SCIENTIFIC ABSTRACT NEMIROVSKIY, YU. V. - NEMKOVA, O. G.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001136520016-6
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: March 14, 2001
• Sequence Number: 16
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

ACC MRs AP6034147 SMCE CODEs UR/0424/66/0)0/005/01 30/0138
,AV=Rt Memirovskiy, Yuo V. (Novosibirsk)
'ORG. none
TITIZ: On the limiting state of layered and structurally orthotropic cylindrical
;shells
I
,SOURCE: Inzhenernyy zhurnalo Kekhanika tvardogo telat noo 5, 1966, 1'.-0-130
,TO-PIC TAGS: shell theory, cylindric shell structure, orthotropic shell, sandwich
istructure, plastic deformation, pl.asticity
I
ABSTPACT: This article deals with some aspects of analyzing inotropio, and structurally
~orthotropic cylindrical shells with layered models, and also with the formlatioj-. of
limiting relationships between gemeralized stresses for these models. Relationships
for two-, three-. and four-layered shells are obtained as special cases, and various
models of structurally orthotropic shells are considered. The material of all elements.
making up the shell is assumed to be ideal stiff-plastic, giving rise to the piecewise
11inear conditions of plasticity which are graphically portrayed in Figures I and 2; L
ithe first figure represents "sheathing" elements# and the second "stiffener" elements.
Limiting relationships of the form -I.. I I
a, + n,0 - hitall (2t, + r,,~) - (2t, - B,,~) (h,tall - qq) r,s / aW
+ 7 "1" (2h + ]P,4') - (24 - Bggl) (h,%? - h,%e) rd / on,
Card 113 - 28AW - 2 (to -.1206) (4161~ - N%,,) r,0 I am"

ACC NRs AP6034147-
Mij - M 034- Alto,$ (2t, Bill) 2 (ts - 1201 (hilgil BgI
IW& + fflT44 - moll -- h,%,s (21, + r., Bill) - (2t, - Bill) (1h%j~ - A,la,l) rVB,?
Mill' - A,%,' (2t, - B111) - 2 (is - t,$-) (h,4a,# rga
kl%ls (211 - Bill) - 2 (t, B"
MI + n,~ - -,44 hI%Iv (2t, + rill - Bill) (212 - Bud) (hi%ll
=01,0 Alla., (21, - B,,') - 2 (1, - to.) maa) rill t*B.,
-I 2ths%,' - 2 (in - tM-) (h.%,, - h,%,g) rill / B,,-
M, + nVal - A,%,' (2s, + r,,,) - (2t, - B,14)(hl%ll - hla,,) r.? BsIg
kl%ll (2t, + rill) - (2t. - B,g4) (hj%? - k,a,4) r.,
4 - t;0, (21;., - B,4)
2(8, - 0,1l) - ~ 6) = 0 0
y
are stated for the get Of limiting conditions satisfying the asatimptions of the
problem, where T, ' - ' '
MI = M. oil=
agill a. hit - h"'
7T -ff*
S,
I
V1
Card
2/3

ACC NR, AP6034147
A,
Fig. 1. Fig. 2.
!Por some special cases there are other "boundary" conditions which occur simul-
Itaneously with the given limiting conditions. Separate discussions are devoted to the!
Ifour-, three-, two-, and general multi-layered shell. For example, limiting condi-
itions for a nonsymmetrical two-layered shell might be
NJ + Mall, - 2A (12 T 1"), -t - 2h,ij + 2h (ig T- is*)0
to - t It'. ts - It - � Is*
Ang + 2hAej - � Ps8sh, 2hts
Ak = hj+ ht. 98'= (01& + OA)I;
'where Wt ht, Z0. ON, =wig
i "t, - hi - -
The model is also extended to cases Involving stiffeners, reinforcetient, and other
cond.itions of plasticity. Orig. art. has: 49 equations and 8 figunts.
~
Card 3/3 SUB CUDEs 661 ORIG RU 1 0031 M REP 1 003
PK_/,B ~O SUBM DATE

ACC NR,
AP6034777
AUTHOR: Nemirovskiy, Yu. V. (Novosibirsk)
OhG: nono
SOURCE' CODk:s
MI-2: On the stability beyond the elasticity limit of layered shells of
nonsymmetrical construction
SOURCE: Inzhenernyy zhurnal. Mekhanika tverdogo telap no- 4P 1956, 97-103
TOPIC TAGS; shell, shell stracture, sandwich structure, elasticity, elastic limit
;,BSTLR2XT-. An analysis is made of the stability of three-layered sloping shells of
nonsymmetrical construction. Of particular interest is the beha,rior of such a shell
beyond the elastic limit. The shell (see Fig. 1) consists of two bearing layers of
717TI it
Fig. 1.
thicknesses and 82, Young's modulus E and E and flow limits and a
1 2 '70v 02'
Cor 1/2
03

ACC NRs AP6034777
light filler of thickness 2h and shear modulus G 3' The Kirchoff.-Lyav hypothesis
applies to the structure, and it is assumed that Poisson's coeff--cient in the same forl
the bearing layers and that I . . 46 E . I
ES 603 ks C2
==~
where and are the tangential and secant moduli, respecti-ely. Amalysis is
rma
made of loading conditions which initiate plastic defo tions. Formulae are derived
for computing the variations of forces and momenta in each layer. A system of
eauations is found for defining the critical loadings for the loEs of stability of the
&lls. The symmetrical case ( 8 1 n 8 2, 0' - 1) is first analyzed, and some
generalizations are discussed for a sloping bimetal shell. The 6pecial case wherein
the materials of the bearing layers are not the same is analyzed, and the limits of
elasticity are found for E 2)' Ble The author notes that certain approximations for
computing the bearing capacity of the structure deserve additional study. Orig. art.
has; 21 equations and 2 figures.'
SUB 'CODE, 5M-13L SM D=s 05-Tul"/ ORIG MWs 00'7/ OW RV- 001
Card 2/2

ACC NR3 AP7006924 SOURCE CODE:
!AUTHOR: VokhmyanJLn,, I, T. (Novosibirsk); j[GM1ravsk1_y._,1U_._V,
,!(Novosibirsk)
.!ORG: Novosibirsk State University
universitet)
i
!TITLE: Load capacity of plain and
(Novosibirokly go3udaratvennyy
stiffened cylindrical shells
SOURCE: Prikladnaya mekhanika, v. 3, no, 1, 196T, 18-23
'.'l It.
TOPIC TAGS: cylJ ndrical shel 1 ice i ed
-teft Mol 041 shel+--Tuad aPac
ABSTRACT:The statte load-carrying capacity of nonstiffened anA ring-stiffened
cylindrical shells clamped along their face adges and subjected to inner
uniform constant pressure is investigated. -An exact solution of this prob-
lem is obtained foe a shell made of a rigid, perfectly plastic material
obeying the Tresca plasticity condition and associated liar of flow.
Equilibrium equations of a plain cylindrical shell, expremsions foe the
low of plastic flow, and boundary conditions of continuity of deformation
and of 3 try are used in deriving axpressloas for determining the exact
;Card

ACC NR-AP7oo6924
value of the limit pr;a:ure.pp for a plain shell as a function of a
geometric parameter o he hell, the statically allowable field of
stresses, and the associated, kinematically possible field of the rates of
strain. A simplified approximate expression for determining P (about
only 22 lower than the exact value) is also given. An expressfon for the
limit pressure P. of a cylindrical shell stiffened by closely spaced rings
and clamped along the face edges Is derived from the expression for Pp by
means of an affine transformation. The procedures to be used calculating
the limit pressure In a case when the stiffening rings are not close enough,
as well as In determining the optimum number (spacing) of rings are out-
lined, Orig. art. has: 2 figures and 11 formulas, (VKI
SUB CODE: 20/ SM DATE: none/ ATD PREW: 5117

I ~. .1 - I II," v ~ ~ V'I ~ , 1-. /V
SHLYAKol-l-, E.M.. Inrhanar, ARI-'!'-"'I
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~ - 7 ar~ --hain vroa,~-' . 3.
(KLRA 10: ?)
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oft of
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21
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Nil,
till
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MA,
QW1,
Ctli

L 081~1-67 ENT ( 1. 1.jP(.-) AT
ACC NR-' AP603352z'l SOURCE CODE: UR/0185/66/011/010/1078/1 8
AUTHOR: liddzhak, Ya. S ; Tgvstyuk. K. D.; Nemish. 1. Yu.
ORG: Chernev State Univirs ity (Chernivets' derzhuniversytet)
S
TITLE: kEff- e'ct of nonparabolicity of energy bands on the kinetic properties of
semiconductors,
SOURCE: Ukrayinslkyy ftzychnyy zhurnal, v. 11, no. 10, 1966, 1078-1088
TOPIC TAG!'): Fermi gas, 'current carrier, relaxation process, integral equation,
energy band, kinetic property, nonparabolicity, semiconductor
ABSTRACT: The concentration of current carriers of some kinetic coefficients
are calculated for the cases of undegenerated and greatly degenerated Fermi gasesi
with nonparabolic isotropic laws of dispersion. The scattering processes are I
described by the relaxation time 'pz;
-2. (-L- ) , where r depends on the
dp
scattering rnechanism only. All kinetic integrals are integrated in general form
for any r and expressed through known special tabulated functions. An analysis is
given for the equations obtained for cases of weak and strong spec,-:rum nonparabolicity.,
Orig. art. has: 5 figures and 42 formulas. [Based on authors' abstract]
SUE, CODE: 201 SUBM DATE: 24Dec65/ ORIG REF: 007/ OTH REF: 008/
I/, nez

ACC NR; AP602i(' )12 SOURCE CODE: uR/GO2l/66,/ooo/oo6/G748/J753
AUTHOR: 111~2 ~Sh Yu. M.
ORG: ]~~rs-ti-tu"te-,)-f-"m-t-,c--h"a-,n,ics k11 URSR (Instytut mekhaniky AN UTR3R)
TITLE: Plane problem in the moment theory of elasticity for a region with a round hole
assuming given boundary translations
SOURCE: AN UkrR3R. Dopovidi, no. 6, 1966, 748-753
TOPIC TAGS: elasticity theory, vector, boundary value problem, ela.3tic plate
FABSTRACT: The author studies a plane problem in the linear theory of elasticity which
.considers stress moments in an isotropic elastic material. In setting up this problem,'
Iformulas are given for the stress moments and translation in terms -)f complex poten-
Itials and the solution of the Helmholz equation. Expressions are given for the prin-
;cipal vec-~or and the principaL moment, and also for boundary conditions in fundamental
!problems of this ty-pe. These formulas are derived on the basis of -:-epresentations for
!the components of the stressed state in terms of the stress functian using the Muskhe-
'lishvili method. The stressed state of an infinite plate with an a~6solutely rigid
:washer sealed in a circular hole is calculated. The entire system is assumed to be
:uniaxial-ly stretched to infin-fty. The plate is located in a rure bending field located
:in the plane of the plate. The article was presented for publication by H. M. Savin.
Orig. art. has: 2 figures, 12 formulas.
SUB CODE: 20/ SUBM DATE: 20Jun65/ ORIG REF: 003/ OTH REF: 001
/,3/
Card 1/1 ,

L 29802-66 EWT(mjj~M~E(,~) IjP(c) EM
ACC NRt AP6011219 (N) SOURCE C019t OR/0-198/66A02/004/0085/0096
ALI THOR: ha Yu. ff. (Kiev)
ORG: Instituto of Mechanics, AN UkrSSR (Institut makhaniki AN UkrSSR)
TIM: Str*na concentration around curvilinear holes in the asymetric theory of
elasticii7y- 7- ~
SOURCE: Pri]dadnaya makhanika, v. 2, no. 4, 1966, 85-96
TOPIC TAGS: elasticity theory, stress concentration, "Mb", approxims-
tion method,, complex function
ABSTRACTi The plane problem for an Isotropic medium in elasticity theory is con-
sidered, An approximate perturbation technique is used to calculate the stress
concentration around curvilinear holes in the plans, which is assumed to be infinite
in extent. 'rho term curvilinear is used in the Bons* that the function s = W
can be mappal on the ~ plane as
a R +
Here, E takes on the values
Card

L 29803-66
ACC Ilds AP60W19
4-b a +b
2
6=�T; k-2.
:hl; k-3
9
for an elliFee, a triangle,, and a square, respictively. 1n the absence of voli=et-
ric forces,, the governing equation for the static problem is give-a by
Vw - 0; VI VI - 0.
The stress functions a" calculated from the series
1 Card 2/3

L 29803-66
ACC NRs Aftolaig
as W
U1 (JR-CO E (er)-+" "(A + 1) a br in mr) -
ar, sin
(Rr)-'A+l bT' cos (s a;
R - I bv" in
F, (r,%) (Rr)-'R-l 0: sin(, + -1) M +
a2) Cos
+ R 4"' sin
T cT'ccs n'
Several numerical examples are given for stress concentration around elliptic,
triargular, and square holes under conditions of umiforn tension. Orig. art, has:
27 equations and 4 figwes.
SUB COIZ: 20/ SUBM DATE: 04Feb66/ ORIG REF.- 005

NVIISOVA, V. V.,(Engr.)
NEk!ISOVA, V. V.,(Erngr.) -- "Particle Structure of' Sols of Vamulium Pentoxide
and Their Properties." Sub 22 Apr 52, Military AcadM, (if Chemical Defense
imerii K. Ye. Iforoshilov. (Dissertation for the Degree of' Candidate in
Chemical Sciences).
Vecternaya Moskva January-Deceriber 1952

I V'~ : r, 1.,
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by iteviiwo, by M. Nemiteattu. F-(-b,'m ~Z:)Il
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SUBJECT USSR/BLAI~ICS/Differentia; equation6l CARI 1/ -14 ?G - 110
AUTHOR 11MzYjJ 11.1.
TITLE Some problems of the qualita,,ive theory of differential eq-iations
(Survey on the modern litera-,uxe).
PERIODICAL Uspechi mat. Nauk.L. 3, 39-56 (1954)
revievred 6/1956
Me author remarks that the qualitative -theory of differentit.1 equaticns in
the last years has become one of the most popular methematic domains of in-
veatigat:,on, and that itE fundamental notions and the theory of method are
transfer::ed io moiiern physics and techmioB. At the same time it must be re-
marked that the mathematical progress was insufficient for these purposes,
because -the mathematics was mainly employed with the solution of -the problems
of local character, while for the application mainly the beh1AViOr of the integral
3urves is of great interest.
The problem of the qualitative theory in the pla:-ie.
The system A - 11(xy), -CIZ - q'x,y) --'-s -,on.sidered. Local inviastigatioas - which
dt d+
were made ti-11 '940 - fall back, and the mathematicians inVe3tigate in the
large. Poinaar6 and Bendixson described the powsibil$.*Oehavi,)r of the integral
curves in regions wth a finite number :)f tiingula3' points. Tieir results are
essentiilly enlarged by the papers of Solnzev (Izvestija Akal. Neuk 2L 3 (1945))
and Vinograd "YJ~en~je Yapiski MOU 135, mathematic.3 Vol.V. "?c2)). Therewith the

Uspechi mat. Nauk )
L 3, 39-56 (1954) CAJU 2114 PG - 110
preblea of the Cl.aSlliri'_~LtiOP Of tho Integral cur-en which ca-.1 ex-L3t in the
plane is entirely solved.
The theorem of Ben-i-Lmson on the exister-ce, c~f a clozed integral. cu:rve in a ring
domain is joined by the investLgatlons of Filippcr fMat.Sborn-k .952)),
Dragilev (Priklad.IUA.Mech. !6. 1 (-.952)) qmd de Castra (Boll..Unione mat.i.tal.
Ser. 3, -8.L 1 (195/3)) who si-coessfu2ly Lnvastigate -,he equatiou *X6+f(Xf;)-i+9~X'J-0.
The metAod of' Dr-,o! uf Fllippc7 and Dragil,av permits an estimation, .~f the
situatir)n of the limit oyc'.eq. I-L. *: r- C- I r~ -- ~! .3tigat_',.-;ns of Gomor., wid Riohmcrd
((Juart. appl. Math. ~L,. 2 (-95-;)) the comparinon method is succensfully applied
which joins the wei. known daplyg-;~-'-) 1-immn and whi,th firstly was formulated
b.f Drag.'.levz Let he g~vert 'rwo systems
an .1.
If' 1 ) f (z.,r) and ~Lre contin:,LLus and satisfy the Lipsch.l.-".z .-ondlltion
in every bounded region outside of the x-axis, 2) C~l V)< 0 1.1 thfl nelghborhood
of the zero Point, 3) xg(m) >0 for 1% 1 >0, then from
4 ) f(x,v~ >
the existence of a paxiodjc solution r;f (B), there follows the-*,e2!.sfen,:e of
a periodic soluTiort of (A), whch lies inside of vph;-~- is '3ounded
by the periodic solution of (B).
IXiff, Levinson, Eckweiler and Diliberto investigate the conditions which must
be satisfied by f(x,.V) and g(x) J.P order that there appears a prescribed
nLimber cf limit cycles.
In the applications, besJde of the system with plane phase space also systems
with cylindric space act a great part. 1,17hese systems may have periodi,,. solutions

3 - 39-56 1) CARD 31' 4 P, - 1110
Uspechi -mat. Naiik 3 V
without singulary p~)int-3. In -(,nn-tio- w,th these questions -~he author
mentions the invest:'.gation3 of (Ana.1i senola, normale Super. di Piza,
Ser 3, (1950)) and '.he papera of 0-:rrwrig.a; (Erincetan 1950) and Reneter.
(Journ. London math.soc. 2Z~L '. No., ~05 ('952)).
To the problem of stability -n the la-ga there belong two clw3sical questions.
1) The question for the center for the existence of a neighborhood
are sought, inside if which all solutions are perindtcl 2) tho question of the
estimation of the region of attra,,tlon of a sinp-lary pUnt. The fIrSt queation
.,L
was treated lese, b-.it the se--ond was t-reated inteneiirel.j in Russia.
Barbagin and Krasso-ski (Doklady Akad. Nqu.x (1952) NO-3) Lmproved Liapunov's
8 LIL
Stabil.Jty cr:iterion and remarkeli 'If alditiona-y to the Liapinov conditions
for evory A a niunber N can be deterinined such that from N there follows
i
(v - Liapunov function), then -lie zero point of the system is
V(x, x,
stable in the large. This theorem ani some conclusions admit to establish several
stability criteria in the large in cannrf!:.e Ca34aO. Most difficult is the
establishment of the corresponding LiapuiLotr function. Erugin, Malkin and Ergov
(Priklad.Mat.Mech 14,, _15. 16~ IL, (~950-*:953)',', uri-estigated in detail the system
-;LJL-
ax Iy ~ f
f.,(x', - 2():) - 'f2(y)
at
i~ppearing in the tl-e.,ry of ajtcma~i.,, -,)r- rc-1. Stt-J,akc9- (Doklcdy Akad.Nauk 82

UspecbJ_ mat. Na.v-k .~L 3,. 39-5C (1954) caz -, / 14 13G - 110
(1952) No.') g2ve .3. me 'h1-1- J ft.) r tlo& -f txD b-ci~-_e : I ,nes i bet wee ri
T
thom here ~ E) a r. sgi:-~-il _r -I e 0ii J- h - ~ -gt a g- ven pc!.nt
,:.f rhe iregral '~Lr :P~ L J b I, -ti w! i are con" a ine,"
The dependert
In thp r4ght part:j - f the equa.~Inn 'A -,,i i r.--rc if *LU.&tQd by DF3 B,igg' , (Dynami cal
systems w! th stable II, ~ -91~,'-'; W- T~ 9. IaT rre'b,~d Bautin (Mat .
SborrLik, n. Sei . 10. ( ;95~_ /' Nc. ) b,~ , - -,- .3 g,:4t,~d the quest ior ofthe existence
of 3iu-it cycles zl&aa the 7.eT,-, p- -in' i-r Y-,x qt.r,y) ai-e pc,Lyncmials of
secone. degrse. It ir pz-o-tred that the 'im: : oyrlet; i- .9 16 3 and an
example wl,-"-.h ej.,a,,t)y thi ee !Jm: t (7: 1 ~f 6*. cer.. Le:-!r1tcri-!r 'Dolclady Akad.
Nauk 19',,',' N).4) inves-"g5tei C-f fve limit yoles from the
sepa,fLtri%. ai:~f (Anr,. Math. Ir,. %-.or Cder-Ad. the .3pecial system
r a! aMa J rj r- (re a!
P and Q-1.axe perlodi.; in t)i with -1he pe-jod 21t , where
F(X, Y, at +,-K,~, - -P(;L, Y, ly, , I r3,,+IT) - -q(y-,j,
and the system pmisesses only isoiarerl -3i.ngulary points. Then Duff investigated
the cftanging of the limJt cycles ir ~iep3aden,~e of al~ and the vanishing and
appearence of ',im:.t cycles from the sin,3%ilary poin-,9.
Three-dimensional problems in t'iF quall,~ative theory.
The question on the behavior of tile irta,grral curves near a singulary point is
not yet entirely i3olred. Apart from thr, "critieal"case where aL arbitrarily

Uspechi mat. Nauk2.L 3, 39-56 (1954)' CARD 5/14 PG - 110
small change of the coefficients invoLves a discontinuous change of the
topological image of the integral cur-7es, the results of Grotmann (Mat.
(1953) I-o-1) must
Sbornik, a. Ser. JLOL (1952) No.11 1~oklady Akad. Nauk 86 1
be mentionedt
1) if among the roots of the characteristic equation there exist at least
two roots, the real parts of which have different signs, then all. solutions
(except such which fill up a manifold of lower dimension) leave a sufficiently
small neighborhood of the zero point for * Pm as well az for t -oD
2) If all real parts are different from zero and have the samie s4n, then
for t -"%,+ oc all integral curves pass zero.
3) The tot7ality of the integral curves decomposes tato a finite number of
classes according to its asymptotic behavior.
Warzevski (Ann.:3oc.Pol.Uath. 21L Vol.II (1949)) remarked that if the real parts
of the roots of the characteristic equation satisfy the condition
0(1 '60(24.... :g. 0(- k-1r'G(k< Mk+1 -4 0( k+2'*'* 4CO(k+p 4~"41:+p+11<
then the set of integral curves which tangent the coordinate plane (xk"'xk+p)'
ha-ve the dimenston k+p.
A complete description of the behavior of the integral curveS in the neighbor-
hocd of a singulary point is possible only with additional assumptions on the
inhomogeneous terms VPi (t I x1 ... xn) . Gxobmann (Doklady Akad. Hauk 86--, (1953) 1)

Us:?eohi mat. N&A IL 3, 39-56 (1954) CARD 6/14 PO - 110
considered the systems
dx
, AX and AY . wbere x .. (xi...x
t dt n) Y, .... rn)
T
ani found the eAditional conditions for whi(:h are necessary in
orler that the form of the integral curves of' both systems is asymptotically
equivalent. These conditions consist In the fact that for I he function g(X)
whare
g(t) -1 ly
1P (t,y) (t-,Ar)
a ,ertain w3ymptotic behavior is demanded. If' the system ha.s negative
characteristic exponents, then the integral curves are asyn~ptotically equi-
vaLent if
f (*,!r) (t,T) I i6 P (r) - 17 - 7 (r k
Iln rl2-m+'+f-
where k and e are certain positive numbers ELnd m+1 is the maximal order of
su.-.h submatrices which correspond to the roots with negati-je rea.1 parts,
11 'a .. flyl , IT I I .
if the charactoristic equation has roots being equal zero, then the behavior
of the solutions is scarcely known. There remain to be mentionec*L the p9 8
of J.Haag (BulJ..Sci.Ms,th..j4 (1946) No.1) and analogous results of e 3 takov
(DDklady Akad.11auk 62. (19481 No.21 ibid. 62 -5)' Desisting from a
,j_ (1948) 110 P
complete qualitative investigation of the neigborhood of a singulary point

Gapechi mat. Nauk IL 3, 39-56 (1954) CLRD 7/ 7 4 P Ir., - I 10
and only putting the question of stability, then the classicaL direct method
of investigation is proved to be the beat for the application3, e.g. Lurje and
Eisermann, on the, automatic control (Gootechizdat 1951 and 1952). From the
theoretical standpoint the results of Massera (,Lnn. of Natb. '1945)So-1) and
Baxbagin (Mat.Sbornik, n. Ser. (1951) No.2) are interoatii:,g, vrho independent
from another forpulated the inversion of Liapwiov's theorem oi-t thet asymptotic
stabtlity. Barbaijin remarks: If a compa-zt, corviaoting, invari~Lnt fiet F devides
its sufficiently small niogborhood into not more than a finit,s number of parts
and if at the saine time it is an asymptotic sett then in a ce--tain neighborhood
of F there exists a continuous function v haviag a continuous derivative relative
to the time in the region U, which satisfies the conditions v >0 and vtl< 0 and
vanishes on F. The same conditions for v are sufficient for t1le stability.
The qualitative investigations of the more- dimensional systema in the large are
still in the initial state, Barbaglin and. Krasovskij (Boklady akad.. Nauk 86
(191j2) 11o.3) give sufficient conditions for the stability in !;he large. The
conlitions are expressed by Liapunov functiodEi. For special e.-stems theme
funn.tions are really constructed (Bax'baC", PrIklad. Mat-Mech. -1(-)L (1952) NO-56
Kra!3ovskij, Priklad. Mat-Mech- J.L (1953) NO-3)-
In the question on the existence of periodic nolutions the aw;hor refers to
the book of Malkin "The methods of Liapuniv and Poincarfi in the theory of none
linear oscillations" (Goatechizdat).

Uspechi mat. Fauk 2A 3, 39-56 (1954) CARD S/ 14 PJ, - 110
Linear systems wi-t~, variable coefficients.
For the treatment of linear systems wl-th variable COeffiCitnt3 the ~ompariscn
wLth other su-table systems is the moat popular method. The beat results in this
d:)main are cbtained by comparison with cons-,ant coefficients. A very good aqy-,np-
tDtic formula is given by Grobmann (D-Alaay A-kad. Hauk 86 (1)13) le)-22~. Let ~~e
dX n
F, a (t):X the given systein
dt 3.1 ij j
n
(2) Z b..Yj (1-1 ~he comY)ari30n 3.fSteM,
It j-1 IJ
m -+1 be th order of the greatest submarrix of the matrix 1) in Jordan's
k f I J.)
form and this order shall correspond ~o the eigenva-lue of the matrix with the
real part Wk. Then from the cond-itton
coo
f t2mk g(t)d-t