SCIENTIFIC ABSTRACT R.L. DOBRUSHIN - D.B. DOBRUSHKIN

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• Collection: Scientific Abstracts
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• Document Creation Date: November 2, 2016
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• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

DOMWSHIN,R.L.
Lemma on the limit of
10 n0-2:157-159 155.
(Probabilities)

Dobrugin F/W
Two limit jkCQXCr&jjbr t C simpleit:l
randoin iafk on it line. Uspehi Mat. Nauk (N.S.) 10

9
no. 3~65),139-146. (Russian)
E~j
be the position,ofa particle after making n steps
V
di
f
i
l
e
i
u
i
a one
mew
nna
tr
n
o
c
t-step, random Nvalk,
symm
\
Let / be a futidion on the integers, with Y,:;. 10)=c,
where the series converges absolutely, Then, if c;t-O, the
distribution" of Zj*/(rj),/(cn1) converges to a limit distri-
bution. If c=0, and if / vanishes except on a finite set,
converges to a limit
the.dis.tribution of j;j"j(rj)/(dw
distribution, Let ~, Yj be mutually independent Gaussian
random variables with zero expectations and unit
variances. Then the above limit distributions are those of
J ~Jlq respectiVely, and d is a positive constant evalu-
ated explicitly ir terms of /. Feller [Trans. Amer. Math.
Soc 67 (1949), 98-119; AIR 11, 2&5) g ;oved a special case
K-
R
l
e
first theor
of
m.
e
ated results ave been proved by
Hallianpur arid, Robbins [Duke Math. J. 21 (1954),
285-307;, MR .160 52.] J. L. Doob (Urbana. Ill.).

DOOB, Joseph Leo I I '0- -, DC8RVSH3,.R.L.,Ctrsn9lmtor)-, YAGLOM , I.M..
(translator . red,, -"- 1 1-
(Stochastie pi%cessesl Verotatuostaye protsessy. Perevod 9
angliiskogo. N6skva. Izd-vo inostrannoi lit-r.-, 1956. 05 p.
(MIRA 11:10)
(Probabilities)

EW L-Sentral finift theorem for non-stationary F \VY
n,-R.
M
Markov ch--m'. 1. Teor Veri:v:anost i Priincrtun
1 (1956), 72-89. (Russian. English surnmarv)
This paper consists of the introduction to a dissertation
and includes, in addition to statements of thtortnis. a
brief outline of some of the proofs. The principal theorenis
are refinements upop those announced previously by the
author (Dokl. Akad. Nauk SSSR (N.S.) 102 (1955), 5-8.
MR 1 .7, 48) and urill be indicated below with the notations
of the review just cited. For any trapsition probability
iunctiv, - P(x. 41'. niuvad, or dite measure ol ergoaicity
p the wathor'no* uses thi`i4odic coefficient"
a=*(P)- I -sup JP(%. A) -Pb,, A)J,
where the bupremum is taken for all x, y, and A. Re-
pl.acing p by ei In theorems 1) and 2) of the review cited we
get 'Neore,m3 I and 2 of the pmgcnt pap-cr, which an-
souiewhat stronger because m,~,p. Mmirenver, in them the
condition bivaliv Mb is bi'st IN)--3iblu Instead of 3) (d t1he
riovievy tile all 8tatf-- the foltlo-4inp more
restdtffheDrern undeTconditio"I (*Lof.the review i! I

".103-A Hld 1.1
hill,

17 l11 7
pruve,: aspo.,ia; L."i
of this th~~oreai. If (b) i.,; kepi but if i, rvpl:irtd tht
i; 'i t Iif) AI
Z !I!, -L'l 3z, U~~

-7
L-
B) -P(,v, I)
Thenp;-~-,-p, xylivrep is the cm,H)CIOll. 01 (11,tiAmly t1dilit'd
tri a previous paper [saine DAI (N,S 102 HQ5F~. 5 i~. NIR
V, 46]. Sev~fal theorms on 0i,
~lf sms of ramdoin van;tlds-,~ iiL
.n lhat Paper Termlill ta-V if
:n- ire amont: furTh, ! 1-
of 04, lf;w.,111,111 tIll" -1;-, 1.', :11
the sum ilt 1,
of n Tandom

i:awizoo~ wen
cen enng an sca tq 14.1 5coffst <
Constants). (11) If
and if
V' Var fj.) =co,
4-1
then Cn is aSyMptotically narmatly distributcd.
-o& (Geneva).
L. Do
:K

%ft" DOBRUSHIN, R.L.
Nwimm- I I
Central limit theorem for inhomogeneous Markov chains [with summarjr
in English]. Part 2. Teor.varoiat.i ee prim. 1 no.4:365-425 '56.
(KM 10-.5)
(Probabilities)

DOBRUSHIN, R.L.
.,-. I . I .
An example of a countable homogeneous Markov process all states of
which are instantaneous [with summary in English]. Teor.veroiat.i es
prim. 1 no.4:481-484 156. (MLRA 10:5)
(Probabilities)

'Do 01 C_L~?
AUTHOR: Dobrushin, Re Le
TITLE: Some Classes of Homogeneous Denumerable Markov Processes.
(Nekotoryye klassy odnorodnykh schetnykh markovskikh
protsessov.)
PERIODICAL: Teoriya Veroyatnostey i Ye e Primeneniya, 1957, Vol.I1,
Nr.3. pp.377-380. (USSRT
ABSTRACT: The problem of finding all Markov processes having a
given system of transition densities is-investigated.
Up to the present time this problem has been completely
solved by Feller (Ref.2) for the regular case when there
is exactly one process. Refs.4, 5 and 6, and others,
have studied at different levels of strictness and
generally, different classes of examples of non-regular
processes. In this paper is given a complete description
of processes for which the densities satisfy two conditions;
the condition of "no beginning", and the condition of a
finite number of ends. The condition of "no beginning" is
Card 1/5 that there need not exist a sequence of non-repeating

some Classes of Homogeneous Denumerable Markov Processes.
Card 2/5
52-3-7/9
states Eik such that the densities a ik +llik -'> 0 for
all k. It would be said that the process which has
n.c-,coo ends Rl, - - -, Rn, if all the states Ei can
be split into n non-intersecting sub-sets Rl, ..*, Rn
such that if we denote by DR the event which is that
for all sufficiently large values of time a chosen
function of the chain belongs to a set of states R, then
n
(1) DRi >0; i-1' ..., n, (2 U DR, is a
ial
Verifiable true event, (3) for RC:Rj the probability
P tDRJ is equal to 0 or to -9 DRi . The following
theorem is proved: let there [e g) ven a compact
homogeneous Markov process with no beginning and with
a finite number of ends Ri, then all non-regular
ends of the process can be split in a unique way into
simple ends and grouns of particular ends. With each

52-3-7/9
Some Classes of Homogeneous Denumerable MarlcovProcesses.
(J) (J)
simple end Rj probabilities qi ri satisfying
00
(Eq.1)
Lz i
can be identified in a single-valued manner. Each
group of parttplar ends 8 can be identified with
quantities ui satisfy4mg conditions
00
k (Eq.3)
Tlv~~ do,-
Card 3/5 7r k_ (Sq.4)

Some Classes of Homogeneous Denumerable Markov Processes.
and
52-3-7/9
(Eq.5)
conversely, lot there be given transition densities
such that to them cotrespond processes with no beginning
and with a finite number of ends: among all the non-
regular ends of the processes let there be given
arbitrary ends called "simple ends", and lot the
remaining non-regular ends be divided into non-inter-
secting groups. Finally let there 'he given a choice of
numbers q Q) , rQ) , and u(j) satisfying ecluati6na
i i i
1, 3, 4 and 5.. Then there is a homogenqous Markov process
which is unique, having these transition densities,the
Card 4/5 ends of which are divided into simple ends and groups of

52--'-7/9
.' Some Classes of Homogeneous Denumerable Markov Processes.
(J) (J) (J)
ends as given, and the quantities qi , ri and uj
so constructed as to correspond with those given.
There are 8 references, 3 of which are Slavic.
AVAILABLE: Library of Congress.
Card 5/5

BOV/52-2-4-7/7
A Summary of Papers Presented at the Sessions of the Scientific
Research Seminar on the Theory of Probabilities. Moscow, Feb-Wy 1957
Tooriya Veroyatnostey i yeye Prbw ) 1957, Y.2, no.-, pp. 478-88
is supposed that the space R is locally bicompact and
has a countable basis. It is further supposed that the
stochastic phenomenon is given by its finite dimensional
Boolean distributions. Dobrushin, R.L., Certain classes
of homogeneous denumerable Markov processes. The contents
of this report have been published in Vol.2, _Nr.3 of this
journal. Rozanov, Yu.A., On linear interpolation of
multi-dimensional stationary sequences in a Hilbert space.
The contents of this report have been published in the
Proceedings of the Academy of Sciences, Vol.116, Nr.6,
1957, pp.923-927. Dobrushin) R.L., On the formulation
of Shannon's fundamenT_a1_t_h_e_o'i~*m. Let 1~ which takes
values in some space X be a random quantity related to
the transmission of information. Let there be given a
space K with some-class V of distributions of pails
of quantities where -3' takes values from X
and it is required that the information 4~ arising in the
transmission of information 1% is such that the distribution
Card 4#X-1 of the pair belongs o V. Let H be the
19

SOV/52-2-4-7/7
A Summary of Papers Presented at the Sessions of the Scientific
Research Seminar on the Theory of Probabilitios.
superior limit of information I(~ and 'Let
G(V)= inf
V
The following theorem is proved: suppose that all the
quantities introduced depend on an index T. If for
any T (1) there are given non-ne tive u:niformlv. bounded
functions of two variables fT(xlg and for any positiv4
number u the set VT(u) consists of all the distributions
Of Pairs Of such that
MPT(tTl ~T) u, (Eq. 2.)
then (2) there exist regular sequences of quantitie~y,
T related to the distribution PT(Y'B) y
B C: Y such that as T o0
i(IT-1
Card
HT

SOV/52-2-4-7/7
A Summary of Papers Presented at the Sessions of the Scientific
Research Seminar on the Theory of Probabilities.
(3) for some sequence of numbers UT there exist regular
-j
sequences of stochastic quantitie B Tn' ; T such that their
distributions belong to VT(uT)
lim.
T -,~ o,
G(VT(UT))
(4) if lim. HT
T -.> a%
lim C(VT(uT)) < 11
T -;~ co HT
then for any F_ > 0 for all sufficiently large T the
Card 6011 information I can be transmitted with accuracy VT(uT-+
2/3

DOBRUSEIN, R. L. (Moscow)
"The Importance of Mathematical Methods in Linquistics."
Theses - Conference on Machine Translations, 15 - 21 May 1958, Mosocow.

DOBRUSHIN, R. L. (Moscow)
"A Test of the Determination of the Concept of the Grammatical Category."
Theses - Conference on Machine Translations, 15 - 21 May 195B, Moscow.

AUTHOR: Dobrushin, R..L.
TITLE: The Continuity Condition for Sample Martingale Punctions.
(Usloviye neprei-jvnosti v-yborochnykli funktsiy Martingala.)
PERIODICAL: Teoriya veroyatnostey i yeye primeneniya, 1958,
Vol.III, Nr.1, pp.97-98. (USSR)
ABSTACT: It is proved that the condition
supAt] > 61 = 000M
t C ro i- (h q. 1
f or 'zy e > 0 as &t -0 is sufficient for
almost all sample functions of a separable stochastic
process [~t, t ( (0, 111 to be continuous. This follows
from the more general result; if Eq.1 is true for a
separable stochastic process, then almost all sample
functions do not have first order discontinuities.
There are 3 references of which 2 are Soviet and 1
English.
SUBMITTED: September 25, 195?-
AVAIIABji;: Library of Congress.
Card 1/1 1. Martingale functions 2. Stochastic processes

.30V/52-5-('--5/10
AUTHOR: Dobrushin R
-TITLE; atistical Problem of Detecting a Signal in the Noise of
a Multi-Channel System Reduced to Stable Distribution Layis
(Odna statisticheskaya zaclacha teorii obnaruzheniya siSnala
na fone shuma v mno-okanallnoy sisteme, privodyashchaya k
ustoychivym zakonam raspredeleniya)
FERIODICAL: Teoriya veroyatnostey i yeye primeneniya, 1958, Vol III,
Nr 2, pp 173-185 (USSR)
ABSTRACT: A system in radio communication is employed with n
channels each having the tension
1 C3 i on its output. The
variable ~i can be considered independently and distributed
isith density probability (Eq.1) where X i is expressed by
Eq.(2). The parameter could be described by two
hypotheses A and B In the first case, with no signal
present, all X i are the same and equal to d>0 (d -
mean noise power). This hypothesis considers the output
tension of the channels as producing only a noise. Ir the
second case a signal is present. All hi except X i
(1~>O) The index j
Card /,, are equal to d while X j = d +- &

SOV/52-3-2-5/10
A Statistical Problem of Detecting a Signal in the Noise of a IAlulti-
Channel System Reduced to Stable Distribution Laws
represents any value of n with probability 1/n This
hypothesis describes the source of tension in all channels
as noises except j's which is the tension of working sig-
nal with the noise superimposed. A possibility that a work-
ing siGnal can be present at several channels simultaneously
is disregarded. The density probability distribution in
both oases can be expressed as p A (xl,..., xn) and
P-G(x,,...qxn) . The ratio p 5/PA can be described by the
statistic (4). If 0 = U/d and ~i is distributed with
the parameter X i then a value ni is found so that the
probabilit-y ?(Qi~>xj can be calculated for 1\< x,,:Z 00
Therefore the statistic (4) in the case of the hypothesis A
has a diatribution which cen be compared with the distribut-
ion of the sum (S) of n independent components i1i .Ath
probability Eq.(6). Similarly, for the hypothesis B this
Card 2/4.

SOV/52-3-2-5/10
A Statistical problem of Detecting a Si-nal in the Noise of a MUl"11-
0 ii
Channel System Reduced to Stable Distribution Laws
probability can be expressed as Eq.(?). The probability
that the hypothesis B is being considered while the hypo-
0
-thesis A is true, can be expressed by ~'13) aad called the
"probability of false alarm". For the probability of hypo-
thesis B beins considered when actually it is true, the
expression (9) is used. It is called the "probability of
detection of true signal". If two values F and D exist
so that O~b(n) is to denote that
0 < ~1,7) a In) <
(n)
The author proves
Theorem 2 : For a symmetric channel with binary input it holds for every
fixed N and n-Yoo
q (N. n) (12)
j7a~-~-.-,n [P"'
N Pat
where g- is the unique root of
Card 5/6 .

9/9 Paso
o96L I LZ IT-Tdv :LT~7jjTjprqfjS
U, 11-\
aj atI'm
Tod L=T
0 Sol Tod
T L(d, ) T Ld
~00/COO/ZOO/LOO/Zq/Z~O/S ... S91Va ITVMS aOj SaPOO SaVUTq jvwi!~do

39004
S/05Y62/007/003/002/004
C111 0333
AUTHOR: Dobrushin, R. L.
TITLE: Asymptotic evaluations of the error probability for the
transmission of messages over a discrete memoryless
communication channel with a symmetric matrix of
transaction probabilities
PERIODICALs Teoriya veroyatnostey i yeye primeneniye, vol. 7, no. 3,
1962t Z-83-311
TEXT. A momoryless channel with a matrix of transaction proba-
is-considered such that any row of I P is a
bilities P pij ij
permutation of any other row, and any column is a petmutation of any
other column. K n F enH i' messages are transmitted, where I a 3 denotes
the largest whole number contained in a, and where H is smaller than the
transmission capacity C of the channel. Here the k-th message is
coded by a word e k , and as the,word Fleaves the channel it is deoided
with the probability r k(') that the k-th message was transmittedl ek
Card

S/052/62/007/003/002/004
i.symptotic evaluations of the error ... C111/C333
and i have the lengthn;
K
r 1. The probability of the error is denoted by
k(i)
k-1K
1 7 `.~- p(e- / ek) r 1 - r the optimal probability of'the error
Ki= i--:- - k
e
P (K) is the infimum of the preceding expression. It is shown that for
n
H - Cit always holds that P n(1c) -:E Pn(K) Pn M, where -P-'is an averaged
probability. Asymptotic expressions are given for F n(K) and P,(K) with
the help of the functions
d log R(h)
(h) (p,,)", m(h) - I "~ 2 (h) dm (h) (1.24)
M dh dh
and under the assumption 62(h) > 0. For example, it holds for every
H --' C;
Card 2/1~

5/052/62/007/003/002/004
Asymptotic evaluations of the error ... CIII'(6333
- 1
A 2h n
Pn (K d -1 a INR(h0 exp f n (1-h.) m(h.)j (1.28)
where h 0 is defined by
log R(h0 Ii0M(h0 -H (1.25)
The asymptotic of the error is determined for H,-,, H up to a constant;
the logarithmic asymptotic is obtained for H n H or6 "Asymptotioally
nonidentical upper and lower estimates are given for H.-- H or" (Here Hor
is that value of H, for which h - 1/2). Finally, the case (;(h):-= 0
1 1. 0
is .considered where ~ n(K 09-An error in Ref. 9 (P. Eli-as, Cqding fcr
two noisy channels, Proe. Lond. Symp. on Inf. Theory, Butteworth Scient.
Publ., Lnd., 1955) is pointed out: the assumption that k 1"PI is false,
it only holds that k 1 - up I+ O(log n).
The most important English language references &rot A. Feinstein,
Card 3/4

S/05 62/007/003/002/004
Asymptotic evaluations of the error C111YO333
Error bounds in noisy channels without memory, IRE Trans. on Inform.
theory, Sept. (1955), 13-14; C. E. Shannon, A mathematical theory of
communication, Bell. Syst. Teohn. Journ., 27 (1948), 379-423, 623~-656;
C. E. Shannon,. Certain results in coding theory for noisy channels. Inf.
and Contr. 1, 1 (1957), 6-25; J- Wolfowitz, Strong converge of the
coding theorem for semicontinuous channelsp Illin. Math*-J-, 3,4 (1955),
477-489)-
SUB.ITTED.: April 11, 1960
74-
Card 4/4

VOIWBIYEV~ NX; red.; GNEDIMIKO, B.V.., red ; DOEUIUSHIN H L red.-
DYNKIN, Ye.B., red.; KOIVOGOIWV, A:N .
[Kubilius, I.P.I. red.; LIIINIK, Tu.V., red.; Priono."Ov, Yu.V.,
red - SMIZOV N.V., red.; STATULYAVICHYUS, V.A.(Statuliavicius,
V.A:J, red.;Y'AGLOIA, A.M., red.; MELINENE, D., red.; PAKERIII,O.,
tekhn. red.
[Trarsactions of the Sixth Conference on Probability Theory and
Mathematical Statistics, and of the Colloquy on Distribations
in Infinite-Dimenaional Spaces]Trudy 6 Vsesoiuznogo soveshcha-
niia po teorii veroiatnostei i matematichoskoi statistike i kol-
lokviuna po raspredeloniiam v beskonebhnomerrykh prostranstvakh.
Vilnius, Palanga) 1960. Villniua; Gos,izd-vo polit. i nauchn.
lit-ry Litovskoi SSR, 1962. 493 p. (MIRA 15:12)
1. Vsesoyuznoye sovesbehaniye po teorii veroyatnostey i matema-
ticheskoy statistike i kollokviuma po raspredeloniyar. v besko-
nechnomernykh prostranstvakh. 6tb, Vilnius, Palanga, 1960.
(Probabilities-Congresses) (Mathematical statistics-Congresses)
(Distribution (Probability theory))-Congresses)

KONDRATOV, Aleksandr Mikhaylovich; DURUSHIN,--R.L., doktor fiz.-
matem. nauk, nauehnyy red.; ZUBKOV, M.A., otv. red-;
PUSHKOVA, S., K., tekhn. red. i
t
[Numbers and thought] Chislo i mysll. Moskva, Detgiz,
1963. 141 P. (MIRA 16:6)
(Cybernetics)
I

DOBRUSHIN, R.L.
Theory of coding. Study of probability error in optimum
transmission techniques. Izv. AN SSSR. Tekh. kib. no.5:
81-84 S-0 163. (MIRA 16:12)

DOBRUSHINt R.L.; TSYBAKOV, B.S.
i ~ .. . 1,
Transmission of information with additional ncise. Probl..
pered. inform. no.14t2l-42 163. (MIRk 16:12)

_D,,3 PUS H) ~J ,
9 - L -
122HOW&A. L. [Dobruehin, R.L.]j CHMGIN, T.I. (Ehurgin., Ya 1.]
MOSEWRI
Problems of the information theory. Rocz wiad matem 6
no*2:205-216 163.

DOBRUSZYNj, R.L. [Dobrushin,, R.L.] (Mookwa)
Mathematical methods in ling#~stics. Rocz wiad matem 6
no*2-.217-W 163,

DOBRUSHIN, R.L. -(Moscow)
Asymptotic optimlity of groap and systematic codes for some chaimels,
Toor, veroiat, i ee prim.18 no.l.,~,211-A 163. %MIRA 1613)
(&~rors, The6ry of)

DOBRUSHIN~ R.L.
Unified methods for transmitting information +.hrough discrete
channels without memory and co=unicationa with independent com-
p,onents. Dokl. AN SS$Rl 148' no.6:1245-1248 F 163. (MM 160)
1. Moskovskiy goeudaretvennyy universitet im. H,V,Lomonosovas
Predstavleno akademikom AoN.Kolmogorovym.
(Information theory)

B112/Bi86
AUTHORS Dobrushing PV L
TITLEs Unitied.metho~e for t e transmission of informations. the
'general cue
PERIODICALz _'Akademiya nauk SSSR. Doklady, Y. 149, no. 1, 1963# 16 ig
TEXT: In'this aper'.the author.investigates the same problems as in,~Ali
(19635p but he does so from a more general point of view. Sys*
148, No. 6
of information S (39-arw-conaidered, thecomponents of wh16h are not .1.
:independent. The numbers %(S) sup
where
a SUPKWD) Q(A)Q(P)j0- have to fulfill the condition
M
f a - followss
aM(S) O(e o1ral-certain The~prinoipal result is as
if the system S sati fies a certain-condit4,on of agreement then
H(t-,S) ~- lim h(t,[SnT)/h.: This reiult'-is.appliaCto channels with and
'without memory.
'Card,1/2

DOERUSHIN, R.L. (Moscow)
Conditions of the aaMtotic existence of the conf1pration
integral of the Gibbs distribution. Teor, veroiat. i ee prim.
9 no.4s626-643 164. (MIRA 17s12)

-7i-Wro)
t 210T%
0)
M(d' )/'RAEM(c WE F.SD(t
ACCESSION Ks kr5w,9,7 5/2582/64/000/012/0113/0123
AUTHOR Dobrushin. R. L. (Moscor)
-TITLE. in co=ection with the sequential deepaing method of Wozenoraft and ReiffeA
SWAM Prcble=j* kibe=etikip no* 12, 1964,, 113-123
MS: itfo=autd-theox7p on
'~Gct~img oodep.- error location ooding,
SMCT: Reretince 19 im~de,.W otfbrii '1W vbmcraft and -Reiffeu
U
N.Y.-London If en thee'
1961). The author contradicts the Wozencraft - Reil hypo, is
stating that the moan number of operatioria (machine eVales) needed to decoa4e one
y
transmitted symbol grows " (log 7) , where p is a email probability of error and
is a constant. A modification to the algorithm was originally su&meted by Koshelay
and Fineker and further developed by the author. A uu=mary is made of coding
nomenclature used by Wozencraft and Reiffen, An is the set of all sequences of van
Card 1/3

7. ~-l-
ACCESSION NR, AT5000719
ENCLOSUIC ol

- - --------- ---
W( WTIF~P(1)-'_ -4 XJP e)
E
d
ACOWSIOR Ri AP015093 UR/0052/65/010/002/0209/0230
AUTHOR: Dobrushin, R. L. Moscow) _~12
TITLEi Existence oi%phaBo transition in two- and three.-dimensionrl Ising, -mr-de-is
V.101-no* 2., 19 3 209430---
'TOPIC TAGS: mthematigal model wdstence theDrem; lattice parameter, phase
trawition
AMR=s A now method was developed to prove quantitatively the exialDence of
these trawitione in %)-dimensionalintagral lattices vith Ising ~odols of poten.
tial
~-The~ method consists of ppo4na the fonowing two theoremsi theorem 1-assume
erp
TIP)
Sexp k (2)
WD
37( t + 40) x P-7 -,1v
where 89 -the volume of a 1) -divisn'sioiWI- s-'phere with a unit surface. Then if

.1 and for any sequence Nt for Which
V, < v < 00
is truethen
k
The proofs of these theorems are Tollowed by a detailed ge-metric c erist4s
ha~xact
ntudy for V lattice arrangements. To this and, with each point X
V
eke connected (see Figb 1 on the Enclosure) with aide I and wI;wXvI
I a cub
card 25~

:PIN R.L.
Existence of a phase transition in tuu-dimensional and three-
dimensional Ising models. Dokl. AN SSSR 160 no-5:1046-1048
F 165. (MIRA 18:2)
1. Submitted September 18, 1964.

:ABSTRACT: In classical statistical mechanics, the state of a system containing
N Identical particles is usually described by a set of their coordinates and momen'-
ta. Since investigattion of such'!~ system can easily be reduced to the case in
which,only particle coordimte; are iiiscus-o'e'd- i'a-s-sume that the state of a system
-by the x
Is given vector x la (xi, . xN),, iiEV- ~ and for simplicity, that V is an
n-dimensional cube. It Is usually assumed th;6A such a system of particles is
described by the Gibbs distribution, which is given by the probability density

where 'i (OD
is a real measurable function that may take the value
C'6 It to usually assumed that the finite limit
log Q ft, N) 1 (9 6)!,
V-,M AV
card

D013RUSHIN, V.A.: XANDMN, A.Te., takhnichooklir redaktor.
[Books on locomotives; a catalog] Knigi lokomotivnowu khoziaistyu;
katalog literatury. Moskva, 1956 . 16 p. rNicrofila](MIRA 10:6)
I.Vae:o.6 nye izdatel'sko-poligrafiehaskoye obmyedinenire "Trans-
zhold rislat."
(Bibliography-Locomotives)

DOBWSHI tv. za vyimsk.; STIKIIHO, T.T.,tekhn. red.
(Taxtbooka and momwls for students taking corrappondence
clar-ces from universities and technical schools] Uchabniki i
uchabnye posobiia dlia zaochni-kov vuzov i takhnik-dmov. [Moskva]
1958. 13 P. (KIM 11;12)
1. Transzholdorizdat, V96soyurnoye izdatellsko-poligrafichookoye
ob"yedineuiye.
(Bib Ii otvaphy-Ra i I road engineering)

DOBRUSHIN, V.A., otvet. za vypuak; MINA. G.P,, tekhn.red,
(Classified plan of literature to be published during 1959
by the State Publishing House for Railroad Transportation
Literature; catalog of literature in print] Tematichaskii
plan vypuska lzdanii tranazheldorizdata na 1959 g.; katalog
literatury, imeiushcheisia v nalichii. Koskva, Gos.transp.
zhel-dor.izd-vo. 1958. 128 P. (KIRA 12:11)
(Bibliography--Railroad engineering)

DOBRUSHIN, Y.A.;HILOYANOT, Y.S.; KARPOTA,N.L., red.; KHITROT, P.A.,
--rarmn-red-i-
(Bibliographical guide to the publications of the State
Publishing4ouse for Railroad Transportation
1950-19591 Bibliogrefichaskii sprnvochnik izdanii tZenri-
sboldorizdata, 1950-1959. Moskva. Toes. izdatellsko-
poligr. abOadinente N-va putei moobehaheniia, 1961. 345 P.
(MIRA 14:5)
(Bibliography-Railroads)

DOBRUSHIN, Ye.S., inzh.
Machine tool for cold banding of pipes without fillers and
some technological paminetere of the bending. Maeh.Bel. no-5:
16-18
(MIRL 12:11)
158.
(Pipe bending)

AUTHOR: Dobrushina I.S. (Moscow) SOV/39-45-3-3/7
TITLE., Typical Irregularities for a Mapping of a k-dimensional
Differentiable Manifold into a (2k-2)-dimensional Vector
Space (Tipio'4inyye neregulyarnosti pri otobrazhenii k-mernogo
differentaiiniyemo mnogoobraziya v (2k - 2)-mernoye vektor-
noye prostranstv07
PERIODICALs Matematicheakiy abornik,1958,Vol 45~Nr 3,PP 333-366 (USSR)
ABSTRACT: The author uses the notions manifold, boundary of a manifold.
irregular point of a mapping, neighborhood of class m of a
mapping to another one, as they are used in the investigation
of Pontryagin [Ref 13 concerning smooth manifolds and their
application in homotopy theory. She considers the mapping of
a compact manifold Mk into the (2k-2)-dimensional vector space
2k-2
A Let f be a smooth mapping of class m>,4 (for k >2 it is
k 2k-2
sufficient m >,3) of M into A Let a be an irregular
point of f and let x Iq*..x k be a local coordinate system in
in the neighborhood of a, so that ?f(a) = 0 . In the case
Card 1/ 4

Typical Irregularities for a Mapping of a k-dimensional SOV/39-45-3-3/7
DIfferentiable Manifold into a (2k-2)-dimensional Vector Space
k >2 the irregular point a is called non-degenerated, if it
holds (B) : For a certain i 2,...,k the system of the
2k-2 vectors
3 d2f (a)
(dxl)2 qX1 dx:i-1 ~.l axi+1 axl ?xk
~f(a) Of(a)
Px2 ?Xk
is linearly independent. In the case k 2 the irregular point
a is called non-degenerat3d, if it holds (C 1) z The vectors
32f (a) and df(a) are linearly independent, or if it holda
(-axl)2 h2
a more complicated condition (C 2)' It is shown that this defi-
nition of nondegeneration with respect to the choice of the
local coordinate system is invariant. The mapping f is
Card 2/ 4

Typical Irregularities for a Mapping of a k-dimensional S071/39-45-3-7/7
Differentiable Manifold into a (2k-2)-dimensional Vector Space
called non-degenerated, if all its irregular points are non-
degenerated and if for k = 2 the boundary Mk-1 of Mk con-
tains no irregular points which satisfy (C 2) -
Main results t In every neighborhood of the class m of the
mapping f there exists a non-degenerated mapping g. The set of
all non-degenerated mappings of class m forms an everywhere
dense domain in the space of all mappings of class m. If a io
a non-degenerated irregular point of the mapping f, then there
exists for each neighborhood U of a and for all sufficiently
near mappings g an irregular point of the same type in the
neighborhood of U. The set of the irregular points of a non-
degenerated mapping forms a smooth one-dimensional manifold of
class m - 1. For k = 2 in a certain neighborhood of an irre-
gular point satisfying (C2) there exists no further irregular
point which satisfies the same condition (C 2)'
The paper suggested by Pontryagin and guided by Boltyanskiy
consists of 23 sections, presents a great deal of Whitney
[Ref 3,4] and Sard tRef 21 and is written in a way difficult
to survey.
Card 3/4

Typical Irregularities for a Mapping of a k-dimensional SOV/39-45-3-3/7
Differentiable Manifold into a (2k-2)-dii,;~-nsional Vector Space
There are 4 references, 1 of which is Soviet, and 3 are
American.
SUBMITTED: February 1, 1957
1~ Mathematics--Theory 2. Topology--Applications 3. Tensor analysis
Card 4/4

STRIKLINA, S.M., sanitarW vrach ; [&,, S . saaitarnyv vrach
- DOBRUH ,6 . a
t%
- "Iiij -
Case of Ovanillism.0 Gig. i san., 21 no.7:52 Jl 156. (MISA 9:9)
1. Iz sanitarno-opidemiologicheakoy stantaii Mookvy.
(VANIIJA--TOXICOLOGY)

- - I , IN -,.- , I "
, - /,- / ~- " ,* P, . ~ " , I,. L,-.,
' '- ' ' ' " . I
DOBRUSiSny 0. / ,
. I--- ,
C-0- Acute hemolytic anemia. Vrach.delo supplement 157:8-9 (MMA 11:3)
1. ChernovitekAyn oblRstnnya klinicheakaya bollnitsa.
(AMIA)

DOBAUSHKIN. D.B.; FADDEYET, B.V., kandidat tekhnicheakikh nauk,
Now types of conveyor belts. Zhim. promo nool:24-30 Ja-IF '57.
(Km 1o:4)
1. STardlovakty savod resinorykh takhnicheskikh Isdelty iUrall
skiy filial Akademit nauk SSSR.
(Conveying machtn:sry)

TAMEM, B.V., kand.tekhn.nauk; WBRUSHKINp D.B., inzh.; MAKAYEV, K.N.p inzh.
"Physical principles of the transmission of driving power by
means of friction "hv A.V.Andreev. Reviewed by B.V.Faddeev. Izv. vys.
ucheb. zave; groe zaurs no*n:131-132 1959. (MIRA 14:5)
(Conveying machinery-Transmiasion devices)
(Androov., A. V. )

Ed,

~Zli

S/138/62/000/001/004/009
A051/A126
AUTHORS: Dobrushkin, D.B.; Ekel', Ye.S.; Orlov, Z.D.
TITLE: The construction of rubber-metal valves
PERIODICAL: Kauchuk i rezina, no. 1, 1962, 11 - 15
TEXT: Four variations of the more frequently used designs of rubber-metal
valves are described. Rubber-metal valves are said to ensure optimum conditions
of hermetic sealing for working pressure in the formation of a closed rubber-
seat contour. Methods are recommended for determining the profile of the seat,
which, in turn, ensures the formation of a closed contour. The working princi-
ple of all 4 valves is as followss the seat is submerged in the rubber deform-
ing it and touching part of its surface where so-called contact tensions occur.
The submerging depth of the seat must be arbitrarily chosen, regardless of the
method used to determine the profile of the seat. The authors then give the ma-
thematical determination of various parameters. There are 7 figures and 7 Sovi-
et-bloc references.
ASSOCIATION: Sverdlovskiy filial nauchno-iS5ledovatellskogo instituta rezinovoy
promyshlennosti (Sverdlovsk Branch of the Scientific Research In-
Card 1/1 stitute of the Rubber Industry)