english russian science dictionary
TRANSCRIPT
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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.
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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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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.
.
, , . , , ,
, .
. . .
, , ! ,, .
, , ., , . , - ! , . , .
.
, , - . .
-, . .. - , . - -. , . , -. , , - .
, -. - . - , .
. , , . . . , . - . , , . .
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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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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).
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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,
see [English.9], p. 1
, 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.
see [English.2], p. 14
f G G/H, , - , G/H G H.
. [Russian.2], . 28
Cartesian coordinate system:
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16 3. English Russian Dictionary
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.
see [English.10], p. 106
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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18 3. English Russian Dictionary
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.
see [English.9], p. 7
, , f= 0.
. [Russian.9], . 14
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20 3. English Russian Dictionary
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:
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22 3. English Russian Dictionary
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.
see [English.1], p. 30
-, , /(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.
see [English.3], p. 24
, , .
. [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.
see [English.7], p. 89
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.
see [English.5], p. 14
XX YY O.
. [Russian.5], . 21
3.14. N
name index: natural mapping: natural morphism: necessary and sufficient:
Example 3.14.1.
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26 3. English Russian Dictionary
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:
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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:
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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:
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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.
see [English.4], p. 59
, , 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
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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
see [English.4], p. 50
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.
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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.
see [English.8], p. 282
- (); , 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.
see [English.6], p. 147
, 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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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
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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,
see [English.9], p. 1
: 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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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.
see [English.8], p. 282
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.
see [English.6], p. 147
: 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.
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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.
see [English.3], p. 24
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
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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
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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
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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.
see [English.9], p. 7
, : 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.
see [English.7], p. 89
: 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).
see [English.9], p. 7
: 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
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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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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
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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
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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
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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
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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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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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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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