-Candidate,Experimentation,Tour-naments,Political Business Cycles.JEL Classification Numbers:D72,D78,H41,J44,J45.¤Address for correspondance:Department of Economics,University of Warwick,Coventry CV47AL, United Kingdom.E-mails:eric.le-borgne@,and B.Lockwood@.y With a di¤erent title:“The Career Concerns of Politicians:E¢ciency in a Representative Democ-racy?”.1.IntroductionIn recent years,economists and political scientists have applied principal-agent theory to study the relationship between voters and elected o¢cials.The literature starts from the idea that there is a moral hazard problem between the elected o¢cial and the electorate: left to his own devices,the o¢cial will pursue his own interests,rather than those of the voters.This is modelled formally by supposing that the o¢cial can supply unobserv-able e¤ort(Ferejohn,1986;Austen-Smith and Banks,1989;Banks and Sundaram,1993, 1998)or has the opportunity to“steal”rent from tax revenue(Barro,1973;Persson and Tabellini,2000).However,this literature modi…es standard principal-agent theory in two crucial ways.First,unlike employees,1elected o¢cials cannot typically be o¤ered mone-tary rewards for their performance on the job:the salaries of political o¢ce are usually independent of short-term performance.Second,dismissal(losing elections)is costly.Under these two conditions,o¢cials can only be motivated(to supply additional e¤ort,to steal less rent)by“career concerns”,2i.e.the fear of losing elections.The recent literature in this area has modelled this process formally,starting with the seminal work of Barro(1973)and Ferejohn(1986).This literature now comprises a variety of models(discussed in more detail in the Conclusion)but with two apparently very robust conclusions;(i)in(sequential)equilibrium,voters follow a cuto¤rule,i.e.will only re-elect the incumbent if his observed performance is above a certain critical level;(ii)the cuto¤rule always motivates the o¢ce-holder(to supply more e¤ort,or extract less rent).This paper argues that conclusion(ii)is in fact not robust.We present a simple two-period model of the agency problem between the electorate and the voters,drawing on the work of Holmström(1982,1999)and Dewatripont,Jewitt,and Tirole(1999),and show that in sequential equilibrium,elections may demotivate:that is,the incumbent will supply less e¤ort than without the“discipline”of an election.The intuition is simple. When the ability and the e¤ort of the o¢ce-holder interact positively,the o¢ce-holder can learn more about his ability by supplying more e¤ort.We call this the experimentation motive for supplying e¤ort.However,if he is exposed to the possible future loss of o¢ce, his motive to experiment will be reduced.This diminution in the experimentation motive may more than o¤set the increase in e¤ort induced by the desire to signal competence to the electorate(the career concerns e¤ect).One way of interpreting the diminution is as short-termism;the incumbent underinvests,anticipating he will lose power(see also Besley and Coate,1998,for examples of this type).1Within a…rm,various incentive mechanisms ranging from promotion and demotion,wage changes, performance contracts(e.g.stock options),are widely used(see Prendergast,1999,and Gibbons and Waldam,1999,for recent surveys).2Career concerns refer to the fact that an agent’s current actions(bour supply,e¤ort on the job)are in part determined by taking into account the e¤ect that these actions have on the agent’s future career prospects even though no explicit incentives(e.g.performance contracts)links the two.1The existence of,and implications of,experimentation in a career-concerns setting is (as far as we know)a new…nding.This is because the existing literature assumes either (i)that potential o¢ce-holders are already fully(privately)informed about their ability, as in Banks and Sundaram(1993,1998);(ii)an additive technology,where information has no value(Holmström,1999);(iii)one period only,in which case information acquired currently cannot be used in the future(Dewatripont et al.,1999);(iv)there is no noise in the production function so that incumbents can perfectly observe their ability from performance at the end of the…rst period of o¢ce(Persson and Tabellini,2000).Our model is the following.3The economy is populated by a number of citizens,who may vary in competence if in political o¢ce.Their performance in o¢ce is described by a production function that maps competence,e¤ort,and a random shock into a scalar variable,the“public good”.Following Holmström(1982,1999),Dewatripont,Jewitt, and Tirole(1999),we assume that citizens do not know their own competence,but can only infer it from their performance in o¢ce.4Initially,we compare two institutions in this setting.The…rst is appointment,where the o¢ce-holder is randomly selected from the population,and is in o¢ce for two periods.The second is democracy,which di¤ers from the appointment in that at the beginning of the second period,there is an election, contested by the…rst-period incumbent and an opponent,the latter randomly selected from the population,with the winner holding o¢ce for the second period.Our…rst…nding is that in this setting,even with appointment,e¤ort may vary over time,due to experimentation,which occurs when the incumbent deviates from the my-opically optimal action that just maximises the current payo¤in order to improve the information content of his signal about his own ability,namely the output of the public good.5We show that experimentation will occur in the…rst period of our two-period setting if and only if e¤ort and ability interact in the production of the public good,and that when it occurs,it unambiguously induces the o¢ce-holder to put in more e¤ort than 3The closest model to ours is the career concerns model of Chapter4.5of Persson and Tabellini(2000),which also builds on Holmstrom’s work,and that we saw after the…rst draft of this paper was completed. We show in Section7that(subject to some inessential quali…cations)their model can be considered as a special case of ours where there is no randomness in the production function.As a consequence,in their model,the incumbent can perfectly observe his competence at the end of the…rst period of o¢ce,and so there is no experimentation e¤ect,which is the main topic of this paper.Our reading of their model is that it is intentionally kept very simple to permit an easy analysis of the way career concerns are a¤ected by electoral rules.4This is in contrast to the more usual assumption in the principal-agent literature,which assumes that agents are privately informed.Empirically,there is support for both assumptions.One proxy for the self-knowledge of an elected o¢cial is the amount of time spent doing the job.In the US,all presidents except F.D.Roosevelt have served either one or two terms.On the other hand,there is considerable variation in o¢ce tenure in the UK,ranging from less than one year for Alec Douglas-Hume to11years for Margaret Thatcher.5The experimentation literature initially studied the problem of a monopolist facing an unknown demand curve(Prescott(1972)and Grossman,Kihlstrom,and Mirman(1977)are early contributions). Mirman,Samuelson,and Urbano(1993)develop a tractable two-period monopolist game and establish conditions under which experimentation occurs.We make use of their results below.Keller and Rady (1999)surveys the literature.2the myopic level.Our key observation is that when we move from appointment to democracy,the incen-tive to experiment unambiguously falls,for the reason described above.Of course,in our model,as in others in the literature,elections also have a positive e¤ect on equilibrium e¤ort via career concerns e¤ect;6the better the observable performance while in o¢ce, the higher the probability of being re-elected and therefore the higher the expected payo¤in the future.As we show,it is possible that the loss of the incentive to experiment may more than o¤set the career concerns e¤ect,so that equilibrium e¤ort may be lower in democracy than with appointment.More generally,we can say that career concerns and experimentation, while both inducing the incumbent to increase e¤ort,are substitutes under symmetric in-complete information:that is,democracy introduces career concerns,but also necessarily reduces the incentive to experiment.In Section5,we show that there is also an important relationship between the“e¢-ciency”of equilibrium with democracy and the presence of an experimentation motive. Consider a constrained social planner who only knows the distribution of the competency variable initially(so he is only as well-informed as the citizens),and has the same powers as citizens,i.e.can“…re”the incumbent if performance falls below some cuto¤value. We say that democracy(with or without endogenous entry of candidates)is constrained e¢cient7if a constrained social planner cannot make every citizen better o¤.It turns out that(subject to a uniqueness condition holding)when technology is additive(so there is no experimentation motive),the equilibrium with democracy is constrained e¢cient,but that this need not be the case with an experimentation motive.A subsidiary objective of this paper is to address two other,related,weaknesses of the existing literature on the principal-agent relationship between voters and o¢ce-holders, namely(i)that the o¢ce-holders(the incumbent and challenger)are assumed to be ran-domly drawn from some population;and(ii)have di¤erent preferences than the voters.8 Our model has already addressed the second problem,by having the incumbent and chal-lenger randomly selected from the same population as the electorate.In Section4of the paper,we extend our model of democracy to deal with(i).Speci…cally,we study democracy with endogenous(candidate)entry,where at the beginning of each of the two periods,any citizen can stand for election,and candidates 6In our model,the career concerns e¤ect can also be thought of as a“tournament”between incumbent and challenger(Lazear and Rosen,1981;Green and Stokey,1983).Whoever wins o¢ce gets“…rst prize”;and whoever loses,“second prize”.7Of course,due to the underlying agency problem,the equilibrium outcome with democracy will never be…rst-best e¢cient,so that the latter is not a very interesting benchmark.8In Banks and Sundaram(1993,1998),the principal(voters)care about the output of the agent,but the agent’s payo¤is independent of this output.The same is true of Persson and Tabellini(2000),where voters care about the output of the public good,but the o¢ce-holder cares only about an exogenous ego-rent and the rents that he can extract from tax revenue.3are voted on by plurality rule,with the winner taking o¢ce for one period(becoming the o¢ce-holder).So,this approach combines the citizen-candidate modelling of selection of o¢ce-holders(Besley and Coate,1997)with the principal-agent relationship between o¢ce-holder and voters.9It turns out that,given the information structure assumed, our main results do not change qualitatively.In particular,as the candidate entry stage cannot reveal any information to voters about their competence in o¢ce,there will still be experimentation in o¢ce.Candidate entry and voting(for all candidates in the…rst period,and for the challenger in the second)will be determined by other characteristics of the candidates.10The rest of the paper is structured as follows.Section2describes the model.Section 3presents the basic results,and Section4extends them to the case of democracy with endogenous entry.Section5is devoted to normative analysis.Section6discusses some extensions.Finally,Section7concludes and discusses related literature.2.The Model2.1.TechnologyThe economy is populated by a set N of citizens with#N=n¸3and evolves over two time periods,t=0;1:There is a political o¢ce that can only be occupied by one citizen, the“o¢ce-holder”.The performance of the o¢ce-holder while in o¢ce is measured by a scalar variable g2<which we call the“public good”.The ability of an o¢ce-holder i2N is measured byµi;and his e¤ort level in period t is a i;t2[0;1):Following Dewatripont,Jewitt,and Tirole(1999),this o¢ce-holder produces g t units of the public good,where:g t=¹(µi+a i;t)+(1¡¹)µi a i;t+"t;t=0;1(2.1) where¹2[0;1]:Also,"0;"1are independently distributed random shocks.In either period,the o¢ce-holder has to decide on a level of e¤ort before observing"t: Note that the general production function(2.1)encompasses two important special cases.The…rst is where¹=1;in which case the technology is purely additive(as in Holmström,1999).The second is where¹=0;in which case the technology is purely multiplicative(in the sense of Dewatripont,Jewitt and Tirole,1999).We assume that eachµi is a random draw from a distribution that can take two values:µH>µL>0with probabilities¼0;1¡¼0respectively.This draw takes place at the beginning of period zero.So,theµi are uncorrelated across citizens.We refer to H; L as the types of the citizens.9This is explored in more detail in a companion paper,Le Borgne and Lockwood(2000).10Following Rogo¤and Sibert(1988),Rogo¤(1990),we allow voters to di¤er in“looks”,i.e.charac-teristics that voters value but are unrelated to competence in o¢ce and therefore economic issues.4We assume that"has a continuous distribution with probability density function f, cumulative distribution function F,and has full support on<.We assume that f satis…es the Monotone Likelihood Ratio Condition(MLRC)that f0(")=f(")is a continuous and decreasing function.11We also assume thatA0.For any a>0;there exists"0;"00;"00>"0;such that f("0¡a)<1<f("00¡a):It is well-known that a large number of distributions satisfy the MLRC(Milgrom,1981), including the Normal,and it is easy to check that if"is Normally distributed,A0is also satis…ed.Our production function,plus the assumption that"t2<;of course implies that g can be negative,and so cannot be literally interpreted as a public good in a public …nance model.The reason for allowing shocks"t to be negative is that if we constrained "t to be positive,i.e.by assuming the lower bound of the support of"t to be zero,then if the incumbent observed g t<¹µH;he could be sure his type was low.This problem of“perfect inference”would complicate the analysis considerably.The simplest way to model non-negativity for g t is to suppose that the random shock is multiplicative,i.e.g t=[¹(µi+a i;t)+(1¡¹)µi a i;t]"t(2.2) and has support[0;1):The qualitative features of the analysis of this paper would be unchanged if we worked with(2.2).2.2.PreferencesIf i2N is an o¢ce-holder in period t;and produces g t,then j=i only cares about the level of performance of the o¢ce-holder,i.e.u j;t=g t:If an agent i2N is an o¢ce-holder in period t;she has payo¤u i;t=g t+R+rg t¡c(a i;t),where g t is the net utility from the public good,as for j=i;R+rg t is an“ego-rent”from being in o¢ce(as in Rogo¤and Sibert,1988),deriving from the prestige in managing public a¤airs,and…nally c(a i;t)is the cost of e¤ort.If r>0,the ego-rent interacts positively with the amount of public good provided.12Following Rogo¤and Sibert(1988),we assume for the moment that r=0(the case of r>0is discussed in Section6.1below).Also,we assume that c(:)is strictly increasing and strictly convex,and13c(0)=0;c0(0)<1.11The MLRC says that,for a given competency type,a high e¤ort increases the probability of obtaining a high visible performance at least as much as it increases the probability of obtaining a low visible performance variable.12Of course,r>0could also model a public duty/altruistic motive for the o¢ce-holder,capturing the fact that holders of public o¢ce may feel some obligation towards the citizens they represent,quite independently from the discipline that elections impose.13The last condition c0(0)<1ensures that myopic e¤ort is positive.52.3.InstitutionsThe agent whose task it is to produce the public good (the o¢ce-holder)is selected in one of two ways.We allow for a third institution in Section 4.1.AppointmentAt the beginning of period t =0,the o¢ce-holder is selected by random draw from the set of citizens,and is in place for both periods.2.DemocracyAt the beginning of period t =0;an o¢ce-holder (the incumbent )is selected by random draw from the set of citizens.This o¢ce-holder is in place during period t =0but faces an election at the beginning of period 1.At this stage,an opponent is selected by random draw from the set of remaining citizens.The citizens then vote on the opponent versus the incumbent,and the winner is the o¢ce-holder in period t =1.Our modelling of democracy abstracts from the entry decisions of candidates (dealt with in Section 4below)while allowing the electorate to “…re”bad o¢ce-holders.It also is quite close to the modelling of the electoral process in Rogo¤and Sibert (1988),and Rogo¤(1990).In all cases,for consistency,we will impose the individual rationality condition that the o¢ce-holder prefers to be in o¢ce than not.rmation StructureFollowing Holmström (1999),and Dewatripont,Jewitt and Tirole (1999),we assume that citizens do not know µ=(µ1;:::;µn ),but all know the joint distribution of µ(symmetric incomplete information ).It is also assumed that the action a is only observable by the incumbent.Because of this,the o¢ce-holder cannot be rewarded on the basis of a:If she receives a salary,this is modelled as a component of R;the “ego-rent”.It is also assumed that g is not veri…able,so the o¢ce-holder cannot be rewarded on the basis of g:2.5.Myopic Choice of E¤ortConsider the choice of e¤ort by an o¢ce-holder who is in power for one period only,and believes he is high-ability with probability ¼:This o¢ce-holder solves the problem v o (¼)=max a ½¼[¹(µH +a )+(1¡¹)µH a ]+(1¡¼)[¹(µL +a )+(1¡¹)µLa ]¡c (a )+R ¾(2.3)The …rst-order condition is¹+(1¡¹)[¼µH +(1¡¼)µL ]¡c 0(a )=0(2.4)This solves to give a ¤(¼);which we call the myopic optimal action by the o¢ce-holder,given a belief that he is competent with probability ¼:If ¹=1;a ¤(¼)´a ¤,for all ¼.6Finally,we can de…ne the utility of the non-o¢ce-holding citizen when both the citizen and the o¢ce-holder believe the o¢ce-holder to be competent with probability¼;v c(¼)=¼[¹(µH+a¤(¼))+(1¡¹)µH a¤(¼)]+(1¡¼)[¹(µL+a¤(¼))+(1¡¹)µL a¤(¼)](2.5) Some useful properties of a¤and the associated value functions v o;v c are the following. First,it is clear from the…rst-order condition(2.4)that@a¤@¼=(1¡¹)(µH¡µL)c00(a¤)(2.6)So,a¤is independent of¼if the technology is purely additive and strictly increasing in¼otherwise.Second,by direct application of the envelope theorem to(2.3),we havev0o(¼)=¹(µH¡µL)+(1¡¹)(µH¡µL)a¤(¼)(2.7) so v o is strictly increasing in¼:By inspection of(2.6),v c is also strictly increasing in¼. Moreover,as R>0,and by the properties of c;v o(¼)>0,and by inspection,v c(¼)>0:3.Positive Analysis3.1.AppointmentWe solve the appointee’s decision problem with the usual dynamic programming approach. In the second period,the appointee faces a myopic problem,so chooses a1=a¤(¼1) where¼1is the appointee’s posterior belief that he is a high-ability type.The individual rationality condition for the appointee is that v o(¼1)¸0which is always satis…ed.Now,note from(2.7)above that as long as the technology has a multiplicative com-ponent,i.e.¹<1;his second-period payo¤is strictly convex in¼1;v00o(¼1)=(1¡¹)(µH¡µL)@a¤@¼1>0(3.1)This means that information aboutµobtained by Bayesian updating is strictly valuable. Now when updating,the appointee can observe both his own output of the public good in the…rst period,g0;and his action in the…rst period,a0.So,from Bayes’rule,the appointee’s posterior belief that he is a high-type is¼1(a0;g0)=Pr(µ=µH j a0;g0)=¼0¼0+(1¡¼0)f L(g0;a0)=f H(g0;a0)(3.2) wheref k(g0;a0)´f(g0¡(1¡¹)µk a0¡¹(µk+a0));k=H;L(3.3)7Note from (3.2)that changes in actions are informative ,i.e.a change in a 0a¤ects the posterior probability that the o¢ce-holder is competent,given output (@¼1(g 0;a 0)=@a 0=0):So,the two well-known 14conditions for optimal experimentation are satis…ed in our model,i.e.the appointee has an incentive to deviate from the myopic e¤ort level in the …rst period.Now we go to the …rst-period problem for the appointee.Note that for a given value of a 0;g 0is a random variable with distribution functionH (g 0;a 0)=¼0F (g 0¡(1¡¹)µH a 0¡¹(µH +a 0))+(3.4)(1¡¼0)F ((g 0¡(1¡¹)µL a 0¡¹(µL +a 0))Consequently,¼1(g 0;a 0)is also a random variable,conditional on a 0;implying an expected optimized second-period payo¤of E g 0[v o (¼1(a 0;g 0))]:So,the problem for the appointee in the …rst period ismax a 0½¼0[¹(µH +a 0)+(1¡¹)µH a 0]+(1¡¼0)[¹(µL +a 0)+(1¡¹)µL a 0]¡c (a 0)+R +E g 0[v o (¼1(a 0;g 0))]¾(3.5)The …rst-order condition can be written[¹+(1¡¹)(¼0µH +(1¡¼0)µL )]+@E g 0[v o (¼1(a 0;g 0))]@a 0=c 0(a 0)(3.6)The …rst term in the square brackets on the left-hand side is the …rst-period (myopic)gain from a small increase in e¤ort.The second term on the left-hand side is the marginal experimentation bene…t or cost from changing a 0from its myopic level a ¤(¼0).Let the value of a 0that solves (3.6)be a A 0:The question is now:what sign is the marginal experimentation term?Following the proof of Lemma 2of Mirman,Samuelson and Urbano (1993)it is possible to show (derivation in Appendix B)that@E g 0[v o (¼1(a 0;g 0))]@a 0=¼0(1¡¹)(µH ¡µL )Z +1¡1v 00o (1¡¼1)d¼1dg 0f H (g 0;a 0)dg 0(3.7)Now,from (3.1),v 00o >0as long as ¹<1;andd¼1dg 0=¼0(1¡¼0)[¼0f H +(1¡¼0)f L ](f L f 0H ¡f 0L f H )>0(3.8)from the MLRC.So,we see that@E g 0[v o (¼1(a 0;g 0))]@a 0>0i¤¹<114See,for instance,Proposition 1of Mirman,Samuelson and Urbano (1993).8i.e.that the experimentation term is strictly positive i¤the technology is partly multi-plicative.So,the following result is immediate from the previous discussion and the strict concavity of c:Proposition1.In the second period,the appointee chooses the myopic level of e¤ort a¤(¼1),conditional on her posterior belief:In the…rst period,the appointee will choose to experiment by choosing a higher e¤ort than the myopic one,a A0>a¤(¼0);unless the technology is purely additive(¹=1);in which case a A0=a¤(¼0).3.2.DemocracyThis case is more complex,as we have a game of incomplete information,where there is both experimentation(unless the technology is additive)and a career concerns e¤ect. We characterise the perfect Bayesian equilibria(PBE)of this game,which turn out to be unique15except that(possibly)the incumbent may choose multiple actions in period0. Suppose…rst that the challenger to the incumbent,j2N;is elected.His choice of action is a j;1=a¤(¼0);because he has no additional information about his own competence.So, the expected utility to any member i=j of the electorate from the opponent is v c(¼0): Now,at the time the electorate votes,every citizen has had the chance to observe g0,…rst-period public good provision.Let¼1be the updated belief on the part of the electorate,having observed g0;that the incumbent is a high-type.Now,when forming the posterior¼1,citizens rationally deduce that in the…rst period,the incumbent has taken equilibrium action a¤0.So,their posterior probability that the incumbent is competent is¼c1(g0)=¼0¼0+(1¡¼0)[f L(g0;a0)=f H(g0;a0)](3.9)Note that we superscript¼c1(g0)to distinguish it from the incumbent’s own posterior, which is de…ned in(3.2).However,note that in equilibrium,¼c1(g0)=¼1(g0;a¤0): Then the expected utility that citizens can expect from the incumbent is v c(¼c1(g0)):So, given the tie-breaking rule,all the citizens(apart possibly from the opponent),will vote for the incumbent when v c(¼c1(g0))¸v c(¼0).As v c is strictly increasing in its argument, this is equivalent to¼c1(g0)¸¼0.From(3.8),(3.9),¼c1(g0)is strictly increasing in g0: Moreover,from this fact and assumption A0,there exists a unique critical value~g0such that¼c1(~g0)=¼0;with¼1>¼0for g0>~g0,and¼1<¼0for g0<~g0.The conclusion is that all voters(except the incumbent)follow the following cuto¤rule:vote for the incumbent i¤g0¸~g0,and for the opponent if g0<~g0:As there are at least three voters by assumption,this cuto¤rule determines the outcome of the election,i.e.how the incumbent votes is irrelevant.15Su¢cient conditions for uniqueness are derived below.9。

银行术语--中英文对照

ABS 资产担保证券（Asset Backed Securities的英文缩写) Accelerated depreciation 加速折旧Acceptor 承兑人；受票人; 接受人Accommodation paper 融通票据；担保借据Accounts payable 应付帐款Accounts receivable 应收帐款Accredited Investors 合资格投资者；受信投资人指符合美国证券交易委员（SEC）条例,可参与一般美国非公开(私募）发行的部份机构和高净值个人投资者。

Accredit value 自然增长值Accrediting 本金增值适用于多种工具，指名义本金在工具(如上限合约、上下限合约、掉期和互换期权)的期限内连续增长.Accrual basis 应计制；权责发生制Accrued interest 应计利息ACE 美国商品交易所Acid Test Ratio 酸性测验比率；速动比率Acquisition 收购Across the board 全面一致;全盘的Acting in concert 一致行动；合谋Active assets 活动资产;有收益资产Active capital 活动资本Actual market 现货市场Actual price 现货价Actual useful life 实际可用年期Actuary 精算师；保险统计专家ADB 亚洲开发银行(Asian Development Bank的英文缩写）ADR 美国存股证;美国预托收据；美国存托凭证(参见AmericanDepository Receipt栏目)ADS 美国存托股份(American Depository Share的英文缩写)Ad valorem 从价;按值Ad valorem stamp duty 从价印花税Adjudicator 审裁员Adjustable rate mortgage调息按揭（ARM）Admitted value 认可值Advance 垫款Affiliated company 关联公司;联营公司After date 发票后，出票后After-hours dealing 收市后交易After-market 后市[股市] 指某只新发行股票在定价和配置后的交易市场.市场参与者关注的是紧随的后市情况，即头几个交易日。