Chapter8-1
计算机组成与结构体系英文课件：Chapter 8 – The Memory System - 1
Big-endian assignment
Little-endian assignment
The Memory System Overview (8)
Memory Locations and Addresses (ctd.)
Little-endian Assignment (ctd.)
Note: In both cases, byte addresses 0, 4, 8, …, are taken as the addresses of successive words in the memory and are the addresses used when specifying memory operations for words.
Internal Memory (Primary Storage)
Internal to the system, directly accessible by the processor.
Example: Main Memory, Cache, Processor Registers
External Memory (Secondary Storage)
External to the system, accessible by the processor via an I/O module.
公司核心第八章习题
Chapter 8Valuing Bonds8-1.A 30-year bond with a face value of $1000 has a coupon rate of 5.5%, with semiannual payments. a. What is the coupon payment for this bond? b. Draw the cash flows for the bond on a timeline. a. The coupon payment is:Coupon Rate Face Value 0.055$1000$27.50.Number of Coupons per Year 2CPN ⨯⨯===b. The timeline for the cash flows for this bond is (the unit of time on this timeline is six-monthperiods):2P 100/(1.055)$89.85==8-2.Assume that a bond will make payments every six months as shown on the following timeline(using six-month periods):a. What is the maturity of the bond (in years)?b. What is the coupon rate (in percent)?c. What is the face value? a. The maturity is 10 years.b. (20/1000) x 2 = 4%, so the coupon rate is 4%.c. The face value is $1000.1 $27.50 02 $27.503 $27.5060$27.50 +$1000Berk/DeMarzo •Corporate Finance, Second Edition 1078-3.The following table summarizes prices of various default-free, zero-coupon bonds (expressed as a percentage of face value):a. Compute the yield to maturity for each bond.b. Plot the zero-coupon yield curve (for the first five years).c. Is the yield curve upward sloping, downward sloping, or flat?a. Use the following equation.1/nn n FV 1YTM P ⎛⎫+= ⎪⎝⎭1/1111001YTM YTM 4.70%95.51⎛⎫+=⇒= ⎪⎝⎭1/2111001YTM YTM 4.80%91.05⎛⎫+=⇒= ⎪⎝⎭1/3331001YTM YTM 5.00%86.38⎛⎫+=⇒= ⎪⎝⎭1/4441001YTM YTM 5.20%81.65⎛⎫+=⇒= ⎪⎝⎭ 1/5551001YTM YTM 5.50%76.51⎛⎫+=⇒= ⎪⎝⎭b. The yield curve is as shown below.Zero Coupon Yield Curve4.64.855.25.45.60246Maturity (Years)Y i e l d t o M a t u r i t yc. The yield curve is upward sloping.108 Berk/DeMarzo• Corporate Finance, Second Edition8-4. Suppose the current zero-coupon yield curve for risk-free bonds is as follows:a. What is the price per $100 face value of a two-year, zero-coupon, risk-free bond?b. What is the price per $100 face value of a four-year, zero-coupon, risk-free bond?c. What is the risk-free interest rate for a five-year maturity? a.2P 100(1.055)$89.85==b. 4P 100/(1.0595)$79.36==c. 6.05%8-5.In the box in Section 8.1, reported that the three-month Treasury bill sold for a price of $100.002556 per $100 face value. What is the yield to maturity of this bond, expressed as an EAR?410010.01022%100.002556⎛⎫-=- ⎪⎝⎭8-6.Suppose a 10-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading for a price of $1034.74.a. What is the bond’s yield to maturity (expressed as an APR with semiannual compounding)?b. If the bond’s yield to maturity changes to 9% APR, what will the bond’s price be? a.2204040401000$1,034.747.5%(1)(1)(1)222YTM YTM YTM YTM +=+++⇒=+++Using the annuity spreadsheet: NPER Rate PV PMT FVExcel Formula Given: 20 -1,034.74 40 1,000Solve For Rate: 3.75%=RATE(20,40,-1034.74,1000)Therefore, YTM = 3.75% × 2 = 7.50% b.2204040401000$934.96..09.09.09(1)(1)(1)222PV L +=+++=+++ Using the spreadsheetWith a 9% YTM = 4.5% per 6 months, the new price is $934.96NPER Rate PV PMT FV Excel Formula Given: 20 4.50% 40 1,000 Solve For PV: (934.96) =PV(0.045,20,40,1000)Berk/DeMarzo • Corporate Finance, Second Edition 1098-7.Suppose a five-year, $1000 bond with annual coupons has a price of $900 and a yield to maturity of 6%. What is the bond’s coupon rate?25C CC 1000900C $36.26, so the coupon rate is 3.626%.(1.06)(1.06)(1.06)+=+++⇒=+++We can use the annuity spreadsheet to solve for the payment. NPER Rate PV PMT FV Excel Formula Given: 5 6.00% -900.00 1,000Solve For PMT: 36.26 =PMT(0.06,5,-900,1000)Therefore, the coupon rate is 3.626%.8-8.The prices of several bonds with face values of $1000 are summarized in the following table:For each bond, state whether it trades at a discount, at par, or at a premium. Bond A trades at a discount. Bond D trades at par. Bonds B and C trade at a premium.8-9.Explain why the yield of a bond that trades at a discount exceeds the bond’s coupon rate. Bonds trading at a discount generate a return both from receiving the coupons and from receiving a face value that exceeds the price paid for the bond. As a result, the yield to maturity of discount bonds exceeds the coupon rate.8-10.Suppose a seven-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading with a yield to maturity of 6.75%.a. Is this bond currently trading at a discount, at par, or at a premium? Explain.b. If the yield to maturity of the bond rises to 7% (APR with semiannual compounding), whatprice will the bond trade for? a. Because the yield to maturity is less than the coupon rate, the bond is trading at a premium. b. 2144040401000$1,054.60(1.035)(1.035)(1.035)++++=+++NPER Rate PV PMT FV Excel Formula Given: 14 3.50% 40 1,000Solve For PV:(1,054.60)=PV(0.035,14,40,1000)8-11.Suppose that General Motors Acceptance Corporation issued a bond with 10 years until maturity, a face value of $1000, and a coupon rate of 7% (annual payments). The yield to maturity on this bond when it was issued was 6%. a. What was the price of this bond when it was issued?b. Assuming the yield to maturity remains constant, what is the price of the bond immediatelybefore it makes its first coupon payment? c. Assuming the yield to maturity remains constant, what is the price of the bond immediatelyafter it makes its first coupon payment?110 Berk/DeMarzo • Corporate Finance, Second Editiona. When it was issued, the price of the bond was1070701000P ...$1073.60.(1.06)(1.06)+=++=++b. Before the first coupon payment, the price of the bond is970701000P 70...$1138.02.(1.06)(1.06)+=++=++c. After the first coupon payment, the price of the bond will be970701000P ...$1068.02.(1.06)(1.06)+=+=++8-12.Suppose you purchase a 10-year bond with 6% annual coupons. You hold the bond for fouryears, and sell it immediately after receiving the fourth coupon. If the bond’s yield to maturity was 5% when you purchased and sold the bond,a. What cash flows will you pay and receive from your investment in the bond per $100 facevalue? b. What is the internal rate of return of your investment?a. First, we compute the initial price of the bond by discounting its 10 annual coupons of $6 and finalface value of $100 at the 5% yield to maturity.NPER Rate PV PMT FV Excel Formula Given:10 5.00%6 100Solve For PV:(107.72)= PV(0.05,10,6,100)Thus, the initial price of the bond = $107.72. (Note that the bond trades above par, as its coupon rate exceeds its yield.)Next we compute the price at which the bond is sold, which is the present value of the bonds cash flows when only 6 years remain until maturity.NPER Rate PV PMT FV Excel Formula Given: 6 5.00%6 100Solve For PV:(105.08)= PV(0.05,6,6,100)Therefore, the bond was sold for a price of $105.08. The cash flows from the investment are therefore as shown in the following timeline.Berk/DeMarzo • Corporate Finance, Second Edition 111b. We can compute the IRR of the investment using the annuity spreadsheet. The PV is the purchaseprice, the PMT is the coupon amount, and the FV is the sale price. The length of the investment N = 4 years. We then calculate the IRR of investment = 5%. Because the YTM was the same at the time of purchase and sale, the IRR of the investment matches the YTM. NPER Rate PV PMT FV Excel Formula Given: 4 –107.72 6 105.08Solve For Rate: 5.00% = RATE(4,6,-107.72,105.08)8-13.Consider the following bonds:a. What is the percentage change in the price of each bond if its yield to maturity falls from 6% to 5%?b. Which of the bonds A –D is most sensitive to a 1% drop in interest rates from 6% to 5% andwhy? Which bond is least sensitive? Provide an intuitive explanation for your answer. a. We can compute the price of each bond at each YTM using Eq. 8.5. For example, with a 6% YTM,the price of bond A per $100 face value is15100P(bond A, 6% YTM)$41.73.1.06== The price of bond D is101011100P(bond D, 6% YTM)81$114.72..06 1.06 1.06⎛⎫=⨯-+= ⎪⎝⎭ One can also use the Excel formula to compute the price: –PV(YTM, NPER, PMT, FV). Once we compute the price of each bond for each YTM, we can compute the % price change as Percent change =()()()Price at 5% YTM Price at 6% YTM .Price at 6% YTM -The results are shown in the table below.Coupon Rate Maturity Price at Price at Percentage Change(annual payments)(years)6% YTM 5% YTM A 0%15$41.73$48.1015.3%B 0%10$55.84$61.399.9%C 4%15$80.58$89.6211.2%D8%10$114.72$123.177.4%Bondb. Bond A is most sensitive, because it has the longest maturity and no coupons. Bond D is the leastsensitive. Intuitively, higher coupon rates and a shorter maturity typically lower a bond’s interest rate sensitivity.112 Berk/DeMarzo • Corporate Finance, Second Edition8-14.Suppose you purchase a 30-year, zero-coupon bond with a yield to maturity of 6%. You hold the bond for five years before selling it.a. If the bond’s yield to maturity is 6% when you sell it, what is the internal rate of return ofyour investment? b. If the bond’s yield to maturity is 7% when you sell it, what is the internal rate of return ofyour investment? c. If the bond’s yield to maturity is 5% when you se ll it, what is the internal rate of return ofyour investment? d. Even if a bond has no chance of default, is your investment risk free if you plan to sell itbefore it matures? Explain. a. Purchase price = 100 / 1.0630 = 17.41. Sale price = 100 / 1.0625 = 23.30. Return = (23.30 / 17.41)1/5– 1 = 6.00%. I.e., since YTM is the same at purchase and sale, IRR = YTM. b. Purchase price = 100 / 1.0630 = 17.41. Sale price = 100 / 1.0725 = 18.42. Return = (18.42 / 17.41)1/5– 1 = 1.13%. I.e., since YTM rises, IRR < initial YTM. c. Purchase price = 100 / 1.0630 = 17.41. Sale price = 100 / 1.0525 = 29.53. Return = (29.53 / 17.41)1/5– 1 = 11.15%. I.e., since YTM falls, IRR > initial YTM. d. Even without default, if you sell prior to maturity, you are exposed to the risk that the YTM maychange.8-15.Suppose you purchase a 30-year Treasury bond with a 5% annual coupon, initially trading at par. In 10 years’ time, the bond’s yield to maturity has risen to 7% (EAR).a. If you sell the bond now, what internal rate of return will you have earned on yourinvestment in the bond? b. If instead you hold the bond to maturity, what internal rate of return will you earn on yourinvestment in the bond? c. Is comparing the IRRs in (a) versus (b) a useful way to evaluate the decision to sell the bond?Explain. a. 3.17% b. 5%c. We can’t simply compare IRRs. By not selling the bond for its current price of $78.81, we willearn the current market return of 7% on that amount going forward.8-16.Suppose the current yield on a one-year, zero coupon bond is 3%, while the yield on a five-year, zero coupon bond is 5%. Neither bond has any risk of default. Suppose you plan to invest for one year. You will earn more over the year by investing in the five-year bond as long as its yield does not rise above what level?The return from investing in the 1 year is the yield. The return for investing in the 5 year for initialprice p 0 and selling after one year at price p1 is 101pp -. We have05151,(1.05)1.(1)p p y ==+Berk/DeMarzo • Corporate Finance, Second Edition 113So you break even when41105545/41/41(1)110.031(1.05)(1.05) 1.03(1)(1.05)1 5.51%.(1.03)p y y p y y +-=-===+=-=For Problems 17–22, assume zero-coupon yields on default-free securities are as summarized in the following table:8-17.What is the price today of a two-year, default-free security with a face value of $1000 and an annual coupon rate of 6%? Does this bond trade at a discount, at par, or at a premium?221260601000...$1032.091(1.04)(1)(1)(1.043)N N CPN CPN CPN FV P YTM YTM YTM ++=+++=+=+++++This bond trades at a premium. The coupon of the bond is greater than each of the zero coupon yields, so the coupon will also be greater than the yield to maturity on this bond. Therefore it trades at a premium8-18.What is the price of a five-year, zero-coupon, default-free security with a face value of $1000? The price of the zero-coupon bond is51000$791.03(1)(10.048)NN FV P YTM ===++ 8-19.What is the price of a three-year, default-free security with a face value of $1000 and an annual coupon rate of 4%? What is the yield to maturity for this bond? The price of the bond is223124040401000...$986.58.1(1.04)(1)(1)(1.043)(1.045)N N CPN CPN CPN FV P YTM YTM YTM ++=+++=++=++++++ The yield to maturity is2...1(1)(1)NCPN CPN CPN FVP YTM YTM YTM +=++++++234040401000$986.58 4.488%(1)(1)(1)YTM YTM YTM YTM +=++⇒=+++8-20.What is the maturity of a default-free security with annual coupon payments and a yield to maturity of 4%? Why?The maturity must be one year. If the maturity were longer than one year, there would be an arbitrage opportunity.114 Berk/DeMarzo • Corporate Finance, Second Edition8-21.Consider a four-year, default-free security with annual coupon payments and a face value of $1000 that is issued at par. What is the coupon rate of this bond? Solve the following equation:2344111110001000(1.04)(1.043)(1.045)(1.047)(1.047)$46.76.CPN CPN ⎛⎫=++++ ⎪+++++⎝⎭=Therefore, the par coupon rate is 4.676%.8-22.Consider a five-year, default-free bond with annual coupons of 5% and a face value of $1000. a. Without doing any calculations, determine whether this bond is trading at a premium or at adiscount. Explain. b. What is the yield to maturity on this bond?c. If the yield to maturity on this bond increased to 5.2%, what would the new price be? a. The bond is trading at a premium because its yield to maturity is a weighted average of the yieldsof the zero coupon bonds. This implied that its yield is below 5%, the coupon rate. b. To compute the yield, first compute the price.2122345...1(1)(1)50505050501000$1010.05(1.04)(1.043)(1.045)(1.047)(1.048)NN CPN CPN CPN FVP YTM YTM YTM +=+++++++=++++=+++++The yield to maturity is:2...1(1)(1)505010001010.05... 4.77%.(1)(1)NN CPN CPN CPN FVP YTM YTM YTM YTM YTM YTM +=+++++++=++⇒=++c. If the yield increased to 5.2%, the new price would be:2...1(1)(1)50501000...$991.39.(1.052)(1.052)NNCPN CPN CPN FV P YTM YTM YTM +=+++++++=++=++8-23.Prices of zero-coupon, default-free securities with face values of $1000 are summarized in thefollowing table:Suppose you observe that a three-year, default-free security with an annual coupon rate of 10% and a face value of $1000 has a price today of $1183.50. Is there an arbitrage opportunity? If so, show specifically how you would take advantage of this opportunity. If not, why not?First, figure out if the price of the coupon bond is consistent with the zero coupon yields implied by the other securities.Berk/DeMarzo • Corporate Finance, Second Edition 115111000970.87 3.0%(1)YTM YTM =→=+ 2221000938.95 3.2%(1)YTM YTM =→=+ 3331000904.56 3.4%(1)YTM YTM =→=+According to these zero coupon yields, the price of the coupon bond should be:231001001001000$1186.00.(1.03)(1.032)(1.034)+++=+++ The price of the coupon bond is too low, so there is an arbitrage opportunity. To take advantage of it:Today1 Year2 Years3 Years Buy 10 Coupon Bonds 11835.00 +1000 +1000 +11,000 Short Sell 1 One-Year Zero +970.87 1000Short Sell 1 Two-Year Zero +938.95 1000Short Sell 11 Three-Year Zeros +9950.16 11,000 Net Cash Flow 24.988-24.Assume there are four default-free bonds with the following prices and future cash flows:Do these bonds present an arbitrage opportunity? If so, how would you take advantage of this opportunity? If not, why not?To determine whether these bonds present an arbitrage opportunity, check whether the pricing is internally consistent. Calculate the spot rates implied by Bonds A, B, and D (the zero coupon bonds), and use this to check Bond C. (You may alternatively compute the spot rates from Bonds A, B, and C, and check Bond D, or some other combination.)111000934.587.0%(1)YTM YTM =⇒=+2221000881.66 6.5%(1)YTM YTM =⇒=+3331000839.62 6.0%(1)YTM YTM =⇒=+Given the spot rates implied by Bonds A, B, and D, the price of Bond C should be $1,105.21. Its price really is $1,118.21, so it is overpriced by $13 per bond. Yes, there is an arbitrage opportunity.To take advantage of this opportunity, you want to (short) Sell Bond C (since it is overpriced). To match future cash flows, one strategy is to sell 10 Bond Cs (it is not the only effective strategy; any multiple of this strategy is also arbitrage). This complete strategy is summarized in the table below.Today 1 Year 2Years 3Years Sell Bond C 11,182.10 –1,000 –1,000–11,000Buy Bond A –934.58 1,0000 0 Buy Bond B –881.66 0 1,0000 Buy 11 Bond D –9,235.82 0 0 11,000Net Cash Flow130.04Notice that your arbitrage profit equals 10 times the mispricing on each bond (subject to rounding error).8-25.Suppose you are given the following information about the default-free, coupon-paying yield curve:a. Use arbitrage to determine the yield to maturity of a two-year, zero-coupon bond.b. What is the zero-coupon yield curve for years 1 through 4?a. We can construct a two-year zero coupon bond using the one and two-year coupon bonds asfollows. Cash Flow in Year: 1 2 3 4 Two-year coupon bond ($1000 Face Value) 100 1,100 Less: One-year bond ($100 Face Value) (100) Two-year zero ($1100 Face Value) - 1,100Now, Price(2-year coupon bond) = 21001100$1115.051.03908 1.03908+=Price(1-year bond) =100$98.04.1.02= By the Law of One Price:Price(2 year zero) = Price(2 year coupon bond) – Price(One-year bond)= 1115.05 – 98.04 = $1017.01Given this price per $1100 face value, the YTM for the 2-year zero is (Eq. 8.3)1/21100(2)1 4.000%.1017.01YTM ⎛⎫=-= ⎪⎝⎭b. We already know YTM(1) = 2%, YTM(2) = 4%. We can construct a 3-year zero as follows:Cash Flow in Year:1 2 3 4Three-year coupon bond ($1000 face value) 60 60 1,060 Less: one-year zero ($60 face value) (60) Less: two-year zero ($60 face value) - (60) Three-year zero ($1060 face value) -- 1,060Now, Price(3-year coupon bond) = 2360601060$1004.29.1.0584 1.0584 1.0584++=By the Law of One Price:Price(3-year zero) = Price(3-year coupon bond) – Price(One-year zero) – Price(Two-year zero) = Price(3-year coupon bond) – PV(coupons in years 1 and 2)= 1004.29 – 60 / 1.02 – 60 / 1.042 = $889.99.Solving for the YTM:1/31060(3)1 6.000%.889.99YTM ⎛⎫=-= ⎪⎝⎭Finally, we can do the same for the 4-year zero:Cash Flow in Year:1 2 3 4Four-year coupon bond ($1000 face value) 120 120 120 1,120 Less: one-year zero ($120 face value) (120) Less: two-year zero ($120 face value) — (120) Less: three-year zero ($120 face value) — — (120) Four-year zero ($1120 face value) —— —1,120Now, Price(4-year coupon bond) = 2341201201201120$1216.50.1.05783 1.05783 1.05783 1.05783+++=By the Law of One Price:Price(4-year zero) = Price(4-year coupon bond) – PV(coupons in years 1–3)= 1216.50 – 120 / 1.02 – 120 / 1.042 – 120 / 1.063 = $887.15. Solving for the YTM:1/41120(4)1 6.000%.887.15YTM ⎛⎫=-= ⎪⎝⎭Thus, we have computed the zero coupon yield curve as shown.8-26.Explain why the expected return of a corporate bond does not equal its yield to maturity. The yield to maturity of a corporate bond is based on the promised payments of the bond. But there is some chance the corporation will default and pay less. Thus, the bond’s expected return is typically less than its YTM.Corporate bonds have credit risk, which is the risk that the borrower will default and not pay all specified payments. As a result, investors pay less for bonds with credit risk than they would for an otherwise identical default-free bond. Because the YTM for a bond is calculated using the promised cash flows, the yields of bonds with credit risk will be higher than that of otherwise identical default-free bonds. However, the YTM of a defaultable bond is always higher than the expected return of investing in the bond because it is calculated using the promised cash flows rather than the expected cash flows.8-27.Grummon Corporation has issued zero-coupon corporate bonds with a five-year maturity. Investors believe there is a 20% chance that Grummon will default on these bonds. If Grummon does default, investors expect to receive only 50 cents per dollar they are owed. If investors require a 6% expected return on their investment in these bonds, what will be the price and yield to maturity on these bonds? Price =5100((1)())67.251.06d d r -+=Yield=1/510018.26%67.25⎛⎫-= ⎪⎝⎭8-28.The following table summarizes the yields to maturity on several one-year, zero-couponsecurities:a. What is the price (expressed as a percentage of the face value) of a one-year, zero-couponcorporate bond with a AAA rating? b. What is the credit spread on AAA-rated corporate bonds? c. What is the credit spread on B-rated corporate bonds? d. How does the credit spread change with the bond rating? Why? a. The price of this bond will be10096.899.1.032P ==+b. The credit spread on AAA-rated corporate bonds is 0.032 – 0.031 = 0.1%.c. The credit spread on B-rated corporate bonds is 0.049 – 0.031 = 1.8%.d. The credit spread increases as the bond rating falls, because lower rated bonds are riskier.8-29.Andrew Industries is contemplating issuing a 30-year bond with a coupon rate of 7% (annual coupon payments) and a face value of $1000. Andrew believes it can get a rating of A from Standard and Poor’s. However, due to recent financial difficulties at the company, Standard and Poor’s is warni ng that it may downgrade Andrew Industries bonds to BBB. Yields on A-rated, long-term bonds are currently 6.5%, and yields on BBB-rated bonds are 6.9%. a. What is the price of the bond if Andrew maintains the A rating for the bond issue? b. What will the price of the bond be if it is downgraded? a. When originally issued, the price of the bonds was3070701000...$1065.29.(10.065)(1.065)P +=++=++b. If the bond is downgraded, its price will fall to3070701000...$1012.53.(10.069)(1.069)P +=++=++8-30.HMK Enterprises would like to raise $10 million to invest in capital expenditures. The companyplans to issue five-year bonds with a face value of $1000 and a coupon rate of 6.5% (annual payments). The following table summarizes the yield to maturity for five-year (annualpay) coupon corporate bonds of various ratings:a. Assuming the bonds will be rated AA, what will the price of the bonds be?b. How much total principal amount of these bonds must HMK issue to raise $10 million today,assuming the bonds are AA rated? (Because HMK cannot issue a fraction of a bond, assume that all fractions are rounded to the nearest whole number.) c. What must the rating of the bonds be for them to sell at par?d. Suppose that when the bonds are issued, the price of each bond is $959.54. What is the likelyrating of the bonds? Are they junk bonds?a. The price will be565651000...$1008.36.(1.063)(1.063)P +=++=++b. Each bond will raise $1008.36, so the firm must issue:$10,000,0009917.139918 bonds.$1008.36=⇒This will correspond to a principle amount of 9918$1000$9,918,000.⨯=c. For the bonds to sell at par, the coupon must equal the yield. Since the coupon is 6.5%, the yieldmust also be 6.5%, or A-rated. d. First, compute the yield on these bonds:565651000959.54...7.5%.(1)(1)YTM YTM YTM +=++⇒=++Given a yield of 7.5%, it is likely these bonds are BB rated. Yes, BB-rated bonds are junk bonds.8-31.A BBB-rated corporate bond has a yield to maturity of 8.2%. A U.S. Treasury security has ayield to maturity of 6.5%. These yields are quoted as APRs with semiannual compounding. Both bonds pay semiannual coupons at a rate of 7% and have five years to maturity.a. What is the price (expressed as a percentage of the face value) of the Treasury bond?b. What is the price (expressed as a percentage of the face value) of the BBB-rated corporatebond? c. What is the credit spread on the BBB bonds? a. 103535 1000...$1,021.06 102.1%(1.0325)(1.0325)P +=++==++b.103535 1000...$951.5895.2%(1.041)(1.041)P +=++==++ c. 0. 178-32.The Isabelle Corporation rents prom dresses in its stores across the southern United States. It has just issued a five-year, zero-coupon corporate bond at a price of $74. You have purchased this bond and intend to hold it until maturity. a. What is the yield to maturity of the bond?b. What is the expected return on your investment (expressed as an EAR) if there is no chanceof default? c. What is the expected return (expressed as an EAR) if there is a 100% probability of defaultand you will recover 90% of the face value? d. What is the expected return (expressed as an EAR) if the probability of default is 50%, thelikelihood of default is higher in bad times than good times, and, in the case of default, you will recover 90% of the face value? e. For parts (b –d), what can you say about the five-year, risk-free interest rate in each case? a.1/51001 6.21%74⎛⎫-= ⎪⎝⎭b. In this case, the expected return equals the yield to maturity.c.1/51000.91 3.99%74⨯⎛⎫-= ⎪⎝⎭d. 1/51000.90.51000.51 5.12%74⨯⨯+⨯⎛⎫-= ⎪⎝⎭e. Risk-free rate is 6.21% in b, 3.99% in c, and less than 5.12% in d.AppendixProblems A.1–A.4 refer to the following table:A.1.What is the forward rate for year 2 (the forward rate quoted today for an investment that beginsin one year and matures in two years)? From Eq 8A.2,22221(1) 1.055117.02%(1) 1.04YTM f YTM +=-=-=+A.2.What is the forward rate for year 3 (the forward rate quoted today for an investment that begins in two years and matures in three years)? What can you conclude about forward rates when the yield curve is flat? From Eq 8A.2,3333222(1) 1.05511 5.50%(1) 1.055YTM f YTM +=-=-=+When the yield curve is flat (spot rates are equal), the forward rate is equal to the spot rate.A.3.What is the forward rate for year 5 (the forward rate quoted today for an investment that begins in four years and matures in five years)? From Eq 8A.2,5555444(1) 1.04511 2.52%(1) 1.050YTM f YTM +=-=-=+When the yield curve is flat (spot rates are equal), the forward rate is equal to the spot rate.A.4.Suppose you wanted to lock in an interest rate for an investment that begins in one year and matures in five years. What rate would you obtain if there are no arbitrage opportunities? Call this rate f 1,5. If we invest for one-year at YTM1, and then for the 4 years from year 1 to 5 at rate f 1,5, after five years we would earn 1YTM 11f 1,54with no risk. No arbitrage means this must equal that amount we would earn investing at the current five year spot rate:(1 + YTM 1)(1 + f 1,5)4 + (1 + YTM 5)5.。
chapter-8高速CMOS逻辑电路设计---副本剖析
内部寄生电容
8.3 逻辑努力
反相器延时的计算
S(>1)倍对称反相器的延迟时间
R Rref S
Cin SCref
C p SC p ,ref
绝对延时
d abs kR(C p Cout ) kRref C p ,ref
相对延时
(h p)
d abs
加前级门的负载电容，导致恶性循环。必须采用
特别的电路设计来解决这个问题。
问题：
如何使反相
器链的总延
时最小？
8.2 驱动大电容
负载优化条件
第一级是标准尺寸反相器，输入电容为C1，FET 电阻为
R1，FET互导为β1，各级单调放大，即有
1 2 3 N 1 N
j R j C j 1
N
N 1
j 1
j 1
N级反相器链的总延时 d j R j C j 1 RN C L
N级反相器链的负载电容 C L C N 1 S N C1
代入尺寸放大关系
R1
j
•
S
C1
R j C j 1 S j 1
N
N
j 1
CGn (2 r )
1 r
g NAND 2
C
ref
Cin CGn (n r )
nr
一倍对称NANDn
CGn (n r )
1 r
g NAND 2
C
ref
n个输入
NOR
每个nFET的尺寸
1个pFET的尺寸
Cin CGn (1 2r )
Chapter 8 Electric Power Generation section 8-1 Coal-Fired Power Plants 电气工程及其自动化专业英语
New Words and Expressions
coal-fired a. 燃煤的 furnace n. 炉，炉膛，燃烧室 pulverizer n. 磨煤机，粉煤机 preheated a. 预热的 boiler n. 锅炉，蒸发器，蒸汽发生器 flue gas 烟气，废气，排烟 electrostatic a. 静电的 precipitator n. 除尘器
Section 1 Coal-Fired Power Plants
the intermediate-pressure (IP) turbine. Leaving the IP turbine, steam (at lower pressure and much expended) is directed to the low-pressure (LP) turbines. The exhaust steam from the LP turbines is cooled in a condenser, and as feed-water, is reheated (with steam extracted from the turbines) and pumped back to the boiler.
Section 1 Coal-Fired Power Plants
In fossil-fuel power plants, coal, oil, or natural gas is burned in a furnace, the combustion products heat water, converting it to steam, and the steam drives a turbine which is mechanically coupled to an electric power generator. A schematic diagram showing a typical coal-fired power plant is given in Fig.8-1. In very brief outline, the operation of the plant is as follows. Coal is taken from storage and fed to a pulverizer (or a mill), mixed with preheated air, and blown into the furnace, where it is burned. The furnace contains a complex of tubes and drums
第八章弹性体的应力和应变-盐城师范学院
第八章弹性体的应力和应变学时安排：3课时教学目的与要求：1、掌握应力和应变的相互关系、拉伸形变的胡克定律及其适用范围；2、了解杨氏模量、泊松比、剪切模量、固体的弹性形变势能、弹性形变势能密度等概念；3、了解梁的弯曲、杆的扭转的基本知识和结论。
教学重点：弹性体的拉伸和压缩。
教学难点：应力、杨氏模量、剪切模量、泊松比等概念的物理意义。
习题：8.1.2 8.1.3 8.1.6Chapter8 弹性体的应力和应变形变的分类：塑性形变：外力撤消后，形变不完全消失；弹性形变：外力撤消后，形变完全消失，此类物体为弹性体——理想模型；本章的研究范围：各向同性的均匀弹性体的弹性形变，均匀弹性体：体内各点的弹性相同。
各向同性的弹性体：体内各点的弹性与方向无关。
弹性形变的种类：伸长、缩短、切变、扭转、弯曲……； 弹性形变的基本种类：长应变、切应变。
§8—1 弹性体的拉伸和压缩一、外力、内力与应力1．外力：对于给定物体，外界（其它物体）对它的作用力2．内力：物体内部各部分之间的相互作用力。
内力的求法：外力→物体形变→内力，为了研究内力，用一假想的平面S 将物体分为两个部分：则S 面的两侧的相互作用力——内力F ' 、F求内力的方法：隔离体法，S 面的两侧分别为一个隔离体。
物体处于平衡时，列出左侧（或右侧）隔离体的平衡方程式，由外力求内力。
S 面上受力不均匀时，在S 面上任一点（O 点）处取面元S ∆，0n 自受力一侧指向施力物一侧，是S ∆的外法向，S ∆确定了即可确定S ∆的受力（内力）。
3．应力：描述物体内部各点处内力强度的物理量（1）定义：①平均应力：F p S ∆=∆ ②应力：0lim S F p S∆→∆=∆ 物理意义：作用于物体某点处某有向面元的平均应力，当面元0S ∆→时的极限——该无限小有向面元上的应力。
③正应力：p n σ=⋅ σ正应力为p 在无穷小有向面元的外法向上的投影，σ取“+”——有向面元的某一侧受到另一侧的拉力σ取“－”——有向面元的某一侧受到另一侧的压力 ④剪切应力：τ，p 在无穷小有向面元的外法线垂直方向上的投影。
专业英语第八章课文翻译1
Chiguo Chapter 8 Section 1 Coal-Fired Power Plants燃煤发电站第一段：在化石燃料发电厂中，煤，石油或者天然气在燃烧室中燃烧，燃烧产生高温的水，然后转换成水蒸气，高温的水蒸气将驱动汽轮机，汽轮机与发电机机械地连接在一起。
图8.1展示了一个典型的图表示意图。
发电厂的运行用一下简洁的语言概述。
从仓库取出煤块放入粉煤机（或者磨粉机）中粉碎，然后与预热的空气混合，最后充入燃烧室中燃烧。
燃烧室包含一个复杂的管道，抽上的水灌输到一个叫锅炉的设备中，锅炉里面水的温度逐渐上升直至它们成为水蒸气。
水蒸气被送至汽轮机中，与此同时，燃烧的废气（烟道气体）通过物理和静电除尘装置除掉99%以上的固体颗粒（灰尘）在通过烟囱或烟囱体排放出去之前。
第二段：刚刚描述的单元，是输入煤粉，空气和水输出水蒸气的单元，这几个方面的系统被统称为蒸汽发电机组，或燃烧室，或者蒸汽发生器。
当考虑根据是燃烧过程的时候常用“燃烧室”这个术语，同时当考虑因素是水汽循环时，“蒸汽发生器”这个术语被更频繁的使用。
水蒸气的3500磅/平方英寸的典型气压和华氏零下1050度的条件，是通过控制和停止（关闭）汽轮机阀门来提供的。
整齐的热能转化为水轮机的机械能。
从排气机中排出的蒸汽在热交换器中成为冷凝器中冷却形成水，再次被泵抽回锅炉里。
通过调节蒸汽的流量变化来控制涡轮发电机的输出。
截止阀具有保护作用，它通常是完全开放的，但可以“跳闸”关闭，以防止汽轮机发电机组超速，使电力输出突然下贱（由于断路器的行动）和控制阀不关闭。
第三段：图8-1表明的是一个单阶段汽轮机，但在实际中一个更加复杂的多级排列被使用以便能实现相对较高的热效率。
一个典型的多级排列如图8-2所示。
它包括四个有着不同蒸汽气压的汽轮机机械地耦合串联在一起。
用常规的概述就是高压蒸汽来自锅炉然后进入高压汽轮机。
在之前离开高压汽轮机的水蒸气回到锅炉（再热器）地区，然后送往中压汽轮机。
《细胞生物学》——细胞8章 细胞骨架1
A 球状肌动蛋白 B 纤维状肌动蛋白
G蛋 C白 D Arp2/3
提交
3. 微丝的组装不包括下列哪个阶段（） A. 成核反应 B. 纤维的延长 C. 踏车行为 D. 解离阶段
单选题 10分
3. 微丝的组装不包括下列哪个阶段()
A 成核反应 B 纤维的延长 C 踏车行为 D 解离阶段
即正极与负极之别
（2）肌动蛋白单体组装成微丝的过程
① 缓慢成核期：肌动蛋白单体与起始复合物结合→形成寡聚体（至少2-3
个单体）。
包括2种肌动蛋白相关蛋白（Arp2/3）和5种
其它蛋白。
② 快速延长期：肌动蛋白单体具有ATP酶活性，可利用水解ATP释放的能
量来快速组装单体。当微丝的组装速度快于肌动蛋白水解ATP的速度时，在
提交
本章主要内容
微丝与细胞运动 微管及其功能 中间丝
第一节 微丝与细胞运动
微丝（microfilament, MF） 肌动蛋白丝（actin filament） 纤维状肌动蛋白
（fibrous, F-actin）
由肌动蛋白单体组装而成的 直径为7 nm的纤维状结构 存在于所有真核细胞中 微丝的组装/去组装 微丝结合蛋白
（MF binding protein）
一、微丝的组成及其组装 二、微丝网络结构的调节与细胞运动
一、微丝的组成及其组装
（一）微丝的结构与成分 （二）微丝的组装及其动力学特性 （三）影响微丝组装的特异性药物
（一）微丝的结构与成分
• 微丝的主要结构成分：肌动蛋白（actin）。
• 肌动蛋白在细胞内有2种存在形式：①球状肌动蛋白（G-actin）： 肌动蛋白单体；②纤维状肌动蛋白（F-actin）：由多个单体组装 而成。
典范英语终极跑鞋chapter8主要内容
典范英语终极跑鞋chapter8主要内容全文共10篇示例，供读者参考篇1Chapter 8 of "The Ultimate Running Shoes" talks about the importance of proper foot support and cushioning in running shoes. The chapter begins by explaining how different types of running shoes are designed to provide support for different foot types. For example, people with high arches may need shoes with extra cushioning to support their feet, while those with flat feet may require shoes with more stability.The chapter goes on to discuss the various materials used in running shoe construction, such as EVA foam and gel inserts, which help to absorb shock and impact while running. It also explains how the design of the shoe, including the shape of the sole and heel counter, can affect the runner's gait and overall performance.One of the key takeaways from Chapter 8 is the importance of proper fit when choosing running shoes. Ill-fitting shoes can lead to discomfort, blisters, and even serious injuries. The chapter provides tips on how to determine the right size and fitfor your feet, including getting professionally fitted at a running store and testing the shoes by running or walking in them.Overall, Chapter 8 emphasizes the crucial role that proper foot support and cushioning play in maximizing performance and preventing injury while running. By choosing the right type of running shoes and ensuring a proper fit, runners can improve their comfort, efficiency, and overall enjoyment of the sport.篇2Chapter 8 of "The Ultimate Running Shoes" is all about speed and performance. In this chapter, we learn about how to choose the right running shoes for racing and how to improve our speed on the track.First off, the chapter talks about what features to look for in a racing shoe. It's important to find a lightweight shoe that provides good support and cushioning. Racing shoes are designed to be sleek and fast, with minimal cushioning to reduce weight and maximize speed.Next, we learn about the importance of proper form and technique when it comes to running fast. It's not just about how fast you can move your legs, but also about how efficiently youcan move them. Proper arm swing, stride length, and foot strike are all important factors in maximizing your speed.The chapter also discusses the role of training in improving speed. Different types of speed workouts, such as interval training and tempo runs, can help build your speed and endurance. It's important to train consistently and push yourself out of your comfort zone to see improvements in your speed.Lastly, the chapter offers tips on how to mentally prepare for a race. Visualizing success, setting realistic goals, and staying focused during a race are all important mental strategies for improving your speed on race day.Overall, Chapter 8 of "The Ultimate Running Shoes" gives us valuable insight into how to choose the right shoes and improve our speed and performance on the track. So lace up those racing shoes and get ready to fly past the competition!篇3Hey guys, guess what? I just finished reading chapter 8 of "The Ultimate Running Shoes"! It was super interesting, so let me tell you all about it!In this chapter, we learned all about different types of running shoes for different types of runners. There are shoes for beginners, shoes for advanced runners, and even shoes for people with special foot conditions. It's really cool how there's a perfect shoe out there for everyone!We also learned about the importance of choosing the right size shoe and how to properly lace them up for a comfortable fit. Did you know that wearing the wrong size shoe can actually cause injuries? Yeah, crazy right?And get this - there are shoes that can track your running stats, like how far you've run and how fast! It's like having a personal trainer right on your feet! Technology is so awesome.But the best part of the chapter was learning about all the latest trends in running shoes. From bright colors to funky designs, there's no limit to how cool your running shoes can be. I can't wait to go shopping for my own pair now!So, if you're into running or just want to learn more about the best shoes for your feet, definitely check out chapter 8 of "The Ultimate Running Shoes". It's a real game-changer!篇4Chapter 8 of "The Ultimate Running Shoes" is all about exploring different types of running shoes and how they can improve your performance. It was super interesting and I learned a lot of cool stuff!First, we talked about cushioning in running shoes. It's like having a comfy bed for your feet while you run. Some shoes have lots of cushioning, which is great for long distances or if you have a history of foot pain. Others have less cushioning, which is better for speed and agility.Next, we learned about stability shoes. These are like the superheroes of running shoes because they help protect your feet and ankles from rolling inwards or outwards. They're perfect for people with flat feet or those who overpronate or supinate when they run.Then, we talked about motion control shoes. These are like the bodyguards of the running shoe world because they provide extra support for people who have severe overpronation. They help keep your feet in line and prevent injuries caused by excessive rolling.Finally, we discussed minimalist shoes. These are like running barefoot but with a little extra protection. They're superlightweight and help improve your running form, but you have to be careful because they offer less cushioning and support.Overall, Chapter 8 of "The Ultimate Running Shoes" was awesome! I can't wait to try out different types of running shoes and see how they can help me become a faster and stronger runner. I'm so excited to put all this new knowledge to the test and find the perfect pair of shoes for me!篇5Hello everyone! Today, I'm going to talk about Chapter 8 of the book "The Ultimate Running Shoes". In this chapter, we learned all about how to choose the perfect pair of running shoes.First, the book talked about the different types of running shoes - neutral, stability, and motion control. Neutral shoes are for runners with a normal arch, stability shoes are for runners with a low arch, and motion control shoes are for runners with flat feet. It's important to know your foot type so you can pick the right shoes for you!Next, the book discussed the importance of getting the right fit. Your running shoes should be snug, but not too tight. They should also have enough room in the toe box so your toes canmove freely. It's a good idea to try on a few different pairs before making a decision.The chapter also talked about the different features to look for in running shoes, like cushioning, support, and breathability. Cushioning helps to absorb impact, support helps to prevent injury, and breathability keeps your feet cool and dry. All of these things are important for a comfortable and safe run.In conclusion, Chapter 8 of "The Ultimate Running Shoes" taught us the importance of choosing the right pair of shoes for our feet. By understanding our foot type, getting the right fit, and looking for the right features, we can find the perfect running shoes for us. Happy running, everyone!篇6Chapter 8 of the Ultimate Running Shoes series is all about choosing the right shoes for your running needs. It's super important to have the right shoes so you can run faster, jump higher, and feel super cool while doing it!First off, you need to think about what type of running you'll be doing. If you're a speed demon and love sprinting, you'll want to go for lightweight shoes with lots of cushioning. These will help you go fast and be comfy at the same time.If you're more of a long distance runner, you'll want shoes with good support and stability. These will help keep your feet happy and healthy as you rack up the miles.There are also shoes for trail running, which have extra grip and protection to handle tough terrain. And don't forget about track spikes for running on the track – they have sharp points on the bottom to help you go even faster!When you're trying on shoes, make sure they fit snugly but not too tight. You want a little wiggle room for your toes, but you also don't want your feet sliding around inside the shoes. And always try them on with the socks you'll be wearing when you run.Remember, the right shoes can make all the difference in your running game. So take your time, try on lots of options, and find the perfect pair that will help you crush your running goals. Happy running, my friends!篇7Chapter 8 of the Ultimate Running Shoes is super cool! In this chapter, we learn all about the advanced technology and cool features of the latest running shoes.First off, we got to know about the innovative cushioning system in the shoes. It's like running on clouds! The special foam material absorbs the impact of each step, making our feet feel super comfy and preventing any injuries.Next, we learned about the unique design of the outsole. It has special grooves and patterns that provide excellent traction on all types of surfaces. So no matter if we're running on the track, road, or trail, our shoes will keep us steady and secure.And let's not forget about the awesome breathable mesh upper! It helps to keep our feet cool and dry, even during intense workouts. Plus, the snug fit of the shoes ensures that our feet stay in place and don't slide around while we're running.Oh, and how could I forget about the stylish colors and designs of the shoes? They look so cool and make us feel like real running champions!Overall, Chapter 8 of the Ultimate Running Shoes taught us that the right pair of shoes can make all the difference in our performance. So let's lace up our shoes, hit the pavement, and run like the wind! ♂️篇8Chapter 8 of the Ultimate Running Shoes series is all about choosing the right shoes for different types of running activities. It's super important to pick the best shoes for your feet so that you can run faster, jump higher, and have fun while doing it! Let's dive into the main points of this chapter.First off, the chapter talks about running shoes forlong-distance running. When you're running a marathon or a long trail race, you need shoes that can provide cushioning and support for miles and miles. Look for shoes with extra padding in the midsole and heel to absorb shock and reduce fatigue. They should also have a breathable upper to keep your feet cool and dry.Next, the chapter covers shoes for sprinting. If you're a speed demon and love sprinting short distances, you need lightweight shoes with a snug fit. Look for shoes with a low heel drop and a stiff sole to help you explode off the starting line. These shoes should also have traction for grip on the track or road.Another important point in this chapter is choosing the right shoes for trail running. Trail running shoes are designed to handle rugged terrain, rocks, and mud. They have aggressive tread patterns for traction and protection for your feet fromsharp objects. Look for shoes with a durable outsole and a protective toe cap for rocky trails.Lastly, the chapter discusses cross-training shoes for other sports and activities. Cross-training shoes are versatile and can be used for running, weightlifting, and other workouts. They should have a stable base for lifting weights, cushioning for running, and flexibility for agility drills. Look for shoes with a comfortable fit and breathability for all-day wear.In conclusion, Chapter 8 of the Ultimate Running Shoes series emphasizes the importance of choosing the right shoes for different types of running activities. Whether you're along-distance runner, sprinter, trail runner, or cross-training enthusiast, there's a perfect pair of shoes out there for you. Remember to consider your foot type, running style, and the terrain you'll be running on when selecting your next pair of running shoes. Happy running!篇9Hi guys, today I'm gonna talk about this super cool book called "Ultimate Running Shoes Chapter 8". It's all about the best running shoes in the world and I can't wait to tell you all about it.In Chapter 8, the book talks about different types of running shoes and how to choose the right ones for you. It explains the importance of having the right shoes for running and how it can make a big difference in your performance.The chapter also goes into detail about the different features of running shoes, like cushioning, stability, and flexibility. It explains why these features are important and how they can help you run better and faster.One of the most interesting parts of the chapter is when it talks about the newest technology in running shoes. It explains how companies are always coming up with new and improved designs to make running shoes even better.Overall, this chapter is super interesting and informative. It's definitely a must-read for anyone who loves to run or is looking to get into running. So next time you're in the store looking for a new pair of running shoes, make sure to check out this chapter to help you make the best choice. Happy running, everyone!篇10Chapter 8 of "The Ultimate Running Shoes" is all about the different types of running shoes you can choose from. It's superimportant to pick the right shoes for your feet to make sure you have a comfy and safe run.First off, there are neutral shoes. These are for peeps who have a regular arch in their feet. They offer cushioning and support without changing your foot's natural movement.Next up are stability shoes. These are for folks with a slight overpronation, which means your foot rolls inward when you run. The shoes have extra support to help keep your foot in the right position.Then there are motion control shoes. These are for peeps with severe overpronation. They have extra support to keep your foot from rolling too much and causing injuries.There are also minimalist shoes, which are super lightweight and don't have much cushioning. They let your feet move naturally, but you gotta be careful cuz they don't offer as much protection.Lastly, there are maximalist shoes. These are like walking on clouds cuz they have extra cushioning for peeps who need it.Remember, the best way to find the right shoes for you is to try them on and see how they feel. And don't forget to replaceyour running shoes every 300-500 miles to make sure they're still doing their job properly.So make sure to pick the right shoes for your feet and happy running! ♂️ ♂️。
ch.8_photosynthesis_guided_reading_answers
Name______________________________Class __________________Date ______________© Pearson Education, Inc. All rights reserved.PhotosynthesisSection 8–1Energy and Life (pages 201–203)This section explains where plants get the energy they need to produce food.It also describes the role of the chemical compound ATP in cellular activities.Autotrophs and Heterotrophs (page 201)1.Where does the energy of food originally come from?Energy in most food comes from the sun.plete the table of types of organisms.Chemical Energy and ATP (pages 202–203)3.What is one of the principal chemical compounds that living thingsuse to store energy?Adenosine triphosphate, or ATP4.How is ATP different from ADP?ATP has three phosphate groups, while ADP has two phosphate groups.bel each part of the ATP molecule illustrated below.Type Description ExamplesAutotrophs Organisms that make their own food PlantsHeterotrophs Organisms that obtain energy from Animals, mushroomsthe food they eatAdenine Ribose 3 Phosphate groups6.When a cell has energy available, how can it store small amountsof that energy?It can add a phosphate group to ADP molecules, producing ATP molecules.7.When is the energy stored in ATP released?It is released when ATP is converted to ADP and a phosphate group.TYPES OF ORGANISMS© P e a r s o n E d u c a t i o n , I n c . A l l r i g h t s r e s e r v e d .Name __________________________________Date _________Class _________________8.For what purpose do the characteristics of ATP make itexceptionally useful to all types of cells?All types of cells use ATP as their basic energysource.9.What are two ways in which cells use the energy provided by ATP?a.Active transportb.Movement within the cellATP and Glucose (page 203)10.Why is it efficient for cells to keep only a small supply of ATP on hand? ATP is not very good for storing large amounts of energy over the long term. A single sugar molecule stores more than 90 times the chemical energy of an ATP molecule.11.Circle the letter of where cells get the energy to regenerate ATP .a.ADPb.phosphatesc.carbohydratesd.organellesSection 8–2Photosynthesis: An Overview(pages 204–207)This section describes what important experiments revealed about how plants grow. It also introduces the overall equation for photosynthesis and explains the roles light and chlorophyll have in the process.Introduction (page 204)1.What occurs in the process of photosynthesis?Plants use the energy of sunlight to convert water and carbon dioxide into high-energy carbohydrates—sugars and starches—and oxygen.Investigating Photosynthesis (pages 204–206)2.What did Jan van Helmont conclude from his experiment?He concluded that most of the mass a plant gained had come from water, because that was the only thing he had added to the pot.3.Circle the letter of the substance produced by the mint plant in Joseph Priestley’s experiment.a.carbon dioxide b.water c.air d.oxygen4.What did Jan Ingenhousz show?He showed that light is necessary for plants to produce oxygen.The Photosynthesis Equation(page 206)5.Write the overall equation for photosynthesis using words.6.Write the overall equation for photosynthesis using chemical formulas.6CO 2+ 6H 2O light 6H 12O 6+ 6O 2© Pearson Education, Inc. All rights reserved.Name______________________________Class __________________Date ______________Chapter 8, Photosynthesis (continued)7.Photosynthesis uses the energy of sunlight to convert water andcarbon dioxide into oxygen and high-energy .Light and Pigments (page 207)8.What does photosynthesis require in addition to water and carbondioxide?It requires light and chlorophyll, a molecule in chloroplasts.9.Plants gather the sun’s energy with light-absorbing moleculescalled .10.What is the principal pigment of plants? 11.Circle the letter of the regions of the visible spectrum in whichchlorophyll absorbs light very well.a.blue regionb.green regionc.red regiond.yellow regionChlorophyllpigmentssugars Reading Skill PracticeBy looking at illustrations in textbooks, you can help yourself remember better what you have read. Look carefully at Figure 8–4 on page 206. What important ideas does this illustration communicate? Do your work on a separate sheet of paper.Photosynthesis uses light energy to convert carbon dioxide and water into sugars and oxygen. This takes place in chloroplasts.Section 8–3The Reactions of Photosynthesis (pages 208–214)This section explains what happens inside chloroplasts during the process of photosynthesis.Inside a Chloroplast (page 208)1.Chloroplasts contain saclike photosynthetic membranes called .2.What is a granum? A granum is a stack of thylakoids.3.The region outside the thylakoid membranes in the chloroplasts iscalled the .4.What are the two stages of photosynthesis called?a.Light-dependent reactionsb.Light-independent reactions, or Calvin cyclestroma thylakoidsLightLight-Name______________________________Class__________________Date______________ Chapter8, Photosynthesis (continued)Light-Dependent Reactions(pages 210–211)10.Circle the letter of each sentence that is true about the light-dependentreactions.a.They convert ADP into ATP.b.They produce oxygen gas.c.They convert oxygen into carbon dioxide.d.They convert NADP+into NADPH.11.Where do the light-dependent reactions take place?Within the thylakoid membranesof chloroplasts12.Circle the letter of each sentence that is true about the light-dependent reactions.a.High-energy electrons move through the electron transportchain from photosystem II to photosystem I.b.Photosynthesis begins when pigments in photosystem I absorblight.c.The difference in charges across the thylakoid membraneprovides the energy to make ATP.d.Pigments in photosystem I use energy from light to reenergizeelectrons.13.How does ATP synthase produce ATP?ATP synthase allows H+ions to pass throughthe thylakoid membrane. As the ions pass through, ATP synthase rotates, binding ADP anda phosphate group together to produce ATP.The Calvin Cycle(pages 212–213)14.What does the Calvin cycle use to produce high-energy sugars?The Calvin cycle uses ATP and NADPH from the light-dependent reactions to produce© Pearson Education, Inc. All rights reserved.high-energy sugars.15.Why are the reactions of the Calvin cycle also called the light-independent reactions?The Calvin cycle does not require light.16.Circle the letter of each statement that is true about the Calvin cycle.a.The main products of the Calvin cycle are six carbon dioxidemolecules.b.Carbon dioxide molecules enter the Calvin cycle from theatmosphere.c.Energy from ATP and high-energy electrons from NADPH areused to convert 3-carbon molecules into similar 3-carbonmolecules.d.The Calvin cycle uses six molecules of carbon dioxide toproduce a single 6-carbon sugar molecule.© P e a r s o n E d u c a t i o n , I n c . A l l r i g h t s r e s e r v e d .Name______________________________Class __________________Date ______________Factors Affecting Photosynthesis(page 214)17.What are three factors that affect the rate at which photosynthesis occurs?a.Availability of waterb.Temperaturec.Intensity of light 18.Is the following sentence true or false? Increasing the intensity oflight decreases the rate of photosynthesis. WordWiseAnswer the questions by writing the correct vocabulary terms from Chapter 8 in the blanks. Use the circled letter from each term to find the hidden word.Then, write a definition for the hidden word.1.What is the process called by which plants use the sun’s energy to make high-energy sugars?2.What is the stage of photosynthesis called in which plants use the energy that ATP and NADPH contain to build high-energy sugars?3.What are the reactions of the first stage of photosynthesis called?–4.What is the region called where the Calvin cycle takes place?5.What is an organism called that obtains energy from the food it consumes?6.What is one of the principle chemical compounds that living things use to store energy?7.What is an organism called that makes its own food?Hidden word:pigment Definition: A pigment is a light-absorbing molecule.hp o r t o t u a e t a h p s o h p i r t e n i s o n e d a hp o r t o r e t e h am o r t s s n o i t c a e r tn e d n e p e d t h g i lel c y c n i v l a C si s e h t n y s o t o h p false。
工厂物理学Chapter_8_1
14
Causes of Variability
•Natural variability •Preemptive outages (breakdowns) •Non-preemptive outages – setups •Operator availability •Recycle
APIC Dr. David Ben-Arieh
t mean process time of a job σ standard deviation of process time c
t
coefficien t of variation, CV
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0 0.75 1.33
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• Effective Process Times:
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APIC Dr. David Ben-Arieh
© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
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Probabilistic Intuition (cont.)
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© Wallace J. Hopp, Mark L. Spearman, 1996, 2000
chapter 8 Objects and Classes (1)
{
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模块之间耦合度高，需求变更时维护代价高昂；
数据开放，不可控的数据修改导致系统既不可靠也不 安全；
优点：运行性能高。
5
哈尔滨工业大学 计算机科学与技术学院
5
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a.show(); b.show(); c.show(); boss.show(); waiter.show();
哈尔滨工业大学 计算机科学与技术学院
6
8.1.2 面向对象的程序设计
易维护、易复用、易扩展
符合我们认识客观世界的规律，降低了复杂系统分析和设计的 复杂性。
只有对象操作需要了解数据存储细节，其它对象访问此数据通 过调用此对象操作进行，因此不必了解数据存储的细节；
Public: 公有成员(类接口)，程序的任何部分都可以访问。
哈尔滨工业大学 计算机科学与技术学院
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210418/4/26
类体的定义
class 类名称 {
public : 公有(接口)成员
private: 私有成员
《固态电子器件》课件8(1)
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国际财务管理课后习题答案chapter 8Word版
CHAPTER 8 MANAGEMENT OF TRANSACTION EXPOSURE SUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTER QUESTIONS AND PROBLEMSQUESTIONS1. How would you define transaction exposure? How is it different from economic exposure?Answer: Transaction exposure is the sensitivity of realized domestic currency values of the firm’s contractual cash flows denominated in foreign currencies to unexpected changes in exchange rates. Unlike economic exposure, transaction exposure is well-defined and short-term.2. Discuss and compare hedging transaction exposure using the forward contract vs. money market instruments. When do the alternative hedging approaches produce the same result?Answer: Hedging transaction exposure by a forward contract is achieved by selling or buying foreign currency receivables or payables forward. On the other hand, money market hedge is achieved by borrowing or lending the present value of foreign currency receivables or payables, thereby creating offsetting foreign currency positions. If the interest rate parity is holding, the two hedging methods are equivalent.3. Discuss and compare the costs of hedging via the forward contract and the options contract.Answer: There is no up-front cost of hedging by forward contracts. In the case of options hedging, however, hedgers should pay the premiums for the contracts up-front. The cost of forward hedging, however, may be realized ex post when the hedger regrets his/her hedging decision.4. What are the advantages of a currency options contract as a hedging tool compared with the forward contract?Answer: The main advantage of using options contracts for hedging is that the hedger can decide whether to exercise options upon observing the realized future exchange rate. Options thus provide a hedge against ex post regret that forward hedger might have to suffer. Hedgers can only eliminate the downside risk while retaining the upside potential.5. Suppose your company has purchased a put option on the German mark to manage exchange exposure associated with an account receivable denominated in that currency. In this case, your company can be said to have an ‘insurance’ policy on its receivable. Explain in what sense this is so.Answer: Your company in this case knows in advance that it will receive a certain minimum dollar amount no matter what might happen to the $/€exchange rate. Furthermore, if the German mark appreciates, your company will benefit from the rising euro.6. Recent surveys of corporate exchange risk management practices indicate that many U.S. firms simply do not hedge. How would you explain this result?Answer: There can be many possible reasons for this. First, many firms may feel that they are not really exposed to exchange risk due to product diversification, diversified markets for their products, etc. Second, firms may be using self-insurance against exchange risk. Third, firms may feel that shareholders can diversify exchange risk themselves, rendering corporate risk management unnecessary.7. Should a firm hedge? Why or why not?Answer: In a perfect capital market, firms may not need to hedge exchange risk. But firms can add to their value by hedging if markets are imperfect. First, if management knows about the firm’s exposure better than shareholders, the firm, not its shareholders, should hedge. Second, firms may be able to hedge at a lower cost. Third, if default costs are significant, corporate hedging can be justifiable because it reduces the probability of default. Fourth, if the firm faces progressive taxes, it can reduce tax obligations by hedging which stabilizes corporate earnings.8. Using an example, discuss the possible effect of hedging on a firm’s tax obligations.Answer: One can use an example similar to the one presented in the chapter.9. Explain contingent exposure and discuss the advantages of using currency options to manage this type of currency exposure.Answer: Companies may encounter a situation where they may or may not face currency exposure. In this situation, companies need options, not obligations, to buy or sell a given amount of foreign exchange they may or may not receive or have to pay. If companies either hedge using forward contracts or do not hedge at all, they may face definite currency exposure.10. Explain cross-hedging and discuss the factors determining its effectiveness.Answer: Cross-hedging involves hedging a position in one asset by taking a position in another asset. The effectiveness of cross-hedging would depend on the strength and stability of the relationship between the two assets.PROBLEMS1. Cray Research sold a super computer to the Max Planck Institute in Germany on credit and invoiced €10 million payable in six months. Currently, the six-month forward exchange rate is $1.10/€ and the foreign exchange advisor for Cray Research predicts that the spot rate is likely to be $1.05/€ in six months.(a) What is the expected gain/loss from the forward hedging?(b) If you were the financial manager of Cray Research, would you recommend hedging this euro receivable? Why or why not?(c) Suppose the foreign exchange advisor predicts that the future spot rate will be the same as the forward exchange rate quoted today. Would you recommend hedging in this case? Why or why not?Solution: (a) Expected gain($) = 10,000,000(1.10 – 1.05)= 10,000,000(.05)= $500,000.(b) I would recommend hedging because Cray Research can increase the expected dollar receipt by $500,000 and also eliminate the exchange risk.(c) Since I eliminate risk without sacrificing dollar receipt, I still would recommend hedging.2. IBM purchased computer chips from NEC, a Japanese electronics concern, and was billed ¥250 million payable in three months. Currently, the spot exchange rate is ¥105/$ and the three-month forward rate is ¥100/$. The three-month money market interest rate is 8 percent per annum in the U.S. and 7 percent per annum in Japan. The management of IBM decided to use the money market hedge to deal with this yen account payable.(a) Explain the process of a money market hedge and compute the dollar cost of meeting the yen obligation.(b) Conduct the cash flow analysis of the money market hedge.Solution: (a). Let’s first compute the PV of ¥250 million, i.e.,250m/1.0175 = ¥245,700,245.7So if the above yen amount is invested today at the Japanese interest rate for three months, the maturity value will be exactly equal to ¥25 million which is the amount of payable.To buy the above yen amount today, it will cost:$2,340,002.34 = ¥250,000,000/105.The dollar cost of meeting this yen obligation is $2,340,002.34 as of today.(b)___________________________________________________________________Transaction CF0 CF1____________________________________________________________________1. Buy yens spot -$2,340,002.34with dollars ¥245,700,245.702. Invest in Japan - ¥245,700,245.70 ¥250,000,0003. Pay yens - ¥250,000,000Net cash flow - $2,340,002.34____________________________________________________________________3. You plan to visit Geneva, Switzerland in three months to attend an international business conference. You expect to incur the total cost of SF 5,000 for lodging, meals and transportation during your stay. As of today, the spot exchange rate is $0.60/SF and the three-month forward rate is $0.63/SF. You can buy the three-month call option on SF with the exercise rate of $0.64/SF for the premium of $0.05 per SF. Assume that your expected future spot exchange rate is the same as the forward rate. The three-month interest rate is 6 percent per annum in the United States and 4 percent per annum in Switzerland.(a) Calculate your expected dollar cost of buying SF5,000 if you choose to hedge via call option on SF.(b) Calculate the future dollar cost of meeting this SF obligation if you decide to hedge using a forward contract.(c) At what future spot exchange rate will you be indifferent between the forward and option market hedges?(d) Illustrate the future dollar costs of meeting the SF payable against the future spot exchange rate under both the options and forward market hedges.Solution: (a) Total option premium = (.05)(5000) = $250. In three months, $250 is worth $253.75 = $250(1.015). At the expected future spot rate of $0.63/SF, which is less than the exercise price, y ou don’t expect to exercise options. Rather, you expect to buy Swiss franc at $0.63/SF. Since you are going to buy SF5,000, you expect to spend $3,150 (=.63x5,000). Thus, the total expected cost of buying SF5,000 will be the sum of $3,150 and $253.75, i.e., $3,403.75.(b) $3,150 = (.63)(5,000).(c) $3,150 = 5,000x + 253.75, where x represents the break-even future spot rate. Solving for x, we obtain x = $0.57925/SF. Note that at the break-even future spot rate, options will not be exercised.(d) If the Swiss franc appreciates beyond $0.64/SF, which is the exercise price of call option, you will exercise the option and buy SF5,000 for $3,200. The total cost of buying SF5,000 will be $3,453.75 = $3,200 + $253.75.This is the maximum you will pay.4. Boeing just signed a contract to sell a Boeing 737 aircraft to Air France. Air France will be billed €20 million which is payable in one year. The current spot exchange rate is $1.05/€ and the one -year forward rate is $1.10/€. The annual interest rate is 6.0% in the U.S. and5.0% in France. Boeing is concerned with the volatile exchange rate between the dollar and the euro and would like to hedge exchange exposure.(a) It is considering two hedging alternatives: sell the euro proceeds from the sale forward or borrow euros from the Credit Lyonnaise against the euro receivable. Which alternative would you recommend? Why?(b) Other things being equal, at what forward exchange rate would Boeing be indifferent between the two hedging methods?Solution: (a) In the case of forward hedge, the future dollar proceeds will be (20,000,000)(1.10) = $22,000,000. In the case of money market hedge (MMH), the firm has to first borrow the PV of its euro receivable, i.e., 20,000,000/1.05 =€19,047,619. Then the firm should exchange this euro amount into dollars at the current spot rate to receive: (€19,047,619)($1.05/€) = $20,000,000, which can be invested at the dollar interest rate for one year to yield:$ Cost Options hedge Forward hedge $3,453.75 $3,150 0 0.579 0.64 (strike price) $/SF$253.75$20,000,000(1.06) = $21,200,000.Clearly, the firm can receive $800,000 more by using forward hedging.(b) According to IRP, F = S(1+i$)/(1+i F). Thus the “indifferent” forward rate will be:F = 1.05(1.06)/1.05 = $1.06/€.5. Suppose that Baltimore Machinery sold a drilling machine to a Swiss firm and gave the Swiss client a choice of paying either $10,000 or SF 15,000 in three months.(a) In the above example, Baltimore Machinery effectively gave the Swiss client a free option to buy up to $10,000 dollars using Swiss franc. What is the ‘implied’ exercise exchange rate?(b) If the spot exchange rate turns out to be $0.62/SF, which currency do you think the Swiss client will choose to use for payment? What is the value of this free option for the Swiss client?(c) What is the best way for Baltimore Machinery to deal with the exchange exposure?Solution: (a) The implied exercise (price) rate is: 10,000/15,000 = $0.6667/SF.(b) If the Swiss client chooses to pay $10,000, it will cost SF16,129 (=10,000/.62). Since the Swiss client has an option to pay SF15,000, it will choose to do so. The value of this option is obviously SF1,129 (=SF16,129-SF15,000).(c) Baltimore Machinery faces a contingent exposure in the sense that it may or may not receive SF15,000 in the future. The firm thus can hedge this exposure by buying a put option on SF15,000.6. Princess Cruise Company (PCC) purchased a ship from Mitsubishi Heavy Industry. PCC owes Mitsubishi Heavy Industry 500 million yen in one year. The current spot rate is 124 yen per dollar and the one-year forward rate is 110 yen per dollar. The annual interest rate is 5% in Japan and 8% in the U.S. PCC can also buy a one-year call option on yen at the strike price of $.0081 per yen for a premium of .014 cents per yen.(a) Compute the future dollar costs of meeting this obligation using the money market hedge and the forward hedges.(b) Assuming that the forward exchange rate is the best predictor of the future spot rate, compute the expected future dollar cost of meeting this obligation when the option hedge is used.(c) At what future spot rate do you think PCC may be indifferent between the option and forward hedge?Solution: (a) In the case of forward hedge, the dollar cost will be 500,000,000/110 = $4,545,455. In the case of money market hedge, the future dollar cost will be: 500,000,000(1.08)/(1.05)(124)= $4,147,465.(b) The option premium is: (.014/100)(500,000,000) = $70,000. Its future value will be $70,000(1.08) = $75,600.At the expected future spot rate of $.0091(=1/110), which is higher than the exercise of $.0081, PCC will exercise its call option and buy ¥500,000,000 for $4,050,000 (=500,000,000x.0081).The total expected cost will thus be $4,125,600, which is the sum of $75,600 and $4,050,000.(c) When the option hedge is used, PCC will spend “at most” $4,125,000. On the other hand, when the forward hedging is used, PCC will have to spend $4,545,455 regardless of the future spot rate. This means that the options hedge dominates the forward hedge. At no future spot rate, PCC will be indifferent between forward and options hedges.7. Airbus sold an aircraft, A400, to Delta Airlines, a U.S. company, and billed $30 million payable in six months. Airbus is concerned with the euro proceeds from international sales and would like to control exchange risk. The current spot exchange rate is $1.05/€ and six-month forward exchange rate is $1.10/€ at the moment. Airbus can buy a six-month put option on U.S. dollars with a strike price of€0.95/$ for a premium of €0.02 per U.S. dollar. Currently, six-month interest rate is 2.5% in the euro zone and 3.0% in theU.S.pute the guaranteed euro proceeds from the American sale if Airbus decides tohedge using a forward contract.b.If Airbus decides to hedge using money market instruments, what action doesAirbus need to take? What would be the guaranteed euro proceeds from the American sale in this case?c.If Airbus decides to hedge using put options on U.S. dollars, what would be the‘expected’ euro proceeds from the American sale? Assume that Airbus regards the current forward exchange rate as an unbiased predictor of the future spot exchange rate.d.At what future spot exchange rate do you think Airbus will be indifferent betweenthe option and money market hedge?Solution:a. Airbus will sell $30 million forward for €27,272,727 = ($30,000,000) / ($1.10/€).b. Airbus will borrow the present value of the dollar receivable, i.e., $29,126,214 = $30,000,000/1.03, and then sell the dollar proceeds spot for euros: €27,739,251. This is the euro amount that Airbus is going to keep.c. Since the expected future spot rate is less than the strike price of the put option, i.e., €0.9091< €0.95, Airbus expects to exercise the option and receive €28,500,000 = ($30,000,000)(€0.95/$). This is gross proceeds. Airbus spent €600,000 (=0.02x30,000,000) upfront for the option and its future cost is equal to €615,000 = €600,000 x 1.025. Thus the net euro proceeds from the American sale is €27,885,000, which is the difference between the gross proceeds and the option costs.d. At the indifferent future spot rate, the following will hold:€28,432,732 = S T(30,000,000) - €615,000.Solving for S T, we obtain the “indifference” future spot exchange rate, i.e., €0.9683/$, or $1.0327/€. Note that €28,432,732 is the future value of the proceeds under money market hedging:€28,432,732 = (€27,739,251) (1.025).Suggested solution for Mini Case: Chase Options, Inc.[See Chapter 13 for the case text]Chase Options, Inc.Hedging Foreign Currency Exposure Through Currency OptionsHarvey A. PoniachekI. Case SummaryThis case reviews the foreign exchange options market and hedging. It presents various international transactions that require currency options hedging strategies by the corporations involved. Seven transactions under a variety of circumstances are introduced that require hedging by currency options. The transactions involve hedging of dividend remittances, portfolio investment exposure, and strategic economic competitiveness. Market quotations are provided for options (and options hedging ratios), forwards, and interest rates for various maturities.II. Case Objective.The case introduces the student to the principles of currency options market and hedging strategies. The transactions are of various types that often confront companies that are involved in extensive international business or multinational corporations. The case induces students to acquire hands-on experience in addressing specific exposure and hedging concerns, including how to apply various market quotations, which hedging strategy is most suitable, and how to address exposure in foreign currency through cross hedging policies.III. Proposed Assignment Solution1. The company expects DM100 million in repatriated profits, and does not want the DM/$ exchange rate at which they convert those profits to rise above 1.70. They can hedge this exposure using DM put options with a strike price of 1.70. If the spot rate rises above 1.70, they can exercise the option, while if that rate falls they can enjoy additional profits from favorable exchange rate movements.To purchase the options would require an up-front premium of:DM 100,000,000 x 0.0164 = DM 1,640,000.With a strike price of 1.70 DM/$, this would assure the U.S. company of receiving at least:DM 100,000,000 – DM 1,640,000 x (1 + 0.085106 x 272/360)= DM 98,254,544/1.70 DM/$ = $57,796,791by exercising the option if the DM depreciated. Note that the proceeds from the repatriated profits are reduced by the premium paid, which is further adjusted by the interest foregone on this amount.However, if the DM were to appreciate relative to the dollar, the company would allow the option to expire, and enjoy greater dollar proceeds from this increase.Should forward contracts be used to hedge this exposure, the proceeds received would be:DM100,000,000/1.6725 DM/$ = $59,790,732,regardless of the movement of the DM/$ exchange rate. While this amount is almost $2 million more than that realized using option hedges above, there is no flexibilityregarding the exercise date; if this date differs from that at which the repatriate profits are available, the company may be exposed to additional further current exposure. Further, there is no opportunity to enjoy any appreciation in the DM.If the company were to buy DM puts as above, and sell an equivalent amount in calls with strike price 1.647, the premium paid would be exactly offset by the premium received. This would assure that the exchange rate realized would fall between 1.647 and 1.700. If the rate rises above 1.700, the company will exercise its put option, and if it fell below 1.647, the other party would use its call; for any rate in between, both options would expire worthless. The proceeds realized would then fall between:DM 100,00,000/1.647 DM/$ = $60,716,454andDM 100,000,000/1.700 DM/$ = $58,823,529.This would allow the company some upside potential, while guaranteeing proceeds at least $1 million greater than the minimum for simply buying a put as above.Buy/Sell OptionsDM/$Spot Put Payoff “Put”ProfitsCallPayoff“Call”Profits Net Profit1.60(1,742,846)01,742,84660,716,45460,716,4541.61(1,742,846)01,742,84660,716,45460,716,454 1.62(1,742,846)01,742,84660,716,45460,716,4541.63(1,742,846)01,742,84660,716,45460,716,4541.64(1,742,846)01,742,84660,716,4560,716,45441.65(1,742,846)60,606,061,742,846060,606,06111.66(1,742,846)60,240,961,742,846060,240,96441,742,846059,880,240 1.67(1,742,846)59,880,241.68(1,742,846)59,523,811,742,846059,523,8101,742,846059,171,598 1.69(1,742,846)59,171,5981.70(1,742,846)58,823,521,742,846058,823,52991,742,846058,823,529 1.71(1,742,846)58,823,5291.72(1,742,846)58,823,521,742,846058,823,52991,742,846058,823,529 1.73(1,742,846)58,823,5291.74(1,742,846)58,823,521,742,846058,823,52991,742,846058,823,529 1.75(1,742,846)58,823,5291.76(1,742,846)58,823,521,742,846058,823,52991.77(1,742,846)58,823,521,742,846058,823,52991.78(1,742,846)58,823,521,742,846058,823,52991.79(1,742,846)58,823,521,742,846058,823,52991,742,846058,823,5291.80(1,742,846)58,823,5291,742,846058,823,5291.81(1,742,846)58,823,5291.82(1,742,846)58,823,521,742,846058,823,52991,742,846058,823,5291.83(1,742,846)58,823,5291.84(1,742,846)58,823,521,742,846058,823,52991,742,846058,823,5291.85(1,742,846)58,823,529Since the firm believes that there is a good chance that the pound sterling will weaken, locking them into a forward contract would not be appropriate, because they would lose the opportunity to profit from this weakening. Their hedge strategy should follow for an upside potential to match their viewpoint. Therefore, they should purchase sterling call options, paying a premium of:5,000,000 STG x 0.0176 = 88,000 STG.If the dollar strengthens against the pound, the firm allows the option to expire, and buys sterling in the spot market at a cheaper price than they would have paid for a forward contract; otherwise, the sterling calls protect against unfavorable depreciation of the dollar.Because the fund manager is uncertain when he will sell the bonds, he requires a hedge which will allow flexibility as to the exercise date. Thus, options are the best instrument for him to use. He can buy A$ puts to lock in a floor of 0.72 A$/$. Since he is willing to forego any further currency appreciation, he can sell A$ calls with a strike price of 0.8025 A$/$ to defray the cost of his hedge (in fact he earns a net premium of A$ 100,000,000 x (0.007234 – 0.007211) = A$ 2,300), while knowing that he can’t receive less than 0.72 A$/$ when redeeming his investment, and can benefit from a small appreciation of the A$.Example #3:Problem: Hedge principal denominated in A$ into US$. Forgo upside potential to buy floor protection.I. Hedge by writing calls and buying puts1) Write calls for $/A$ @ 0.8025Buy puts for $/A$ @ 0.72# contracts needed = Principal in A$/Contract size100,000,000A$/100,000 A$ = 1002) Revenue from sale of calls = (# contracts)(size of contract)(premium)$75,573 = (100)(100,000 A$)(.007234 $/A$)(1 + .0825 195/360)3) Total cost of puts = (# contracts)(size of contract)(premium)$75,332 = (100)(100,000 A$)(.007211 $/A$)(1 + .0825 195/360)4) Put payoffIf spot falls below 0.72, fund manager will exercise putIf spot rises above 0.72, fund manager will let put expire5) Call payoffIf spot rises above .8025, call will be exercised If spot falls below .8025, call will expire6) Net payoffSee following Table for net payoffAustralian Dollar Bond HedgeStrikePrice Put Payoff “Put”PrincipalCallPayoff“Call”Principal Net Profit0.60(75,332)72,000,0075,573072,000,2410.61(75,332)72,000,0075,573072,000,2410.62(75,332)72,000,0075,573072,000,2410.63(75,332)72,000,0075,573072,000,2410.64(75,332)72,000,0075,573072,000,2410.65(75,332)72,000,0075,573072,000,2410.66(75,332)72,000,0075,573072,000,2410.67(75,332)72,000,0075,573072,000,2410.68(75,332)72,000,0075,573072,000,2410.69(75,332)72,000,0075,573072,000,2410.70(75,332)72,000,0075,573072,000,2410.71(75,332)72,000,0075,573072,000,2410.72(75,332)72,000,0075,573072,000,2410.73(75,332)73,000,0075,573073,000,2410.74(75,332)74,000,0075,573074,000,2410.75(75,332)75,000,0075,573075,000,2410.76(75,332)76,000,0075,573076,000,24175,573077,000,2410.77(75,332)77,000,000.78(75,332)78,000,0075,573078,000,24175,573079,000,2410.79(75,332)79,000,000.80(75,332)80,000,0075,573080,000,24180,250,2410.81(75,332)075,57380,250,000.82(75,332)075,57380,250,0080,250,24180,250,2410.83(75,332)075,57380,250,000.84(75,332)075,57380,250,0080,250,24180,250,2410.85(75,332)075,57380,250,004. The German company is bidding on a contract which they cannot be certain of winning. Thus, the need to execute a currency transaction is similarly uncertain, and using a forward or futures as a hedge is inappropriate, because it would force them to perform even if they do not win the contract.Using a sterling put option as a hedge for this transaction makes the most sense. Fora premium of:12 million STG x 0.0161 = 193,200 STG,they can assure themselves that adverse movements in the pound sterling exchange rate will not diminish the profitability of the project (and hence the feasibility oftheir bid), while at the same time allowing the potential for gains from sterling appreciation.5. Since AMC in concerned about the adverse effects that a strengthening of the dollar would have on its business, we need to create a situation in which it will profit from such an appreciation. Purchasing a yen put or a dollar call will achieve this objective. The data in Exhibit 1, row 7 represent a 10 percent appreciation of the dollar (128.15 strike vs. 116.5 forward rate) and can be used to hedge against a similar appreciation of the dollar.For every million yen of hedging, the cost would be:Yen 100,000,000 x 0.000127 = 127 Yen.To determine the breakeven point, we need to compute the value of this option if the dollar appreciated 10 percent (spot rose to 128.15), and subtract from it the premium we paid. This profit would be compared with the profit earned on five to 10 percent of AMC’s sales (which would be lost as a result of the dollar appreciation). The number of options to be purchased which would equalize these two quantities would represent the breakeven point.Example #5:Hedge the economic cost of the depreciating Yen to AMC.If we assume that AMC sales fall in direct proportion to depreciation in the yen (i.e., a 10 percent decline in yen and 10 percent decline in sales), then we can hedge the full value of AMC’s sales. I have a ssumed $100 million in sales.1) Buy yen puts# contracts needed = Expected Sales *Current ¥/$ Rate / Contract size9600 = ($100,000,000)(120¥/$) / ¥1,250,0002) Total Cost = (# contracts)(contract size)(premium)$1,524,000 = (9600)( ¥1,250,000)($0.0001275/¥)3) Floor rate = Exercise – Premium128.1499¥/$ = 128.15¥/$ - $1,524,000/12,000,000,000¥4) The payoff changes depending on the level of the ¥/$ rate. The following tablesummarizes the payoffs. An equilibrium is reached when the spot rate equals the floor rate.AMC ProfitabilityYen/$ Spot Put Payoff Sales Net Profit 120(1,524,990)100,000,00098,475,010 121(1,524,990)99,173,66497,648,564 122(1,524,990)98,360,65696,835,666 123(1,524,990)97,560,97686,035,986 124(1,524,990)96,774,19495,249,204 125(1,524,990)96,000,00094,475,010 126(1,524,990)95,238,09593,713,105 127(847,829)94,488,18993,640,360 128(109,640)93,750,00093,640,360 129617,10493,023,25693,640,360 1301,332,66892,307,69293,640,360 1312,037,30791,603,05393,640,360 1322,731,26990,909,09193,640,360 1333,414,79690,225,66493,640,360 1344,088,12289,552,23993,640,360 1354,751,43188,888,88993,640,360 1365,405,06688,235,29493,640,360 1376,049,11887,591,24193,640,360 1386,683,83986,966,52293,640,360 1397,308,42586,330,93693,640,360 1407,926,07585,714,28693,640,360 1418,533,97785,106,38393,640,360 1429,133,31884,507,04293,640,360 1439,724,27683,916,08493,640,360 14410,307,02783,333,33393,640,360 14510,881,74082,758,62193,640,360 14611,448,57982,191,78193,640,360。
机械弹性动力学基础
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机械动力学
Chapter8 机械弹性动力学基础
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机械动力学
Chapter8 机械弹性动力学基础
3、作用在横向振动梁单元上的广义力
振动方程中的广义力列阵， 根据虚位移原理推导。
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静力学问题： 动力学
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机械动力学
Chapter8 机械弹性动力学基础
静力学问题：
KU F （线性代数方程）
动力学问题：
MU KU F （微分方程）
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Chapter 1-8 解释句子
解释句子：(9A Chapter1-8)1.If you work harder, you will pass the exam.= Work harder, or you won’t pass the exam.2.We will not finish the work in time unless you give us help.= We can’t finish the work in time without your help.3.We found that it was necessary to write down her address.= We found it necessary to write down her address.4.You never forget what you should do.= You never forget what to do.5.You have got an amazing memory.= What an amazing memory you have got!6.We use it to remember phone numbers.= We remember phone numbers with it.7.How much do you weigh?= What’s your weight?= How heavy are you?= What’s the weight of you?8.Some parts of our brains can’t grow bigger if we do not use them a lot.= Some parts of our brains can’t grow bigger unless we use them a lot.9.If you exercise every day, you will have a strong body.= If you do sports every day, you’ll be strong.10.What happened when you were shopping yesterday?= What took place when you went shopping yesterday?11.My brother is no longer a naughty boy.= My brother is not a naughty boy any more.12.This mobile phone is now the most popular one.= This mobile phone is now more popular than any other mobile phone.13.To begin with, some basic ideas for a story are necessary.= Firstly / First of all, we need some basic ideas for a story.14.For example, a plot needs to be thought of.= For instance, a plot needs thinking of.15.In the second stage, the type of characters and their voices are decided.= Second, let’s decide the type of characters and their voices.16.Fanny is a tall, pleasant girl.= What a tall, pleasant girl Fanny is!17.He always forgets things.= He is forgetful.18.She is frightened of snakes. = She is afraid of snakes.19.What do you think of the animated cartoon?= How do you like the animated cartoon?20.We have decided how to draw the characters.= We have decided how we’ll draw the characters.21.The students left classroom separately.= The students left the classroom one by one.22.What fun it is to draw comic strips! = It’s fun to draw comic strips.nd pollution is caused by the deposit of solid waste.= The deposit of solid waste causes land pollution.24.It is vital that we do something to save the earth.=It is very important for us to do something to save the earth.25.We don’t know what to do with the rubbish.= We don’t know how to deal with the rubbish.26.The Blacks do not throw away as many cans as the Whites,= The Whites throw away more cans than the Blacks.27.There is no difference between Alice’s dress and mine.= Alice’s dress looks the same as mine.28.Mrs. Lin was a kind woman , so everyone respected her.= Mrs. Lin was a kind woman , so everyone had a good opinion of her.29.Fortunately, the fire did not do much damage.= Luckily, the fire did not do much harm.30.These are the basic grammar rules.= These are simple but important grammar rules.31.Humans are polluting the earth. = Humans are making the earth dirty.32.It’s vital for us to do something to save earth.= It’s important and necessary for us to do something to save earth.33.Without ozone, the sun would burn us up.= If there was no ozone, the sun would burn us up.34.The atmosphere is essential to living things.= The air round earth is very important to living things.35.The glass keeps much of the heat from getting out.= The glass prevents much of the heat from getting out.36.The greenhouse effect may cause the level of the sea to rise= The greenhouse effect may make the level of the sea to rise.37.They are actually video cameras.= In fact, they are video cameras.38.Finally, each frame is photographed separately.= In the end / At last, each frame is photographed separately.39.When I was walking down the street, I met an old friend of mine.= When walking down the street, I met an old friend of mine.40.She began to play the violin when she was four.= She began to play the violin at the age of four.41.We were surprised when we heard the news.= We were surprised at the news.= We were surprised to hear the news42.She lost her purse when she went to the post office.= She lost her purse on her way to the post office.43.We got plenty of rest so that we could remember the new words better.= We got plenty of rest in order to remember the new words better. 44.The maths problem is so difficult that I cannot work it out.= The maths problem is too difficult to work out.45.No living thing can live if there is no air.= No living thing can live without air.46.He died 2 years ago.= He has been dead for 2 years.47.He suspected that the crown was not completely made of gold.= He didn’t believe that the crown was completely made of gold.48.The bath was full of water.= The bath was filled with water.49.We all respect Mr. Wang because of his kindness.= We all have a good opinion of Mr. Wang because he is very kind.50.They have a daughter whose name is Cathy.= They have a daughter called/named Cathy.51.Why not send him to prison? = Why don’t you send him to prison?52.They promised to find out the killer.= They made a promise to find out the killer.53.The sports meeting was put off（推迟）as a result of the weather.= The sports meeting was put off because of the weather.54.Annie finished school.= Annie graduated from school.55.She loves shopping, so she decided to apply for the job.= She made up her mind to apply for the job, because she loves shopping.56.She described herself to her pen-friend.= She told her pen-friend something about herself.57.We’ve got prepared for the coming exam.= We’ve already got ready for the coming exam.58.I’m sure that he will come here.= I believe that he will come here59.My mother is always busy with her housework.= My mother is always busy doing her housework.60.She attended an important meeting yesterday.= She went to an important meeting yesterday.61.He didn’t watch TV until he finished his homework.= He watched TV after he finished his homework.= He didn’t watch TV before he finished his homework.62.Annie got nervous when she thought about the interview.= Annie felt worried and afraid when she thought about the interview. 63.Would you please tell me how to behave at an interview?= Would you please tell me how to act at an interview?64.The police put the thief behind bars.= The police put the thief in prison.65.John admitted breaking the window.=John said that he had broken the window.66.The students was unaware of his mistakes.=The students didn’t know about his mistakes.67.People rarely eat snake in the UK.=People don't often eat snake in the UK68.She always obeys her parents without question.= She always listens to her parents without question.69.I’m as old as my pencil.= I’m the same age as my pencil.70.This table is one metre long. That table is one metre long, too.= This table is as long as that one.= This table is the same length as that one.71.The two streams are both two metres in width.=This stream is as wide as that one.=This stream is the same width as that one.72.This mountain is as high as that one.=The two mountains are of the same height.73.This bag of rice is 25 kilograms. That bag of rice is 25 kilograms, too.=This bag of rice is as heavy as that one.=This bag of rice is the same weight as that one.74.What did you do that for? =Why did you do that?75.This flower is more beautiful than that one.=That flower is less beautiful than this one.=That flower isn’t as beautiful as this one.76.Jill studies harder than Tracy.=Tracy doesn’t study as hard as Jill.77.He was too young to go to school.=He was so young that he couldn’t go to school.78.Y ou never seem to be short of pocket money.=It seems that you don’t have enough pocket money.79.Y ou use the keyboard for typing in information.=You use the keyboard to type in information.80.N ow they are everywhere.=Now they are here and there.81.Y ou are more dependent on computers than you realize.=You depend on computer more than you understand.82. What happened to…?=What’s the matter with …?=What’s wrong with …?83. I can’t solve the problem. = I’m not able to work out the problem.84. He bought a vase for 200 yuan.=He paid 200 yuan for a vase.=He spent 200yuan on a vase.=He spent 200 yuan (in) buying a vase.=A vase cost him 200 yuan.85. Jenny admitted stealing the vase.=Jenny agreed that he stole the vase.86. Why do you like working as a detective?=Why do you enjoy being a detective?87. They both denied stealing the vase.=Both of them didn’t admitted stealing the vase.=Neither of them admitted stealing the vase.88. A good detective never jumps to conclusions.=A good detective never makes up his mind too quickly.。
8相变过程
马氏体转变特点：
1）相变前后存在习 性平面和晶面定向 关系。
2）快速。可达声速
3）无扩散
4）无特定温度：
四、按成核特点分类（略）
温度段。
均质转变：发生在单一均质中。
非均质转变：有相界面存在。
五、按成分、结构的变化分（略）
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此时，生长速率达极大值，一般约在10-5cm/s范围。
上图是GeO2晶体生长速率和过冷度的关系。
可见生长速度随过冷度的增加先增大后减小，具有峰值。这是由于 高温段主要有液相变成晶相的速率控制，增大过冷度对该过程有利； 在低温段由扩散控制，低温对扩散不利，所以生长速度减慢。
重构式转变
位移式转变
§8－2 成核与生长的机理
一、析晶相变过程的热力学
相变过程的不平衡状态及亚稳区
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过冷。 c、当加入杂质，可在亚稳区
形成新相，此时亚稳区 缩小。
原因：当发生相变时，是以微小液滴或晶粒出现，由于颗粒很小， 因此其饱和蒸汽压和溶解度>>平面态蒸汽压和溶解度，在相平衡温 度下，这些微粒还未达到饱和而重新蒸发和溶解。
广义相变：包括过程前后相组成的变化。
g L (凝聚、蒸发) g S (凝聚、升华) L S (结晶、熔融、溶解) S1 S2 (晶型转变、有序-无序转变) L1 L2 (液体) A＋BC 亚稳分相 (Spinodal分相)
A Glimpse of Chinese Culture《中国文化概论》讲义-chapters 1-8
Chapter 1The Origin of Chinese Culture文化词汇Confucian philosophy 儒家哲学Confucius孔子Mencius孟子the descendants of Yan and Huang 炎黄子孙the Spring and Autumn and the Warring States Periods 春秋战国时期The Art of War《孙子兵法》porcelain 瓷器三皇五帝Three Emperors and Five Sovereigns)Gregorian calendar/ solar calendar格里高利历,是国际通用的历法,即公历lunar calendar阴历the Twenty-four Solar Terms二十四节气Chinese Zodiac生肖Chinese Culture---Past and PresentChinese history began with two legendary figures—Emperor Huang and Emperor Yan, who, together with their tribes, inhabited the drainage area along the middle reaches（中游）of the Yellow River. By the time of Xia Dynasty, after centuries of living side by side, these two tribes had gradually merged into（合并，融合）one. Consequently, the Chinese people usually call themselves “the descendants of Yan and Huang”.People at that time believed that the land they lived on was the center of the world, and called their state the "Middle Kingdom"(中国), thus giving China its country name.Traditional Chinese culture is recorded not only in history books and documents, but also in archeological records(考古记载), such as ancient city walls, palaces（宫殿）, temples（寺庙）, pagodas（宝塔）, and grottos（洞窟）; artifacts（史前古器物）, such as bronze objects, weapons, bronze mirrors, coins, jade and pottery objects, and curios; and folk culture, including song and dance, embroidery（刺绣）, cuisine（烹饪）, clothing, tea ceremonies, drinking games, lanterns, riddles, martial arts（武术）, chess and kites. With a continuous history of 5,000 years, it has undergone frequent transformations to produce a rich and vital cultural heritage.In the modern day, with the rise of western economic and military power beginning in the mid-19th century, Western systems of social and political organization have gained adherents in China. Indeed, within today’s globalized environment, modern cultures interact and cooperate increasingly more with each other. China’s culture of the future will most likely reflect this cross-cultural dimension. Thus, obtaining a solid understanding of China’s culture of the past is necessary in order to successfully embrace all that the culture has to offer to the world.The Appellation of ChinaChina is the appellation of our country given by foreigners. The porcelain china is the transliteration of the place name Changnan(昌南), which was the old name for Jingdezhen（景德镇）. The porcelain made in Changnan was smooth and bright, and earned another name of artificial jade. It became famous both home and abroad and was exported to Europe in large quantities.As time passed, people in Europe forgot the meaning of Changnan and switched the original meaning of porcelain of the word “china” to the place of its origin.The Alternative Names of China⏹Chixian, Shenzhou(赤县、神州)⏹Jiuzhou (九州)⏹Hua ( 华)⏹Huaxia(华夏)⏹Zhonghua(中华)⏹Hainei(海内)Chinese MythologyChinese Mythology is a collection of cultural history, folktales（民间故事）, and religions that have been passed down in oral or written form. Chinese mythology is similar to modern religion in that they both believe in relationships between mankind and a higher power.Historians have conjectured（推测）that Chinese mythology began in 12th century BC (close to the time of the Trojan War 特洛伊战争). The myths and legends were passed down in oral form for over a thousand years, before being written down in early book such as Shui Jing Zhu and Shan Hai Jing.The classification of myth神话的分类Creation myth 创世神话：Nvwa Created Man(女娲造人）Hero myth 英雄神话：Houyi Shooting the Sun(后羿射日)War myth 战争神话：Yellow Emperor Tackled Human-God(黄帝擒蚩尤)Cultural MosaicHeavenly Stems and Earthly BranchesThe standard Gregorian calendar is generally referred to as the solar calendar in China. The traditional Chinese lunar calendar, also known as the Jiazi calendar, counts the years in sixty-year cycles by combining two series of numbers---the 10 Heavenly Stems and 12 Earthly Branches.The Twenty-four Solar TermsThe traditional Chinese lunar year is divided into twenty-four solar terms, according to the position of the sun on the ecliptic in relationship to the earth. The solar terms designate agricultural periods, and can predict changing seasonal conditions, temperature, and weather throughout the course of the year. They are extremely important to agricultural production.Changes in the four seasons are determined by eight solar terms:立春( the Beginning of Spring),春分( the Spring Equinox ),立夏(the Beginning of Summer ),夏至(the Summer Solstice),立秋(the Beginning of Autumn),秋分( the Autumnal Equinox),立冬( the Beginning of Winter),冬至(the Winter Solstice )Changes in temperature are indicated by five solar terms:小暑Slight Heat ,大暑Great Heat ,处暑the Limit of Heat ,小寒Slight Cold ,大寒Great ColdChanging weather conditions are indicated by seven solar terms:雨水Rain Water ,谷雨Grain Rain ,白露White Dew ,寒露Cold Dew,霜降Frost's Descent ,小雪Slight Snow ,大雪Great Snow .Recurring natural phenomena are indicated by four solar terms:惊蛰the Waking of Insects ,清明Pure Brightness ,小满Grain Full,芒种Grain in EarChinese ZodiacIn ancient times, our ancestors counted the years with 10 heavenly stems and 12 earthly branches. Although this was scientific, most people were illiterate and could not memorize or calculate easily. Thus the animals that influenced people's lives were chosen to symbolize the terrestrial branches: the rat, ox, tiger, rabbit, dragon, snake, horse, sheep, monkey , rooster, dog and pig.Chapter 2 Culinary Culture文化词汇culinary厨房的，烹饪的;烹调用的cuisine烹饪，烹调法;菜肴main food主食,主粮（staple food ）Fire temperature火候food tonic 食补“Food is the first necessity of the people”(“民以食为天。
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R iL L
t
i L ( ) d 0
R diL L dt
1 LC
iL 0
iL
Solution
+
R
L
C
_
uC u L u R
Step 1. Apply KCL to the parallel RLC.
(b) parallel RLC circuit
i R i L iC 0
• In theory, the simplest circuit that generates sinusoidal waveforms is LC circuit. Such an electronic circuit is an idealized oscillator circuit. Oscillator circuits play an important role in many communication and instrumentation systems.
d 0
series RLC circuit b R / L c 1 / L C parallel RLC circuit b 1 / R C c 1 / L C
For appropriate constants b and c, where x is either uC or iL. Solution Step 1. Substitute Kest
Based on
d uC dt
d uC dt
2
1
LC
uC
and
2
u C ( t ) K co s( t )
d uC dt
2
K s in ( t )
1 LC
K c o s ( t ) u C
2 2
2
or
1 LC
The values of K and θ depend on the initial conditions.
Linear Circuit Analysis
Warming up snacks in a microwave oven
Second-Order Circuit
1. What is second-order circuit?
A second-order circuit is characterized by a second-order differential equation. It consists of resistors and the equivalent of two energy storage elements.
2
b R/L
R 2
c 1 / LC
L C
R L
1 2
s t s t x (0 ) K 1e 1 K 2e 2
t0
K1 K2
s t s t x ( 0 ) K 1 e 1 K 2 e 2
t0
s1 K 1 s 2 K 2
Series RLC circuit
b 4c
3. Source-free second-order linear networks
R L
C
i R i L iC
• Development of differential equation models for series and parallel RLC circuits + uC Solution _ Step 1. Apply KVL to the series RLC.
K
2
d e dt
2
st
2
bK
de
st
cK e
st
K e ( s bs c ) 0
st 2
dt
s bs c 0
characteristic equation
b 4c
2
Step 2. Solve characteristic equation, the roots are:
iC C uL L d uC dt diL dt iL uC
_
Step 2. Obtain differential equations in the capacitor voltage uC and inductor current iL.
d uC dt
2
2 2
1 LC
uC
d uC dt
2 2
R d uC L dt
1 LC
uC 0
(b) parallel RLC circuit
diL dt 1 C
Step 3. Choose iL as circuit variable and express uR, uC, and uL in terms of iL.
d iL dt
Typical examples of second-order circuits:
R
+
L
US
C
IS
R
L
C
_
(a) series RLC circuit
(b) parallel RLC circuit
R
L
L
C
C
R
L
C
Zero-state response or complete response
+
u R u L uC 0
(a) series RLC circuit
Step 2. Choose uC as circuit variable and express uR, uL, and iC in terms of uC.
R L C
R iC L d iC dt uC 0
s1 , s 2 b
natural frequencies
2
Step 3. Discuss three distinct possibilities Case 1. b2 — 4c >0 , two distinct real roots. x ( t ) K 1 e s t K 2 e s t The constants K1 and K2 depend on the initial conditions of the differential equation, which depend on the initial voltages and currents in the circuit.
LC 1
iL 0
d iL
R
L
C
dt
2
2
diL
R C dt 1 RC d uC dt
LC 1
iL 0
d uC dt
2
LC
uC 0
(b) parallel RLC circuit
d x dt
2 2
series RLC circuit
b dx dt cx 0
b
R L 1
2
Thus one reasonable assumes that the solutions of differential equations have the general forms:
u C ( t ) K co s( t ) i L ( t ) K co s( t )
1 GL c
c 1 LC
1 LC
parallel RLC circuit b
RC
• Solution of the general second-order differential equation model All four differential equations have the general form:
d iL dt
2
1 LC
iL
Step 3. Construct the waveforms uC(t) and iL(t). Specifically recall the differentiation properties of the sine and cosine functions:
d dt d dt s in ( t ) c o s ( t ) c o s ( t ) s in ( t )
d
2 2
s in ( t ) s in ( t )
2
dt 2 d dt
2
c o s ( t ) c o s ( t )
uC R
L
1
t
u C ( )d C
d uC dt
0
d uC dt
2
2
1 RC
d uC dt
1 LC
uC 0
R
L
d uC
2
C
dt
2
2
R d uC L dt
1 LC 1
uC 0
d iL
(a) series RLC circuit
dt
2
2
R diL L dt 1
R
L
Zero-input response
US
C IS
R
L
C
_
+
U
S
L
R1
R2
+
U
S
L1
R