ch03[共30页]

Ch3酸碱与酸碱平衡P78－1,7 ,8 ,12；14,15,16；20,23[3－1] 指出下列酸的共轭碱：酸 O H 2、+O H 3、32CO H 、-3HCO 、3NH 、+4NH共轭碱 -OH 、O H 2、-3HCO 、 -23CO、 -2NH、3NH[3-5]已知H 2SO 3的O 1a pK=1.81，O 2a pK=6.91。

在pH4.00和4.45时，溶液中H 2SO 3、HSO 3－和SO 32－三种形式的分布系数δ2δ1δ0各为多少？解： ()[]O O O +++⋅++=21122322a a a KKKH HH SO H δ()[][][]O O O ++O +-⋅++=2111231a a a a KKKH HK H HSOδ()[][]122230121121δδδ--=⋅++⋅=O O O ++OO-a a a a a KKKH H K K SOpH4.00： δ2=[][][]2.785.185.142424101010101010------⋅++=0.00703δ1=[][][]2.785.185.142485.1410101010101010-------⋅+⨯+⨯=0.99297δ0=1-δ2-δ1=1-0.00702969-0.99297=0.0000004（或0.001）pH 4.45：δ2=[][][]2.785.185.15.425.425.4101010101010------⋅+⨯+=2.23372×10-3δ1=[][][]2.785.185.15.425.485.15.410101010101010-------⋅+⨯+⨯=0.9977662δ0=1-δ2-δ1=1-2.23372×10-3-0.9977662=2.06×10-8[3－7] 写出下列物质在水溶液中的质子条件式： ○1NH 3·H 2O ： [][][]-++=+OH H NH 4[H +]= [OH －]－[NH 4+]○2NH 4Ac ： [][][][]-++=+OH NH HAc H 3[H +]= [NH 3] + [OH －] －[HAc]○3(NH 4)2HPO 4： [H 2PO 4 －]+2[H 3PO 4]+ [H +]= [NH 3] +[PO 4 －3] +[OH －][H +]= [NH 3] +[PO 4 －3] +[OH －]－[H 2PO 4 －]－2[H 3PO 4]○4CHOOH ： [][][]--++=OH COOH H○5H 2S ： [][][][]---+++=OH S HS H 22 ○6Na 2C 2O 4： [][][][]-+-=++OH HO C H O HC 422422[H +]=[OH －]－[HC 2O 4－]－2[H 2C 2O 4 ][3－8] 12%的氨水溶液，相对密度为0.953，求此氨水的OH －浓度和pH 值。

Chapter 3Preferences and UtilitySolutions to Problems3.2 Consider the single-good utility function U(x) = 3x2, with a marginal utility given by MU x= 6x. Plot the utility and marginal utility functions on two separate graphs. Does this utility function satisfy the principle of diminishing marginal utility? Explain.The two graphs are shown below. It can be seen from both graphs that this function does not satisfy the law of diminishing marginal utility. The first figure shows that utility increases with x, and moreover, that it increases at an increasing rate. For example, an increase in x from 2 to 3, increases utility from 12 to 27 (an increase of 15), while an increase in x from 3 to 4 induces an increase in utility from 27 to 48 (an increase of 21).This fact is easier to see in the second figure. The marginal utility is an increasing function of x. Higher values of x imply a greater marginal utility. Therefore this function exhibits increasing marginal utility.U(x) = 3x2MU x = 6x3.4 Consider the utility function U (x , y ) = y √x with the marginal utilities MU x = y/(2√x ) and MU y = √x .a) Does the consumer believe that more is better for each good?b) Do the consumer’s preferences exhibit a diminishing marg inal utility of x ? Is the marginal utility of y diminishing?3.4 a) Since U increases whenever x or y increases, more of each good is better. This is also confirmed by noting that MU x and MU y are both positive for any positive values of x and y . b)Since x MU =x increases (holding y constant), x MU falls. Therefore the marginal utility of xis diminishing. However, y MU =y increases, MU y does not change. Therefore the preferences exhibit a constant, not diminishing, marginal utility of y .3.6 For the following sets of goods draw two indifference curves, U 1 and U 2, with U 2 > U 1. Draw each graph placing the amount of the first good on the horizontal axis.a) Hot dogs and chili (the consumer likes both and has a diminishing marginal rate of substitution of hot dogs for chili)b) Sugar and Sweet’N Low (the consumer likes both and will accept an ounce of Sweet’N Low or an ounce of sugar with equal satisfaction)c) Peanut butter and jelly (the consumer likes exactly 2 ounces of peanut butter for every ounce of jelly)d) Nuts (which the consumer neither likes nor dislikes) and ice cream (which the consumer likes)e) Apples (which the consumer likes) and liver (which the consumer dislikes) a)Hot DogsChiliU 2U 1b)Sweet’N Lowc)Butter2412 U 2d)NutsIce CreamU 1U 2e)ApplesLiverU 1U 23.13 Draw indifference curves to represent the following types of consumer preferences. a) I like both peanut butter and jelly, and always get the same additional satisfaction from an ounce of peanut butter as I do from 2 ounces of jelly. b) I like peanut butter, but neither like nor dislike jelly. c) I like peanut butter, but dislike jelly.d) I like peanut butter and jelly, but I only want 2 ounces of peanut butter for every ounce of jelly.In the following pictures, U 2 > U 1. a)Peanut ButterJelly 1 224 U 2 U 1b)Peanut ButterJellyU 1U 2c)Peanut ButterJellyU 2U 1d)243.15 Consider the utility function U (x , y ) = 3x + y , with MU x = 3 and MU y = 1. a) Is the assumption that more is better satisfied for both goods?b) Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x ? Explain. c) What is MRS x , y ?d) Is MRS x , y diminishing, constant, or increasing as the consumer substitutes x for y along an indifference curve?e) On a graph with x on the horizontal axis and y on the vertical axis, draw a typicalindifference curve (it need not be exactly to scale, but it needs to reflect accurately whether there is a diminishing MRS x , y ). Also indicate on your graph whether the indifference curve will intersect either or both axes. Label the curve U 1.f ) On the same graph draw a second indifference curve U 2, with U 2 > U 1. a) Yes, the “more is better” assumption is satisfied for both goods since both marginal utilities are always positive. b) The marginal utility of x remains constant at 3 for all values of x .c)3, y x MRS d) The y x MRS , remains constant moving along the indifference curve.e & f) See figure belowXYU 1 U 23.16 Answer all parts of Problem 3.15 for the utility function U (x , y ) = √xy . The marginal utilities are MU x = √y/(2√x ) and MU y = √x/(2√y ). a) Yes, the “more is better” assumption is satisfied for both goods since both marginal utilities are always positive. b) The marginal utility of x diminishes as the consumer buys more x .c) x yx y x y MRS y x =⎪⎪⎭⎫ ⎝⎛⎪⎪⎭⎫⎝⎛=22, d) As the consumer substitutes x for y , the y x MRS , will diminish.e & f) See figure below. The indifference curves will not intersect either axis.3.17 Answer all parts of Problem 3.15 for the utility function U (x , y ) = xy + x . The marginal utilities are MU x = y + 1 and MU y = x . a) Yes, the “more is better” assumption is satisfied for bot h goods since both marginal utilities are always positive. b) The marginal utility of x remains constant as the consumer buys more x .c) xy MRS y x 1,+=d) As the consumer substitutes x for y , the y x MRS , will diminish.e & f) See figure below. The indifference curves intersect the x -axis, since it is possible that U > 0 even if y = 0.3.18 Answer all parts of Problem 3.15 for the utility function U (x , y ) = x 0.4y 0.6. The marginal utilities are MU x = 0.4 (y 0.6/x 0.6) and MU y = 0.6 (x 0.4/y 0.4). a) Yes, the “more is better” assumption is satisfied for both goods since both marginal utilities are always positive. b) The marginal utility of x diminishes as the consumer buys more x .c) xyy x x y MRS y x 6.04.0)/(6.)/(4.4.04.06.06.0,==d) As the consumer substitutes x for y , the y x MRS , will diminish.e & f) See figure below. The indifference curves do not intersect either axis.3.19 Answer all parts of Problem 3.15 for the utility function U = √x + 2√y . The marginal utilities for x and y are, respectively, MU x = 1/(2√x ) and MU y = 1/√y . a) Yes, the “more is better” assumption is satisfied for both goods since both marginal utilities are always positive. b) The marginal utility of x diminishes as the consumer buys more x .c) x y y x MRS y x 2/1)2/(1,==d) As the consumer substitutes x for y , the y x MRS , will diminish.e & f) See figure below. Since it is possible to have U > 0 if either x = 0 (and y > 0) or y = 0 (and x > 0), the indifference curves intersect both axes.3.20 Answer all parts of Problem 3.15 for the utility function U (x , y ) = x 2 + y 2. The marginal utilities are MU x = 2x and MU y = 2y . a) Yes, the “more is better” assumption is satisfied for bo th goods since both marginal utilities are always positive. b) The marginal utility of x increases as the consumer buys more x .c) yxy x MRS y x ==22,d) As the consumer substitutes x for y , the y x MRS , will increase.e & f) See figure below. Since it is possible to have U > 0 if either x = 0 (and y > 0) or y = 0 (and x > 0), the indifference curves intersect both axes.3.21 Suppose a consumer’s preferences for two goods can be represented by the Cobb–Douglas utility function U = Ax αy β , where A , α, and β are positive constants. The marginal utilities are MU x = αAx α−1y β and MU y = βAx αy β−1. Answer all parts of Problem 3.15 for this utility function. a) Yes, the “more is better” assumption is satisfied for both goods since both margin al utilities are always positive. b) Since we do not know the value of α, only that it is positive, we need to specify three possible cases:When 1<α, the marginal utility of x diminishes as x increases.When 1=α, the marginal utility of x remains constant as x increases. When 1>α, the marginal utility of x increases as x increases.c) xyy Ax y Ax MRS y x βαβαβαβα==--11,d) As the consumer substitutes x for y , the y x MRS , will diminish.e & f) The graph below depicts indifference curves for the case where 1=A and .5.0==βα Thus 5.05.0),(y x y x U =. Regardless, the indifference curves will never intersect either axis.3.22 Suppose a consumer has preferences over two goods that can be represented by the quasi-linear utility function U (x , y ) = 2√x + y . The marginal utilities are MU x = 1/√x and MU y = 1.a) Is the assumption that more is better satisfied for both goods?b) Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x ? Explain.c) What is the expression for MRS x ,y ?d) Is the MRS x ,y diminishing, constant, or increasing as the consumer substitutes more x for y along an indifference curve?e) On a graph with x on the horizontal axis and y on the vertical axis, draw a typicalindifference curve (it need not be exactly to scale, but it should accurately reflect whether there is a diminishing MRS x ,y ). Indicate on your graph whether the indifference curve will intersect either or both axes.f) Show that the slope of every indifference curve will be the same when x = 4. What is the value of that slope? a)Yes, the “more is better” assumption is satisfied for both goods since both marginal utilities are always positive. b) The marginal utility of x decreases as the consumer buys more x .c) ,x y MRS ==d) As the consumer substitutes x for y , the y x MRS , will diminish. e) Since it is possible to have U > 0 if either x = 0 (and y > 0) or y = 0 (and x > 0), the indifference curves intersect both axes.Besanko & Braeutigam – Microeconomics, 4th edition Solutions ManualCopyright © 2011 John Wiley & Sons, Inc. Chapter 3 - 11f) The slope of a typical indifference curve at some basket ),(y x is the,x y MRS =. At4=x , ,0.5x y MRS ==. Note that this holds regardless of the value of y . Therefore, the slope of any indifference curve at 4=x will be 0.5-.。

第3章 TMS320C54x指令系统教学提示：TMS320C54x是TMS320系列中的一种定点数字信号处理器。

由于C54x 系列DSP的CPU内核结构均相同，所以其汇编语言程序向下兼容。

因此，本章介绍的C54x 指令系统适用于所有具有相同CPU内核的C54x DSP，尽管这些DSP的型号可能不同。

C54x DSP汇编语言和单片机、微型计算机等一般汇编语言的组成和结构类似，但又有其特殊性，学习时要注意它们的不同点。

C54x DSP的指令系统包括汇编语言指令、汇编伪指令、宏指令，本章主要介绍汇编语言指令，其他指令在第4章介绍。

教学要求：了解汇编源程序的书写格式。

掌握指令的7种寻址方式，尤其是间接寻址方式。

掌握算术运算、逻辑运算、程序控制、存储和装入4种基本类型的汇编语言指令。

3.1 汇编源程序格式汇编语言指令的书写形式有两种：助记符形式和代数式形式，本章以助记符指令系统为主介绍。

汇编语言是DSP应用软件的基础，编写汇编语言必须要符合相应的格式，这样汇编器才能将源文件转换为机器语言的目标文件。

TMS320C54x汇编语言源程序由源说明语句组成，包括汇编语言指令、汇编伪指令(汇编命令)、宏指令(宏命令)和注释等，一般一句程序占据编辑器的一行。

由于汇编器每行最多只能读200个字符，所以源语句的字符数不能超过200个。

一旦长度超过200个字符，汇编器将自行截去行尾的多余字符并给出警告信息。

汇编语言语句格式可以包含4个部分：标号域、指令域、操作数域和注释域。

格式如下：[标号] [:] 指令[操作数列表] [；注释]其中[ ]内的部分是可选项。

每个域必须由1个或多个空格分开，制表符等效于空格。

例如：begin： LD #40， AR1 ；将立即数40传送给辅助寄存器ARl1. 标号域标号供本程序的其他部分或其他程序调用。

对于所有C54x汇编指令和大多数汇编伪指令，标号都是可选项，但伪指令.set和.equ除外，二者需要标号。