intermediate technical japanese volume 1 readings and grammatical patterns

Table of Contents-Volume 1Preface Explanatory Notes Lesson 0: Review of Verbs and Verb Forms Lesson 1: Mathematics I numbers and sets Lesson 2: Mathematics IT matrices, variables and fun

Also available in the Technical Japanese Series

Reflections on Science byNakaya Ukichiro

An Advanced Japanese Reader

Translated and edited by Edward E Daub

and Shiro Asano

((Snow crystals are letters sent from the heavens ))

-Nakaya Ukichiro

For anyone learning to comprehend scientific articles in

Japanese, this reader offers selections from the writings

of well-known Japanese scientist, Nakayo Ukichiro At

the time of his death in 1962, the American Meteorological

Society Bulletin heralded him as " the world's

outstand-ing scientific investigator of snow crystals."

Nakaya was a popularizer of science and a brilliant

essayist Here are included excerpts from his classic book

The Methods ofScience (I(agaku no Hoohoo) and other

literary essays discussing various cultural and social topics

in relation to science English translations accompany the

Japanese texts, followed by a glossary

2003 Paper ISBN 0-299-18104-9

Basic Technical japanese

Edward E Daub, R Byron Bird, and Nobuo Inoue

Even with no previous training in Japanese language,

readers of this book can learn to translate technical

man-uals, research publications, and reference works Basic

Technical Japanese provides step-by-step instruction,

from an introduction to the Japanese writing system

through a mastery of grammar and scientific vocabulary

to practice in reading actual texts in Japanese With

extensive character charts and vocabulary lists, the book

is entirely self-contained; no dictionaries or other

refer-ence works are needed The authors are scientists and

engineers with extensive experience in translating

Japanese

1990 Cloth ISBN 0-299-12730-3

!(anJ·i-Flash/BTj

Craig T Van Degrift

This DOS software is an electronic flashcard companion

to Basic Technical Japanese It follows the text chapter

by chapter, providing exercises to test the pronunciation

and meaning of all 510 kanji and 4000 compound words

introduced in the textbook It also allows missed words

to be saved for retesting The program requires VGA or

color EGA graphics

1992 Software ISBN 0-299-97077-9

Solid-State Physics and EngineeringTechnical Japanese Supplement

Craig T Van Degrift

This book is a supplement to the textbook Basic Technical Japanese It introduces 100 new kanji and more than

700 new words and phrases that appear frequently indocuments dealing with solid-state physics The textoffers ten lessons, each presenting key vocabulary and

ten new kanji that reappear in the exercises for that

lesson and in subsequent lessons, reinforcing learning

The exercises emphasize vocabulary building, kanji

recognition, definition matching, and translation skills

Anintroductory lesson reviews the katakana and hiragana writing systems.

1995 Paper ISBN 0-299-14734-7

BiotechnologyTechnical Japanese Supplement

R Byron Bird and Sigmund Floyd

This supplement to Basic Technical Japanese introduces

an additional 100 kanji to build vocabulary for readingand translating Japanese literature related to polymerscience and engineering

Intermediate Technical Japanese

Volume 1:

Readings and Grammatical Patterns

Intermediate Technical Japanese

Readings and Grammatical Patterns

James L Davis

University of Wisconsin-Madison

The University of Wisconsin Press

The University ofWisconsin Press

1930 Monroe StreetMadison, Wisconsin 53711www.wisc.edu/wisconsinpress/

Copyright©2002The Board of Regents of the University of Wisconsin System

All rights reserved

Printed in the United States ofAmerica

Cataloging-in-Publication data is available from the Library of Congress

ISBN 0-299-18554-0

Table of Contents-Volume 1

Preface

Explanatory Notes

Lesson 0: Review of Verbs and Verb Forms

Lesson 1: Mathematics I (numbers and sets)

Lesson 2: Mathematics IT (matrices, variables and functions)

Lesson 3: Mathematics ill (solutions, statistics and models)

Lesson 4: Computer Science I (fundamentals; part I)

Lesson 5: Computer Science IT (fundamentals; part II)

Lesson 6: Computer Science III (applications; part I)

Lesson 7: Computer Science IV (applications; part II)

Lesson 8: Mechanics I (pressure and vacuum)

Lesson 9: Mechanics II (motion and flow)

Lesson 10: Thermodynamics I (fundamentals)

Lesson 11: Thermodynamics II (applications)

Lesson 12: Light I (fundamentals)

Lesson 13: Light II (wave properties)

Lesson 14: Light III (applications)

Lesson 15: Sound I (fundamentals)

Lesson 16: Sound II (applications)

Lesson 17: Magnetism I (fundamentals)

Lesson 18: Magnetism II (applications)

Lesson 19: Electricity I (fundamentals)

Lesson 20: Electricity II (applications)

Lesson 21: Electricity III (semiconductors and superconductors)

Lesson 22: Electronics I (transistors and diodes)

Lesson 23: Electronics II (other circuit elements and basic circuits)

Lesson 24: Electronics III (ICs)

Lesson 25: Electronics IV (other circuits and devices)

Lesson 26: Signals and Signal Processing I (fundamentals)

Lesson 27: Signals and Signal Processing II (applications)

Lesson 28: Computer Hardware I general)

Lesson 29: Computer Hardware II (memory and recording)

Lesson 30: Polymers I (fundamentals)

Lesson 31: Polymers II (MW, DP, viscosity and processing)

Lesson 32: Polymers III (properties and applications)

Lesson 33: Materials I (ceramics; fundamentals)

v

-vii ix17 172945 61 75 89 105 119 133 145 155 165 177 189 199 209 221 231 243 255 265 275 285 295 305 317 327 335 343 353 363 373

Lesson 34: Materials II (ceramics; applications) 383

Lesson 39: Interdisciplinary Topics I (magnetic and electrical interactions) 435 Lesson 40: Interdisciplinary Topics II (electrochemical, biochemical and bioelectronic

This two-volume set is designed to prepare scientists, engineers and translators to read Japanesetechnical documents The reader is presumed to have already studied Japanese for at least one year.These volumes were prepared for use in a two-semester sequence of technical Japanese courses atthe intermediate level, but they are also well suited for use as self-study materials The primaryobjectives are to help the reader build a technical vocabulary in Japanese, to reinforce the reader'sunderstanding of important grammatical constructions, to improve the reader's reading-

comprehension ability, and to provide practice in translating technical passages from Japanese intoEnglish Authentic materials have been incorporated, so that the reader will gain exposure to

realistic examples that include frequently used grammatical patterns and essential vocabulary items.The disciplines covered in these volumes are mathematics, computer science, physics, mechanicalengineering, electrical and computer engineering, and advanced materials

Volume 1 contains a review of verb forms and forty field-specific lessons, which have beengrouped into fourteen units Each of the forty lessons features fifteen KANn that are important inthe field that is the focus of that lesson In addition to ON and KUN readings and the variousmeanings for the KANn, each entry includes two important terms that contain the KANn in question Experience has shown that memorizing KANn in the context of specific terms (ratherthan attempting to memorize the KANn in isolation) increases the likelihood that the learner willremember both the KANTI and the terms All of the readings listed in the current Japanese

government document, 1itmi~~l{· mf~1li1j~v~(1987) (ISBN 4-17-214500-0), are

included for each of the six hundred KANn featured in this volume A complete KANn index(with entries arranged in d!> v~5 ;t:.t:3 order) may be found at the end of this volume

Each of the first nine field-specific lessons also introduces a number of grammatical patterns thatthe reader should master in order to understand Japanese technical documents At least three

example sentences accompany each grammatical pattern, so that the reader can understand the

us~geof the grammatical pattern in context To ensure that the reader will gain the maximumamount of reinforcement in vocabulary building, each example sentence has been taken from anessay that is included in one of the lessons A complete listing (in a combination of alphabeticalorder and d!> v~5 ;t:.t:3 order) of the one hundred grammatical patterns appears after Lesson 40.The major portion of each lesson is devoted to reading selections on topics related to the theme ofthe lesson The essays within a lesson have been arranged so that the reader may apply knowledgeand vocabulary from earlier essays when reading subsequent essays More fundamental topics arepresented early in the lesson; applications and more specialized topics appear later A list of thesources from which the reading selections were taken is included in the Explanatory Notes

Volume 1 contains seven hundred twenty-one technical essays of various lengths Lesson 0 andthe first nine field-specific lessons should be studied by all readers The reader may then selecttopics of interest from the remaining thirty-one lessons to produce a customized course of study

V l l

-Volume2contains a complete glossary for the example sentences and the essays that appear in Volume 1 Each individual vocabulary list is keyed by number to a specific grammatical pattern or essay Each word that appears for the first time in an example sentence is listed in the glossary under the number of that grammatical pattern Each word that appears for the first time in an essay

is listed in the glossary under the number of that reading selection Since all example sentences have been taken from essays, some items appear in the glossary twice.

Japanese is a fascinating language, but it is a language that requires many hours of study in order for a native speaker of English (or any other Indo-European language) to read comfortably about topics in hislher field of interest It is my hope that these volumes will ease the reader along the path to enhanced reading ability and a clearer understanding of Japanese texts.

Numerous individuals have patiently answered questions and graciously reviewed drafts of these volumes In particular, I wish to thank R Byron Bird, Professor Emeritus at the University of Wisconsin-Madison, Edward E Daub, Professor Emeritus at the University of Wisconsin-

Madison, David O Mills, Associate Professor at the University of Pittsburgh, Michio Tsutsui, Associate Professor at the University of Washington, Junko Mori, Associate Professor at the University of Wisconsin-Madison, Dr Ken Lunde of Adobe Systems and Mr Mitsuo Fujita of Daicel Chemical Industries for their assistance Any errors that remain are entirely my own.

Financial support from the Department of Engineering Professional Development at the University

ofWisco~sin-Madisonfor the preparation and publication of these volumes is gratefully

acknowledged.

The reader who has questions or comments about anything that appears in either volume, or who wishes to be advised of any revisions, is encouraged to contact me at the email address that appears below These volumes are dedicated to my wife, Zhen, and to our daughter, Ruth, without whose support I could not have completed this project.

James L Davis

Madison, Wisconsin

jdavis@engr.wisc.edu

August2002

Explanatory Notes

1 AllaN readings are written in KATAKANA; all KUN readings are written in HIRAGANA.

2 When introducing new KANn at the start of a lesson, OKURIGANA are enclosed within parentheses.

3 When more than one verb can be created from a single KANn, an intransitive verb is identified

as {vi} and a transitive verb is identified as {vt}

4 In the presentation of new KANn multiple ON readings or multiple KUN readings for a single KANn are separated by semicolons Multiple meanings associated with a single ON or KUN reading are separated by commas Throughout both volumes multiple meanings associated with a single Japanese word or phrase are separated by commas.

5 The readings for KANn that appear in grammatical patterns are enclosed within brackets.

6 Grammatical patterns are numbered by lesson as follows:

to the reader also appear within braces.

10 The appearance of a hyphen before or after a specific KANn (or KANn compound) indicates that the KANn (or KANn compound) in question is used primarily as a suffix or a prefix,

respectively.

l X

-11 The source for each reading selection that appears in Volume 1 is identified by the abbreviation and page number(s) that follow the title of the essay The abbreviation and complete information for each source follow:

-e '7 -e '7 ~ 'Y!7 A !$:A;A§;ISBN 4-621-03041-8; 1986

9Gilffij 9Gilffij.Tlt~.:A; ~-I14~-;1991

12 Information for the glossary was gathered from many sources, including the books listed above and the following:

Kenkyusha's New Japanese-English Dictionary (Fourth Edition);

Kenkyusha; ISBN 4-7674-2025-3; 1974 The Modem Reader's Japanese-English Character Dictionary (Second Revised Edition);

A~;ISBN 4-621-03546-0; 1991

Lesson 0: Review of Verbs and Verb Forms

In this lesson we review the major verbs and verb forms that are frequently encountered inJapanese technical documents Since this lesson is intended to serve as a review, the explanationprovided for each verb or verb form is brief The reader who would like more information isencouraged to consult the following reference books:

Basic Technical Japanese

E E Daub, R B Bird and N Inoue

The University of Wisconsin Press; 1990

ISBN 0-299-12730-3

Dictionary of Basic Japanese Grammar

S Makino and M Tsutsui

The Japan Times; 1986

ISBN 4-7890-0299-3

Dictionary of Intermediate Japanese Grammar

S Makino and M Tsutsui

The Japan Times; 1995

ISBN 4-7890-0775-8

Note 1: In principle, there are three ways to end a clause or a sentence in Japanese: with an v)

-adjective (for which the present/future affirmative form ends in v)), with a verb (for which thepresent/future affirmative form ends either with Q-denoted as"ru"-or with some other syllablethat contains the vowel "u"-denoted as "xu"), or with the copula (which is usually expressed intechnical Japanese as some variation of-c'~Q [in the affirmative] or -c' (~J:) tJ: v) [in the

negative]) In this book the term "predicate" will be used collectively to include all three options

Note 2: All Japanese verbs can be thought to belong to either the"ru"category (also known as

"-ru" verbs) or the "xu" category (also known as "-u" verbs) However, some verbs in eachcategory are irregular in certain forms Thus, ~ ~ andfT <canbeconsidered "xu" verbs that areirregular in some forms Similarly, <Q and9 Q can be considered "ru" verbs that are irregular

in some forms In the discussions of verb forms in this book, only the specific forms of these fourverbs that are irregular will be mentioned Thus, unless it is indicated otherwise, the reader mayassume that all other forms of these four verbs are conjugated as might be expected based on thecategory to which each verb belongs

1

-GraDlDlatical Patterns

0.1) connective form of a verb

The connective affirmative form (also known as the gerund) is created by replacing the final t~

or t~of the past affirmative form with L or -r:, respectively The connective negative form is made by replacing the final t~v~ of the present negative form with t~< L This verb form can be used to link clauses, and it appears in other special patterns that are discussed later By way of analogy, the connective affirmative form of -r:~.Q is expressed as either -r:~ ~L or simply -r:; the connective negative form of -r:~.Q becomes -r: (~d:) t~< L.

2 a =a+ib=(a +iO) +(b +iO) (0 + il)-r:~.QtJ)G, a+ib ~d:.t~.Q~2i%-r:t~< L, Jf7*C:~L J::v~.

3. ~~ A O)7CiJ~a, b, c, -r:~.Q C:~, A ={a, b, c, } C:.V~L, ~~A ~d:

7C a, b, c, tJ) Gt~.QC: v~:>

0.2) conjunctive form of a verb

The conjunctive affirmative form (also known as the infinitive) is created by dropping the final Q from the present/future affirmative form of an ru-verb (J!.Q ~ J!) or by replacing the xu with

xi for an xu-verb(~9 ~ ~G) Irregular verbs are treated as follows: < Q ~ ~;9.Q ~ G The conjunctive negative form is made by replacing thefinalt~v~ of the present negative form with t~< This verb form can be used to link clauses, and it appears in other special patterns that are discussed later By way of analogy, the conjunctive affirmative form of -r:~.Q is expressed as

-r:~ lJ ; the conjunctive negative form of -r:~ ~ becomes -r:t~< (Note: When linking clauses, the conjunctive form often indicates a greater degree of independence between the clauses than would be the case if the connective form were to be used.)

1. x, y E R ~=~tGL, ~nl3O)fl1 x +Y C:~9Q~WE R iJ~t~t~ 1 -:JJE* lJ, x +Y =y

passive verbs are classified as ru-verbs, so the present negative form of any passive verb is made

by replacing the final Q of the present/future affirmative form (of the passive verb) with t~v~ Apassive verb in Japanese is most commonly used to express passive voice, but it can also be used(generally in conversation) to raise the level of politeness

2 *~J~A~~:~d:~.-Titif, t&M~t~ cO)~~m~~:£'":5<!LIc7J~-r?J{tl::f~t~!L~~JC:

G LflJm~tlQ.

0.4) potential verb

The present/future affirmative form of a potential verb is created by replacing the final Q with

G tlQ for an ru-verb(f~Q ~ f~G tlQ)or by replacing the xu with xe+ Qfor an xu-verb(t)]

<.~ tJJ~tQ). Irregular verbs are treated as follows: < Q~ : G tlQ; 9 Q ~ -c:~Q.Allpotential verbs are classified as ru-verbs, so the present negative form of any potential verb is made

by replacing the final Q of the present/future affirmative form (of the potential verb) with t~v~ Apotential verb indicates that a certain action is (or is not) possible (Note: For an ru-verb the

potential verb and the passive verb are identical.)

which means "has come (from somewhere else) and is still here," and~'":J L v~.Q,which means

"has become." (Note: In written Japanese the connective form of a passive verb is frequently

combined with v~.Q. Such a combination is usually translated "is+verb [past participle]." Forexample, the verb~7JltlLV~.Q means "is written" andJJ.¥~ttlL v~.Q means "is called" or~is

known as.") (Note: The combination of a verb in the connective form and-t3 tJ is described inpattern 4.6.)

1. z:tl~J:, ~~t=¥t!0)~/7°'J /~C: '7/~ ~ft:, il$~~im~O)~ ~:I V ~ 3 / ,

~mmit~~~~~~O)~Jlf~O)~tJJ,~tJJmtJJ7~0)~jj$?J{U)£t~C~:mV~GtlLV~.Q

2. !L~ ~mv~, il$~~~~~uilifg{~tJJ~J:-~~=t /7 • :JJ jyDt! C: et~ttl LV~.Q

3

-3 -~,:, 65~~.g XO)7I:~~A9~=cn)Wf~tl-Ct/~~X:~x ~~ltct)~·), x~~

0.6) provisional form of a verb

The provisional affirmative form is createdbyreplacing the final ~ from the present/futureaffinnative form ofan ru-verb withtl~i (Ji~ -7J!tltt)orbyreplacing the xuwithxe+~tior an xu-verb(~9 -7 ~it~t).The provisional negative fonn is madebyreplacingthefinal

~It)of the present negative form witht~ ~ttltf.This verbfonnis used to express an"if~statement \vhen the desiredgoalis clearly un~erstoodand \vill be realized·'provided that" a

certainstate is attaineJor a certain action occurs It alsoappears inother special patterns that arediscussed later.By\vay of analogy, the provisional affinnati ve fonn of<: 65~ is expressed as-r65tt~i; the provisional negative fonn of<:~ ~ becomes C:tet ~ttl~i

3 K n~JiJ~-r AB = C -r~tl~i, 'SA = Ie -r:~ ~

0.7) causative verb

The present/future affirmative form of a causative verb is createdbyreplacing the final Q

with ~it~ foranru-verb(~.Q ~ f~ ~itQ)or by replacing thexuwithxa+ it~ for anxu-verb(111 <~111 n\ it~).Irregular verbs are treated as follows: <~ ~ ~ ~it~;9 ~ -7

~it~.All causative verbs are classified as ru-verbs, so the present negative form of any

causative vt;rb is madebyreplacing thefinal Q of the present/future affirmative form(ofthecausativeverb) withtJ v). Acausative verb indicates that someone (or something)iscausingsomeone (or something) else to carry out a certain action or is allowing someone to carry out acertain action

1.~~a ~:~tG-C, ~*~ a +iO ~~t~~i!tt~t, ~~(})JJt!c:~*lkO)-=t!C:~d:-fk

0.8) representative form of a verb

The representative fonn (also known as the frequentative) iscreatedbyadding t) to the pastaffirmativefonn.This form most frequently appears in the pattern \\/hereby two different verbsare used in succession, followedby9 Q: VIt::. fJV2t:: fJ 9 ~ or \' 1t:: t)V2t::.tJ G t:: Onoccasion, only one verb or three different verbsmaybe used in this \\'ay.This form serves to

express representative actions orstates~which are selected from a potentially longer list of

actions or states The two examples given above could be translated u(I> (will) do such things as

VI orV2,~'or~'(I)did such things as VI or V2," respectively

1 ~0):: c'i, lJl~O)t>0)(.:-.Jlt~L~.9~o)l:, ~*O).m~~lt)~ra,n~tr~n\Jt~t>, IYJE~tl§ ~t1~m.-r ~J t:: tJ, ~ t~ ~d:~f4:~ft(J)~.:6~lt*-c' ~J t~fJ 9 ~ t~CO)~

miJ\ t;, ~tl;6~:lFiiJ~*t::,,~d:m.-r~Q1iit':mIt)~tt-Clt)~

2. t:: C;t~i, 7J~EJ(J~JJJO)rtJ'~~~t1c:~1Dfit~C~@lm-rt&-:Jt:: t), ~~~O)rtJ'~~7J

~*-r:S~tJ~;tt:: fJ9~

3. t:: C: X tf, iti{tJt~j:ftJml·:mIt)Q;O\~lm ~:ffl ~)?J tr~ -c:~'iE ~:t~J t::. fJ/F~'iE ,:t~J t~

~J9~

0.9) tentative form of a verb

The tentative form (also known as the volitional) is created by replacing the final ~ with J:

:> for an ru-verb(Jt~ ~JtJ::-j)or by replacing the xu with xo+ -5 for an xu-verb(JJ'9~

~~'5 ). Irregular verbs are treated as follows: <~ ~ ~J:: 5 ; 9 ¢ ~ L, J:: :>.When used atthe end of a sentence that involves human action, this verb form canbeused to express the

writer's volition or will, thus saying, "Let's " or "We shall " In allother instances, this fonnindicates the writer's hesitation or uncertainty regarding the content of the sentence In theseinstances, a word such as~'probably," "perhaps" or "may(be)" canbeadded to the content of thesentence to convey the tentative nature of the statement The combination of the tentative form of

a verb and C 9 ~ indicates either that an attempt is being made tocarryout the action indicated

bythe verb, often with the suggestion that this attempt is not successful, or that the action

indicated by.the verb is about to occur In each instance, the reader must determine from thecontext which meaning is intended

1 z:O)d1.~tt~~~ft L,d:::> ~9 ~c:~, Ara'(1)g~l:J:: ~ L~1Dfi~.n¢ :t>(1)*C'~

0.10) desiderative form of a verb

The desiderative affirmative fonn of a verb is createdbyadding t::: v\ to the conjunctive

affirmative fonn This form is used to express the writer's (or speaker's) wish to carry out acertain action, and could be translated as t.'(l/we) wish to " or "(Jlwe) would like to " Thedesiderative affirmative fonn can be converted into many other forms In such conversions the

5

-desiderative is conjugated as an V~-adjective. Thus, the desiderative negative form is made by replacing the final v~ of the desiderative affirmative form with <t~v~.This form indicates that the writer (or speaker) does not wish to carry out a certain action.

2. *.z*~~ 0t~ vlJmf~)tTtJ:b~SJZ)t~d:.K 1 ~mv~-Cnf~f~~tt, nf~)tc:t~~

3. ~ G~:ArJ3,-m~* ~:~v~-r, ~1&13"J~:~d:7°D 7"7 A~tJlUf~ t) ~: EI~ ~m-c'mff~~

f~/FGt~ v~c: vl 55iV~~~7J~d!> ~

jJ'Ycombine; ::Jry fit, suit

~('5)to fit, to suit {vi}; ~(bit.Q)to join together {vt}

mathematicslogic

set, collectioninstance, case

l:I / limit, restriction

iJ)~'(.Q )to limit, to restrict

1R€~R.ft

~~R_ft

bl:l/~::Lry:1ry::Lryl:l/~::Lry:1ry

infinite setfinite set

experiment, trialreal number

~ ~ =z.ry£ollection, gathering

~-::>(~ Q )to assemble, to meet{vi}; ~J (~ Q )to collect, to gather{vt}

~_ft !Jry~::L ry :1ry empty set

~3 ry disposition, nature; t'1 attribute, gender, nature

7

-stabilitycharacteristic

~ A; '/ simple, uncovered; element, principle

real number logarithm

'* ~ '1 grand, great, huge, large; -!1+'1 grand, great, huge, large

.:t3.:t3(~v~) grand, great, large;.:t3.:t3(~ ~)size; :t3.:t3(~tel:)grand, great, large

M ~ '1 opposite, versus; 'Y '1 pair

absolute value subject, object, target

;! '* r) law, principle, rule

$j{fj15$

It. 1) principle, reason

GraDlDlatical Patterns

C II¥ [J::] ~~ to name , to call , to know as

cf#J\ [Y3 '.7] T Q to name , to call • , to know as

(Note: The phrase "noun C v) 5"is often used simply to focus the reader's attention

on a particular concept or technical tenn In such cases C v)~ is not translated.)

2 fT~Ij~.~T Q7Caik ~~O)(i, k) ~7.tclP¥~S~

3. x, y E R ~:~;fG-C, ~tlGO)~xy cffJ\T:Q~W E R tJ!t::.ti. 1'JJE*:Q.

1.2) X [*t~] and X [*t~] ~1

The word ~t:: is frequently used at the beginning of a sentence to introduce additional

information, which may support or reinforce a previous statement It is often translated as

"furthennore," "moreover" or "in addition." The expression * t:: ~j:occurs between two

nouns (or noun phrases) and corresponds very closely to a logical "or" operator It may be

translated as "and" or as "or," depending upon the context

1.3) ~:'M [?7~] TQ with respect to , with regard to , for

~:'M [?7~] ~-c with respect to , with regard to , for •

~:'M [?7~] ~ with respect to , with regard to , for

(Note: The phrase ~=~tg-:Q modifies a noun that appears later in the sentence; the phrases

~:~tGLand ~:~tGmodify a verb that appears later in the sentence.)

1. *t:: x ~ 0 ~=~tGL~j:Ixl = x, x <0 ~:.~tGL~j:Ixl = -x c~G, ~I ~x O)~~tf~cv) 5.

2 f:f::to) IE0) 2 ~a, b ~:~tG -C, ~\ 9~:Q EJ~~ n tJ!fi1£ GL a < nb Ct~:Q

1.4) ~ [tJ:] tJ li [t~] J and ~li [-e~ 1)~] To

These verbs exemplify a situation in which·two different verbs can be made using the same twokanji As might be expected, the verb that carries the ON readings andg-.Q is more formal in tone,

9

-while the verb that is expressed with the KUN readings tends to be more colloquial Both of these verbs can be applied to four general situations The first meaning is associated with organization; it can be translated variously as "to be formed," "to be organized" or "to be composed." The second meaning is associated with an abstract concept taking on definite form; translations include "to be realized," "to materialize" and "to come into being." The third meaning is associated with the action

of concluding or signing an agreement The final meaning, "tobevalid" or "to hold true," was formerly associated only with ~t]tLJ, but these days it can be associated with both verbs This meaning is particularly common in technical Japanese.

2. ~~~:~v~-c~d:, AVB ~d:A ~J:.tJB O)~tJ:< c~-jjiO~~tLTQC:v~'5Z:c:~~,*T~

1.5) I:: J: Q depending upon • , due to , by means of

1~J: ~L depending upon , due to •••, by means of

l~J: fJ depending upon •., due to ••., by means of •• (Note: The phrase ~:J: ~ modifies a noun that appears later in the sentence; the phrases

~:J:.J -c and ~:J: tJ modify a verb that appears later in the sentence.)

1. fT~tlO)fD A + B ~d:jitij~iO~1RJ C~O)tJj~~:t2'~tA + B =(a ,K + bik ) ~:J:.J -C~~~tlQ.

2. ~tlG ~£~O)R~c: G-C1J{UQ ~ c~:J:: tJ, E2 O)15-}~O)~e;¢~~~Q

QWJ~~£{~c: v~'5 z: c:iO~d!> Q.

1.6) l::~ ~tQ in • , for , regarding

1~.av~L in , for , regarding •

(Note: The phrase ~:~~t ~ modifies a noun; the phrase ~:~v~-c modifies a verb The expression ~:~ v~ L~d:in written Japanese is essentially equivalent in meaning to the double particle l:~d:,but carries a more formal tone.)

~TQc ~~:, A =B cTQ.

1.7) !t [~Q] ~:\~j:

The expression ~ ~v)~d:occurs between two nouns (or noun phrases) and indicates that thetwo nouns (or noun phrases) maybetreated as alternatives No emphasis or preference is placed

on either alternative This expression is almost always translated as "or."

thought to mean "all (ot)," "every" or "the entire," as this expression modifies the noun that

follows 9~LO).However, the word9~Lcan alsobeused as an adverb, meaning "entirely,"

"wholly" or "completely." Thus, when the word9 ~L appears by itself, the reader is cautioned

to ascertain from the context whether9 «Lis intended to function as a noun or as an adverb

1.9) t~t~ and t~t~1J

The wordt:: tican appear as part of the expression t:: ti(J),which means "ordinary" or

"hardly worthy of mention," or it can be used alone In some easily recognizable situationst:: ti

means "free" or "without charge," but in most instances t~ti is used as an adverb to conveymeanings such as "only," "solely," "but," "however," "merely," or "simply." The word t~tiG

can mean "however" or "provided that," but in many instances a translation such as "here" or "inthis case" is more appropriate These instances tend to be situations in which the writer is

providing supplementary information that is pertinent to the situation under consideration or isproviding information that is contrary to the reader's expectation

2. t~ti., ~O)~)]mO)tI~ft~~~~d:§~~mO)~.~, i§mft~O).G~ ~i&1/J\~fiffi

G-c:t30, 1b< O)m.~:filrmGt~

3. t~tiG Ex ~d:x iO~p(x) ':~J-c7tm9 G~O)C1Jt~C~0)3flf$){ii~~9

1 1

1.12) ~'[i1\tel:6l -r and ~, [i1\tel:6l -rL,~

The word n)tJ:~ ~is used with an affirmative predicate to mean "always" or "necessarily." The expression n)tJ: ~ ~G~ is used with a negative predicate to mean "not always" or "not necessarily."

3 f3lJJftJfJ.O)ilAJ]!fRB~d:, ~~~lvcO)t.I~lliAfJiO):Jllil:HfJo).~7,( - ~l,y7ftJfJ

.~AT l\~l& tJ1Jk:>.

1.14) l]{ [-13J:] rJ

The word"& rJ.links two nouns or two symbols, either of which may be modified by an

adjective or a modifying clause Although & rJcarries the meaning "and," its usage is quite

limited & rJ.cannotbeused as a conjunction to link two clauses

no mattter what/which, any

1. fA:~1j {an} ~::.t3V)L, v)n)t~QIEO)fA: c ~I&~ L~, ~~lJ{7J)G9cO)T.AtLO)lJ{an'

am ~:~tG'L Ian - ami<ciO~~t)li:J C:~, {an} ~£*fA:~J*t~~d: Cauchy fA:~J ~v):>.

-Reading Selections 1-1:

~~~-f*(1).~~R -e~Tc~, R ~j:~~:~~.Qaltt.~t>'J

I)4j{1j~~~:~T~jt1• i)x, ye R ~:M~L, ~nGO)fllx+y c~T~lcwE R

tJ~t~ti 1 'J)E* tJ, x + Y = Y + x("ilJ~~J{Ij), (x + y) +Z= x + (y + z) (*6~~j{lJ) tJ~~ tJ lL :J. *t~*fZIJO)Ic0 tJ~fil£GL, f£~O)~x ~:~tGLx + 0 =x it~~tJ ll'J (oO)fil£).

J!~::x E R ~::MGL x + (-x) = 0 ctel:~ -x E R tJ~t~t! 1 'Jfil£T~ ii) x, YE R ~:MG

L, ~nG(1)fI xy cflJ\T~IcW E R tJ~t~ti 1-:J)E*tJ, xy = yx ("ilJ~~j{Ij), (xy) z = x

(y z)(~~~Jtlj), (x + y) z =xz+ y z(?tfi2~J{Ij) tJ~~tJ tL'J * t~*fEIJ 0)1c 1tJ~fil£G L ,

4) 2mO)Ic~J {an}' {b n} ~:SV~L, at ~a 2 ~ ••• ~an ~ ••• ~b n~ ••• ~b 2~ bl I¢\'J lim(b n

- an) = 0 -r:d!>n~t, lim an= limb n=C ctel:Q C E R iO~(tc.ti. 1J) fi1£T~ (grp'./J\~o)mtJll!).

5)Ic~J {an} ~:.t3v~L, v~iO\tel:~iEo)~ C ~~~ -C~, ~QlJ{I¢\ G;tO)T~LO)lJ{

an' am ~:'MGL lan-aml<cl¢!~tJtL:Jc~, {an} ~~*Ic~J*t~~J:Cauchy~~Jcv~5

~IcO)~*Ic~J~j:~, rtl~R ~t>J (~IcO)5G«Ujt1)

~tL-r:IRJ-?t~~:~5il*~Ic(1)~~~~i2.~t~~m~~J, c v~:> (1)iO~!LIc~Jd!>Qv~~j:!L~~(1)~*~tJ:)E.-r:d!>~ ~n~j:, ~M=F~0)'!T/71J /7· c '7/~bft, il*

~d~.0)~~~V-~3/, ~m~?t~~~~~~O).~~O)~.,M~.~~(1)~.m~)EtJ:c~::.m lt~GnLlt~~ !LIc~.mV~, il*~~~~~U)l!ft{M~~1-~l::-t / 7 ·

7J)vD~ C e:t~1tt-Cv~Q ~~~~*~fJJ~~)ta9~~J:: fJ tt>~tJ: v~=Frl3'~~~Qi1i$a9JJ~O) JJJtmJ~iOt~~ ~tt-c v~Q. ~m1: G~tG~1, !L~c ~J:~ O).~!L~ ~mT.1-4:

IJ\mtltJ:~L~~~d:)v-v'Y ~O)e:t 5tJ:if$a9tJ:tI.~:e:t-:J-CfFttQ. *mtl~:~d:~

-Tft1i, t&MfI~tJ:CO)~Jl~a~::t!vj'<!L~n~7?lIJ:If'fl~tJ:!L~~jc G -cflJm~ tt~ GtJ~ G~.flfljmO)t~~~:~d:, tt~~.~tJ:lj{.-c'~~~tt~}ajWl~j~, M!mTQ~~::tt

At-C}a]Wlnt+7t~::~<, 1}ajWll:~tt>$7t~~: tt>~ G7J\tJ:mJ{ljtt7J~tJ:<, 7t~~JtIjc~!R

liJ~~::OOT~~~~afi~~~::~mT~~{~~L~nt1fm~~Q •~!Lf{~J {Uk} ~d: to, 1,

, N-l} (t::.t!.GN = nS ::> 1, n ~d:fI~m 1mO)*~~) l:0).1I-~7t~~::~v~, vk =

uklN ~d:ilIf~a9~:: (0, 1) l:0)i!!~-~7t~~::~5 fmO)if$aiil~d:TAt-C, ~tt7J\Gii~tJ:~.~:e:tJ L~~~~~• •waJtJ:i!!rt7t~~f{F( •)~tt>:J!Lf{~d: F-1(V k ) ~~)fTtt

~1e:t V~7Jt, -f?iJ3t~1f*jR.W~tJ: cO)if$~tJ:ttJ5~::J::fJ atJJ~jj$~~~ GttQ ~ C7J~

1950~{-t~: J von Neumann ~::J:: fJ7J'~tl, ~O)f~1b<o)I=Jc7J~tJ: ~ttLV~Q

1-5:

~Lf{O)~~~~M~~:WlJAtQ~::~J: 1.*~~c~1Ltt~~ce:t~1tt~~at~ai~~~iimT~ 0<vk<I~1l5]j\wk=[mvk]E{0,1,···,m-l}~1l57J\, {uk}O)1f~~j~l

bd)l(c 2+tf)+i«be - ad)l(c+tf» (t~ti.Gc 2+tf ~0) ~:e:t-:Jl)t~~ 1JD$c*~~::JV~-CJJJ~$JtIJ, *S~$JtIj, 7t~$JtljiOt~ t)1L!>, 0 = 0 +iO ~1JO$O)~7G, 1 = 1 +iO ~*

ib ~:~tGl, a -ib ~ a O)3t~~fl~f{C v~5

1 5

0)~f*7J)GtJ:.o.~~ {xlax)} d!>.o v)~j: {x;ax)} c:~g- .g;J;t~~{a} ~d:7Cat~t! 1:J7J)

GtJ:.o.~-c'd!>fJ, a:/;bO)c~ {a, b} ~d:2:J0)7Ca, b7J)l3tJ:.o.~~d!>.o •~A

n~~~RmO)7Cn)l3tJ:Qc~A ~~~R.~cv)v), A n~~~mO)7C~-2iuc~ A ~~~R.~cv)5.

• ~A, B ~:::t3v)-C, A O)7C7J~g-~LB ~::~g-.oC~, A ~J:B O)$?t.~-ed!>Q C: v) v), *tc.A ~d:B ~::-2i*tl.o, d!>Qv)~d:B ~J:A ~-2iUcv)5 ~O)c~~2~AcB~m

v)G. ~O)~)E~A<ZB c~g- {:EJito).~ A ~::~tGL ~cA ~d!>.Q A cB :t3J:rtB

cC~G~AcC-ed!>Q.AcB:t3J:rtBcA~G~A=B-ed!>Q.AcB~A:/;BO)

c~, A ~d:B O)~$?t.~~d!>Gc v) 5.

~2~~~~~J:, f(~0)d!>G~.Q?tlf~::~im~::mv)Gtl~~~a9tJ:~~~f(~a9~2~i!

~mv)-Cif~g- Qf(~d!>~ v)~J:~~~O) 1$r~-c'd!>JL, f(~~~~(f(~a9~J.m~)

*tc.~J:J.m~a9~~~c~J:~~tlQ Z:Z:-c'if~~tlQ '~J.ma9' tJ:~~~::, :t30):t30)0)

J.m~~::~~0)~J.m~~~~:J~t1JD;tQz: c ~::J:J -C, MJ< 0)f(~a9J.m~iO~1~ GtlQ O)-c' d!>G.

'A *tc.~J:B' 'A 7J):JB' 'A tJ:l3~tB' 'A -c'tJ:v) , C:v)5trrlm~, ~tl~tl,

A vB, A A B, A ~B, -,A

C v) 5~2~-c'~g- A v B ~trrlmA, B O)~J.mfl1*tc.~d:.~, A AB ~~~fJl*t~Jd:~

A~B c.~, 'A C: B C~J:(PJ~*tc.~J:(PJfrnI-c'd!>Q' C~U f(~~:::t3v)-c~J:, A vB

~J:A:t3J:.rtB O)1/'tJ:< c:'b-1J7J~JJXlig-~c:v)5 ::,c~Jit~g-~ *t~, 'g-~-Co)

~-i-r :¥3 rJ row, line; :JrJ journey, line

v) ( <) to go; t3 :.t~( 5 ) to conduct, to perform

relation function

significance, meaning definition

series high grade/class

matrix square matrix

coordinate system coordinate axis

mode, method, form, system equation

numerical differentiation differential equation

_ 1::3 r) mark, signpost, target

~~{~ 1:: 3 r):;.:t/jJ

standardization sample

~ :t part, percentage; 7 / minute; :t / dividing, part, segment

V(7J)~) to understand {vi}; V(~t ~) to divide {vt}

~ A / change, strange

jQ)(;t.Q)to change, to revise {vt}; jQ)(V.Q) to change, to differ{vi}

n $ r) direction, side, way

jQ)t:: direction, manner, person {honorific}, type

inverse matrix zero matrix

Grammatical PatterllS

2.1) ••• ~c:IJfa, [t3t3] lt~

Jlft [Itl> ttl] tJta, [t:>.s] tt~

C~1Jta,[t3t3l It~

it often happens that , often •

it often happens that • , often •••

it often happens that • , often •.•

2 -~,:, ~Q~ra'J:~=~~*~~/"\ '9~C~, :cO)~ra'pq,: 1JO)£lil~wa~m)E9tl~t, ~tt~=J::J -c~~*n)-~':~* ~~f;iJ'~~~)

3 f{~O)~Wr'7tffC'~j:, -t-0)~~'=£-:5't,,)-C, -t-tlttlO)~lt)it~-C~J&~ t,,)'3~~

fflt·J~ ~ c:tt~~t,,).

respectively, individuallyrespective, individual, each

1.~=A, 'A = -A c-a~ (1£11)fi~lj~~ntn~tftJ\f-rY!J, ~ftfi9fJ*t~'·j:~~tf*fi~IJ,

2.4) ••• I: [:tJ /] TQ concerning , related to _., for •••

I~R[13 /] L,T concerning •., related to •••, for •••

••• I~DU[13 /] L, concerning ,relatedto _., for •••

(Note:The phrase ~:009Q modifiesanoun; the phrases ':00 Gland l:R G

modifya verb.)

I. ~'5 9 QC, K l:O)fPlC:~O)fi~JO)~-1*~i1J[]it':J~ L,.-C KhD1f¥~t~9

1 9

-2. y O)x ~:~9:Qmn ~~~O)~~~~ y', y",

3. m~0)l&*~:OO9:Q-t3 ~tJ:It! ~d!>~j:Q

2.5) J: '5tI.

This adjective indicates a similarity or other relationship between the noun that it modifies and the word or phrase that precedes it If J:~tJ: is preceded by a demonstrative adjective (see

example 1), it is usually translated " kind" or " type." However, when J: ~tJ: is preceded by

a noun and the particle0) (see example 2), it is usually translated "like " or "such as " If J:: '5

tJ: is preceded by an affirmative predicate (see example 3) or a negative predicate (see example 4),

it may be translated "that ," "such that ," "for which " or "of the type that " The choice among these four possibilities is influenced by whether the subject of the predicate is the noun modified by J::~tJ: or whether the subject appears along with the predicate in the modifying clause that precedes J::~ tJ:.

a noun and the particle 0) (see example 2), it is usually translated "like " or "as (with) " If J::

5 ~: is preceded by an affirmative verb (see example 3) or a negative verb, it indicates that the action described by the verb that follows J:: 5 ~: is being carried out to achieve or to avoid,

respectively, the action or state described by the verb that precedes J:: 5 ~: In this case J::~ ~: is most commonly translated "so that ," "in such a way that " or "in order that "

1. ~tl*O)~~ 7 ~7 A~Bt~~~tJ:c~d:, ~.*it~::O)J::5 ~:mv~ Gn~~{?iJc v)jt

~.

2. fT~IjO)m (tr.t;) O)~lt~fT, ~ (1:~) O)~lt~~1jcPflt, J:~CfT~Ij~(a ik ) O)J:: '5 ~:

3 ~tlt1ilJHlt, ~1iDHK:ff, Htm-lttJ: c,t, ~O)J:: 5 tJ:ff.1I(J)t::-rlJ, -rtt~tlO)m~,:

Ji9~J: 5l=~<~t1t~ ~(J)-r:65~

2.7)t~~tand ~;t

The particlet~~tusually carries the meaning "'only" or "solely." When t~~trefers to aspecific numerical value it maybetranslated "only," but it may also mean4~exactly"or~Justthisamount-no more, no less." The panicle ~.it means "if only" or "so long as" when combinedwith a verb in the conditional fonn, but means "even" when used after a noun In some cases theparticle-r:is inserted after the noun and before ~it.

1 MAB~d:AO)~J~c: B O)fT~tJ~-~9 ~!jJ}-g.,:t~~tAB=(C ik ) (c il=LaiJb jt ) ':J:J-r~

it sometimes happens that _., sometimes •

it sometimes happens that •••, sometimes •••

it sometimes happens that •••, sometimes

in other words, namely, that is (tosay)

in other words, namely, thatis (tosay)

-2.10) nounl ~/~j: noun2 cTo

clause + cTo

(we) let nount be noun2, (we) denote nounl by noun2, (we) take nounl as noun2 (we) suppose (clause)

1 Euclid 1JZmlE 2 l:~:, 1J~ O~Thl~9 ~ 2 Thl x'x, Y'Y ~c tJ, {}[O)!k~ 1 ~~&)-Ct)~t~t, E 2 O)Thl~&.*7J~l~Gtt~

2. {~Icli9tJ:7tIf-r~d:, -~~:1*~~tJ:C~ 1J~&)Lt)V)-C, ~tt~::fii~C:Q~O)~

~d:cannot be used as a conjunction to link two clauses.

1 ~ GPk(X), q(x) iJ~D -c'lEj{JjtJ: 6 ~t, (2) ~mt~GD -c'iEj{fj (~\'-9G ~ 1flffi-c'tJ:lti ) tJ:

my(x) 7J~t~ti.1 :Jfftt9Q

2. ~ G~2:.~:~d:-~O)*~li9tJ:~ tJ~f~rffl7J~-2i~ttLV)tJ: vi~9tt~t, • tJ JS G1TVttt~.?ltlO)~~~d:11ll~li9tJ:~rzg~:0)~~ c~<~O) c~it GttQ.

fljffl9 QJ~-r~&fI T~ ~«~A ~A T b, ~T~~«~A ~A T b ~rRBIJ~ttQ.

2.13) ltiO~t> moreover, furthermore, in addition, not only that

1 D I*J-r:y(x), y'(x), , y(n)(x) ~~9«-Cil~-r:~QJ:: 5 t~ (1) (J)flilt.y(x) ~~ 1J lt~\'t>

we know that , it is known that ,

we find that , we have learned that

Reading Selections

ffJIJ (f{219-220)

K ~J:ff:~O)!I~t~~J: (~~PJ~)~C9:Q (K C L,-C~f{~ R ~t~~J:.*f{~ C ~~X:Q

~friO~~v) KJ:O)fT~Jc~d:, K~:~9:Qmn1i0)7Caik(i=1, , m;k=l, , n)

(J)'$ (J)J: :>tJ:~1JWO)ft2~~ v) v), fT~J~f¥jJ5X:9:Q7Caik ~~O) (i, k) J5X:7tCPf~~

a l l al2 a1n

a21 a22 a2n

J:~~rr~J~<V G <~d:(m, n)~fT~1jCv):>. *f~:(n, n)~rr~J~n '$ O)iE1JfT~1jCv)

5. -~(J)~0)~mWfT~ljcv)5~c~~:Q fT~IjO).(~ti)O)~lt~rr, .(J:r)O)~lt~~JcPflt, J:~~fT~J~(aik) O)J: '5 ~:Pm~C9:Q ~ c ~~:Q aik=O (i =l-:k)~~~iE1J1T~Ij~~tftJfT~J, ~tftJfT~Ij~9«LO) au iO~~ L,v) ~(J)~An7-fT~1j c v)'5.

*f~: t~ t~ 1fT7J\ 6tJ:Q fT~Ij (a l ••• an) ~ K J:0) n '$ O)lT/'\ 7 1')v~ t~ ~d:./'\.7 1')v,

~v) 5. fT~IjO)fl1A +B ~d:Jilij~iO!fP1 C:~O)~fr~:ti~tA +B =(a ik+b ik ) ~:J:J L~~~

n, fiAB ~J:A O)~ljf{cB 0)1Tf{iO~-~9.Qtifr~:ti~tAB=(C ik) (C ik= "Laijbjk) ~:J:J

~t::: K 0)71:C:1T~1JC:O)fi~ a(aik)=(aaik), (aik)a= (aika) ~:J:: ~ L~~9.Q ~'5 9.Q

C, K l:O)fPJG~0)1T~1J0)3k~~J:1J[I~~:~GL K1J[I$~tJ:9 ~t:::'1T~IjO)fJ~=JV~L

~J:~fr7*JtJj, 7t~27*J{Jj;O~J5X:li9G. ~JL K J:(J) n'$ ~fT~J!IC v) v), Mn(k) ~t~ ~J:

i}[7C ctJ:G 9 «LO)J5X:?tiO~ 0 -r~.QJ: 5tJ:fT~Ij~~fT~1jCV)JL, fP1 G < 0 -r~9

~t::: (i, k) /1X:?tti~tiO!1 -rft!!O)/1X:?tn!::' C:~'c: < 0 ~~Q1T~Ij~ E ik C:9n~i,

~fT~J¥{ll:C: v) 5.

*t:::.Mn(K) O)fT~JA ~:~t L" L AA- I=A-IA =I c:tJ:~fT~JA-I lO~ffl£T~ C: ~, A-I ~

A O)~fT~1jC: v) v), ~fT~J ~*.fT ~fT~J ~ (K ~:-t3 ~t ~) IERrjfT~J*t~ ~J:m~fT~J cltFT

~ A O)~fT~J~J:~ Gffl£Ttl~i, -it~:~*~ KIO~m~tJ:G~1, fT~JA lO~iERrjfT~J

-c'd!>~t:::.~O)~ftF~d:fT~IjJ:t JAIIO~KO)m~Jt-c'd!>:Q:: C:-c'd!> t), C: <~: K1O~f*~tJ:ittt,

(m, n) ~fT~1jA =(a ik) O)fTC:~1jC:~Atl~~ -C-c'~:Q (n, m) ~fT~1jA'=(b ik ) (b ik=

a k ) ~A O)titlfT~1jC: v)v), tA -c'7J'T::C:7J~?9v) K n~m~-c'AB = C-c'd!>tl~1, tBtA = tC-c'd!>:Q tA =A, tA = -A c:tJ::Q (lE15)fT~Ij~~tl:ftl~t~fT~J, 3Cf\:;fT~Ij*t:::'~d:~~t

ltFfT~J, &:~tltFfT~J C:P¥v'S~ IE15fT~1j A =(a ik ) -c' a ik=0 (i < k) -c'd!>:Q ~0)~ ~-Jl)fT~Ij,

aik=0(i >k)-c'd!>:Q~0)~ J:=Jl)fT~Ij, jJIij#'@jbit-C¥~:=Jl)fT~J C: v) 5.

Euclid.lJlWE 2J:~:, 1J~ o~ill3CTG 2 ill*j x'x, Y'Y ~c t), ¥{ll:0)*~ 1 ~~&)L-t3~t~i, E20)ill3C~~*1O~1~Gtl~ TtJ:b!> , 2ill.x'x, Y'Y~c!>G~J~O~OcT :Q~~ill R C:J!tJ: L" L, E2(J) 1J~P tJ) G:: 0) 2 ill*j~:-t30 Gt:::.~.O).@ ~~ tl:ftlx, y c:Ttl~1, J~ P E E 2 ~d:, ~(J)~~c J::~itl:Q~f{o)~Jl (x, y)E R 2 ~:J::J

-~~:, d!>:Q~r~'J:~:~~*~~AT:Q C:~, ~O)~ra'f1\J~: 1JO)t!Uf~w~m~T

tl~i, ~tl~:etJ L~~*tJ~-:li~:~* ~~'@jIO~?9V) .lJlW £2 J:O)ill3C~~*~~d:,

L?ltl~::'C~:ett), E20)~J~0)~~IO~~*G tJ:-t3, m~~:J::J-c~d:, E20)~~$dJ~tfJmO)~f{ill*jc GtJ:v)l:', JI~tJ:~f{RO)§!l£~J~tt:::.~O)~mv)G::'CIO!d!>G. ~t

f{15DN*If, ~$15DN*If, ft~t*IftJ: c~J:, :: (J)J:::>tJ:fJ!~O)t:::.~, ~tl:ftlO)m~~:JlTGJ:::> ~:J< Gtlt:::.~o)-c'd!>G

f{~o)-~~~=:Bv)-c, ~f{~~~c:~<(PJC::li~~:mv)G::' cn!?9v). ~O)!j!'@j~d:,-:li~t~C(PJc:~O)-c'd!> G GtJ) G, ~J cJ.tv):li~~:mv)-C, C: <~:-~~t~O):: c

~ l1afi~f{, (-ite'tJ:v)) -~O)~t~O)::c ~?91afi~~cv):> :: C~d!>Q.

~~O)~wr~?tJfl:'~d:, ~O)~5e~:t!"=Jv)-c, ~tl:ftlO)~v):li~-c'~~c v):>~H~

m v) Q :: C:7J~?9v). $fJT~tJ:?tJfe'~J:, 1~n!~~* t:::.~d:~*~0)::' C: n!?9 <, ~G <~J:

~tl~tl~~1~~f{*t:::,~d:~*f{1~~~C:J:v'S~ C <~:, ~~~~~f{d!>Qv)~d:~*f{O)m'@j-cd!>Q~~~=~d:, ~n~n~~f{*t:::'~d:~*~~cJ::v'$~~ c ~d!>Q *t:::., ~~

~n!~f{~ra'~:~*tlGJ::> tJ:~f{ (*t:::'~d:fjl*~) 1~~~~d:~Jt~~c:J::~ttlQ:' c ~

2 5

-~ tJ, 7c(J) Ifj~ GLm~~~~~~nQ f~~EJ9tJ:7}lf~~j:, -~~::'!*~!ItJ:C~ 1':)~&'JL:t3v~L, ~tL~::iii~ c~ ~(J)~~~ce:t~~:: cn~~~ ~(J)tjj~~j:, ~~~(J)

.~~::~CLlI~tJ:~~iO~.~n, ~~~::~CL~lJIJtJ:~iO~J~t6nQ t~c;t~~, ~.~, iii~iO~c ~~::~~(J)~~~~Q C~, /(t) =/(-t) ~3;Q~~f ~f~~~, /(t) =

-/(-t)-c'3;Q~~/~~~~Ctt~:> *t~~~O)JmJ¥:~f*~f*':)~~,TtJ:V!> t 1<t 2 tJ:

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