english russian science dictionary

7/27/2019 English Russian Science Dictionary

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arXiv:math/0609472v6

[math.H

O]2Apr2012

English Russian Science Dictionary

E-mail address: [email protected]: http://sites.google.com/site/alekskleyn/URL: http://arxiv.org/a/kleyn_a_1URL: http://AleksKleyn.blogspot.com/
http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6http://arxiv.org/abs/math/0609472v6mailto:[email protected]://sites.google.com/site/alekskleyn/http://arxiv.org/a/kleyn_a_1http://alekskleyn.blogspot.com/http://alekskleyn.blogspot.com/http://arxiv.org/a/kleyn_a_1http://sites.google.com/site/alekskleyn/mailto:[email protected]://arxiv.org/abs/math/0609472v6


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. English Russian and Russian English dictionaries presented in

this book are dedicated to help translate a text from one language to another.

I also included the bilingual name index into this book. - - , -

, - .

.


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1. Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3. English Russian Dictionary . . . . . . . . . . . . . . . . . . . . . . 133.1. A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.2. B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.3. C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.4. D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.5. E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.6. F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.7. G . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.8. H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.9. I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.10. J . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.11. K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.12. L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.13. M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.14. N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.15. O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.16. P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.17. Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.18. R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.19. S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.20. T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.21. U . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.22. V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.23. W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.24. Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4. . . . . . . . . . . . . . . . . . . . . . 354.1. A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2. C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.3. D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.4. R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.5. S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3


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4

4.10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.18. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.22. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.23. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.26. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.28. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.29. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5. Name index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

6. . . . . . . . . . . . . . . . . . . . . . . . . . . 61

7. . . . . . . . . . . . . . . . . . . . . . . . . . . 65

8. . . . . . . . . . . . . . . . . . . . . . . . . . . 67


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1

Preface

According to legend, all people spoke one language. Then they decided to buildup the tower of Babel in order to climb up to the sky. To stop project, L-rd confusedtheir languages.

Much water has flowed since then. A lot of different occupations appeared.Occupation of interpreter is one of the most ancient and important. At the sametime this is art.1.1

Lively text contains phraseology, slang. It is hard to translate it one to one.Translation of sonnets by Shakespeare from English into Russian is very strikingexample. You can compare translations of sonnets by Shakespeare made by S. J.Marshak and A. M. Finkel. They are different works of art although original iscommon.

I use sonnet 90 for the purposes of illustration.

Then hate me when thou wilt; if ever, now;Now, while the world is bent my deeds to cross,Join with the spite of fortune, make me bow,And do not drop in for an after-loss:Ah! do not, when my heart hath scaped this sorrow,Come in the rearward of a conquered woe;Give not a windy night a rainy morrow,To linger out a purposed overthrow.If thou wilt leave me, do not leave me last,When other petty griefs have done their spite,But in the onset come: so shall I tasteAt first the very worst of fortunes might;And other strains of woe, which now seem woe,Compared with loss of thee, will not seem so.

Translation by S. J. Marshak.

,

, . , !

,

1.1It looks as in spite of this human is not ready to build up new tower of Babel. I believe

people should learn to understand each other, no matter what views they may have. Mankind

must become mature to get this goal.

5


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6 1. Preface

.

.

, , . , , ,

, .

Translation by A. M. Finkel.

, , ! ,

, . , , ., , . , - ! , . , .

.

No doubt, to appreciate the difference of these translations at its true value,we need to know well both languages. However I add few notes.

Although both translations describe similar situation in the life, there is onestrong difference. Translation by Finkel is foreboding of disaster which is possiblyunavoidable. Translation by Marshak is epicenter. Although translations are different,each of them leaves indelible track. Each of translations reflects individual perceptionof interpreter, his emotional experience. The strength of translations is that Marshakand Finkel are co-authors of Shakespeare.

There exists opinion that it is much easier to translate technical text. Unambiguityof translation of term is one of the reasons. Another reason is existence of set ofphrases; using of such phrases make easier realization of the text.

However I do not agree with this point of view. It is not enough to write

good theorems for writing of the paper. We expect that somebody reads the paper.And good style is important here. This is more important when we translate apaper from one language to other. Sometimes it is not easy task to put text intoframe prepared in advance. Moreover, any text has emotional color which expressesauthors relationship. In this case we need somebodys help.


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1. Preface 7

Writing papers I frequently use outside assistance during translation. Today wecan find such help because of development of software and internet. For instance,you can find a lot of forums on web page

http://forum.lingvo.ru/actualforum.aspx

and somebody in these forums can help you to translate text. I frequently use helpof the forum "English-Russian-English translation"

http://forum.lingvo.ru/actualtopics.aspx?bid=18

and I am very grateful to everybody who helps me to translate my papers.Usually I am looking for help in the forum either I meet unusual grammatical

form, or expression which I cannot translate unambiguously. Very often when Itranslate I feel that I need to change original sentence in order to make it moresufficient to my ideas in both languages.

When I feel that I need additional assistance, I visit Google, book search,

http://books.google.com/bkshp?tab=wp

where I can find appropriate terminology or sample how to write proper sentence.In Russian literature there is good custom to mention name of interpreter.Because I turn for help to forum, it is hard for me to follow this custom. ThereforeI decided to tell about people who help me in the book dedicated to process oftranslation.

Initially I started this vocabulary as immediate helper to write papers. I wrotevocabulary slowly. I put into vocabulary terms and definitions which was importantfor me and I met in books published on both languages. When vocabulary becamelarge enough I decided to make it available for others. I also took into account thewishes expressed in response to previous versions of vocabulary. This vocabularyinvolves only physical and mathematical terminology. Word may have an alternativetranslation or different meaning in common speech. However I did not include thisinformation into vocabulary

I also included the bilingual name index into this book. I added into this listonly names which I met in both Russian and English texts. However there is onemore problem which I meet when I translate papers. Sometimes the relationshipbetween the writing and and the pronunciation is not clear. It would be good ideato add transcription, however I did not make it because I did not have reliablesource.
http://forum.lingvo.ru/actualforum.aspxhttp://forum.lingvo.ru/actualtopics.aspx?bid=18http://books.google.com/bkshp?tab=wphttp://books.google.com/bkshp?tab=wphttp://forum.lingvo.ru/actualtopics.aspx?bid=18http://forum.lingvo.ru/actualforum.aspx


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9/67

2

, . - , . , - .

. . - . -.2.1

, . , -. - . , . . . . . , .

90.

Then hate me when thou wilt; if ever, now;Now, while the world is bent my deeds to cross,Join with the spite of fortune, make me bow,And do not drop in for an after-loss:Ah! do not, when my heart hath scaped this sorrow,Come in the rearward of a conquered woe;Give not a windy night a rainy morrow,To linger out a purposed overthrow.If thou wilt leave me, do not leave me last,When other petty griefs have done their spite,But in the onset come: so shall I tasteAt first the very worst of fortunes might;And other strains of woe, which now seem woe,Compared with loss of thee, will not seem so.

. . .

,, .

, !

, .

2.1 , , . -

, ,

. .

9


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10 2.

.

, , . , , ,

, .

. . .

, , ! ,, .

, , ., , . , - ! , . , .

.

, , - . .

-, . .. - , . - -. , . , -. , , - .

, -. - . - , .

. , , . . . , . - . , , . .


11/67

2. 11

, -. , , , . ,

http://forum.lingvo.ru/actualforum.aspx

, . "--"

http://forum.lingvo.ru/actualtopics.aspx?bid=18

, .

- , , . , .

, , , google, book search,

http://books.google.com/bkshp?tab=wp

.

-. , . , , .

. . -, , . .

. -, . . , - .

. , , - . , . - . , , .
http://forum.lingvo.ru/actualforum.aspxhttp://forum.lingvo.ru/actualtopics.aspx?bid=18http://books.google.com/bkshp?tab=wphttp://books.google.com/bkshp?tab=wphttp://forum.lingvo.ru/actualtopics.aspx?bid=18http://forum.lingvo.ru/actualforum.aspx


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13/67

3

English Russian Dictionary

3.1. A

A-valued function: A- Abelian group: absolute value: ;

Example 3.1.1.

Absolute value on skew field D is a mapping

d D |d| R

which satisfies the following axioms |a| 0 |a|= 0 if, and only if, a= 0 |ab|= |a| |b| |a + b| |a| + |b|

D -

d D |d| R

, |a| 0

|a|= 0a = 0 |ab|= |a| |b| |a + b| |a| + |b|

absorption of photon: acceleration: accelerator: according to theorem 2.1: 2.1

Example 3.1.2.According to theorem 2.1, triangles ABC and DBCequal. 2.1 ABC DBC.

acute angle: additive group: adjacent angle: adjoin:

Example 3.1.3.We adjoin to (2.7) all the equations obtained by equating

to 0 those commutators which are not expressible in the form(2,10).

13


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14 3. English Russian Dictionary

see [English.9], p. 7

(2.7) , -

0 , (2.10).

. [Russian.9], . 13, 14

adjoint group: algebra bundle: algebraic: algebraic complement of matrix: -

algebraic extension: amplitude: analytic in x (x is variable): x (x - )

Example 3.1.4.The following treatment applies to a domain in which ai are

analytic in the s and xs,


, ai - x.

. [Russian.9], . 7

angle: angle of incidence: angle of reflection:

angle of refraction: angular momentum: anholonomic coordinates: anholonomity: anholonomity object: annihilation operator: annihilator: apocentre: approximation: arccosecant: arccosine: arccotangent: arcsecant: arcsine: arctangent: arity: as small as we please: associative: associative law: associativity:


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3.3. C 15

at first glance: at first sight: at least:

Example 3.1.5.At least in the neighborhood of the identity. , .

attractor: auto parallel line: axiom of choice:

3.2. B

Banach algebra: Banach space: base of fibered correspondence:

base of topology: basis for vector space: ; -

basis of vector space: ; -

behavior: Bells theorem: bijection: bimodule: binary: Bott periodicity: boundary: boundary conditions:

By Theorem 2,1: 2.1

Example 3.2.1.By Theorem 2.1, a= b. 2.1, a = b.

3.3. C

canonical map:

Example 3.3.1.The map fofGontoG/Hconstructed above is called canonical

map, and G/H is called the factor group ofG byH.


f G G/H, , - , G/H G H.

. [Russian.2], . 28

Cartesian coordinate system:


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Cartesian power: Cartesian product: category: Cauchy sequence: causal relationship: - causal scalar field: causal vector field: chain rule: change of coordinates: change of variable: chaos: chart over U: Uclosure of the set: closure operator: closure system:

cluster point: coarsest topology: cofactor of matrix: colloquia: colloquium: column vector: combinatorics: commutative diagram: commutativity: commutator: commute:

Example 3.3.2.Because P commutes with H, the proper states ofH can be

labeled by proper values ofP.


P H, H P.

compact-open topology: - comparable topology: complete division ring: complete field: complete lattice: complete space: complete system:

completely integrable: complex field: componentwise: conditions of integrability: conformal transformation: congruence: ; conjugate quaternion: connected group:


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3.3. C 17

connection coefficients: conservation law: consider:

Example 3.3.3.Consider correspondence from set A to set B. A B .

continuous in neighborhood: continuous in x: xcontradiction:

Example 3.3.4.The contradiction completes the proof of the theorem. .

contravariant:

convection: convention:

Example 3.3.5.We use the convention that we present any set of vectors of

the vector space as a row. , -

.

converge:

Example 3.3.6.Filter Fconverges to x. F x.

conversely: convex function: coordinate chart: correlation: correspondence from A to B: A Bcosecant: cosine: cotangent: countable set: counter: covariant: cover: covering space:

Example 3.3.7.Consider the covering space R S1 of the circle S1 defined

byp(t) = (sin t, cos t) for any t R. R S1 S1, -

p(t) = (sin t, cos t) t R.

Cramers Rule:

D-vector space:

D-


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creation operator: crystal lattice: curve: curvilinear coordinates: cycle: cyclic group:

3.4. D

D-vector space: D-

decomposition of map: define:

Example 3.4.1.This equation defines the inverse transformation. .

degree of map: denominator:

Example 3.4.2.Let us reduce items to a common denominator. .

dependence: derivative of second or greater order with respect: -

develop equation: diagram of correspondences: difference: difference module:

differentiability: differentiable function: differentiable in the Frechet sense: differentiable in the Gateaux sense: differentiate the function with respect to x: -

xdiffraction: diffusion: discrete space: discrete topology: distributive law: distributive property of multiplication over addition:

division ring: ( )domain: Doppler shift: downstairs:

Example 3.4.3.We sum over any index which appears twice in the same

term, once upstairs and once downstairs.


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3.5. E 19

, - , , - .

D

-linearly dependent: D

- D

-linearly independent: D-

D-vector function: D--D

-vector space: D-

D-linearly dependent: D- D-linearly independent: D- dual module: dual space: dynamics:

3.5. E

eccentricity: eclipse: elementary particle: emission of photon: endomorphism: energy: engine: enhanced: entropy: envelope of a family of plane curves:

enveloping algebra: equation is satisfied identically: -

equivalence class: equivalence relation: Erlanger Program: essential parameters in a set of functions:

Euclidean metric: Euclidean space: evaluating by equating x to the a: a xevent horizon: event space: evidence: evidently:

Example 3.5.1.The only solution is evidently f= 0.


, , f= 0.

. [Russian.9], . 14


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exact sequence of modules: extension field: extension of correspondence: exterior differential: exterior product: external algebra: external power: extremal: extreme: extreme line:

3.6. F

factor: ; ;

Example 3.6.1.To factor a polynomial means to find two or more polynomials

whose product is the given polynomial. ,

, -.

factor group: factorization: fiber: fibered correspondence: fibered map: fibered product: field-strength tensor: filter:

filter base: finest topology: finite dimensional: finite set: Finsler metric: Finslerian metric: force:

Example 3.6.2.In 1935, Hideki Yukawa proposed a quite different field theory

of the nuclear force.

see [English.1], p. 29, 30

1935 - .

. [Russian.1], . 39

the Frechet derivative: the Frechet differential: free representation:


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3.8. H 21

frequency: friction: ; function f ofx: f xfunctional: functor: fundamental sequence:

3.7. G

G-principal bundle: G-galaxy: the Gateaux derivative: the Gateaux differential: gauge invariance: general relativity: generally speaking:

generated: Example 3.7.1.Algebra A generated by the set S is a K-algebra A, S, K-.

generator: geometry: Global Positioning System: gluing functions: Gram-Schmidt orthogonalization procedure: -

graph: graph theory:

gravity probe: group bundle:

3.8. H

Hadamard inverse: has relevance to: head of vector: helical structure: helicity: hermitian form: highest common factor ofp and q: p qholonomic coordinates:

homeomorphic: homeomorphism: homogeneous: homogeneous Lorentz group: homology: homomorphism: homotopic: homotopy:


22/67


hyperfine splitting: hyperplane:

3.9. I

identical particles: identification: identification morphism: identity: iff: ,

Example 3.9.1.a= 0 iffaji = 0 for any i, j.

a= 0 , aji = 0 i, j.

image under map:

Example

3.9.2.

We define the image of the set A under correspondence according to law

A = {b: (a, b) , a A}

A

A = {b: (a, b) , a A}

in a similar way:

Example 3.9.3.

In a similar way, we can introduce a coordinate referenceframe.

.

in general:

Example 3.9.4.However in general this product is not D-linear map., , D--

.

indicatrix: inequation: infinitesimal: ; inhomogeneous: inhomogeneous Lorentz group: injection: insulator: ; interaction:


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3.12. L 23

Example 3.9.5.The observed range of the strong interactions whitin nuclei

led Yukawa to estimate that /c is of the order of 200 electronmasses.


-, , /(c)200 .

. [Russian.1], . 39

interaction picture: interference: inverse transformation: irreducible representation:

is related to: isotropic vector: it is evident that: ,

Example 3.9.6.From (2.2) it is evident that any solution of (2.7) satisfies

(2.9). (2.2) , (2.7)

(2.9).

3.10. J

Jacobian: Jacobian matrix:

3.11. K

kernel: ()Kerr metric: kinematics: Klein bottle: knot:

3.12. L

Lagrangian: lattice: ( )left side of equation: left-distributive:

LHospitals rule: lift of correspondence: ; lift of morphism: ; lift of vector field: ; limit: limit of correspondence with respect to the filter:


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limit of sequence: limit p oint: limit set: linearly dependent: linearly independent: little group: locally compact space: loop (quasigroup with unit element): ( )

Example 3.12.1.An algebra Q=< Q, . ./, > equiped with binary operation of

multiplication(.)and right division (/)and with a constant Qis called a right loop if< Q, . , / > is a right quasigroup such thatadditional identity .x= x is satisfied.


, , .

. [Russian.3], . 39

Lorentz transformation: lower index:

3.13. M

the Mach principle: manifolds with affine connections: mapping: mass:

massive particle: massless particle: mathematical: mathematician: mathematics: mean value theorem: measure: measurement: metric-affine manifold: - Milky Way: mixed system: Moebius band: momentum:

monic polynomial: ; monomial: monotone function: monotonic function: multiple root: multiplication: multiplication table: multiplicative group:


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3.14. N 25

multiplicity ofx in f: x f

Example 3.13.1.

If the multiplicity ofa is greater then 1, a is called a multipleroot.

a, 1, a .

multiply by 2: 2multiply by b: bmuon: mutually orthogonal: ; -

;

Example 3.13.2.Let i be in Jp; since ei Tp and T is the direct sum of the

mutually orthogonal subspacesT0, T1, ...,Ts, the hyperplane ofT

orthogonal to ei is of the form Li+ Tp, whereLi is the hyperplaneofTp orthogonal to ei.


i Jp. ei Tp T - - T0, T1, ..., Ts, T, ei, Li+ Tp, Li - Tp, ei.

. [Russian.7], . 106

mutually perpendicular: ; -

Example 3.13.3.We shall take two mutually perpendicular axes XX andY Y

on a plane, with their point of intersection O as origin on each.


XX YY O.

. [Russian.5], . 21

3.14. N

name index: natural mapping: natural morphism: necessary and sufficient:

Example 3.14.1.


26/67


In order that a system of equations (1) admit solution necessaryand sufficient that there exist a positive integer N such thatequations F1, ..., FN are compatible.

, (1) , -, N, F1, ..., FN .

neighborhood: neutrino: neutron: neutron star: non-Abelian group: nondegenerate form: nontrivial: norm:

Example3.14.2

.

Norm on D-vector space V over non-discrete valued skew

field D is a mapping

v V p(v) R

which satisfies the following axioms p(v) 0 p(v) = 0 if, and only if, v= 0 p(v+ w) p(v) +p(w) p(av) =|a|p(v) for all a D and all v V

D- V - D -

v V p(v) R

, p(v) 0 p(v) = 0v = 0 p(v+ w) p(v) +p(w) p(av) =|a|p(v) a D v V

normed space: nucleus: ()numerator:

3.15. O

obtain by differentiating:

obtuse angle: Occams razor: operate:

Example 3.15.1.Operating on equation (1) with operator V yields an integral

equation.


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3.16. P 27

(1) V, - .

opposite preordering: ordered set: ordering: orthonormal basis:

3.16. P

parallel transport: parallelepiped: parity: partial differential equation: partial ordering: partition of unity: ; Paschs axiom: passage to the limit: pericentre: perturbation: pfaffian derivative: phenomena: phenomenon: photon: physical: physicist: physics: point: ; polology:

polyadditive map: polylinear form: polynomial: ; polyvector: poolback bundle: ; positive definite form: positive integer: power of set: precession: preordering: prime ideal: principal bundle: probability:

problem: proceeding in this way: ; -

projection: projective plane: proof by induction: propagation: proper state:


28/67


proper value: pseudo-Euclidean space: pulsar:

3.17. Q

quantum entanglement: quark: quasar: quasigroup:

Example 3.17.1.An algebra Q =< Q, ., / > equipped with binary operations

of multiplications (.) and right division (/) which satisfy theidentities

(x/y).y = x (x. y)/y= x

is called a right quasigroupp.see [English.3], p. 23

, a, b -

ax= b, ya= b

.

. [Russian.3], . 39

quaternion: quotient bundle: quotient group:

quotient ring: quotient set: quotient topology:

3.18. R

radiation belt: range: ; rational field:

D-linearly dependent: D-

D-linearly independent: D-

D-vector space: D-

real function: real valued function: reciprocal image: reduced Cartesian product of bundles: -

reduced fibered correspondence: reduction of similar terms: reference frame: reflexive:


29/67

3.19. S 29

regression: relation: relevance: ; ;

Example 3.18.1.Distinction between Lorentz and Poincare groups is of no

relevance here.

.

remainder: repeated root: represent: residue: resistance: resistivity:

resonance: restriction of correspondence to set C: C

retract: retraction: right angle: right side of equation: right-distributive: ring of characteristic p: pring of integers: rotation group: row vector:

3.19. Sscale: scattering: scattering amplitude: scattering from crystal: scattering theory: secant: section: segment: seismology: semiconductor: semigroup: series: ( )set of functions: set of power of continuum: sieve of Eratosthenes: similar triangles: simple polyvector: simple ring: simple root:


30/67


simplex: simply connected: sine: single transitive representation: skew field: ( )skew product of vectors: skew-symmetric form: skew-symmetric tensor: solar eclipse: solution of differential equation: -

solve for the c: c

Example 3.19.1.Equation may be solved for the c. c.

spacelike vector: special relativity: sphere: spherical triangle: splittable algebra: D-linearly dependent: D- D-linearly independent: D- star-shaped domain:

Example 3.19.2.This result, known as the Poincare lemma, will hold for

star-shaped domains M Rm, where "star-shaped" means thatwhenever x M, so is the entire line segment joining x to the

origin: {x: 0 1} M.


, , MRm. "" , x M , x :{x: 0 1} M.

. [Russian.4], . 94

stationary state: strictly monotone function:

strictly monotonic function: strongly monotone function: strongly monotonic function: structural constants: structure constants:

Example 3.19.3.Suppose gis any finite-dimensional Lie algebra, so by Theorem

1.54 g is the Lie algebra of some Lie group G. If we introduce


31/67

3.20. T 31

a basis {v1,...,vr} of g, then the Lie bracket of any two basisvectors must again be in g . Thus there are certain constants ckij ,i, j, k= 1,...,r, called the structure constants ofg such that

[vi, vj ] =r

k=1

ckijvk i, j = 1,...,r


g - , 1.54 g - G. g {v1,...,vr}, - g. , ckij , i, j, k = 1,...,r, - g , ,

[vi, vj ] =

r

k=1 c

k

ijvk i, j = 1,...,r

. [Russian.4], . 82

subordinate:

Example 3.19.4.For each open coverUa ofXthere is a partition of unity {b}

subordinate to the cover. Ua X

{b}, .

subtrahend:

summation convention: summer solstice: surjection: symmetric: symmetry: synchronization procedure: synchrotron: system of total differential equations: -

3.20. T

tail of vector: tangent: Taylor series: tensor of order 2: 2tensor product: there exist:

Example 3.20.1.There exists a positive integer N such that equations F1, ...,

FN are compatible.


32/67


33/67

3.22. V 33

Example 3.21.1.Simply-connected commutative Lie groups are called vector

(Lie) groups; unless stated otherwise, they are always given theR-vector space structure defined above.


- (); , R-- .

. [Russian.8], . 7

Example 3.21.2.In this section, E denotes a locally convex space and E its

dual. Whenever we talk of the polar M

of a set M in E (resp.E), we shall always mean, unless otherwise stated, the polar ofM relative to the duality between E and E.


, E - , E ,, M (. M) M E(. M E), , , -M(.M) E (.E), E E.

. [Russian.6], . 212

up to notation:

Example 3.21.3.I can repeat, up to notation, proof of theorem 2.1. -

2.1.

upper index: upstairs:

Example 3.21.4.We sum over any index which appears twice in the same

term, once upstairs and once downstairs.

, - , , - .

3.22. V

valued division ring: valued field: valued skew field: variable:


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35/67

4

4.1. A

A- : A-valued function

4.2. C

D- : D-vector space

4.3. D

D- : D

-vector spaceD- : D-vector spaceD--: D-vector functionD- : D-linearly dependentD- : D-linearly independentD- : D-linearly dependentD- : D-linearly independent

4.4. R

D- : D-vector space

D- :

D-linearly dependentD- : D-linearly independent

4.5. S

D- : D-linearly dependentD- : D-linearly independent

4.6.

: Abelian group : absolute value : auto parallel line : additive group : axiom of choice

: Paschs axiom: algebraic : algebraic complement of matrix;

cofactor of matrix : algebraic extension: amplitude : scattering amplitude

35


36/67

36 4.

x (x - ): analytic inx (x is variable)

4.6.1.

, - ai x.

. [Russian.9], . 7

The following treatment applies to a domain in whichai are analyticin the s andxs,


: annihilator: apocentre: arccosecant: arccosine: arccotangent: arcsecant: arcsine: arctangent: arity: associativity: associative: attractor- : metric-affine manifold

4.7.

: base of fibered correspondence

: basis for vector space; basis of vectorspace : basis for vector space; basis of vector

space : base of topology : filter base : Banach algebra : Banach space : massless particle : infinitesimal : infinitesimal: bijection: bimodule

: binary : Occams razor : Klein bottle

4.8.

: relevance


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38/67


39/67

4.11. 39

4.10.

: engine

: two-sided ideal: operate

4.10.1. (1) V,

.Operating on equation (1) with operator Vyields an integral equation.

: Cartesian coordinate system : Cartesian power : Cartesian product : zero divisor : diagram of correspondences

: dynamics : discrete topology : discrete space : left-distributive : right-distributive : distributive

property of multiplication over addition: diffraction : the Gateaux differential : the Frechet differential x: differentiate the function with respect

tox : differentiable function: differentiability : differentiable in the Gateaux sense : differentiable in the Frechet sense: diffusion: insulator : proof by induction : dual space : dual module

4.11.

: unit sphere : identity

: unless otherwise stated 4.11.1. -

(); -, - R- .

. [Russian.8], . 7


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40 4.

Simply-connected commutative Lie groups are called vector (Lie) groups;unless stated otherwise, they are always given the R-vector space structuredefined above.


4.11.2. , E -

, E , , M (. M) M E (. M E), , -, M (. M) E

(. E), E E.

. [Russian.6], . 212

In this section, Edenotes a locally convex space and E

its dual.Whenever we talk of the polar M of a set M in E (resp. E), we shallalways mean, unless otherwise stated, the polar ofMrelative to the dualitybetweenEand E.


: natural mapping : natural morphism

4.12.

: dependence: problem

: associative law : distributive law : conservation law : change of coordinates : change of variable : closure of the set: eclipse : solar eclipse : star-shaped domain

4.12.1. , , -

M Rm. "" -

, x M ,x : {x: 0 1} M.

. [Russian.4], . 94

This result, known as the Poincare lemma, will hold for star-shapeddomainsMRm, where "star-shaped" means that wheneverx M, sois the entire line segment joining x to the origin: {x: 0 1} M.


41/67


42/67


43/67

4.16. 43

: skew-symmetric tensor: cotangent : connection coefficients x f: multiplicity ofx in f

4.14.4. a , 1, a

.If the multiplicity ofais greater then1,ais called a multiple root.

: multiple root; repeated root: curve : curvilinear coordinates : crystal lattice: torsion

4.15.

: Lagrangian : left side of equation : summer solstice : total ordering : linearly dependent : linearly independent : Moebius band : lift of vector field : lift of morphism : lift of correspondence : locally compact space ( ): loop (quasigroup with unit element)

4.15.1., , .

. [Russian.3], . 39

An algebra Q=< Q, . ./, > equiped with binary operation of multiplication(.) and right division (/) and with a constant Q is called a right loopif< Q, ., / > is a right quasigroup such that additional identity .x = xis satisfied.


4.16.

: to be finer than

4.16.1. F B.Filter Fis finer than filter B.

4.16.2. T1 T2.Topology T1 is finer than topology T2.


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44 4.

: little group: mass : massive particle: scale: mathematician: mathematics: mathematical : Jacobian matrix : Kerr metric: to be coarser than

4.16.3. F B.Filter Fis coarser than filter B.

4.16.4.

T1 T2.Topology T1 is coarser than topology T2.

: Milky Way: polynomial : range : set of power of continuum: factor : angular momentum : monotone function; monotonic function : identification morphism : fibered map : power of set : multiplicative group: muon

4.17.

: at first glance; at first sight p q: highest common factor ofp and

q: covering space

4.17.1. R S1 S1, -

p(t) = (sin t, cos t) t R.Consider the covering spaceR S1 of the circleS1 defined byp(t) =

(sin t, cos t) for any t R.

: positive integer : tail of vector : without loss of generality : without loss of generality : non-Abelian group : nondegenerate form: anholonomity


45/67

4.17. 45

: anholonomic coordinates: neutrino: neutron : neutron star : necessary and sufficient

4.17.2. , (1) , -

, N, F1, ..., FN .

In order that a system of equations (1) admit solution necessary andsufficient that there exist a positive integer Nsuch that equations F1, ...,FN are compatible.

: inhomogeneous Lorentz group: inhomogeneous

: verify directly 4.17.3. , A -

.We verify directly that A is linear map.

4.17.4. -

.We verify the statement of the theorem directly.

: continuous in neighborhood x: continuous in x : irreducible representation: inequation: nontrivial : lower index: absolute value; norm

4.17.5. D

- V - D -

v V p(v) R

, p(v) 0 p(v) = 0 v= 0

p(v+ w) p(v) +p(w) p(av) =|a|p(v) a D v V

Norm onD-vector spaceVover non-discrete valued skew field D isa mapping

v V p(v) R

which satisfies the following axioms p(v) 0 p(v) = 0if, and only if, v = 0


46/67

46 4.

p(v+ w) p(v) +p(w) p(av) =|a|p(v) for all a D and all v V

4.17.6. D -

d D |d| R

, |a| 0 |a|= 0 a= 0 |ab|= |a| |b| |a + b| |a| + |b|

Absolute value on skew fieldD is a mapping

d D |d| R

which satisfies the following axioms |a| 0 |a|= 0if, and only if, a = 0 |ab|= |a| |b| |a + b| |a| + |b|

: valued field : normed space : valued division ring; valued skew field

4.18.

: enveloping algebra

: range : domain : image under map

4.18.1. A

A = {b: (a, b) , a A}

We define the image of the set A under correspondence accordingto law

A = {b: (a, b) , a A}

: generator: conversely : inverse transformation : reciprocal image : poolback bundle : Hadamard inverse : general relativity


47/67

4.19. 47

: anholonomity object : envelope of a family of plane

curves : homogeneous Lorentz group: homogeneous: simply connected : single transitive representation: monomial: neighborhood : closure operator : creation operator : annihilation operator: define

4.18.2. .

This equation defines the inverse transformation.

: mutually orthogonal : orthonormal basis: remainder : acute angle: relation: mapping: identification: segment: evidently

4.18.3., , f= 0.

. [Russian.9], . 14

The only solution is evidentlyf= 0.


, : it is evident that

4.18.4. (2.2) , -

(2.7) (2.9).From (2.2) it is evident that any solution of (2.7) satisfies (2.9).

: evidence

4.19.

: parallelepiped : parallel transport : twin representation: variable : Bott periodicity


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48 4.

: pericentre : mutually perpendicular : at least

4.19.1. , .At least in the neighborhood of the identity.

: behavior : absorption of photon : similar triangles : in a similar way

4.19.2.

.In a similar way, we can introduce a coordinate reference frame.

a x: evaluating by equatingx to the a: subordinate

4.19.3. Ua X -

{b}, .For each open cover UaofXthere is a partition of unity {b} subordinate

to the cover.

: lift of vector field : lift of morphism : lift of correspondence: componentwise

: cover : complex field : rational field : polyadditive map: polyvector : polylinear form: polynomial : complete system : complete lattice : complete field : complete space : complete division ring : total differential

: positive definite form: polology: semigroup: semiconductor : obtain by differentiating : mutually orthogonal

4.19.4.


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4.19. 49

i Jp. ei Tp T - T0, T1, ..., Ts, - T, ei, Li+ T

p, Li - -

Tp, ei.

. [Russian.7], . 106

Leti be in Jp; sinceei Tp and T is the direct sum of the mutuallyorthogonal subspacesT0, T1, ..., Ts, the hyperplane ofTorthogonal to eiis of the formLi+ Tp, where Li is the hyperplane ofTp orthogonal toei.


: generated

4.19.5. A, S, K--

.AlgebraA generated by the set S is aK-algebra

: Cauchy sequence : right side of equation : chain rule : Cramers Rule : LHospitals rule : summation convention: limit : limit of sequence : limit of correspondence with respect

to the filter

: limit point : limit set : passage to the limit : interaction picture: represent: preordering : Lorentz transformation: precession: approximation : reduction of similar terms : reduced Cartesian

product of bundles : reduced fibered correspondence : monic polynomial : tidal acceleration : the Mach principle : adjoint group: adjoin

4.19.6.


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50 4.

(2.7) , - 0 , (2.10).

. [Russian.9], . 13, 14

We adjoin to (2.7) all the equations obtained by equating to 0 thosecommutators which are not expressible in the form (2,10).


: causal vector field : causal scalar field- : causal relationship : proceeding in this way : extension of correspondence

: proceeding in this way : projective plane: projection : derivative

of second or greater order with respect : the Gateaux derivative : the Frechet derivative : poolback bundle : simple ring : prime ideal : simple root : simple polyvector : spacelike vector

: manifolds with affine connections : event space : opposite preordering: contradiction

4.19.7. .The contradiction completes the proof of the theorem.

: synchronization procedure : Gram-Schmidt orthogonalization

procedure : right angle : pseudo-Euclidean space: pulsar : pfaffian derivative

4.20.

: uniform continuity : uniformly continuous function : uniform space


51/67

4.21. 51

: radiation belt : partition of unity : partition of unity : factorization : decomposition of map : factor

4.20.1. ,

, .

To factor a polynomial means to find two or more polynomials whoseproduct is the given polynomial.

: difference c: solve for the c

4.20.2. c.Equation may be solved for the c.

: propagation: scattering : scattering from crystal : algebra bundle : group bundle : fibered product : fibered correspondence: consider

4.20.3. A

B.Consider correspondence from set A to setB .

: extension field: enhanced : splittable algebra: regression: resonance: retract: retraction: reflexive : solution of differential equation

: sieve of Eratosthenes ( ): series : Taylor series

4.21.

: up to notation


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53/67


54/67


55/67

4.24. 55

: exact sequence of modules: trajectory: transitive: friction: triangle U: chart over U: trivial: trigonometrical: trigonometry : Tunguska Cosmic Body : obtuse angle: turbulence

4.23.

: angle

: angle of reflection : angle of incidence : angle of refraction : resistivity: knot: multiplication 2: multiply by 2 b: multiply by b : monic polynomial : ordered set: ordering : partial differential equation : equation is satisfied identically

: acceleration: accelerator : conditions of integrability

4.24.

: quotient set : difference module : quotient bundle: factor group; quotient group: quotient ring: quotient topology: physicist

: physics: physical: filter : Finsler metric; Finslerian metric: photon : fundamental sequence: functor : gluing functions


56/67


57/67

5

Name index

Yakir Aharonov

James Waddell Alexander

Victor Amazaspovich Ambartsumian

Andre-Marie Ampere -

Carl David Anderson

Archimedes

EmilArtin

Cesare Arzela

Alain Aspect

Michael Atiyah

Pierre Victor Auger

Amedeo Avogadro

Walter Baade

John C. Baez .

Stefan Banach

John Bardeen

Asim Orhan Barut

Tatyana Baturina

John Stewart Bell

Felix Alexandrovich Berezin

Peter Gabriel Bergmann . .

Jacob Bernoulli

George Birkhoff

Nikolai Bogoliubov

David Joseph Bohm

Niels Bohr

Ludwig Boltzmann

Bernhard Bolzano

Fel ix Borel

Max Born

Satyendra Nath Bose Raoul Bott

Nicolas Bourbaki

Eugenio Calabi

Georg Cantor

Constantin Caratheodory

Sadi Carnot

Lewis Carroll

Elie Joseph Cartan

Henri Paul Cartan a

Hendrik Casimir

Guido Castelnuovo

Augustin Louis Cauchy Owen Chamberlain

Shiing-Shen Chern -

N. A. Chernikov . .

Geoffrey Foucar Chew

Elwin Bruno Chritoffel

William Clifford

Paul Moritz Cohn .

Alain Connes

John Horton Conway

Leon Niels Cooper

Gabriel Cramer

Luigi Cremona

Jean Le Rond dAlembert

Leonardo da Vinci

Louis de Broglie

Rene Descartes

James Dewar

Bryce S. DeWitt .

Jean Alexandre Eugene Dieudonne

Paul Dirac

Johann Peter Gustav Lejeune Dirichlet

Christian Doppler

Frank Watson Dyson

Freeman John Dyson

Arthur Stanley Eddington

Werner Ehrenberg

Paul Ehrenfest

57


58/67


59/67


60/67

60 Name index

Valerii Vinokur

Max von Laue

Wilhelm Eduard Weber

Karl Theodor Wilhelm Weierstrass

Andre Weil

Steven Weinberg

Hermann Weyl

John Archibald Wheeler

Alfred North Whitehead

Hassler Whitney

Eugene Wigner

FrankWilczek

Robert Wilson

Chen Ning Yang Shing-Tung Yau -

Hideki Yukawa

Oscar Zariski

Yakov BorisovichZeldovich

Ernst Friedrich Ferdinand Zermelo


61/67

6

Yakir Aharonov

Amedeo Avogadro

Jacques Hadamard

James

Waddell Alexander

Victor Amazaspovich Ambartsumian

- Andre-Marie

Ampere

Carl David

Anderson

Emil Artin

Archimedes

Cesare Arzela

Alain Aspect

Michael Atiyah

Walter Baade

. John C. Baez

Stefan Banach

John Bardeen

Asim Orhan Barut

Tatyana Baturina

John Stewart Bell

Benjamin

Franklin

. . Peter Gabriel Bergmann

Felix

Alexandrovich Berezin

Jacob Bernoulli

George Birkhoff

Nikolai Bogoliubov

Satyendra Nath Bose

Bernhard Bolzano

Ludwig Boltzmann

David Joseph Bohm

Niels Bohr Felix Borel

Max Born

Raoul Bott

Nicolas Bourbaki

Steven Weinberg

James Van Allen

Wilhelm

Eduard Weber

Karl Theodor Wilhelm Weierstrass

Andre Weil

Hermann Weyl Eugene Wigner

Alex Vilenkin

Frank Wilczek

Robert Wilson

Valerii Vinokur

Galileo Galilei

Galois

Georg

Karl Wilhelm Hamel

William

Rowan Hamilton

Rene Eugene Gateaux

Samuel

Abraham Goudsmit

Carl Friedrich Gauss

Werner Heisenberg

- Murray Gell-Mann

Israel

Moiseevich Gelfand

Heinrich Rudolf

Hertz

Victor Franz Hess

Josiah Willard

Gibbs

David Hilbert

Marvin

Leonard Goldberger

Walter Gordon

Hermann

Gunther Grassmann Marcel Grossman

A Grothendieck

Adolf Hurwitz

Jean Le Rond

dAlembert

Leonardo da Vinci

61


62/67

62

Frank Watson

Dyson

Freeman John

Dyson Louis de Broglie

. Bryce S. DeWitt

Rene Descartes

Nathan Jacobson

Paul Dirac

Johann Peter Gustav Lejeune Dirichlet

Christian Doppler

Jean

Alexandre Eugene Dieudonne

James Dewar

Oscar Zariski

Yakov

Borisovich Zeldovich

Arnold

Sommerfeld

Dmitri

Iwanenko

Leopold Infeld

Pascual Jordan

Hendrik Casimir

Eugenio Calabi

- Heike

Kamerlingh Onnes

Georg Cantor

Pyotr Kapitsa

Constantin

Caratheodory

Sadi Carnot

a Henri Paul Cartan

Elie Joseph Cartan

Max Karoubi

Guido Castelnuovo

Johann Kepler

Roy Patrick Kerr

Gustav Robert

Kirchhoff

Oskar Klein

Felix Klein

William Clifford

. Shoshichi Kobayashi

Andrei Nikolaevich Kolmogorov

. Paul Moritz Cohn John Horton

Conway

Alain Connes

Augustin Louis Cauchy

Robert Kraichnan

Gabriel Cramer

Luigi Cremona

Elwin

Bruno Chritoffel

Leopold Kronecker

Martin Kruskal Leon Niels Cooper

Kazimierz

Kuratowski

Lewis Carroll

Guillaume Francois de LHopital

Joseph Louis

Lagrange

Lev Landau

- Pierre-Simon

Laplace

Henri Lebesgue

Leon Max

Lederman

Adrien-Marie

Legendre

Gottfried

Wilhelm Leibniz

Joel Lebowitz

Serge Lang

Joseph Lense

Andrei Linde

Joseph Liouville

Andre Lichnerowicz

Nikolai Ivanovich Lobachevsky

Hendrik Antoon

Lorentz

Edward Norton

Lorenz

James Clerk

Maxwell

Lise Meitner

Charles W. Misner

Robert Millikan

John Willard

Milnor

Hermann

Minkowski

Eliakim Hastings

Moore

Holger Mueller

John von Neyman

Emmy Noether. Katsumi Nomizu

Newton

Yuri Obukhov

Pierre Victor Auger

William of Ockham

Peter Olver


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63

Robert

Oppenheimer

Blaise Paskal Wolfgang Pauli

Cecil Frank Powell

Moritz Pasch

Giuseppe Peano

James Peebles

Max Planck

Julius Plucker

George Polya

Isaac

Pomeranchuk

- Jean-Francois

Pommaret

Lev

Semenovich Pontryagin

Jules Henri

Poincare

- Simeon-D eni s

Poisson

Isidor Isaac Rabi

Bertrand Russell

Ernest Rutherford

Kurt Werner Friedrich Reidemeister

William Reynolds

Ole Christensen

Roemer

Bernhard Riemann

Martin Rees

Gregorio Ricci

Carlo Rovelli Marshall

Nicholas Rosenbluth

Michel Rolle

Ryszard Ra. czka

Karl David

Tolme Runge

Hanno Rund

Anthony Sudbery

Edwin Ernest

Salpeter

Leonard Susskind

Corrado Segre

Waclaw Sierpinski

Jean-Pierre Serre

James HarrisSimons

Dmitriy

Skobeltsin

Lee Smolin

Eduard Study

Shlomo Sternberg

Thomas

Joannes Stieltjes

Norman Steenrod

James Stirling

George Gabriel

Stokes Leo Szilard

Alfred Tarski

Walter Thirring

Hans Thirring

Richard Tolman

George Paget

Thomson

Kip S. Thorne

Alfred North

Whitehead

John Archibald

Wheeler

Hassler Whitney

GeorgeEugene Uhlenbeck

Michael Faraday

Richard Feynman

Carl Faith

Pierre Fermat

Enrico Fermi

Armand-

Hippolyte-Louis Fizeau

Sergei

Pavlovich Finikov

Paul Finsler

Grigorii Mikhailovich Fikhtengolts

John Ambrose

Fleming

Sergei

Vasilevich Fomin

Max von Laue

James Forbes

George Francis

Maurice Rene Frechet

Alexander

Friedmann

Joseph Fourier

Edwin Hubble

Felix Hausdorff

Friedrich W. Hehl

. . S. W. Hawking

Heinz Hopf Antony Hewish

Ernst Friedrich Ferdinand Zermelo

Owen Chamberlain

- Shiing-Shen Chern

. . N. A. Chernikov


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64

Geoffrey Foucar

Chew

. Jacob Schwartz Karl Schwarzschild

Julian Schwinger

Schmidt

Erwin Schrodinger

John Schrieffer

Paul Steinhardt

Eduard Stiefel

Jacques

Charles Fracois Sturm

Euclid

Arthur

Stanley Eddington

. . Luther Pfahler

Eisenhart

Samuel Eilenberg Leonhard Euler

Albert Einstein

. . Lev Elsgolts

Federigo Enriques

Werner Ehrenberg

Paul Ehrenfest

Hideki Yukawa

Carl Jacobi

Chen Ning Yang

- Shing-Tung Yau


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[English.1] Steven Weinberg. The Quantum Theory of Fields. Volume I. Foundations.Cambridge university press, 1995

[English.2] Serge Lang, Algebra, Springer, 2002[English.3] Lev V. Sabinin, Smooth Quasigroups and Loops, Kluwer Academic Publisher,

1999[English.4] Peter J. Olver, Applications of Lie groups to differential equations,

Springer, 2000[English.5] V. I. Smirnov, A Course of Higher Mathematics, volume I.

Translated by D. E. Brown.Translation, edited and additions made by I. N. Sneddon.Pergamon Press, Addison-Wesley Publishing Company, 1964

[English.6] N. Bourbaki, Topological Vector Spaces, Chapters 1 - 5, Transl. by H. G.Eggleston& S. Madan, Springer, 2003

[English.7] N. Bourbaki, Lie Groups and Lie Algebras, Chapters 4 - 6, TranslatorAndrew Pressley, Springer, 2002

[English.8] N. Bourbaki, Lie Groups and Lie Algebras, Chapters 7 - 9, TranslatorAndrew Pressley, Springer, 2005

[English.9] Eisenhart, Continuous Groups of Transformations, Dover Publications,New York, 1961

[English.10] Edward Uhler Condon, Halis Odabasi, Atomic Structure, CUP Archive,1980

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