SCIENTIFIC ABSTRACT FR:OGIYEVICH, I.B. TO:OGIYENKO, V.S.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001237800015-6
• Release Decision: RIF
• Original Classification: U
• Document Creation Date: November 2, 2016
• Sequence Number: 15
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTR

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~, a92a.5-6;~~, ~~r (m) ~.. _.___.__..__~.__~_.~_.:s~tr~c.~ co~~: ii~7ooa%~~ 166/a,i;Ja~i~g/oa~z,
' AL'TFfOR; _`.~~vetski V. ~.; Polubarinov~ x. V. ~~~.,
ORG ~ Jai~~t,~Instit,ute i'or ~3ucleearch ~Obt'ypdinennyy institut ~~adernykh
iss~,edova~.~iy)
TxT1:~: T~teory oi' a ne~~;trraZ.. ma~js~.vo tensor f~.eld w~.th _~;~ ~,
5GL~F~CE. ,!~N SSSR. I~ok~.~ClcFy, v. 1G6, no. 1~, ~.qGb, ~33q-~1~2
~~
TOP;[C TAG~i: nuclear p:k~,ysics, nuc~.ear spin
A&iT~CT; An intAr~acti.ng syrrmtetrical tensor field h~E`(h7~~` = hf`y) m;~y define spins 2
and 1 aizd two spin~u 0. A theory of such interacting mass tensor fil.~.d was devE:loped,
der;ivir~ ~ supplem,entary tiilbE:rt--Lorentz type g;erieralized condition from trte equation
of motiAn. Tn tr~i,s thEjory, the h~`'~ field may define only spins 2 a~~.d 0, excluding
the othc.x~ 0 spin grid ~,1~~ spin ~. because the sign of the spin 1 energy is oppos'~te of
that of ;pins 2 and 0. The interaction of tha tensor fiol.d with itself ataci with the
scalar fiold was examined; a i;wo~parameter farn9.ly of naneguivalent theoriec~ r~a,s
obtained #'or �he mass i~ensor afield. The �quation obtained differed from E:~nst~sinrs
equation b,,r peas"3$17ing a cosrac?logica:! term which disturba the general coves�ianl~e
and the ~.,heory a'" ~.3~ua.'valance. This papQr was pradented b;yr academician,_N.....N.._.
-�a~y�~ 1~ P~"'y ~.'~b~ . `17~e authors thank ~!. N. ~'~",~UUU1re'~~ N~. _ ~.~~~~v ~~nd ~~,.,,~ .~
Smorodinr~kiv for u:~,-eful discw~eions,~ (}r~.g. r~rt. bass z2 a"ormu~as. NA]
sUB cans� za / suar~ nAT~: ~.oriay~-~ / ~xG Rte: Qo~
4 Carol ~'"~-' - ___ UDC�: 0.
,.
.~ ~._. ,
,. _._._-___.___~- .._....._._~.....~..~._..~~,w........
i~,,.,y,,,.,k,,._ .. ... _.. ~.. _ _......_. ...._....__._.. .....,..._..r._ _
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. � __~. ~ _ ~- ~ ~ _ ~ _~.1 ':.:taF..{~y :?~M~nro.K/;:.r}`i.3`~'akH P~r...t~ t. .; " _ ._~ _ _
- _ ,. ,..:+'r.,a,.� ~�. '..~~N.7d . catrix ele:~ent' for a Process with n gha~,gns is
found Lc be
Cf~ S~i>~u...~ ...~ ...u (q~s1j=' (g2sPj...F ~(o",nsrij.
~1 tin M 14 ~2 ~+ 1~n
uquiva7.e:nt 1'~.~s s~ey be oht,ained wherk thi, field st.ren~th tensor :~y(~:j i~a
rePlac~:c' by �~ ax �y� �~.
Card 1/2
~~
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Sl05f~~2/0~3~cQ4/G32;~'G6l
r~~~f ~~,i ~ $108~~B1i~2
nUT~fai~;~: U~iy~~v~;t:,kiy, 'J. X. , podgaretskiy, t~:. 7.
1"ITi, Some interference phenomr:na in K�Ko systems
P~RIau~:(::.~. Zhurria3, ekgperimen�al'noy i teoretichea,ko;~ fiziki, v. ,~3,
no. ~~(�~a), 1962, ~ 36~-1;64
TEXT: !;ontinuin~; eat^lier work (`Lhr',Tx, 4~, 7.2a, 1962 tlae authors st~idied
the nat~.:re of beats of the Pais-Piccioni type in the d�~~ay of KoKo p+~irs.
Such b+r,ts T? : (~~;iyevets~:i.y, '/. a.
TImI,I;;: On the Interaction Det~~een K- and n-rsgesons (0 vzaimor(eystvii
c~ezhclu Y- i n-r~ezonawi)
PERIODIOAL: 2;huxnal e~:spnrir~ental'noy i teoreticheekoy fizik;i, 1;fa9:
Vol 36, Nr 2, pp 642-6q3 (IISSR)
ADaTfi_AGT: in a recently published a~a]~er by A. Pais (PayFS) the ]'ollowing
interesting hypothesis is c3iacus~;ed : The intea~na;l parities of
charged and nautr~al K-mesons dif'f'e~� Exam each other. In this
cr~se~ severe limitations of the S,a~ran~ians o]" strop{ inter-
actions follow from the condition of char,;e invariance in the
pion-nuclea~n system. Many reactions, for f.nMtfince
K+ + n -~ Ko + , ar� forbidden. n oxc~er t F~void this d' ff ' -
culty, the CK~n~ -interaction ~K~~~ = f (?.m )~K + K�r+ �~ K�K~n
K
is introduced t~~here m denotes the mass of thE: F~-rrieson. Parity
i:~ conserved in this ~nteractiori, but the sytrraetry a]' stronff
rteractions is no loner valid. For the veri]'iaatiozi of the
~Rn~ interaction, the ~at?thars su~;ljest carrfinK; out an er.-
Cerc] 1~2 peximent concerning the pair production of K-mesons
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The Pr~aperties of G:~arge SJw..~etxy s.r~d tre
Rf,prea~~ntationa of 'the Exten~.ed Croup of ?~oxent;~ i:1
the Theory of Elementary Partic~.es

tr:is.~r~epresentat:ios:p the #'xee field ~+ has tree l~agxs.rg.ian
L a ,~ (1x~~,,, iectYQdynami^a ~.:~
s,pps,rent~y bf~~Ad only u~~or~ the fact that thy. $exS.es {1 ~ :Is a~y~aptot:.c sand ths:t
tYie cou~~l~ir,.~ constant is ~�e:ry sr~all~
The re~;xesrmtatiQn (,j~ pera-:its a development acoordin~ to inve~cge powers of t~~e
coupl~.n~ oc~nstarit g by the development of
e~is~~ ~;cco~rc~~.n~ to the po~'ers o~ the s.r~~amen+,, ~'ox fx,,m (3) t~:~exe fc~llo+vs
S ,~ ~~ ._c.~.~ .fin (~ 3n (~-,,~ yn ~, ~ ~(s~ M ~.~ ~~ ~~ (2 ~ ~o) ~ ds~ ~.~' thM~ d~av~el.~apmt~r~t
n~ ~ ) �~ ~.
acc�r~ipT.~ yo ~~g exis,ts�
I~tSTTTT3:~'T+aI~ : Electrophysica? Laboratory of the Aoademy of Soie:o.cy in the USS~a
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a, r+.t1 ~ n ~i l~ c v s. ~ ,l T
t t-~if mass ~}~ th~~ elec,~r~1r. ih~ pe~t;;,~�~a?;z c.
-,,r~:~r:,^s`. ~ ~ f~p7 ;~. Hr re !~ det~.c ~:
�
B
,,. the s~--~.fls
� ~.tia~ a .r a �~r:~.~~sh~s fox L
� ~? ~ ~ 2?~ ~ ~1, ~n~-~ ,~r~ Here Ii dR''i^;:e;~ -~h:=
~.,~; ~A r,,n! rf ~~;.,~..:~~~~(?rA,~' ~ Uzi ~I ~t,� c: 2n
.a ~ m z- ~ , ~ XS ~ W ~ ~ Ja ,~
n L T L \ J" 'l ~r ~ rr 1 A~~~ ~~~~~~1~' ~ !?
t�.,,~ I, r. 4~i r. ~~t: TI ~ `~ s: ~~it~ ~~r i 111
w}~;t~'~~1~1L a~ n't..,r~lex's~ % 'i ~ ~ .1 ;: ul~r., iii
z~,j.~ e 5~~1.t~i t}res e;ccepti~~Ci
` ~~ ~~~f :~l ~ >'ci~ abo~A sex�ies ~~~.�,rs.:.-~;e~ 1Ti t~iN ^c~sF~ of
iJ.'i
o- ~;~ ~ r~?lcl i s asfmpf cat t c; ; ,~~erefxG~; TOF FIB ccn~ ~.U.cte s that triEl pertu:cbat i oria
~~ ~ ~' ~ nr ~ ~ r~ ~?;a ~.u u:~c3.ess .1~1 spy to ~~r tr;e fact t'r;r3t the
:a~:� ~ c~-~ci : F~~a~ ~ii~ tc~ a d:z . c.rea; i.n~ ,,e..
f ~~~;~1;.,.n ~~;,:,cl Expression fc~:r 3~' c~~.stu.�.
'~tt-~x�~: ~. a~ rio~ sho~~vn. th{~t i;he sum^iat~i.;t~i of thy. ment~.or,ad de�re7.op~i~;nt ~n seri.er.
F ~ , f ~ ~ rl. z ix:rna. ~ rio~+ the= r, ~:~rrc~,~p~~zltittn~ fc~r~nulfi i'c~:e L� ~ iheae de ,.
f c~M ~. ~;~ ~UR~~, ~ m.~ thy; .
l~h~~z~,.tiuii~ do nc,�~ ~rd~,~ut;4~ ~tr,~: ~xselE~s35n.oss of the for~~ai71a ~~.1ren fax L' bti~ t~-1~
frzc:t tti~.t s,z;n~!a.t~.an r~,~.~yt b~, ~n.ae~^stoQd irk a more ~ene:~a,1 than the ^la.ssica~.
.,~;~,se~
F;~s, %'!;~ ti C:r11`I;f.'T`llly rtli~tZ.L7C :`l 1; j.~ tT'1ze ~.tl 'E~.~~ tE*j)X'E?Ei~TI~iElt.1.GT`i CJx th8 111t~r~,C ~.�..aiTl
r {~
~,t ~. ~ ~
ry i. ;:, ~s~a�.~}_~ ~rritt~:Fn .~~~~n. rafs a :~e ~ -s a.cw~rf3.;n~ to pe:wex's off' the coup7:.r~
~,~,n:~t~~x c ~;
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the .~rz'cexpreta.tir~n off` the ~e~z`ies 4t~ r~h~, p
she ~~~.zanttzrn mheary of the Fy~:1d
reviewed, 10 ~ 1~~6

~~~,c~ur;1~G~, r5;; the opinicr~ af' v~,~riuus authors the Fzforei,ent.ioned. sex�~f~; f.a:ri b~
r. ~ ~,�orur,ct- ~~1so ~.~ the iz~fin.itie s axe ~~accluded frt>m indir;due,? terms, ?~~~z�~~ :.~;
~.~;i ~r;1;~J! ';t'lAtu CGx't~31.T% V3.J,t:~ iA$y" '~:,c' a~~:�~'3.~7~d tC & ~3E'r~iurbatiottal ~~:rae~ :f zx.
:~~ .ryz?te~p.~~=ted ~n +r.~~ spirit oaf t-ae sum~~,at3c~r.~ ~etrxodg {G H~iiRliY'~ ~'ULz.jlr~e~.t
;i?Z�~'~" Pu>>li.shirg j:io}asE fc;r Fc~:C`ei~n ~zteratur.c;~ ~r~oscow 1~~1~ s,n.;i s~C~t x~:~ #:}2e
,n-..~ro;~ : ~.~s:-ical ~~enae of C~TJGhY- ~br mo~~r:s of thE: theory cif ~eneral~,;:~.r-~ fwzzr-
't 7.'?;' ~ ,'i it1~~~~O~ CiJ" 9Llip:a~G1.~~Ti ~�f i~"t}'2~,1"r~C~'u her�, ~c.i.th th~~ Yzelp of 'a~.n~cr d ;~epxer
;~(,~truc.~J_~i.~a of tY~-e i~az~~.tsax .~.3 f'ozznd tY~at :~s ruaxe ~s.c~:ept;~ble ths,n the z:isua:l ozze
-ar,~ ~tz~.c ~., zr pri:~7ci;ale. pexr+itg an~.~.ysi.:3 aaoorditt� to negativ~P powea~u o'~
~: J.zY;,.:7~. aanstant~,s<
:`i't+ ~.a�? c. begins w:i;h an �interesying e:x,arr~ple b,yr U~Lgiyevice' tsbyg~iy, V. I.
::' A4~C~.FBI'~d~.~i"�.,~-f'r~`'"98:'~~.9ii`."~":',li~',ti'4~-"Tt" :.
Title '~~-ngular distribution of gamma radiation at great depth: of pene-
t~ration into matter
Periodical Zhur. eksp. i teor. fiz., 29, October 1955, 464-472
Abstract T'he author-finds the distribution of gamma rays aecordi.ng to s,ngles
and energies at great depths of penetration into mattez~ in the {ease
of constant coefficient of absorption and in the case cif coefficient
linearly dependent upan the gave length. He considers the passage
of gamma rays through an inhomogeneous medium.
Institution
Submitted June 25, ~�95~E
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~~-1~C` U'~--~ ~ v`~~~ V If
"
'
~'
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~ + 3~ y
t
uSSR~~luclear ~:'hysi+~s _ G,aamantx rays
Card 1/1
dub . 14~ - 7/19

Author Ogiyevetskiy, ~. x�
~~~.~-:

� ~
';~:~',~~`.~ ~~.~ ~: s through matter
henry of the pro~~s,~;ation of gam-na ray
Title
29, October 1955, 45~~ -463
fix .
Pcxiadic:al ~ ,
2',hur , eks~~ . i teor ,
7.~s
r~n
t

'~
t ~~.,:
o
aa~na rayn accord~.rag
7'he author fi.tids the di;~tributian of g
th of
de
h
ter
~o
n'
xac
Abs p
e
The
Fznd energies as e~ function of t
several rRev
of
of the order
rays i4; in-�
in the ea~ae of initial energy
allel beam of monochromatic gam 1'
ow
;
~~rablem ~.~~: Xf E~ par
cident pe,:`Pendicu].ar~.y to the flat slaxfa5edef endlupo~ I~ePmtshtt~'ri.m~~ry
i
p
on
~aill the i~ngular and energy distribut
ti
tter`: The 3.nvesti
~.a-
~
�
be
ot~ier
~ven
ener , a,ad propl~l'tiess of ma
i
gY
enetration wil g
f
p
tribution at great c~.epths o
~� nelen'~y and Ye. L� Fe.m"
a
�
work. The author thanks Professors
Eight references: e�g� S. Z'
Taman
Y
e .
berg and Academic iar I �
asanicheskikyi luchakh [shower p' cc�-
1'
.
I~eleia'kiy, Lt~,vinnyye pratvessy v
Slate Technical Pie~~, Moscow~Leningrad
s
,
esses in. cosm:tc ray
1848�
Institia.tion
Submitted June 25, 1954
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'I 5 -6
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for ,~be1 ank
methods ~,~)~eP~'ap~~"
"{;a~~h~.'~~t~ of , ~ ate. 4~yeVet~aki.3~~. a
~ b ~+'tian, rt ~ngia~e~'s ~m L. 1i~� ~. ~z~a-
~~~ ~) ~ of. Tr~na~a
tro'~k Ana
vich 231-~3~,
~ ~55R l yob- 9~ t ~~ 2, pP
~' of ~,be1 acid ~esa~~o and. many
~.~ dc~ub~-e aer3.e'S
~ta,te~ y:~at th+~ methods tion
mete f`~r~ h~~~th~r~ are ~~rie~ b~, b~
pi~,hex ~cabl ~ e ` aY'e ntrt std
axe not camF Bence the
bel method wla~.c
b the A Ge vex'sP~.
.the ~e~ ro ,~e~ha~, and ~ ~~,~~"~9 _
f~Il~p~~'~~n'~iar~ ~E.~~;q,,..
egtabl3.shing ~;o~~&Pab1e� C~a~b~
~,nteresi~~ in methada are etic means ~
fox wh3ck~ these f ax3.tknm
tit the ~pethac3. o. ~~f~ .~ ~~~~,
.~,~ also ~ ~, ~'
p~,-es~nt~ ~l . _ .
,::,
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~?a~s~
~/oil/~ ~/ooo/oo~./oa~.,'ao~
On Caue~hy's proble~a for the a .. N251/D~US
Thf' fal.lawing reau,:lt is obtained r If the initial funet:ions Ul (x)
anti U~ (x) sa�tisfy
/ui(x)/~, C exp~~/x/ln(1 +/x/)~p ~. rh c 1, i ~~ 1, 2, (6)
thE~n tb.e solution of Cauchy ~ s problem for (1) and (2) ~~ives (4 )
anti (5) and this solution is uniquep and continuously ~~epende~nt
on the initial fun~ctiona ul;x) and u~(x)~, [Abstractor~~3 notes
Apparent change of notation j o (4) and (5) may be diffelrentia~t,ed
an arbitrary number of times, provided that the result:L:ng sex~ies
area uniformly convergent to an arbitrary finite integr~~l of too
These a,re 6 Soviet bloc :references.
AS~IoCIA,TIO~I ~ y?nipropetra~vs'kyy derzhavn y universytet I; State Uni4b
verity of ~?nepropetrov'sk~
PRI~SEN'tET~e by V.N. Hnyedenko, Academic~.an AS U~CrSSR
SUkIMITT Ef~ t February 22, lq6�
Card 5/5
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2'~~b~
S/OZl 61/404/O~C~l/441/448
~ t e ... L~25].~305
4n Cauchy s problem far h
where I;n(x~ ie an n-th c-rder Wessel function. This formula i~ the
soluticln of Cauchy's probleme oacillationf ofeacbeamffere:ntial ana--
logue c:f the ec~uatlon of th
i~ ~L1 �+, ~4u .,,, 4 .
,~t~ ~x4 �
In, the case r = 1 then, after various transformations ~(4~ became~s
,,,,,...---- ------ ~ 2t ' ~t t
2T- d~u,(x -~- khj.
~~,_~, ~~-moo
1
wY-ich .ls the solution of Cauchy's problem for the difi'~erence�-dij'fe-
r~:ntia:l analogue of the wave equation
~~u ~2u
C,~,rd 4 /5
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S~a~1~2~,~5~~~8-a ~~~
- (71x the Summa~bi:i1,y of ~Er~.es of Barel ~ s h~e'th~~d of Fracti~~nal Qrder
of total inclusion that .it is con.vE~x. that the a v ni' e
v ~ d e .ag of
~ this met;',hod :incxeases with Gt. and tkiat Schnx~.dt~s taubE;ri.arl
theaxgm :for exparaenta.~a;l methc~da ~?f ,~ummab~~.ity (which carxes~
I pond.3 tuc:J-~~ in t}~e authorgs des.i.~raatic~n~ holds far method
($oG[~ with any~.~ The CB:; fJCi metl~-oet i.s al.-o compared with
Ahal. ~ s ~;~aneral method and wx #;h thE- methods of Eu I.ex, Cesaxo
a�d Voro~~-oy,
There arla Ei xeferenceeY ~ of ~rh~.ck;G ~~xe Sovist~ 2 Frenc,h~
~ 2 Germans l Eng:I.ish a,nd 1 Italian.
i
A 5~.;',CIATIONa ~Dazepropetxovski,y gasu~iaxstvennyy ur~iversa.tefi~) (Dnepropetrovsk
State Un;tvers i ty j a
A:~t edenk~
PRE:>ENTEDo By Bo V.~~Gnedenko)~ Metnbery AS Ukr55~i.
SUB;'QITTED~ Ff~bruary 18s 159
Car~;t 2~~
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1
i
i6 I; i } 50~~/zi~59��8-i~26
AiITI�:OR a uhiyevets '`k3~s I. I . (~7giyevetsxiy~ I, 1. }
� ~+~ ��~~ rte.::
'~STI;~E; On thy: Su,mmr~bil,ity af' Series by Bore].'s Met;~iad of ~yract~.onal
Order
PER:I:ODICAL< Dapavidi Akademi nauk Ukrains'kc RSR9 lg5~lp Nr 8,, pp 815
i B18 (U'SS~R}
E ABS'.C'RACTt The classical methods of summak~ility of Eor~ol (inttdral and
exponential} are well knowne Ref. 1~~. The vrork oi" E. Le
Roy 'Ref . z,] and to a certain extent the reclently ~>ublished
similax works of Vladarskiy fRaf4 3.19 are dE~dicated to the
generalization of thpge methods. in this az�ticle the
author di.scuases an interesting paper by Sa:r~nia ~RF-f . ~ in
which he introduces a sequence of methods of summaty:llity of
ali integer ardersq Hore~'s integral. and ex~ronen`ta.Fdl method
being particular cases of this sequence. Tri this I3apery
Sannian's defini+ion is extended to every rElal indE;x
~,._.. c:~~ ~ ~' ~ ~o and the properties of this def.~nitiony
denoted as (B~~} are considered in detailo It is f~hown~
Carla 7./z that the method cif ~aummability (E,GG} satisfj.es the condition
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\\\\
!
I t
{
3~'r ,
J.l~ ~ la ~. ~ F! .~ ~'~' f ~{ ~
c~-.l .~.~, ,~r t J (OI ~ ~^ ~", f ~ f. i't f~ ~ f.
m.tT1~~ , Oz~ tpic ThFOry of� 5~zrru~, -;n ;~ t~.~~r~~:iE?d 5,.: ~ ;~.y~, F . ti"J ~h r~~~~ ~r 1 '
TrJepl.i ~z h~atri ^e k: (K ,ef?xil s~~rnm~_~�~:z~d~s,n r.,.,;r.~-n:i;cs~t~r~;~~~?,
~O;~~.F?d::; ~ate'~ �;,t;s fey' rrl~.�T~.-~sarr'..,. ~'r;nl.3_~,~a.)
:~~A7~I; ~C~'~L Iz~4~~es ~~i.ya �r�~sshi. kr! uch~~brykh ^a J~~dts:~i.y~ tv~,~,~;~,;r,fi,~ .k~, ~! ;} ;4
~r ~~ ~, Pp .~ f33-~ ~ ~E3 (USSR.
A}~;jT'Rj!.G"L I:~~t x 't)r' ~, nF~qupxrc~k c~z' a:e~.l.. r~~~mhr~~;�;~� Ar~:.,aa~.iir~ ~,~ .~. fir.. ~?.:..:~.r
~'Rt� f FY..% �~he s 1.quYric:e:~ x~ vyc~ ~ f.~y~ fl ,-~:~ are ~{,;~ _a.eci 1 Lnf~~.ri' ~~~ `
C 4 f F : ~ ~ ~i ~: ~ Y ~. T ~ 't; l!. ~' 1 r'1 F~ ~} i. ~. ~ ~ r~1 ~ lI .~~ :. X. l 1..f .i ~ ~ Ct X' ~' r ?~ `~ !: ?~ Z'
,h,. tr}~~ i~.?~:es.r 4umbinF~t ~~)x~ ~.x, .,~~o.~..~~c cvi~h ~r :i_~ r,~,s
~:~~arnrrr~'c ,.~: ~ A ~;'~.yret~. &F' ~ of c>~u.rdelz st;q'uF;rr.ces is c;~~l;iF:3 ~_i.}F.ar=.~
:~)~d~pVrxdt~rt; w~:~~h :~F~pF?::t t0 T ~f arr arb;trary f:4r~ite m~mbe ~;:
;; rr,~;],F.:I~< t - {~~' ~rY,.} ~ ~c a .l.fi.+ ~._LI~F3d~~,y .2"ad.r'~3E:71~F'2'f �! W.. ~ri :r'e.,J N-r r,5
'1'1-rr:.c~x�~�m:, a'!~ e~~.:ary 'I ~~~?re e~:~.~t r~:3~~dex~um~xably rr}sry b~,,.nt;~- i
^,-~,~.:rr~- . ~.r.:{:{~.xa.y inde~endt:r;~ ~~i~rrespE; :t ~~> ~C,. EaF~:.~;~r l c~i~~. :.
~.~zmr:~ a ~c~t~r,3ad di~~F~r~~:n~ aeq~::~:~r%c~y suns ~?~r,--_d,.,r~t,.me~:~b;y m~� I
~:t?l,iP~,eC~ ~~~;~N;ri^~~ VYh:~.t v ,~ ~? Sjm~lrs.nec41,=~~-.l Z7} "r: cc"zi.i 'tT~ ~ _.
`h di. rF . g~ ,. 1)
FSRIQDIC.~IL~ Doklady Akademii, Nauk ,1958, Vo1.118, Nr, 3, pp. ~43~-~4~ (IIBBR)'
~B9TRA~CT"~ Let Enf (x} be tr-e best approximation by tri.gonom~ric polynomials
of f(x) in the metric Lp. Let f(x+2'~') ~ f(x), f(x) dot t).
0
Let the fractional integral of the order aCbe denoted by
0o A (~e) oD Hy(x}
,;~
v~1 y~1
There ,~Ay(x} dFinote~ the Fourier series o;E' f(x) ~;nd ~ By,(ac)
denotes the conejugate aeries. Let fa(~c) fa(x) denote the
Card 1 f 2 f~raotional `derivative of order vtof f(x).
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9uma~ati~~n oi' Double Series kith Methods of Cesara and SOY~Q~c'-13-b-~14~33
dbel In the Bounded Sense
~.~~-~ ,~ Bo(na) rar fi.~~;*~
~tfn ~o(na) for 3 � a+1
6m 'n ~~ o (m'P)
~ o~m~)
for c~~' ~ +1
fox ~ ~ ~+i
a~~
(Em,n ~~ C if m,n j~M, M integral.
Then (1) is bou,ndedly summa'ale with the suca s according to
Abel.
There are 9 rsf'erences, 7 of which are Soviet, 1 ~termarz, and
1 Polish.
SvBMITT~;Ds :ldarch 15, 1957
Card 3,~3
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~s Wlth ~etl~od~~ e)~ ~epaxa and ;~av~~12--;3~6~�~4f 33
Summatior~ o~ .bouble 3e~1
Abel in the Bounded Sen$e
� const. Let (1} be bounded:~.y summable with the sum s
thod G, d , ) if lim ~~~9 ~ ~Y s B
to thEl me ( ~ n
a,caording (my~~~~
1 me~-ne ~,h~i~ .1 ~ m ~.1` - let; there exist the ~,im:it va"~y~ue }
(,m,n) ~ n ~'um3Aab1~ 4~41iaj't~~.X-g `�~'
i'or ever~r ~~ 1� (~) is called boundedly
r-ith the sum s if tin l'(xgY) ~ s, where 4'(xgy)
~~be l (z ~ ~,1~ �~ 1
~ 7~ 1 ar~td (x:,y r~e~~ns
~+ 8�x~'y~, the limit exists far every ~}
!-~ ~ J
i~o,~~o
that "~~ y ~~' W 'y
~ ( ) -bounded and (G s ~ ' ~ ~ b summable
Theorem: If (~ ,~ is C, ~' hen (~ } is also bounded.Iy
summablr~ with iuhe sum s, to Abel.
with the sum s according bounded and (G, `~, ~) baundedly
Theorems If (~ ~ is (r' ~' ~ ~ ~.~) boundecl.ly summable
s~:mmable, then it is also (C, ~~ :
(ti and ~ are ar~itrary ~~ositi~~!~ numbers} .
with the same sum }-boundedly summable with res~ecl~
Theorem: Let (1} be ~C,~'~~
to s, let
Gard 2!~
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AUTHORS ,..._ _ Ogiyevetskiy, I.I. _ _ SOD/Q2~13-F,.-14/33
TITL~s Summation of Double Series With Methods of Gegaro and Abel in
th� Bounded Sense (Summirovaniye dvoynykh ryadov tt~etcdam~.
Ghezaro i Abelya v ogranichennom smysle)
iERIOD:ICI~L: Uspekhi matematioheskikh nauk, 1958,Yo1 13,Nr 6,p~,~ 119-125 (Ui~SR)
ABSTRACT: For the double aeries
(1) ~aiJ
m n
let S ~ ~, a . , S` rri ~ ~ A~w~ A~~~ Skl ~, ~rhere
kl i=o,jao iJ m k~o,l~o
Am mm a�+1 ~+2~.` � . � ~+~. The Ce9aro m�an of thy: nx~der
v r~_1, ~~~1 is
~'�~R
~ ~ - R Se._,.....L.~..
m,n~ AaA~
m n ~ ~' ~
(1) is ar~lled (C,O(, ~)-bounded it' ~ ~: r. ~~Co (IItrr.=0,~,~,..., ~o
Gard 1f3 r
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~ yWnww,YM{M..aWrwti+Yrw+~ti~_ ~l ~ ...,
'ter*~`~~;~pi~"~t`~t~at ~~'t~a ~r `M;~ ~x
~8~ ~, 411 ~`~ ,pia f~IttC~+~. ~~ ~k~"~'o~~ taCl~ VW~1t ~; ,n,~
' ,~~~ ~~~~ viii ~a~he~~ ~ het- ~~x, ~~ ~ ~'. ~ ;';
_ - I~ +~s~tr~~t~ !`t~rt~t~c~ ~~fin~~ fir a~ i~~l ~ ~r~~d ~~
~1ya'~a~y ~,p *an ~ ~ ~ 4
a _ i - :iirr~ l~fY~x--.~f:K~~-~~1i+I~- ~jdudu~ ~ ti
t - ~i ,
._ _ '~e1t the game u~~lit~r holds. with ,K replaced ~y- - ~ - ~ . ~ " `
, ,~abitras-y #uuctions~ ~'~ ~ L~4~oo, cxs~ {~= ~, :2).1~~e px~,~f- ~ ~ ;
i~ ~. aii~pl~ ac~apta~l~in of Lt'e~er'~ xa~uberkan tl~caren~.
' ` ,~~ ~nal~g~~s: re5u~t ;~~old~ fir l~~ilFn tratrsfur~ns. Applti
~~ ~. W ~' sti~a~~ arc mute ~o All axt~i ~~, l j suFn~ittabalii}~ rat d~ulilc. :`'
~:
~~, ~ :~~c~t~ces ~trid tcy ~~`; a, ~~ su~rirrtaljility ~f d~uE7I~' int~~;ralst ~ ~ ~'~ ~ -
- E. f~c'~s~it~t (`u~slttit~, i~~sli.)
,, t._
aa,
e
~: -
f, ` '
;::
!~ r
a. a
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21.-58-~-428
Gene~~alization of Po Civin's Inequality fox the Fractional 1}erivative of a
Trigonometric Polynomial to a Case of Dp - Spaoe
case of LFI -metric, where p } 1. Assuming
~ ~ ~
i~f' ~i P= ~ f ~~ x
w
the author shows that the fo:llawing inequality holds
P ~~ ~'
where C(~x } denotes some constant depending can Ex alone
Thi;3 inequality represents a generalization 'ef Civints in-
equality to which it reduces for p ~~ aQ .
There are 7 references, l of which :ls Soviets 3 Americans
2 English and l Hungarians
ASSOC'IATIQNs Dnep;~apetrovskiy goaudarstverihyy universitet (Dnepropetrovsk
Stai,a University)
PRESt~NTED: By h2~~mber of the AS UkrSSRs BaV� Cnedenko
Card 2~3
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li4. /~J ~~/7 1
Y '
AUTHt:~R: Ugiyevetekfy, T:~In ~':~-58-5-4f28
TTTS,Ii~. ~en~3raliaatfon of Pg Civin~e Tnequal,ity for 'the ~`ractivnal
b Derivative of a Trigonometric Palync-mial to ~~ Case of L
-
p
Spa~~e (Obobshoheniys neravenatva Sayvina o proizvodnoy drob~
nvg~a poryac3ka trigonometriohask~go mnogoohlen.a na sluchay
pra,stranstva Lp)
PERTC, DTC:.AL r. Dopav~.di Akademi% rauk Ukraina' koi RSR ~ 1958 ., Nr 5 ~ pp 486-
' 488 (USSR)
ABSTF;.ACI'o P, Ci ~;~in ~ Ref 1 7 has generalized the Bernstein inequality
concerning derivative of a triganometric polynomial to a
case of a fractional derivative of the order a which is de-
fined as follows:
j a. (a; .,_ COS .i7 a ~S `~~ cX~ .T 5 t ~~ ,,"1' ~'_, ~(~` ,~, Cx
n ~ z K 2 K

K=1 k,~
whEre Ak(x) = akcaskx + bksinkx; B (x) - aksa.:nkx - bkcas:kx
for a trig~~nometric polynomial of the form;
r~ ~~

Kx!
Card 1~3 The authar proves that an analogous result holds also fo:r a
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f i-
T~�~unsac~(;ions of the T'hir~l All-union MathezaatiealC ongr~es~~ ~ Cont8$~ s
Jun-Jul Q56i ,`.~"rudy 'S6, V. 1, Sect. Rp~s., I7,date].'stva AID S3SR, Mo~ieow~ 1956 ~ crJw
Nat,ansor~, Y. P. (Le~Lingrad) . Qenerali2at~:on of the Theoa;~em ~ 37 pp.
of P. I. Romanovskki,y +~n Singular IntegralEt as a Cane of
Stielt~je~~s Ialtegral~~N
Natansot:;, C`n I, (Leningrad). Sorn~e questions of ~xriction
Approxin~~ation by Stux~-Liouville Functions.
Natanson, I. P. (Len;ingrad ). Supplement: to the Nausdorf~'
T'heoretn~i on Moment S~equenaes.
Ogiyevetskiy~, I. I. (]~epropetrovak).
~'~t'i~~rr-`~''~"Mui,tiple i'bvr Series.
The~�e axle 2 r�ferences,
English.
bn the Th+~ory of
l of which is USSR, and the other
4gi~reve t ~~kiy, I. Xe � (I~teX~rope trovsk) . Some Taube:rian
T4~iec>rems on 3equence~s WitY~ Bounded Slow psi;illations.
There ax~c3 3 referenc,ees, ~. of which is USSR,, 1 le-h
a~~d 1 t~e;t~n~an.
card 2g/~;:~o
-~ -
92
92-~3
~3-9~+
9~
~~
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OaIYB~TSK:IY, T. I.
'~t~~e ~ ~'~er Sler~,e~e: ll ;~ ,;
t~
~`- ~~t ~,t~ivh~ ~f ~. ~. ~~~te~y
"n~~ ~ ~8~ ~~~ vai z~xx~rx~, ~o ~, ~ 20,E
DevelQpiug the methods of ~'a~ and ~4 I. A,kh~
the ~ author obta~itie an, e~,ct ~.ttvs far c evr ~t
Un~~~x}/ ~.n the ease ~~' one ~ ,~ ~ ~
~e x~a1. c~.ase of ~-
ees, t~.eh ~.nclmdee a utrmber o~ ~,~am~i~r meth df
sw~natf,on; here ~, the ~~ Fcatt~~,~r series of
$ mat~~,~ q. ~~o~~~ the ~.aterest as~d ~s
~~~~~~
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