tsukuba graduate school entrance exam 2009/08

8/14/2019 Tsukuba Graduate School Entrance Exam 2009/08

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University of Tsukuba

Graduate School of Systems and Information Engineering

Master's Program in Social Systems Engineering

ENTRANCE EXAMINATION

August 20, 2009

Foreign LanguageEnglish

Write your application number on the top of each answer sheet.


2/26

2008823

Read the following extract from an article in the August 23, 2008 issue of the Japan Times Weekly,

and answer the questions entirely in English or in Japanese. For each of the following question,

give your answers in complete sentence.

QuestionEach question carries the same weight.

1. 1 Gordian knot

Explain what Gordian knot means in the context of this article.

Note: Gordian knot is described as follows in Wikipedia:

The Gordian Knot is a legend associated with Alexander the Great (). It is

often used as a metaphor for an intractable problem, solved by a bold stroke ("cutting the Gordian

knot").

2.

What is the technological advance that can solve the energy problem? Explain its detail. Also

describe how the innovation can be applied in practice.

3.

List the three representative renewable energy sources according to the article, and describe their

merits and demerits.

4. EU

How and to what extent could Japanese experience contribute to solve EUs energy problem?

Explain.

5. EU

Even if the technological innovation is technically feasible and implementable, what are other

obstacles that must be overcome to solve EUs energy problem? Explain.


3/26

RENEWABLE ENERGY

EU's energy needs require complex geopolitical solution

By ALEXANDER JACOBY

In a world of complex connections, the problems, and their possible solutions, are more intricate

than ever. This applies particularly to the enduring issue of the environment. Our continuing

dependence on fossil fuels contributes to climate change, with the long-term consequence of

environmental degradation and political instability in those countries adversely affected by that

change. We are all familiar with the problem. But the sheer variety of ways in which technologically

advanced societies are dependent on fossil fuels, the fact that we take for granted the ability to travel

internationally, and to commute on a daily basis between our homes and our workplaces, plus the

growing demand for energy in developing nations such as India and China, make any simple, single

solution seem remote.

Could a technological advance cut this Gordian knot1? A recent article in Britain's Guardian

newspaper suggested that it might. The solution is a network of high-voltage direct-current cables,

potentially a practical means of long-distance transmission of electricity. Hitherto, we have relied on

alternating-current cables, which lose too much energy to be used over long distances. But scientists

working for the European Union claim that modern DC cables could one day allow all of Europe's

energy needs to be supplied by renewable energy. These cables will carry solar energy from North

Africa, geothermal energy from Icelandic volcanoes, and wind power from Britain and Denmark.

When one form of energy is lacking (for instance, when there is no wind in Northern Europe),

another will supply the shortfall (there will still be sunlight in the Sahara).

Anything that could enable a shift to renewable energy on a grand scale merits urgent consideration.

But this proposed solution to an environmental problem overlooks the related geopolitical one.

The current dependence of the West and other developed countries on fossil fuels is a problem not

only because of its environmental dangers but also because the largest deposits of our most vital

fossil fuel, oil, are located in countries that are politically unstable and in many ways ideologically

inimical to the nations that are the biggest consumers. This latter problem will not be resolved by the

EU plan to shift toward renewable energy.

Saharan solar power is vital to the plan. But sunshine-rich North Africa, no less than the oil-rich

Middle East, is a politically unstable region. The government of Algeria has said that it "aims to

export 6,000 megawatts of solar-generated power to Europe by 2020." But it is doubtful that


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Algeria's Islamist militants, who have continued to pursue a low-level insurgency since the end of

full-scale civil war in 2002, share this ambition. The EU plan requires a political stability that cannot

be guaranteed in the uneasy 21st century.

From a geopolitical perspective, then, it is surely desirable that in unstable times nations strive as

much as possible for self-sufficiency. This is not an argument for isolationism. But the EU, at least,

as an increasingly close-knit grouping of broadly like-minded countries, with similar political

assumptions, social concerns and economic priorities, should ideally strive to be able to generate the

energy it needs on its own territory.

Yet this raises questions of practicality. Solar panels in Spain would be politically more secure than

solar panels in Algeria, and some are already in place; but Spain lacks the vast deserts of North

Africa. Without the key contribution of Saharan solar power, geothermal energy from Iceland (an

EU country in all but name), Northern European wind power or other renewable sources may not be

able to provide a volume of energy sufficient to satisfy the continent's needs.

Geothermal energy is perhaps the most promising of the alternatives since it is thought that the

amount of energy currently drawn from such sources is a fraction of the possible total. Indeed, this is

a matter that might also be of relevance to Japan, which despite the widespread subterranean heat

that warms thousands of onsen, generates less than 1 percent of its energy from geothermal sources.

But for Europe and elsewhere, the technology to exploit geothermal sources fully is, sadly, still in

the future.

The EU plan certainly has many virtues. It has a firm technological basis and it sees the importance

of diversification; it does not pretend that any one energy source could supply all our needs. But we

cannot assume that technological advances will solve our problems without tackling the political

disagreements that are so pervasive today. We need to learn again that pragmatic solutions to

practical problems are not enough. We need also a more just and equitable answer to the political

questions of our century.


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[1]

University of Tsukuba

Graduate School of Systems and Information Engineering

Master's Program in Social Systems Engineering

ENTRANCE EXAMINATION

August 20, 2009

Major Subjects

(1) This package contains questions from the following 4 subject areas. Choose onesubject area to answer.

(2) Write your application number on the top of each answer sheet.(3) Write the subject area and question number (e.g., Mathematics [1] ) on the top of

your answer. Use a separate answer sheet for each question.

Subject Areas

Mathematics

Economics

Management Engineering

Urban and Regional Planning


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Mathematics

19 3

[1]

(1).

0 4 1 2 14 0 3 0 2

1 3 0 1 22 0 1 0 2

1 2 2 2 0

.

(2).

a b + c bc

b c + a ca

c a + b ab

.

(3).

3 a + b + c a2 + b2 + c2

a + b + c a2 + b2 + c2 a3 + b3 + c3

a2 + b2 + c2 a3 + b3 + c3 a4 + b4 + c4

.

[2] {an} T{an} + {bn} = {an + bn}k{an} = {kan}

an+2 = 2an an+1 (n = 1, 2, . . . ) ()

{an} T S

(1). ({an}) = {an+1} S

(2). a1 = 1, a2 = 0 () e1 = {1, 0, 2, 2, . . . }a1 = 0, a2 = 1 () e2 = {0, 1, 1, 3, . . . } S

(3). a1 = 1, a2 = 2 () f1 = {1, 2, 4, 8, . . . }a1 = 1, a2 = 1() f2 = {1, 1, 1, 1, . . . } S


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(4). {e1, e2} e

(5). {f1, f2} f

(6). S {an} = {a1, a2, . . . } an a1, a2, n

[3] A

(1). tAA

(2). tAA = B2B

(3). A = P S P S

[4] 0 < < 1

(1). n n+1n

1

xdx 1

n

(2).

n=1

1

n

[5] I(t)J(t)

I(t) =

t0

etx sin xdx, J(t) =

t0

etx cos xdx

(1). I(t) t

(2). I(t)I(t) J(t)

(3). I(t) J(t) t

[6] 2R2DD = {(x, y) R2|x2 + y2 1}

(1). (x, y) Dx y


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(2). D

(x y)2dxdy

(3).

D

(ax + by)(x y)dxdy = 0

D(ax + by)2dxdy = 1 (a, b)

[7]

f(x) =

3500 (25 x2) for 5 < x < 50 elsewhere

(1). 3

(2). 1

(3). 2 3

(4). 4

[8] (A)(B)(C)(D)

1 x1, x2, x3, . . . , and xn

y =n

i=1

x2i

= n (A)

2 x (B)(B)

b(x; n, ) =

nx

x(1 )nx for x = 0, 1, 2, . . . , n

3 x (C)(C)

p(x; n, ) =xe

x!for x = 0, 1, 2, . . .


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4 x (D)(D)

n(x; , ) =1

2e

1

2(x

)2 for < x <

> 0

[9] 100kg

5 98.9kg 4.4kg

= 100 < 100 5%( = 0.05)( 4

5% t 2.132)


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Choose three questions from Questions [1] through [9], and use a separate set of answer

sheets for each question.

[1] Compute each of the following determinants.

(1).

0

4 1

2 1

4 0 3 0 21 3 0 1 22 0 1 0 2

1 2 2 2 0

.

(2).

a b + c bc

b c + a ca

c a + b ab

.

(3).

3 a + b + c a2 + b2 + c2

a + b + c a2 + b2 + c2 a3 + b3 + c3a2 + b2 + c2 a3 + b3 + c3 a4 + b4 + c4

.

[2] Let T be the linear space consisting of all real sequences {an} where the additionand the scalar multiplication are defined by {an} + {bn} = {an + bn} and k{an} = {kan},respectively. Consider the linear sub-space S ofT consisting of all sequences {an} satisfyingthe following recurrence relation:

an+2 = 2an an+1 (n = 1, 2, . . . ) ()

Answer each of the following questions.

(1). Show that the map define by ({an}) = {an+1} is a linear transformation on S.

(2). Let e1 = {1, 0, 2, 2, . . . } be the sequence defined by a1 = 1, a2 = 0 and (), ande2 = {0, 1, 1, 3, . . . } be the sequence defined by a1 = 0, a2 = 1 and (). Show that{e1, e2} forms a basis of S.

(3). Let f1 = {1, 2, 4, 8, . . . } be the sequence defined by a1 = 1, a2 = 2 and (), andf2 = {1, 1, 1, 1, . . . } be the sequence defined by a1 = 1, a2 = 1 and (). Show that

{f1

, f2}

forms another basis of S.

(4). Find the linear transformation matrix e of on the basis {e1, e2}.

(5). Find the linear transformation matrix f of on the basis {f1, f2}.

(6). Express the general term an of the sequence {an} = {a1, a2, . . . } S in terms ofa1, a2and n.


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[3] Let A be a real invertible matrix. Answer each of the following questions.

(1). Prove that the eigenvalues of tAA are all positive.

(2). Show that there exists a real invertible symmetric matrix B such that tAA = B2.

(3). Show that there exist an orthogonal matrix P and a real symmetric matrix S such

that A = P S.

[4] Let be a real number such that 0 < < 1. Answer the following questions.

(1). For any natural number n, show the following inequality:

n+1n

1

xdx 1

n

(2). Does the following infinite sum of series converge or diverge? Why?

n=1

1

n

[5] For the functions I(t) and J(t) defined below, answer the following questions.

I(t) =

t0

etx sin xdx, J(t) =

t0

etx cos xdx

(1). Find the derivative of I(t) with respect to t.

(2). Applying the integration by parts formula to I(t), find the equation on the relation

between I(t) and J(t).

(3). Find the explicit formula of I(t) and J(t) as a function of t.

[6] Let R2 be the 2-dimensional Euclidean space, and let D be a subset of R2 satisfying

D = {(x, y) R2|x2 + y2 1}. Answer the following questions.

(1). Find the minimum and maximum of x

y when (x, y) is in D.

(2). Find the following integration. D

(x y)2dxdy

(3). Find a tuple of (a, b) which satisfies both

D(ax + by)(x y)dxdy = 0 and

D(ax +

by)2dxdy = 1.


12/26

[7] The number of minutes that a flight from Tokyo to Osaka is early or late is a random

variable whose probability density is given by

f(x) =

3500 (25 x2) for 5 < x < 50 elsewhere,

were negative values are indicative of the flights being early and positive values are indica-tive of its being late. Find the probabilities that one of these flights will be

(1). at least 3 minutes early;

(2). at least 1 minute late;

(3). anywhere from 2 to 3 minutes early;

(4). exactly 4 minutes late.

[8] Answer the name of distribution that applies to following (A), (B), (C), and (D), and

answer the features and the main usages of each distribution.

definition 1 If x1, x2, x3, . . . , and xn are independent random variables having standard

normal distributions, then

y =n

i=1

x2i

has the (A) distribution with = n degrees of freedom.

definition 2 A random variable x has a (B) distribution, and it is referred to as a (B)

random variable, if and only if its probability distribution is given by

b(x; n, ) =

n

x

x(1 )nx for x = 0, 1, 2, . . . , n .

definition 3 A random variable x has a (C) distribution, and it is referred to as a (C)


p(x; n, ) =xe

x!for x = 0, 1, 2, . . . .

definition 4 A random variable x has a (D) distribution, and it is referred to as a (D)


n(x; , ) =1

2e

1

2(x

)2 for < x <

where > 0.


13/26

[9] Suppose that the specifications for a certain kind of ribbon call for a mean breaking

strength of 100 kilograms, and that five pieces randomly selected from different rolls have

a mean breaking strength of 98.9 kilograms with a standard deviation of 4.4 kilograms.

Assuming that we can look upon the data as a random sample from a normal population,

test the null hypothesis = 100 against the alternative hypothesis < 100 at = 0.05

(5% significance level), where 2.132 is the value of t.05,4.


14/26

[1][2]

[1] ( ) 120 D p p= p

2 2

2

( )2

yC y = y

(1) (2) (3)

(4) 30

(5) (4)


15/26

[2]

,

,

,,)1(

),,(

1

1

nL

LL

ICY

sYSIKK

LKFY

t

tt

ttt

tt

ttt

ttt

=

+=

=

+=

=

+

+

t t tt

Yt

Kt

L

t t t

tI

tS

0

tC (.,.)F

1


16/26

Economics

Answer both questions, [1] and [2]. Use a separate answer sheet for each question.

[1] Japanese consumers have a demand function for towels which has the form ,

where the price of towels is denoted by p. Towels are supplied by two firms, a Japanese firm

and a foreign firm. The two firms behave competitively. The total cost function for producing

towels is given by

( ) 120 D p p=

2

( )2

yC y = in each firm, where the production quantity of each firm is

denoted as y.

(1) Derive the total supply function for towels

(2) Derive the market price and the total supply.

(3) The total surplus in Japan is the sum of the consumer surplus and the profit of the Japanese

firm. Find the total surplus in Japan.

(4) Now, the Japanese firm lobbies for protection, and the Japanese government accepts the

request and puts a tariff of 30 on the foreign towels. What is the new price for towels paid

by customers?

(5) Under the same conditions as in (4), derive production quantity of the Japanese firm and the

foreign firm, and find the total surplus in Japan.


17/26

[2] Consider the Solow growth model described by the following equations:

,

,

,,)1(

),,(

1

1

nL

LL

ICY

sYSIKK

LKFY

t

tt

ttt

tt

ttt

ttt

=

+=

=

+=

=

+

+

where is output in period t, is the capital stock at the beginning of period t, is the

number of workers in period t,

tY

tK

tL

is the depreciation rate, is investment in period t,

is saving in period t, and is consumption in period t. The production function is

constant returns to scale, and the marginal product of capital and labor is positive and

diminishing. We also assume that the Inada conditions are satisfied, and that

tI

tS

1

tC (.,.)

0

F


18/26

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19/26

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20/26

[2]

2

(1) JavaNode

(2) key 2 Java

(3) Java

C D

() c = c.leftchild() c = c.rightchild.rightchild() preScan(n)() preScan(n.leftchild)() c = c.leftchild.leftchild

() return c() return null() preScan(n.rightchild)() c = c.rightchild() preScan(null)

1: public Node find(int key) {

2: Node c = root;

3: while (c.key != key) {

4: if (key < c.key)

5: A ;6: else

7: B ;8: if (c == null) break;

9: }

10: return c;11: }

1: public void preScan(Node n) {

2: if (n != null) {

3: System.out.println(Key is + n.key);

4: C ;5: D ;6: }

7: }


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[3]

(1) 0 , 1 , . . . , 3 1, 1, 1, 2

(2)

[4]

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3

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(2)


22/26

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23/26

[2] In the binary search tree shown in Figure 1, the item value of each node is larger than the values

of all the items in its left subtree but is smaller than the values of all the items in its right

subtree.

Figure 1 Binary search tree

(1) Show a Java classNode to represent a node on the binary search tree shown in Figure 1.

(2) Figure 2 shows a Java program for searching a given key, key, in a binary search tree. Fill

in the blank fields and to complete the program using the following selection

statements.

(3) Figure 3 shows a Java program for traversing a binary search tree in preorder and printing

out the item value of the visited node. Fill in the blank fields C and D to complete the

program using the following selection statements

Selection statements

(a) c = c.leftchild(b) c = c.rightchild.rightchild(c)

preScan(n)

(d) preScan(n.leftchild)(e) c = c.leftchild.leftchild

(f) return c(g) return null(h)

preScan(n.rightchild)

(i) c = c.rightchild(j) preScan(null)

1: public Node find(int key) {

2: Node c = root;

3: while (c.key != key) {

4: if (key < c.key)

5: A ;6: else

7: B ;8: if (c == null) break;

9: }

10: return c;

11: }

Figure 2 Search program on a binary search tree

1: public void preScan(Node n) {

2: if (n != null) {

3: System.out.println(Key is + n.key);

4: C ;5: D ;6: }

7: }

Figure 3 Scan program of a binary search tree in pre-order


24/26

[3] Answer the following two questions

(1) Assume that the cash flow at the -th periods 0,1,2,3 of an investmentisgiven by 1, 1, 1, 2. Calculate the internal rate of return ofthis investment

(2) For stock options, it is known that the put-call parity exists between the prices of

European put and call options. Explain the meaning of the put-call parity, and explain

why it holds.

[4] Concerning intergroup conflict within an organization, answer the following questions.

(1) In general, the following three elements are considered to be important so as to understand

the process of how intergroup conflict could be generated:

1) group identification;

2) observable group differences; and

3) frustration against other group(s).

Discuss how intergroup conflict could evolve from the three elements.

(2) There are two types of intergroup conflict. Horizontal conflict occurs between groups or

departments at the same level in the organizational hierarchy, while vertical conflict arises

among groups at different levels along the vertical hierarchy. Describe one concrete

example for each type.


25/26

[1][4]2

[1]

(1) TOD(Transit Oriented Development)

(2)

(3) Jane Jacobs

(4)

(5)

(6)

[2]

[3]

[4]


26/26

Urban and Regional Planning

Choose two questions from Questions [1] through [4], and use a separate answer sheet for each

question.

[1] Choose four terms/topics out of the following six, and explain their meanings and/or concepts

from the viewpoint of urban and regional planning.

(1) Transit Oriented Development

(2) The Athens Charter

(3) Jane Jacobs

(4) District Plan

(5) Development Permission System

(6) Urbanization Promotion Area, Urbanization Control Area

[2] Describe the functions of urban green spaces, and explain how to increase the green spaces in

urbanized area referring the existing planning legislation.

[3] Explain the features of New Town Development in Japan, and then describe the problems of

New Towns and the countermeasures for them.

[4] Explain the process and the mechanism of the decline of central districts in local cities in Japan.

Then describe the direction of their revitalization.

tsukuba graduate school entrance exam 2009/08

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