SCIENTIFIC ABSTRACT KREYN, S. E. - KREYN, S. G.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000826420019-9
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: January 3, 2017
• Document Release Date: July 31, 2000
• Sequence Number: 19
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

L 10123-63
ACCESSION NE: AP3001320
oxidizability was evaluated from the isotherms of cocygen absorption, the nature
and quantity oP oxidation products, and the anowit of sediment formed.
Oxidizability vas shaqn to depend primarily upon the concentration arA type of
organosialfur compounds present. These ccupounds oxidize more readily than hy-
drocarbons. and vhen present in small quantities Inhibit the oxidation of
hydror-arbons by decomposing peroxides formed in hydrocart.,on media. In lazrger
quantities the organosulfur compounds are oxidizedby oxygen as well, and tU5
accelerate oxidation of the oil, Oxidation of S-containing oils result3 in the
formation of sulfonic and coxboxylic acids. When S content ia sufft'cier;tly high,
the concentration of these acids is a linear function of the totall S co-t':-nt.
A parabolic dependence was established bet-ween the amount of aedim-ent formed
az a na!~Ut of the oxidation of S-containing oils aivi the total S cor~tent.
A fomula f or calculating the amount of sediment fom,.ed wa.-3 derive4 and
verified experJrentally. Oils containing aboul. 0.45% S are most resista'nt to
oxidation and form the mmUest quantity of oyidetic-i pr;-Aucts and sediment.
Ori g. art. has: '6 f igurea and---! formulas. -
ASSOCIATION: none
SUBMI7T'.'--. 00 DATE ACQ; 28May63 ENCL: 00
SUB CODE: 00 NO REF SOVI. 009 OTHER: 002
Cord 2/ 2

KREYN, S.E.; RUBInSHTEYN, I.A.; POPOVA, Te.A.
Effect of chemical composition of oile on their stability
during oxidation. Neftekhimiia 3 no-41584-593 -Tl-Ag 163.
(MIRA 16:11)

-KREYN, S.E.; VIPFFR, A.B.; SHEKH-FEP, Yu.N.
Solubilization of' the contqainatirn pr(yiucto Or rrotor oils by
the cleaning action of metal sulfonate,2. Khim.i tekh.topl.i masel
8 nc).11:52-57 N 163. (MIRA 1-6:12 )

WLIDBEMP D.O.; DEYNO S.E.; KAIAYTAN, Ye.N.; KICHKIN, G.I.;
MINKHAYROVA, S.A.; TRUBENKOVA, 11.ft
Methods for obtaining oils with Improved low-temperature
properties frm sour curde. Trudy BashNII NP no.6:105..Ill 163.
(~M 17:5)

KULIYEV, All 1.11usayevich, prof.; E" :,E..
nauk, red.; YEEISHERUM, O.M.0 r0a,
(Lubrication oil additives; ehvmI.,itr-j and 'Iri-
sadki k smazochnym maslam; khimiia i tekhnologiia. 11103kva,
Khimiia, 1964. 321 p. (MI-RA 18:3)

11614-66 "T~J'T(m)
ACC NRt AP6005236
W
SOURCE CODE: UR/0413/66/000/001/
ITIVENTOR: Pa2R~,_K._K.; Kreyn, So Es; Vipper, A. B.; Zuseva, B. So; Garzanov, Go Yes;
i h - ___Y. As
Vinner, Go Go; Dobkin, I Ye77, A =anas'yev,
q cli~skaya,
Botkin,_P. P.; Kuliyev, A. Hs; Zoynalova. Go A.
ORG: none V
TITLE: Preparation of motor oil. Class 23, Ho. 177579
SOURCE: Izobreteniya, promyshlennyye obraztsy, tovarnyye znaki, no. 1, 1966, 74
TOPIC TAGS: motor oil, antivear additive, detergent additive
ABSTRACT: An Author Certificate has been Issued for a preparat&ve method for motor
oil, Involving addition of a detergent and an antiwear additivellto the oil base. Th4
method provides for the use of an alkyl-formaldeFyde condensation product and of a
dialkyl dithiophosphate based on C12-C16 alcohols as the additives. (BO)
SUB CODE: 1l/ SUBH DATE: 16Apr64/ ATD PRFSS:1110
-Card 1/1-

L 145678-66 FeIT (m) /T DJ ATE
ACC NRi 6023624-------- ---SOURCE-Congi-tjR/O)-18/66/000/004/0021/0024
AUTHOR3 Botkinp Pe P.;
V1222S.L A. B.; Zusevap B. S.; Kreyn, S. E.; Papoks K. K-;
Somov, V. A
ORG: none
additive
TITIS: New composition of diesel oil
SOURCEI Noftepererabotka I neftekhimiya, no. 4, 1966t 21-24
TOPIC TAG31 diesel oilp antioxidant additivot lubricant additive
ABSTRACT: A composition of additives to motor fuels was developed in order to match
innorted additives in their effectiveness w n taken in similar concentrations. The
co;Dosition includes the additives BFK (4%) and LANI-317'/(0.25%). The BFK additive
ir. ~ho barium salt of the products77 condensation of alkylphenol with formaldehyde,
and the LAIII-317 additive is zinc dialkyldithiophosphate In Isopropyl alcohol and
C12-C16 alcohols. In wetting and antioxidation properties, the now composition is
practically equivalent to foreign additives (t1ioso of the Monsanto Co.) designed for
oils of the first series of the inLornational classification. The now composition
also has advantages over antiwearilarnd wetting agents in the operation of a diesel
motor on low-sulfur fuel. The use of the now composition of additives increases the
motor potential of fast dissol engines and reduces their oil consumption. Orig. art.
Card.1/2
UDCt 665.4s66-022.3i621.892

L 11-5 ~ P) t ~ -16
ACC NR,-- 'A?6u-j624-
h-as 1 3 tables.
ii/ SUBN DAM: non,)/ ORIG REFI 007/ OVI REF: 001
fv
Lcard 2/2

ACC NRt AP6023960 SOURCE CODES UR/0204/66/006/002/024110248
AUTHORS ~=t S. E.; Rubinshteyn, 1. A.; Popova, Ye.-A.
ORGI none
ff
TITI-It AdloftLant pj2pqrtied of organic sulfur compounds present in petroleum oilst
and possible formation of aryl sulfide complexes
SOURCES Noftokhimiya, v. 6, no. 2, 1966, 241-248
TOPIC TAGS: organic sulfur compound, antioxidant additive
ABSTRAM The paper discusses the antioxidant properties of organic sulfur compounds
contained in narrow chromatographic fractions isolated form the Sul-fur aromatic con-
centrate of the Tuymazy petroleum distillate with Vl()Oo = 10 centistokes. The anti-
oxidant properties of the compounds wore found to Increase with the degree of their
cyclic character; their inhibiting capacity considerably exceeds that of the hydro-
carbons 1with which they are associated. The various organic sulfur compounds present
in the distillate differ in the mechanism of their action and manifest their maximum
effectiveness at certain definite concentrations in the oil which are characteristic
of each group. The organic sulfur inhibitors may form associates with aromatic hydro-
carbons and organic sulfur compounds whose molecules contain aromatic polymuclei. Th,
formation of associates decreases the antioxidant effect of organic sulfur and aromat,
ic inhibitors. Orig. art. has$ 2 figures and 5 tables.
uDci 665-521-5:665-547.7.

ACC NR, AP6023960
SUB CODES if/ SUBM DAM 23kig65/ ORIG REFS 0061 OTH REFS 001
Card 2/2-fC

L 01303-67 EWT(m)/EL,,P(J)/ ip~t)j I 'B /RN
p(
ACC NRt AP6003433 (4) SOURCE CODE: UR/0065/66/000/-;01/004,3/0051
Lollborg, _A* Lq; Vaynshtok, V, Vo; Kreyn, Se E.; Shokhter) Yu, 110;
Poddu1onyy, V.
ORG: none
V1
TITLE: Production of nitrated potrolat=-base corrosion inhibitors
SOU11CE: Khimiya i tekhnologiya topliv i masel, no.lp 1966# 48-51
.TOPIC TAGS: potroloLp productj corrosion inhibitor, steol.,
PBSTRACT; Ozocerite and petrolatum-base corrosion inhibitorste nov mado by
with air at 13o-16oC in the presence of a catalyst. The preparation takes 10-24 hr.
i
A less time-consuming method was offered for producing a corrosion inhibitor fron
petrolatum. It consisted of treating petrolatum with a 62% FIN340-olution neutralizln:,
;the reaction product with a 20% aqueous solution of NaOH witho rawval of the spent
1FN03, and dehydration. The nitrated and neutralized petrolatum was completely solub'Q
in oil and insoluble in water* The test or, the corro3ion-protectiva properties of the
5% solution of nitrated petrolatum in transformer oil made with St,45 steel proved tha",
1 13 ~-
as a corrosion inhibitor, the product was not inforriar, if not s-,.iperior.. to the oxidized
i
petrolatum. Tho optimal con~Fption of E03 wa:; dette.-mincd as 101C. Nitrating petrolatun I
Eth large amounts of !~;33(~30%) contributed in noma cases to its corrosive properties! F
i
CcrJ -1/2 uDc: 665-521.5 : 66.095,81 ; 620,193

A' c N.,,: ,1)6C03433
~h
i to the Tho trea'non' of oxidized petrolattm with small amounts
(5-'-5,1,),-" 1:"N0,,,.;it1i noutl-a-lization ~(NaOH and dehydration yielded an inhibitor
coluIble L04.
th in wU'*'.or tuid in ails. Thin permitted it to be used in the form of either
~oill or wat-:ir solutions. 7he most effective corrosion inhibitors for the steel was the
:oxidized petrolatum, having an acid number of X-L-415 after treatment with 15% addition
~of the 62/'" B03 solution. The quality of the inhibitors depended greatly on the purity
jof the final product. For this.purpose the nitrated oxidized petrolatum was purified
~3f spent M;03 by settling and treated with NaOH to a neutral reaction& The product of
!,nitration of oxidized petrolatum was tested as a corrosion inhibitor for ferrous and
Inonferrous metals (All duraluninl Cu,.Fb,, Snl bronze., Mg alloys, steels., solderl cast
liron, and in combinations of metal-dood and metal-rubber). In all cases it provided for
ilong-lasting and reliable protection. The nitration of oxidized petrolatum from the
lKazan NFZ was made In a pilot plant installation with 62% HNO (consumption 15%) at
i7O-90C for 4 hr without settling out any of the spent ELIO 3* Pne nitrated product had
ian acid number of 90 mg KOH. The final neutralized inaibit6r had an ash content of 7.5%
,an alkalinity by phenolphthalein of 1.2 mg KOH and by bromophenol blue of 65*7 mg KOHp
la water content of 1,6% Dean and Stark, and good protective properties of the 5% solu-
Ition-in transformer oil for Sto45 steel: more than 30 days In water before the appearano
!;of corrosion nuclei* The nitrated petrolatum and the nitration of oxidized petrolatum
-:,-n be made in the same simple apparatus which is used for the nitration of mineral
jz:,ils. Origa art. has$ 5 tables*
CODE:/(j13/ SU13M DATE: none/ ORIG REFs 006/ OTH REF: 002
Card

L 42173-66 FW7 (m) IT TV
ACC NRt AR6014532 ( 4 SOURCE COW: UR/0081/65/000/010018#018
AUTHORS: Badyshtova, K. M.; Vipper. A. B.; Vorozhikhina, V. I.; Donisenko, Ke-K**#
- a- 3 1
Kroyn, 5. 6.; Pyati-lotova., N. I*; Mazanov. L. a; Yastrebov, Us is,
TITIZ: Effect of the extent of refinQ'of the distillate and residual co=ponents-b.
of DS-14 oil from sulfurous petrol-eu-m upon their operational properties
SOURCE: Ref. zh. Khimiya, Abs. 19P129
REF SOURCE: Tr. Ku7byphevsk. n.-i. in-t neft. prom-sti, vyp. 25, 1964, 85-95
TOPIC TAGS: lubricating oil, petroleum refining, phenol / DS-14 lubricating oil,,
11,1S-20 lubricating oil,, DS-11 lubricating oil
ABSTRACT: Laboratory study a4d testing on the engine Yan-204 of f ive samples Of
DS-24 oil of Novokuybyphev M,~(differing by the technology of their processing) havq
been performed. The study shows that the changes in the extent of phenolic refining!
of distillate and residual components (within the limits of 160-180 and 250--~320.5
of phenol, respectively) have no effect on the detergency, antioxidative,, d ti-;
an an
wear zourtieW\of DS-14 oil containing effective additives. Economically, the mos'~.
cIonveniont-me-thod for producing DS-14 oil is to mix the residual and distillate cori-
ponents of Diesel oil, 60 and 40%,, respectively, (i.e., components treated to a 1e
extensive phenolic refining), This leads to lowering the price of DS-14 oil by 15~"'
and to increasing its yield by 4%, as compared with the prodlu tion of DS-14 oil by,
=Wng oils 16-20 and DS-no\\ As N. LTrarkation of abstract
CODEs

KREEYN, Selim G.
"On an Inner Characteristic of the Set of All Continuous Functions Defined
on a Bicompaut Hamsdorff Space,," Dokl. AN SSSR, 27, No.5, 1940
Odessa State U... Kiev

KRUNP S. 0.
"Semi-Arranged Rings)n Dokl. AN SSSR, 30, No.8, 1941
Kiev State U., Math. Imt. Ukr SSR Acad Sci

~4F Al
r'I A
S. G.- JU(bektviour of Izasodx2anxic facton; neat--3
the-raffrW a Strwag wave. Rep. Wopovidij Acaff.
Sci. Ukrainim SSR no. 3-4, It-t6 (1.946). (Ukrainian
and English)
The author wriies down the one-dimensional equatinn4
governing the trunsition 61 pr6sure, density and vt4c0, there
exists r.>0such that for 0,,O be funotionals defined on E the gradients of which are
continuous operators on E* ~(X) . max ~,(x)-J(x) are those indices i for
i
which 'Pi(x) - ~(x) for given x. Then the following lemma is valids if f(X,t)

Doklady Akad. Nauk 102, 13-16 (1955) CARD 2/3 PG - 74
BatisfieD the condition
(2) ( ri (,)x,f (x,t)) e-.L I ~(x)]-W(t),
where (1,x) denotes the value of the linear functional 1 on the element x,
and if x(t) is the solution of (1) for t1-< t 4t., then
t2 Vx(Y]
(3) -T ( t) dt -,> du
f f LTU7
ti Ox(ti)]
From the lemma follows the theor4pkA If (2).- satisfied, for qxg--.-,oo also
(x) ---), oo and for every A> 0
00
(4) du 00,
f LFUY
A
then all solutionB of (1) are continuable on the intervalft0'001
This theorem can be applied for the investigation of a system
dxi
dt i(x1P ... Xnft)
ifit is considered as an equation (1) defined in the n-dimensional euclidean
space. Choosing for q(x) several functions of the n variablest then for (5)

Doklady Akad. Nauk 102, 13-16 (1955) CARD 3/3 PG - 74
one can obt in several non-local existence theorems. In three cases for
different T(x) the concrete condition (2) is given#
From the lemma follows still a general theorem of uniqueness; x an XI(t)
and x - x2(t) be two solutions of (1) satisfying the same initial condition.
Let be ~(O) - 0 and
( r -,< L
j(x i-x,)(xl-x2)' f(xl't)-f(x2lt)) 01-x2)] 'T(t'
where for every E > 0
du
77 ~ 00,
0
theii x1(t) M x2(t)'
The given theorems can be used for the proof of the non-local theorems of
existence and uniqueness of theintegro-differential equations.
INSTITUTIONs Public University Voronei.

SOV/124-57-9-10375
Translation from: Referativnyy zhurnal, Mekhanika, 1957, Nr 9, p 69 (USSR)
AUTHOR: Kreyn, S. G.
TITLE: Mathematical Aspects of the Theory of the Motion of a Solid Body With
Cavities Filled With Fluid (Matematicheskiye voprosy teorii dvizheniya
tverdogo tela s polostyami, napolnennymi zhidkostlyu)
PERIODICAL.: T r. 3- go Vses. matem. s"yezda.Vol 1. Moscow, AN SSSR, 1956, pp ZO
ABSTRACT: The paper analyzes aspects of the existence of a motion of a viscous
incompressible fluid and of eddy motions of an ideal fluid during a
given motion of the,body containing it and with given initial conditions.
Nonlinear and linearized problems are analyzed. The author studies
the problems of the existence of small oscillations of the fluid, of the
totality of the system of nor'frTal oscillations, and of the characteris-
tics of the frequency spectrum in three cases: The motions of an ideal
fluid approximating a state of equilibrium with the presence of a free
surface, the motions of an ideal fluid approximating its rotation as a
solid body, and the -.oscillations of a viscous fluid approximating sta-,
tionary motion. In the latter part of the paper the combined oscilla-
Card 1/1 tions of a solid body and a fluid are studied on.aimilar't4s". Annot.

Call Hr: AF 1108825
T-ransactions of the Third All-union Mathematical Congress (Conto ) Mosc(~w J,
Jun-Jul '5 Trud , Sect t3.6n1Vaetej15tv0AN SP4R, f4oscow, 1956, 237 pp.
Krasnosel 1~dkiy, YMAX.Vtv"broneihi~ h nvestigation
of Bifurcation Points of Non-linear Equation. 2011-205
Kreyn, S. a. (Voronezh). Mathematical Problems In
-the--Mv;~y~f Motion of Solid Bodies With Fluid-
filled Cavities. 205
Kupradze, V. D. (Tbilisi). On Some New Research at
the University of Tbilisi in the Mathematical Theory
of Elasticity. 205
Mikhaylov, G. K. (Moscow). Precise Solution of a
Problem on Stabilized Motion of Ground Water in Vertical
Plane With Free Surface and Feeding Zone. 205-2o6
Mention is made of Polubarinova-Kochina, P. Ya.
Movchan, A. A. (Moscow). Linear Oscillations of a Plate
Movin in Gas at High Velocity. 2o6
Card 98/80

IjaiccW, Yu~ L. and Krerhi S. G. Tategratioa and dif.
F i vil
iri m' and
aprIlvatiom to
GI Only. 'Trud, LL fiO. I

4nd.3pvIirati;3ns-m! giWJI Of Zt f0rML&I for-

Hui k, a but'PrI&I oi;f t1i!kx-
cntiabk: for t ill t~ornv-, i~i t1w r,--ki bw.,, ;,wi f ~j
functiul, with co 6 loug_ k-_,,M "Al'.TS "Al k1 %14nit
li;z
ill tjv~ of diAtmai-un. f hi- i-i
f-
6
(Iifill
IP
f
f
-U

e-, a &
wbere EA(4 is ti 14~i
The fornAula i3 extr-0---d to higher order dewrativc-3 by
fterat,au, and a Tavicir's ti-C-Or-M., wifli th(~ int('"gLif fonn
of the rt.-mainder, is proved. The difit rf.-ntial co-Afici-nti of
the o1wrator fwictions and the int,,:gak are und u,sicjYJ 'a
th
exist in:fhe sen3e of cunvergericc by rtprratur norms.
propertias oUthe qlielijes integral with resix-a to the
spectral ftuiction are-discLLi.-icd in ~rxn(- Bv taking
to be a function cqiial-to .1 isolated. jy)rtion of
tht: sjxctrumt rind Zero tun tht! 5p-ctrurn of 11,
z~pp!fcation5 arc gken to perturbatiou Eheury; the f-.jr-
mulac simplify considerably when H(fj is linf~ar in t.
Estimates for the error Urm, in the Taylor'& c-xpansion
are given. The principal roults appearM without

'
N,~
proof in DoW. Mad Nwuk '-qS R 70 (1,73 t), 13 -16;
Dapovidi Akad. Naa- -Ukrain.
HSR 1951, 2-14-233 I'M It
12,617; 16, 264]~ L. B. Cwp,-y (Cardifl).

S()V/ 1 ~7 7 i (I I
T -.A,, -!at -in, Ret u., a r,, y zhu r r a I, Me I it "t. rgiya, I', ~ 7 Nr 110 15 "I.,SSR)
AUTHORS, Kre~ r S. G. Reshct~ -,. Kh- S,
T!TLE ci "~.e Fie?d an Elect--cmagnet:c Separator With
A.'Ic,%va,-(e I-,:- -.11C MOUal Eltick-1- c: Avjacert_ Po;e Tcrrn_ral~,
Rschvt po'v~ ~Iektrcmagn;-rcm separatore - u0ieton-l
zd.rlll(,Igo I;van'!%,n 5( Sed!"~h P',!';U~3r;y~h
PER'OD'GAL SI, f.r. Krr,c-ozh_;~, gorrioruc-. 19561 Nr pp 1 ~4 148
A! I S'l R A (".'r Et,,''(-, a 11,A(1 beC!'_ Madv ci !tic twc nitvetc
I eld arising between the intinitely thin poles, either wedge --shaped
o., ~_a.. of a magnet (DerVacti, 11. G. , Gornvv zh. , IQ50. Nr 1).
The r!f-;e!.t ixcft~ .': de,cled to I,,. e_'0;'gM:o't 0' Ox fieW exi-itifig
with iuch a sys!-rn o! po'.rted po'e! Funuarnt-nt,! het e, :s !he
cl,Cce cl a d'sta%ci: between the po'rit*~a vcIes ut wh'ch the mutual
IT',I'LWf-.Ce M i~,.e re~ipecC-e poles woul'o. ric, lead to any ct',ceable
r- tt;e magv el.:.c torce exerted oi a partlcle ci ore.
Erjudtor-5 a.-e put lorth ~or c,,Iculat.or. of the muiual e'..,ectz' of like
PC i e~ of 1he m ignet:C torce, ard ot the intcns~tv oi the lield. it
C-A! (4 1 /2 ts toul"d that the riptimum rad,'u.~ ci cur dtUre is r z 0. 15 1

SOV'i 17 57 10 i8584
A-al~ F;ela ar. E'cc-rornagne,7c Separd,cr ~Cc-l
ar avg'e f *19 the m~r'rrium &,!,i,-, e !~etwvcr (-pr-)cjs'.te
pc'(:,, 0 ti,e magretEi the rzie'u-4 c: cur a0ire o1 -~ rourded mag, et at its
7("%Ve .1, pt
A, 51-.,
C '! a

7 1
/K 1.10 s' % ~lk~ffl' A,, and Kreta, S. G 0 n a class of
eum- thmems far-ME
~W %' jfx~ V1.
Uspchi Ma 2r9--? S'
t. Nauk (N.S.) 11 (1956), no. 1(67), -1
ussiau)
Considex the'-pt-oblem y',., y), vvith
if ig co"nilnuotm on R thlen an im-
prw"e-nent by Imon MML. 1, 28 (1928). 216-219, C.;
thfurem of Ro!;enbktt ields uniquentss of tht: Soil,
ki~, I - The principtil result in the paper wider i!i , 1-i-at
if '-dsrl j/(x' yj'j-/"X' Y2)~jsPjYj-Y2f2
and 0-,ctO) for every t. At first the linear equation
dx
-rt. Ax + f M
is considered, where A is Independent of t. Let q be the linear operat--~r

Doklady Akad.Nauk 1_11.,, 19-22 (1956) CARD 2/3 PG 7';'
t
T(t-x)x(_C)aC,
0
Theoremi a) q acts and in continuous in the space C L of functionj which
satisfy the Lipschitz condition, If for ~ :-- 0 the semigroup T( ~ ) is cor,--
tinuoug with respect to the norm (condition C n according to Hill), "!aer, q
acts from CL to C 1 and is continuous. b) if A- I is completely contlnlo-ilti~
then Q an an operator from C L to C .-s completely continuous toc,.
Theorem: Let T(~ ) satisfy the condition Cn and let f(t) be continuous anJ_
have a strongly bounded variation. For x 04r--D(A) the formula
x(t) - T(t'x + Qf(t)
) 0
yields the solution-of (1)-(2). dx
Let be given a homogeneous linear equation __ . A(t)x and let be satisfied
dt
the condition Do C(t) - 1(t) d .1"'(t) bounded and strongly cont2nuous in
dt
Theorem: If c'( ) is satisfied, then 1) the operators A(t) have u common regicn

Doklady Akad.Nauk Ill, 19-22 (1956) CARD 313 PG - 711
of definition, 2) the operators B(t,B) - A(t)l -1 (s) are continuous with respect
to the norm in t and a and 3) the derivative 9B(t,s) is strongly continuous
at
for every s in t.
If 1) and 3) are satisfied, then CK) is satisfied too. This theorem and a further
one are int'direct connection with the investigations of Kato (J.11ath.Soc.Jap
5,L no.2, (1953)).
Then the non-linear equation (1) is treated. A. generalized solution of (1)-0)
means a function x(t) which satisfies the operator equation
(3) X(t) - Qf Itox(t)] + U(t'O)xo
For the proof of the theorems of existence theorems of fixed points are used,
For a sufficient smoothness of f(t,x) in some cases it can be shown that the
generalized solutions the existence of which was proved, are ordinary solutions
of (1). Some examples are considered.

SUBJECT USSR/MATHEMATICS/Algebra CA10) PG - 736
AU Til OR BEREZATISKI Ju.1a., KREJN B.G.
TITLE Hypercomplex systems with an infinite basis.
PMODICAL Uspechi mat.Nauk 12L 1, 147-152 (1957)
reviewed 5/1957
An ordinary hypercomplex system the elements of which are n-dimensional
vectors x, can be underntood as a ring of complex-valued functions x(j) - xi
which are defined on a basis Q consisting of n points, where the ordinary
addition and multiplication with a scalar and the composition
n
(X * YM) - T x(j)y(k)cjkl
J,k-1
C, jkl -structural constants, are valid. The authors extend the notion of the
Lommutative hypercomplex system to the case that Q is a locally compact
metric space, The authors restrict themselves to positive structural constants.
Then it is shown that by restricting to (in a certain sense) symmetric hyper-
complex systems, to these systems the principal results of the harmonic
analysis on commutative locally compact groups can be transferred. Numerous
examples aro given.

-SUBJECT USSR/ITATHEMATICS/Differential equations CARD 112 PG - 760
AUTHOR X"JN S. G.
TITLE Differential equations In the Banach space and their
application In hydromechanics.
PERIODICAL Uspeohi mat.Nauk 12, 1, 208-211 (1957)
reviewed 5/1957
The author considers the motion of a tenacious fluid in a closed vessel
which carries out a given motion around a fixed point. The system of motion
equations is non-linear and not of the type of Cauchy-Kowalevski since the
derivative with respect to the time of one of the wanted functions (.�z
dt
p - pressure) does not appear in the equations. The author shows that by
introduction of a suitable Hilbert space and by decomposition of it into an
orthogonal sum of two subspaces the unknown function p can be eliminated,
while for the other unknown function v (relative velocity) an equation of
the type
dv
(1) dt . Av + g(t,v,B1V,...,BnV)
is obtained. Here A is a negative definite operator in the Hilbert space
112
and the operators BI depend on (-A) .With the aid of the operator

Uspechi mat.Nauk 12, 1, 208-211 (1957) CARD 212 PG - 780
q - (A the non-linear equation (1) can be reduced to an integral
dt
equation which has a solution in a sufficiently short time.
With this consideration the author wishes to point out the importance of
the investigation of differential equations in Banach spaces.

ERASNOSELISKIY, M.A.; KMN, B.G.; KYSHKIS, A.D.
The broadened sessions of the Voronezh Seminar on Functional
Analysis in March 1957. Usp.mat.nauk 12 no.4:241-250 JI-Ag 157.
(HIIIA 10: 10)
(Voronezh--Functional analysis)

AUTHOR; K r "oscow) 40-21-2-3/22
e _&, L:OiBeyev, (Voronezh,,
TITLE: On the Oscillations of a Solid Body in the Interior of "Which
There is a Fluid With a Free :;urface (0 kolebaniyakh tverdo-
go tela, soderzhashchego zhidkost' so svobodnoy paverlhnostl-
yu)
PERIODICAM Prikladnaya Matematika i Ifekhanika,1957,Vol 21, Tir 2
pp 169-174 (USSR)
ABSTRACTj Under the influence of conservative forces a solid body with
a cavity partially filled with a fluid carries out small on-
cillations which are described by the following equations
(due to N.N.Moyseyev,Thesis, Mathematical Institute) Academy
of Sciences )41oscosy 1955),
Y'.' + (P) (P , t) dP+ /,L2Y + (P) "g (p, t) dP t)
M 6 6
(p, t) + H(P, (Q, t)d-,l +ZLYn"'tn(P)+L Yn 9n (P~.O
n' n-1
Here the Y i are the 3,eneralized coordinates of the body,
Card 1/ 3

On the Oscillations of a Solid Body in the Interior of Which 40-21-2-3/22
There is a Fluid With a Free 3urface
z - ~(P,t) is the equation of the free surface; vi and y,
are functions of the point ,7hich are determined only by the
-avity; A&2
geometrical properties of the c i are constants
which determine the conservative reforces; Q i(t) - outer
forces; S - the plane domain corresponding to the free sur-
face in the state of equilibrium; y-density of the fluid;
g - constant field tension; H(P,Q) - the Green's function
for the Neumann's problem for the domain occupied by the
fluid. The motions for a i z 0 are said to be free oscilla-
tions.
'.11ith the aid of function-theoretical methods the authors
provet For motions of the considered body around the state
of equilibrium there appear normal oscillations, i.e. (1)
has solutions of the form
iw t iv t
(2) Y n n
jn . qjn e Cn n 0
In order that the atate of equilibrium is stable (i.e. (2)
remains bounded for all t) it is necessary and sufficient
that the matrix
Card 2/3

On the Oscillations of a 'jolid Body in the Interior of "hich 40-21-2-3/22
There is a Filuid With a FrPe :*;urface
2 1
6-k (P)Q (P)dP;
k
is positive definite (S jk - Kronecker's C). Then all frequen-
ciesi) are real and 2 as n --I, oo . Besides then in
n n
the metric of the L 2t (2) is a complete system of solutions.
In this case the Cauchy problem has a unique solution defined
for all t if the Q i(t) are of bounded variation on every fi-
nite interval.
There are 8 roferonce8i 7 of -which are Soviet and 1 America.,
SUB17ITTED: March 9, 1956
AVAILABLEx Library of Congress
1. Solids-0saillatims-Thewy
Card 3/3

K R
SUBJECT USSR/11ATHEI(ATICS/ftnotional analysis CARD 1/3 PG - 874
AUTHOR EUSNOSZLISXIJ I.A.t KUJI S.G., SOBOLEVSKIJ P.E.
TITLE On differential equations with unbounded operators in the
Hilbert space.
PERIODICAL Dokl:dy Akad.Nauk 112, 990-993 (1957)
revi wed 6/1957
Joining a paper of Kato (i.math.Soo.Japan, 5-1. 2, (1953)) the authors
investigate the equation
(1) -k + A(t)x - f (t)
dt
in the Hilbert space ff. Kato constructed the solution of (1) in the Banach
space in the form
(2) X(t) - U(t,O)X0 + qf(t),
where the solution of the homogeneous equation has the form
X(t) - U(tjG)X.
with a continuous aAd bounded operator U(t,s) and with the initial condition

Doklady Akad.5auk 112, 990-993 (1957) CARD 2/3 PQ - 874
X(S) - X0 and t
f U(t,s)f(s)ds.
0
In the special case considered by the authorap about U and Q more exact
assertions can be made. Here it is assumed that 1) A(t) is selfadjoint and
(x,x), 2) for 0:6 caL and suf f iciently small it holds s
jjBv1j 4, jl_~ IlAvil + L-:1 vj
~'r
The operator S is called elliptic, if S = A+B , where A
is self-adjoint and positive-definite and B is of fractional
order with regard to A. If A is elliptic in (1), then (1) -
(2) is correct. Let U A (t) in this case be the semigroup
generated by (1) . Por each v~Sll and t;),0 the function
'UA(t)v satisfies the equation (1) . All the solutions U A (t)v
are analytic in larg tj< -f0 (1po does not depend on v),
There areg references, 3 of which are Soviet.
Card 2/3

Differential Equation With Abstract Elliptic Operator in 20-118-2-7/60
the Hilbert Space
PRESENTEDs July 11, 1957, by I.G. Petrovskiy, Academician
SUBMITTED: JulY 8, 1957
AVAILABLEi Library of Congress
Card 3/3

AUTHORSs Glushko,V.P. and Kreyn, S.G. SOV/20-122-6-2/49
TITLE: Fractional Powers of Differential Operators and Embedding
Theorems (Drobnyye stepeni differentsiallnykh operatorov i
teoremy vlozheniya)
PERIODICALs Doklady Akademii nauk,SSSR,1958,Vol 122,Nr 6,pp 963-966 (USSR)
ABSTRACTs Let G be a bounded domain of the n-dimensional space (n>,2)
which is star-ahaped with respect to a sphere. In the Hilbert
space L2 (G) let a self-adjoint positive-definite operator A
be considered which is generated by a differential operator
of even order and by a system of homogeneous boundary con-
ditions. A is called strongly invertible, if
A-'f 11 .4~ C ilf 11 (f E L where W 1 is a Sobolev space.
W1 L2 2) 2
2 n
Theorems Let A be strongly invertible, 0 ,Y, the get Ea is contained in the space EO(q is dense in it and
I I x 110( !~~ 11 x3for x C-- E ,~
2, from o(-0 3 :5z B and x G E,,there follows
2-
x x x
13
Let F and F 1 be two Banach spaces, where
(6) FIL F F 1 dense in F J! x flF x F x& F,
Card 1/ 3

i'-)'q
on t~,e Notion of Normal Space Scale ,/020/60/132/03/06/066
On 0' 1 let be given a normal i3cale of the spaces E',e' 9 whnre
(7) F 0(-E 0 ? F 1 E,I X 11 E 'X 11 F x F 0)
0
X 11 E 1 X H F (X FI)
(8) lim x F. 2= X 11 E (x,:-E,
B > 1 1
Tt in said that the scale E-,- bases on the spaces F 0 and
hf~,,ore,m I . Among the normal scales which base on F and IF there exists
ncalr- G, b
,)nc is dense
- (0 !~': cA' -e-1) with the properties a) Go -a ;
~.n G, ; C) for every normal sca)e EX which bases on F0 and F1 it holds
if x 11 -- -
E X ii Go,, (0, xt--. F,
This scale is called maximal,
Theorem 2 : Let the spaces F 0 and F 1 satisfy let GX be tho 11aximal
Card 2/3

On the Notion of Normal Space Scale ''/020/60/132/03/06/066
scale for F 0, F 1 ; let be an arbitrar,-,- on T0,11 wl,:ch satisfies
(8). Let the linear operator A be defined on F 1 and let it satisfy the
condition
Ax 11 -~C I(x IIF Ax 11 r C It x 11 x E: F
Eo 0 0 F1 1
Then for 0 -~' ck :E- I it holds
(9) 1l Ax 11 ~G, the :solution actually pertains to , he, space H
t nding
#priori estimate is true. The paper presents theorems on homeomorphism for
the intermediate spaces Hk and normal homogeneous boundary- conditions. These
A
t-heorems are applied to local increase of smoothness of the solution down to the -
boundary. The proof rests on the uiterpGl4tion theorem which consists in the
rollowing: if Rtand Rt are 2 Hilbert scales of space and the operator R operates
C4*d 3/ 4