SCIENTIFIC ABSTRACT ULYANOV, N.A. - ULYANOV, P.L.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001857920015-3
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: March 14, 2001
• Sequence Number: 15
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

ULOYANOV, N.A., kind.takhn.aauk
..............................
Ivaluating tractive properties of wheel drives in earthmoving machines.
Stroi.i dor.mashinostr. 5' no.3-16-20 Mr 160. (MIRA 13-.6)
(Traction engines)
(lartbmoving machinery)

MIXHAYLOV, B.I., inzh.; ULIYANOV, N.A., kand.takhn.nauk
Automatic adjustment of motor grader operations. Stroi.i dor.
mashinostr. 5 no.7:6-7 Jl 16o. 04VU 13:7)
(Automatic control)
(Graders (Xirthmoving machinery))

ULIYANOVY 1. A., dotsents kand. takhn. nauk
Choice of parameters and operating conditions of a wheel-
mounted motor of continuous earthmovere with cutting blades.
Sbor. trud. MISI no.39.-268-274 '61. (MIRA 16.-/,)
(Earthmoving machinery)

UL'YANOV,, Nikolay Aleksandrovich kand. takhn. naukI BAWOV, A.F.,
--~'~.~tekhn~.nauk, retsenzent; KONONENKO,, N.A., inzh., red
SAVEL17EV, Ye.Ya., red.izd-va; SMIRNOVA, G.V., tekhn.red.
[Fundamentals of the theory and design of wheeled tractors
for excavating machinery] 0snovy teorii i rascheta kolesnogo
dvizhitelia zemleroinykh mashin. Moskva, Mashgiz, 1962.
206 ~. (MIRA 16:4)
kTractors-Design and construction)
(Excavating machinery)

ULIIANOV, N.A., kand.tekhn.nauk
Method of makin traction cwputations for rollers on
pneumatic tires. Stroi. i dar. mash. 7 no.8:15-16 Ag 162.
(HIRL 15:9)
(Rollers (Earthwork))

ALEKSEYEVA, T.V., kand. tekhn. nauk; ARTDIIYEV, K.A., kand. tekhn.
nauk; BROM]MG, A.A., prof.; VGYTSEKHOVSKIY, R.L., inzh.;
U 17 OV qu ; Prinimal uchastiye
OV N,,A.,, kand. tekhn. n
KON1fflN%K-O)---'O.--P'.'W.,, inzh.; FEEDORCYV,- D. I.., kand. tekhn. nauk,
reteenzent.,
(Machines for earthwork; theory and calculation] Mashiny
dlia zemliaAykh rabot; teoriia i raschet. (By] T.V.
Alekseeva i dr. Izd.2., perer. i dop. Moskva, Izd-vo
"Mashinostroenie," 1964. 467 P. (MIRA 17:5)

0
ULIYAOV. N.G.
'2eeting an experlmental hydraulic clutch in & Zjs-150 Car. Sborn.trad.
lab.prob.bystr.mash. 3:205-213 153. (K[aA 9 e.9)
(Automobile-4ransmission devices)

USILVIEVA, N.N.; ULIYAIICV, N.K.7
Geobotanica.1 studies as a method of prospecting for ore deposits
in central Kazakhstan. InfoxT4,sbor*VSEGEI no.5Os83-94 161.
WM 15--8)
(Kazakhstan-Prospecting) (Kazakh tan--Phytogeography)

TSYKUY&OVA9 N.A.; ULIYANOV.. N.K.
Occurrences of metals in eluvial and talus formations of some ore
deposits in central Kazakhstan. Inform,sbor.VSEGEI no.50:71-81
161. Off-FA 15:8)
Kazakhstan-Y,eta3z,, Rare and minor)
tzakhatan-Nonferrous metals)

MAROCHM, N.I., glav. red.; I-VIRKOVSKIY, A.P., zam. glav. red.;
TJLIYAI,ICV. &&4 zam. glav. red.; CIAIMSHIN, G.S., red.;
ZAYTSEV, I.K., red.; KNIPOVICH, Yu.N.,, red,; KULIKOV, M.V., red.;
LABAZINI G.S., red.; LURIYE, M.L., red',- SR-1011EIRM, T.P., red.;
SPIZHAMKIY, T.N., red.; STERLIN, D.Ya:, red.; TATARITOV, P.M., red.;
BELYAKOVAO Ye.Ye., nauchnyy red.; 11MUSHIN, V.A., tekhn. red.
[yearbook of the results of studies,by the All-Union Geological
Institut] Ezhegodnik po rezul'tatam rabot VSEGEL Lenirgrad,
Otdel nauchn.-tekhn. informataiip 1961, 203 p. (Leningrad.
Vsesoiyznyi geologicheskii institut. Informatsionnyi sbornik
no.49.) Nim 15: 6~
(Geology)

ULIYANOV.0 N.H.#- inzh&j SHPOMIUN, V.I.., inzhe
Distributing device for the refluxing of packed colu=0. Xhiz.
mashinostr. no.3:3-4. My-Je 163. (14IRA 16:11)

ARUTYMAU., B,8b.; BORISOV, V.N.; ZHEPLINSKrY, B.M.; MESROPYAU~ N.N.;
14WHMUMAKOV, X.P.; UL!YANOV, N.S.
~
Apparatus for the destruction of flotation froth, 'Khim, r ma
no,2:346-147 F 163. (KMA 16:7~ 0
(Flotation)

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A.0 ONCOMAS Wofs
Flotatim so-4ro*mtim staLwith
TOAXWW of the Rysism-Akrilm an L the -0-tty
do its, _S.
so P04OW11-W, waak.14av
Sofmiyth R&J? %wjo,b Nebw Nduck. 1.d~ l"J'Aktalw.
Imieffleft"idaft la. V. SomwUm 1039, No. Mo. 6w
J; Kke". ROOrat. Zkar. 1940. No. d. R.- -Rusittut; (hv.
W"hm Ry*un-Akriloy ocr. betaft "lion, in a IIWY.
III- trPw furnace for 40--W Inin. lftipcvm con4dashly thv
wisdity of the fintati,"I vimentralf. litinsing the 1~tmffnt
'it PAh to DD- I % avA RM to 4 J -6.3 DurstioaW the
bAsit dWatkM b 16 ItAll. &Rd Purilic1l. of the ctwcn-
trate 8 m1u. The amts. of the mgents used are soda 0.0-
6.5. 46dole 6. kcrosme 6 and water glass 0.776 kg./ton.
W R. Henn
-00
too
goo
600
too
a**
Coo
41
400
A S A. 11. A "I'Al,~VOkAL LITMI(M CLASUPICAMM
13.. art Milled aw am, III
u w .11 00
4,11P "Patton 011411111 "atilt K I I in

1 1 10 it U a w is 4 V~ III a LIU JANNIF 1111to it 4634841
L Is A A I L
00 A
/
00
e-
ff-
i
-
00
*0
I 00
makda of pbeepborks are at the Pordsad balm at
do ftu'vv Gre d-Osits. tl'y-ajwv And V. N1. 00
NW. SWMA XWb- 4YOUCk- 1411. I'Jdi%ff*iWW i
1'. Nswelk" 1940, No. W. W-
-Wf
103
KNO
ZIWW
No
% 114 4
ft
00
Wow
-
-
-
~
A
,
:
,
v
ibe Portland am an a 035-mm, wrern ptcwftkfvd a t0,23 -00
113M. coommitrate coniff. PA 21.9. RA 9.4 and JnwA. so*
90.3 midue 17.94%. The optimum Amom of the a" is 100 0 0
"Wpb, with no rmf than 7% of f1w r"kltw remillf"I m
000 it* wrvm. Tits lWitilas mWats went vorbosyll. 400
druls 1.7. vister sh" 1.0 and hitif LO kg.1fd". I" the
o4114 jPu)PI)wfmIIGO0WI*Id***I~4. Aftirrilatallon.the 000
**w coobtvatmic comitaWd PA VA-9741, RA)& 3.9-4,6 and

11 twd.midmed.0-8.8%, Tbvextn.wmsqJ,j%. AOj&
go
00 min. lWation produd produced a coamtmo rowrg.
R
'04 14-15% of P60b, wbkb cmus t* ubed to produre pbopborite aro
W. R.
Rml~
. Coo

Soo

4400
iloo
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00
I low 119taltv" 60.00

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Zkow. 119011, No. 6. PA.-Proper candi.
lk . . 6. wrM omk*cd ham 6b. No Semi-
M -00

A
A * ptudWim upit. wW a qw.4. vA a quaint. Yclicaw for en.
6
Th
'00
- e ogv
ikUj the 1~~n pbw*Mritft p"O.
X) so fiwkb a 0-10% Mw1w 41 The Illiew).
a -00

allw can be tm*4 out *Itbwt w%IN of The fine
v
l
alimes. with a 34M 1001fimlion of the, raww1trale aml S .00
d %ingir puriAmthm III vite tailbip. After theArd putifi4*.
d " RA
d PA 27 b-:r
t
i
h
..
ne
e mwen
rate tvatig
tion t
4.37-4,70%. The 11,0, exta. wws 93.4413.01% of the a**
visaml ccuscentrale. The main flotatkin IMIrrils took
13-A min purificallmi of the ninventrate 13.0-18.8 m1n.
The rt~xvma
and ~"lWn d the Whip 13 min
u,
.
the main notation wM aubuilylic lu-61
utped C too
and cuboxylic xM suit 0.21S kg./ton. Niificatiou of the
sox tailinp required carboxylic wM I A4-IM and cubmylic
salt 0.14 kgjtaa. No water glAm vu rectuired.
FArenwald nwhion m suitable for IWAIW ol 1
i~t,ppcr vilinit P?wN)hOrjjL4, W. R. fictin

ASA.SLA METALLMOICAL UTIVIATM CLASUPICATION
. ... .... IIII(It" wee
r
b u I I., It it it It 19 S a he 0 M
a & to I IF of 1 4 a 1 6 v
4
0 0 0 0 4111 e a 0 0 0
411 40 0 w 0

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a
1 4 6, a I 1 11 0 It Q it M It 4 1 11 M M U is it Q a) 0, 46
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1* of" wM 4
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and V. 0. Koatsm! FM OF1101,
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ow i Ixtewiv
b
f
U4
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y
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No. fi
ep
IN)
120-=; KNin
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No
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4
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us"
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to
. w&
Washed groun
k-
di
l
d
i
t
ont. con
ons.
er mena
for the preliminary tout
ug un
The conspit. of the concentrate was PA 22.3-21.79 and
RA 9*411,41,31%, The 11.0g, wait 4. in Pololus
oll -Mk
Theloaat4
nout
lhv
h
in
l moo
.
av
uraw"
ga
1g
ly Wat In a 12-chavibirr Fahren"Itl
=
N%J
Z

fie kitvt writ oblabled.orwolithich (414% of the
~
=h
0 total) tvitialned 30% PA and 4% RA. Juld The alher (112%
tio
t
in
Th
filt
i
d 21
1
PA
l n0.111
ra
n fa
.
e
a
.
e
of The tots
) conta
ne
% BID*
so dM varmato filter was 420 kg./6q. in., as compared 3
w with 501ts./sti. ni. with The unrostated orv. Thervaptits zoo
00.4 umd we" sioda 6.0-6.6. acklo" 2, cruile oil 0.6, Is**
kerosene A.6 and water glabs 0,2 hil.1ton for the Ist Pull-
fication and 0.15 kg.tton for the 20d Purification. Th.
duration of the Biala llistation wall) min., 0(the Ist Purifi- 400
cation 5.0-6h mia., of the 3M Purification 8.0-4.5 min.

and of the 3rd Purification IGJO-18.3 min. The ratio 6800
solid: fiquM in the pulp was IA. Cf. C. A, 36,4frfla, anti
490
prftv*dWjr absir. W. R. Ilran
I
wo*

. .
It favoirs -0 1 1420411 "At 041 Get

U's-AT a ill; it of W S v
JA A I a rA a 0 0 a 1,
a 0 o 0 o o
I
. . as . . . . .

41 140
.

-
Nf"tk
m of Phosphorite or* fmm tho 8
lodavow depos.
oil -
ho. ri.S.VI'Yilnovmdv.M.Rau:wv
ska
*. ObftdSR-
j
.
'
b,q Soack. last. i~dfq arargifiddav Ms. 1
.
S
t4
19"
N
60
X
amv
wd
o. 1
. 1 1;
tn. x4f."r, Zheir.
.
1%0. No. 0. 8&-G~-'llbr av. content in the Shchismy

t
0 0 d The raw tmmt Is to 150-ZA)
:gets is 12%.
' .
Carboxylic adds are used to. A con.
t
t
bt
i
5
d
l
28
P
0
- .
m
m
e was o
ne
eau
a
.
g.
OW RA
^
3.7-4. 1 %; tailings containtd Poh 3.87%; tmn, was 75-
W. R. lfrno

00
AIN.SLA S"ALLUMICAL W22AUNIC CLAIMICATM
va~ 67wallvo ISOM VWAAT
90
'Too
'lee
Ob
lee
I I I I a no a " 4 1 W a 9 a 4 3 9 v
W. U 00 U An
0.0 0,0.0 0000
116 0 :-v:,1*.** ** 0 *-*-*-O-o 00 00

if I
15
u= x 11 U U It
j# Iv if to 4 0 a a a 0
'" IJI
J.- --Am_ _1
j _A
i., A" ~i Ito-#* fil Ift, I
Coo-,-

RZhudou of glaccouke and the W1,10
of Conumtratins Plants of the Igoc'ev and Upper Kwu
t ' N
d
I
A
I
*
F
r AC
e
*
pos
3
VM
M
0.1fankm,
'
=
Gf
.
.
i Ra" ivauch. 11151. 7
'

d 1
4&eMiYuM i Isualefax WdFF Y4. V. SOMOUPO 1939.
-
M-W
r
Kh in
erds
zh
low
N
6
HO
O
l
.
.
a
.
o.
.
;
.
,
'
-
h
h
U
h
i
f
rv and
or
te ore
tom t
"Mmuff p
asp
e Egor
pper
I Kav= drpooits gives iow exta. a( PM. The tailings con-
lai pbwphorite, but also glauconite (hydrous
go .1. e of Fe. K, Ca. Mx), which is used for soften-
inghardwater. The method used to obtain the glaucooke a*
concentrate from tailing%iochides condensati.sn, classifics-

i
b
i
d
i
l
i
i
see
t
o
t
on,
c sepn. and nwist
ng, magnet
ng. The a
ry
ng,
initial material. when Vmud to t" mesli. Coutains, a
00 tual. amt. of glauconite. 71se +0.6 Mm. friction, Ob-
tained dwing bolting. before the magnetic sepn., and the
tailings of the sepcL friction are used to enrich phoo. a* 0
phorites. Flotation with dark naphtha amp gives a con. CO

vrntrate coutg. 18-121% I'M. Such emkirment intreasci O
the 12,0peldn, from(S-5~701oM%. Amettustforenrichium
'
the ham
ev dcpoWix om is dewtibed,. W. R. Ifeun

U06
off
C""TuNg Cal"WCAT"
lam 1"Bij " *a*." 6"101V
'A OPAIJI of a" ASS

U
0 Av so as r4 An L S It IW 0 0 0 1 IF 0 9 A 4 a T

of tv 0, it 0
01 It It it i ~
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0
I
.
*

ULIYANOV, N.S.
"Extraction of Glauconite and Phosphorite frcm the Tailings of
Con6entrating plants of the E.-orlyev and Upper Kama Depostis,"
N.S. Ullyanov, Obogashcheniye Fosforitov, Gl&ukonitov i Sernykh
RuU, 35-or-M-Rabot Nauch Inst Ubobreniyam i Insektofungisidam im
Ta. V. Sampylov, 1939, No 150. pp 152-66; Khim Referat Zhur 1940,
No 6, pp 86 (SEE: Inst. Ins~ct/iungi. in Ya. V. Samoylov)
SO: U-237/49, a April 1949

T,TLIYANOV, N. S.
"Flotation of Phosphorite Ore*of the Portland Horizon of the
Egorlyev Ore Deposits," -N. S. Ullyanov, and V. M. Ezuchevskaya,
(Above Feriodical) PP 96-103, Xhim Keferat Khur 1940, No 6,
PP 84-5 (SEE: Inst. Insect/Fungi. in Ya, V. Samoylov)
SO: U-237/49, 8 April 1949

TT N. S.-
-, L I YANGTJ
"Flotation of the Upper Kam Phosphorite Ore Deposits.*" N. S.
Ullyanov., Above Periodical PP 103-20; lChim Aeferat Zhur.-T74-0., No
6; 85 pp (SEE: Inst. Insect ungi. in Ia. V. Sampylov)
SO: U-237/49, 6 April 1949

'ULM'i
KV, N.
"Flotation of*the Upper Aama Phosphorite Ores with a Preliminary
Roasting," N. S. Ullyanov, V. M. Vidonov, and V. G. Konstantimov,
(Above Periodical3 PP 120-132; Khim Referat Zhur 1940, No 6, pp 85
(SEE: Inst. Insect/Fungi. in fa. V. Samoylov)
50t U-237/49x d April 1949

I - - -- TjTL1YJ4NGV)- N. S. - - - - -- -
"Flotation of Phosphorite Ore from the Shchigrov Deposits, of
H. 5, Ullyanov, and V. M. Ezuchevakaya, (Above Periodical) PP 145-511
KhTm RefeM Z ur 1940, No, 6, pp 85-6 (sEE: Inst. Insect/
Fungi. in Ya. V. Samoylov)
SO:, U-237/49, 8 April 1949

L t Y.411101d., 'j-
"Flotation on a Oemiproduction c-cale, with Preliminary Roasting of
the Ryazan-Akvilon Ore from the Egorlyev Ure 'Jeposits 11 N S. U11yanov,
V. M. 'Vidonov, and N. V. Makarenko, (Above Periodicall PP*5y:73, Khim
Referat Zhur 1940, No 6 pp 84 (SEE: Inst. Insect/Fungi. in Ya. V.
samoylov)
SO: U-237/49, 8 April 1949

USSR/Chemist -4ei-~i
ry diz rs FD-3000
Card 1/1 Pub- 50-1/17
Author Ullyanov, N. S.
Title The most immediate tasks of the mined chemical raw materials
industry
Periodical Khim. prom. No 6, 321-324, Sep 1955
Abstract Discusses the mining of phosphate and potassium minerals, sug-
gesting improvements. On the basis of USA and German experience,
recommends enrichment of potassium salts by flotation and ex-
presses the opinion that the use of a hydrocyclone in combination
with flotation methods is advisable. States that the gravita-
tional method for the enrichment of Chulak-Tau and Ak-Say phos-
phorites is still in need of improvement, while enrichment of
phosphorites by flotation has yielded good results. Says that
research on the replacement of the autoclave method of melting
out sulfur has lagged and should be expedited.
Institution Main Administration of the Mined Chemical Raw Materials Industry
(*Chief)

ULIYANOV, N.S.
Phosphate raw material and potassium fertilizerso Khim.prow,
no.7: 430-432 O-N 157. (MIRA 10:12)
(Phosphates) (Potassium salts)

ULIYANOV, H.S.
Conference on problems of the development of the potash industz7.
Xhim. prom. no.1:54-55 Ja-F 158. (KIRA 11.63)
(Potash industry-Congresses)

mean m won -Ma'-A
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f f6 1,
q 3 1. I

U I- LISTOV ) I.V.1 red.; MELINIKOV, V.I.,
tek1m. red.
(Outstanding people of Luzinol Znatuye liudi Luzino. Omsk
Omskoe knizbnoe 12datellstvop 1960. '70 (MIRA 14:121
(Ullyanovskii District (Omsk Province~LAgricultural workers)

LEKAyE~ V.M.; YELKIN,L.K.; ULI.TANOV ..,N.S., kand, takhn. nauk,,
red.
do ' tnei hod
(YO a of sulfur recovery from sulfur ores]
Sov1-w"w,w"U sposoby polucheniia sery ix sernykh rud;
uche,li&-, posoble. Moskva,, Moak. khimiko-tekhnolog. in-t im.
D.I.Nedeleyeva, 1961. 75 P. (MIRA 16:10)
(sulfur)

ULIYANOV, N.Se
Problems in the development of miping, ore dressing, and chemical
processing industries. Gor. shwe. no-5:3-5 N 163. (MM 16:5)
l"4osudarstvennyy komitet po, khimii pri Gooplane SSSR.
(Apatite) (Phosphates) (Potassi4) (Sulfur)

I 'T' T L a
CITED SOURCE: Nauclrin- f.. 95

al Kum lmnvu~y vqv W J~v
it
The corriparative error A ju be nrii, 1. ~:n

capable ot rapia CUM PCTISULI(Al aL
DIM
Card 31

E -- -- - -- - - - - - - -- -- - - --
0. -
131,1YANOV) -1 -
Designing a ferrodynamic galvanometer. Zzv.Vfs.ucheb.za-i.; p-,7ib.
7 nO.2W-,-52 164. (MIRA 18:4)
1. Kuybyshevskiy politekhnicheakiy institut imeni Kuyltrsheva.
Rekomendovana kafedroy izmei-itelIncy takliniki.

UL'YANOTI-Pa-, polkovnik.
The eastern Pomeranian operation. Voen.snan, 29 ao.9:10-11 8 153.
(KLHA 6:12)
(WorlA War, 1939-1945--Compaigns)

ULIYAHOV, P, (Astrakhan')
--- A-i"
-~,4 1Con't accounting courses for radio
1 (Astrakhan Province-Radio-Study
operators. Radio no.8S40 Ag 156.
and teaching) (KERA 9:10)

ABnMOV, A.A.,'redaktor; BOLTyANsKlY, V.G., rodaktor; VASIL'Y19VI A.M.@
redaktor; MV=V, B.V., redaktor; MYSHKIS, A.D., redaktor;
NIKOLISKIY, S.M., otvetstvewVy redaktor; POSTNIXOT, A.G., redaktor;
FROXHOROV, Yu.V., redaktor; RYBNIKOV, K.A., redaktor; ULITAN(,?
redaitor; USPINSKIT, V.A.. redaktor; CHETAYXV. N.G., i V*o
SHILOVO G.Te., redaktor; BEIRSHOV, A.I., redaktor; SIMKINAO ie'.N..
tekhnicheskikh redaktor
[Proceedings of the third All-Uniou mathematical congress] Trudy
tretiego veasoiuznogo matematicheskogo ~Oezda. Mos%:va, Izd-vo
Aiadomii nauk SSSR. Vol.l. [Reports of the sections] Sektsionnye
'doklad,v. 1956. 236 p. (MLPA 9:7)
1. VoesoyuzW matematicheskiy s"yezd.3rd Moscow, 1956.
(Mathematics)

BEMOVIKO, P.; KOZHEVNJV. N., inzh.-tekhnolog; fl~L'IIIKOV. A- *,
ULITANOV, P. f konditer
Advice to the cook. Obahchostv.pit. no.11:16-17 N 159.
(14IRL 1313)
1. Upravlentye rabochego snabzhoniya Sverdlovskogo sovnarkhaza
(for Kozhevnikov).
(Cookeu)

UWTANOV, P.
Party organization of the interfarm building organizationo.
Sell.stroi. 15 no.8:3-2-14 Ag 160. (KM 13:8)
1. Sekretarl partorganizataii Gullkovichakogo xezbkDlkhozstroya
Krasnodarokogo kraya.
(Krasnodar Territor7-Building)
(Collective farms-Interfarm cooperation)

UMTOOVO P.,v kand.economichaskikh nauk
Socialist economy is the indestructible basis for our country's defenses.
Tyl 1 snab.Sov.Voor.Sil 21 no.2:10-15 F 161, (MIRA 14:6)
(Russia-Economic conditions)

ULIYANOV, P., kand.ekonomicheskikh nauk
Communism is an abundance. Komm.Vooruzh.Sil 2 no-3:39-47 F 162,
(MIRA 15:1)
(Cost and standard of living)

AID Nr 971-17 20 Ifty
VACUUM CLADDIM OF REFRACTORY METALS (USSR)
Ullyanov, A.. N. D. Tarasov, and S. F. Koftun. Tavetnyye"metally,
no. 3, Wip- '1963, 74-76. S/136163/000/003/003/004
The-cladding of Nb, Mo. and Ta with 1X18H9T [AISI-321.) stainless steel,-Ni-
chrome, Ur602 alloy 1316 Fe, 0.35-0.75% Al and Ti, 0 .416 Mn, 19-22116 Cr,
1.8-2.30/6 Mo, 0.8176 Si, 0.0876 C, 1.3-1.8% Nbj, and zirconiurn has been in-
,restigated experimentally. Cladding was performed in a vatuum rolling mill
designed by the Physicotechnical Institute of the Ukrainian Acader~y of Sci-
ences. Refractory billets were mechanically. cleaned or pickled, spot welded
or riveted to the cladding material, heated in vacuum to the rolling tempera-
ture, and then rolled to the reqi4ired thickness. Pressure in the vacuum ays-
tem during beating and rolling was maintained at 4- 10- 5 mm Hg or lower. In
order to prevent work hardening, the rolling temperatur a was maintained
above that of the recrystallization,of the rolled metal. -The strength of the
Card 2/2
'W_

AID Ur. 971-17 20 Mar
VACUUH CIADDEQ (Cont'd] 6/13(Y/63/000/003/003/004
bond between the cladding and the base metal was found to increase with in- 7
creasin reduction and with higher rolling temperatures. Microhardness
- 9
tests showed that Mo and Cr-Ni alloy claddings do not form chemical com-
pounds in the interface zone; A sharp increase of interface microhardness
from - 230 to 740 kg/mm2 was observed in Nb clad with N-602 a I loy.
Some hardness increase was observed in Nb clad with Zr or TI. Aging at
1200*t for 2 hrs had little or no effect on the structure or strength of the
-_.bondl between Mo or Nb. and Cr-N -alloy cladding ;~.aging at 1200!C-for-10-hre
increased. bond strength by M- 20016, Shear strength of -the bond between Wt-
obium and zirconium cladding rolled at 1100*C with 'reductions of 20 or 4010
was - 30 or 64 kg/mm~ respectively, and that between xnolybdenum and
314 -602 cladding rolled'at 1190*C with reductions of 20 or 45016.-was - 28
.,:.or: 43 kg/mm 2~ respectively. [AZ)
C%rd 2/2

ULITANOV, P.L.
Soriem in H"r's system. Vent. Xoak. un. Ser. 1s Mat , mekh,
20 no.405-43 Tl.-A& !65. (MiRA 18j 9)
1. Xafedra tooril funktaii i fw*tsionaltnogo analiza Moskovskogo
gosWarstyennogo universiteta imeni M,Vb Lmonomovs,

us S
Ul'yanov, P. L. On some equiva!ent conditions of '.Gn-
--J s. U s Mat
vergence off s,:rics .ind integr pehi N el". auk
(N 3 133 141 (1953). ~'Rus-,Ian'i
h.- Fcl, S
(A the. t::r -t- t, 'f~x !i:d L~e
%.1i1;'v- 1h" ci~.- :int the
0
CL5e
the
~.J: the
well Lilov~;: t co"':N1 u; III f;ijfllt~ C.I~H-s Wher! the
sequelic, w(k" too rapidly tile [InItelieS3 0 the
series is equivalent to that of the integral obtained~by re-
Placing Jf(x+1)-f(x-1)j by a higher difference. ------
G. Klein (South Hadley, ?vfasq.).:
-Kr ;AN-5,1

lent to the condition k -r (4 Nol
Dlied to the du,t of f imd tim
VIM
W.Y,

z
7_
Wyanny, P. L On Idironoingtdc series with idonotonically
decreasing coefficients. Doklady Akad. Nauk SSSR
(N.S.) 90, 33-36'(1933). (Rus3ian)
The author consider.; the functions f(z) - Zk".jak cos kx,
J(x) = T_Ztak sin kx, under the condition that ak--#O and I
Aa. I < m. It is well known that neiti:er series need be,'
matical -Revlqws,~
Nathe integration is,
a Fourier series under this condition,
: N0.1
Vol e 15 Lebesgue integration. The author says that a measurable
..
Tari 6 - 1954 function O(x) is A-integrable'on (a, b) if the measure of the'

Sin set when (x) I L~Pn is o(l/n) and the Lebesgue integral oe

'
'
'
the
f unctiA
Obtained. by tru=iting O(x) at +n approaches
limit. Cse~,--e.g.~~Qtart_ Mat. Sbornik. N.S. 28(70), 293-
(1951); these Rev. 13, 20.],rhe following theorems are
tv~eti- (1) ThieKries for f(x) and J(x) are the A-Fourier
ser
aes of their itims. (2) If O(x) iu a function of bounded
variation whose conjugate ~(x) is also of bounded variation.
(A)f_fj~ (A)fljo. (3) If 0(x) is a bounded measurable
function, the definition of ~(x) as,ja JDitichy integral ngrees
almost everywhere with the clefinilion of j(x) asan A-ime-
gral. (4) For all x, J(x) N lite nega6ve of the A-ronjtij,.i1(- I'(
f(x); except perhaps at 0. +1r, f(.%) is Ow
of J(X). R. P. Boas. .11.

USM/Ma hematics Fourier series
Card 1/1 : Pub. 04 - 5/9
Author : Ullyanov, P. L. (Moscow)
Title : Application of A-integration to a class of trigonometric series
Periodical : Mat- sbor., 35 (77), pp 469-49o, Nov-Dec 1954
FD-1427
Abstract : The main results of this work were formulated without proof in the author Is
article "Ti-igonometric series with monotonically drcreasing coefficients.
"DAN SSSR, 90, No 1, 33-36, 1953- In the present work the author gives
the principal definitions and cites certain works devoted to the same
problem. He proves that f (x)..ao+-I: ak-cos kx is a Fourier (A) series
of f(x) and its sine-conjugate f (x). Thirteen references, 2 USSR.
Institution :
Submitted : October,28j, 1953

P.A. Some questions of A-fintegration. Dokl..
Ulyanov,

-'d' N
,
:
102 1077-1060
M
k SSSR
S
N
)
.
.
.
au
.
a
. -
(
(Russian)
A measurable real-valued function on (a, 61 is said to,
be A-integrable if
in(x: x t [a, 1/(%)j 1) and has period It, then
10
for almost all x c (0, 2:0, A forimila is also giv(-.n for
ansform Ll(-,r, a)). Proofs are
inverting tile tr,
"Gwcton, N,
E, flovi, 1-,(.
A~77
MR,

tj 4 qN o 11) P- ~- -
SUBJECT USSR/MATHEMATICS/Theary -)t fune-tions CARD 1/2 P%G - 182
AUTHOR ULJANOV P.L.
TITLE On the continuation of functions.
PERIODICAL Doklady Akad. Nauk 1 913-915 (1955)
i2~1
reviewed 7/1956
The author considers a function f(x) which is defined on and or-
la,b]r. LOL,P] has the property i. He seeks a function fl(x~ which is defined
on (c,dj (where (c,d)--) [a,b3), on [a,b] identical with f(x) kLnd on [o,d]
POSBOSSeS the property At Beside of f(z) its conjugate function
Y(X) lim f(x+t)-f(x-t) dt
E-+ 0 2 tg .1 t
2
is considered.
For integrable and continuous functions the following theorems are formulated
and a sketohy proof is givens 1. Let the periodic funotion f(x) EL(012TO have
the property that f(x) and Y(x) are integrable on La,b] C [0,21T) and for a
F_ ~P- 0 holds:
f(b+t)dt - 0 (in 1 )-1-E ff (&+t) dt - 0 f(la E
f Tn-1 Ini
0 0
Then there exists a funotion T(x) such that NOW - f(X on [a,b] and
x) EL(0#21r be periodic, f(x) and
(x) CL L(O f 21T ). ItJ(x)E L(Op21r)* ?* Let f(

boklady Akad.Nauk 195L 913-915 (1955) OARD 2/2 PG - 182
T(x) cont'nuous 'i?n La,b] C [0,27r] . Then f.(x) can be conzinued from Ca,b] to
[0,27TIsuch that' it and Its oonjugate Cuncttoa are oontinuc-os on the whole
interval [0,21A). 3. Let11(x) 6L(012"V) be periodiop f(x) and Y(x) essentially
bounded on [sib] c Co,2!r end
t t
f(a+r,)dn - O(Ifl) f(btn)dn - O(jtj)
Tr f(a+n)-f(a-n) - fjjL+nL-_fLb-n
Tim 17-
dn 4 OQ .1m, I dn ~ < c3
h -.*oI I I h -.voh
then f(x) can be continued from la,~l to LO,2Wj euch that the property of
the essential boundedness for f and f remains true.
INSTITUTIONt LomonOBSOV University, Moscow

ARRAMOV, A.A., redaktor; BOIMYANSKIY, V,G., redaktor; VABILIYIIV, A,M,,
redaktor; MADVIDEV, B.T., redalctor; KYSHKIS, A.D., redaktor;
NIKOLISKIY, S.M., otvatetvann3rj, redaitor; POSTHIKOY, A.G., redaktor;
PROKHCROV, Yu.V., redaktor; RYPNIKOV. X.A., redaktor; QtjUa"P.L..
redaktor; USPXUSXIY. V.A., redektori CHITAYEV, N.G., radaktor;
SHILOV, Moo, redaktor; SHIRSEOV, A.I., reds.ktor; SIKKINA, Ye.H..
tekhnicheskiy redaktor
[Proceedings of the all-Union Mathematical Congress] Trudy tretlego
vuesoiusnogo Katematichaskogo s0azda; Moskva iiunl-itull 1956.
Moskva. Isd-vo Akademii nauk SSSR* Vol.2. (Brief summaries of
reporta]'Kratkoe sodarzhanis obzornykh i sektsionnykh dokladov.
1956. 166 p. (MIaA 9:9)
1. Tseso7uznyy matematicheakiy 807azd. 3, Moscow, 1956.
(Kathematics)

cauctly lare oi its bandary vamem Var~us wrolaria
p p

SUBJECT USSR/MLTHEULTICS/Fourier series CARD 1/2 PG - 742
AUTHOR ULJAJZOV P. L.
TITLE On almost everywhere permanently convergent series.
PERIODICAL Mat.Sbornik,n.Ser. 40,, 1, 95-100 (1956)
reviewed 5/1957
An almost everywhere permanently convergent function series is a series
which converges almost everywhere for an arbitrary transposition of the
terms.
Let J'P (x)j (n-0,1,2,...) be a system of polyn6mials,being defined on
I n 2
La,b], being complete with respect to L and closed with respect to L which
is orthonormalized with the wfiight -C(x) (C(x) is defined on Ca,b], positive
and integrable). The series
OD
M E c k Pk(x)
k-o
is called the Fourier series of the integrable function f(x) if
b
ck f f(:x)C(x)pk(z)dx (k-O,1p2p...)*
a
Let 0 ( &,f) be the modulus of continuity of f on [a,b3 with the length of

Yat.Sbornikon.Ser- 40, 95-100 (1956) CARD 2/2 PC - 742
steps S. Joining the results of Kolmogorov Doklady Lkad.Hauk _1L 291-294 (1934))
and Natanson (Boklady 1kad.Hauk 2, 209-2il 8934)) the author proves the
theoremes
1. If f(x)E L(a,b) and
Q( 8 If) for +0,
01 -9 1 6) i
In I (In In 1 '+E
then the Fourier series (1) of the function f(x) on Ca,b] converges almost
everywhere for an arbitrary arrangement of the terms.
2. If f(x) is of bounded variation on a,b and if
0 0, 0( > 0. If the analytic function
F(z) is representable in G by an L-integral of the Cauchy type, i.e. if
F(z) - 1 (L) f LM d (zC-G, f(~)EL(1)),
21ri 1 S -Z

. 71oklady Akad.Nauk 112, 383--385 (1957)
then F(Z) - i d ~,
21Ti (A) f r -Z
1
CARD 3/3 PG - 724
where Pi( ~) are the limit values of the function F(z) if z coming from the
interior of G reaches 1. Some conclusions ars given.

4/A L/
AUTHOR: ULIYANOV'jp~-L- 20-4-12/51
TITLEs On Permutations of- a T-rigonametric System (0 pirrestanavkakh
trigonometrichaskoy sistany)
PERIODICALs Moklady Akadsmii Nauk SSSR, 1957,V01- 116tNr-41PP-568-571 (USSR)
1BSTRACTs Let
M so+ 00 cos k x + b sin.k x)
_2 Z (&k k
W
be the Fourier series of f(x)C-L(O,21r)q f(x+21r) - f(x). (1) is
called unconditionally , -oonv*r#*xt almost, *vwrywkere if it
convazgan- &]Aoxt-. toz ~ aw.arbitrary, porautatioa of
the terms. :Lot EM(f).be-the -boW.approxination, of-f(x) in the
n
metric of the L2 by trigononstric polynomials of the order (n-1).
(o (1n.1 n) I+ Ein a ~Z2 (f )J2 '_ 00 0, tbls n ( 1
Theorems If YK n
n 10
converges un.conditioz&lly. 0- *t.overywhere on [0,2-91.
Theorems If-for V_>O there holds
ir 21t lin ti lin lin t1l 1+ z 2
Card 1/2 f t - [f (x+ t) - f (x- t)] dx dt < w
~ 0

On Permutatians-..of.&-Trlgonometric-System 20-4-12/51
thsa..(-I-)~ Is unconditionally.-.c*zLrArgarit. almost -svvrywhsxo~ on
EO, 21rj.
Thoorent-There *xists a continuous 21V -poriodic:function f(x)
the-Fourior~sorios of.which after a certain permutation of the
terms does not converge on [0,210for every q;-2 in the metric
q
of the L
Several.further.similar results are..givon whioh gonloralisjo
well known rosulta due to Marcinkiewi4z fRof 3,7. and Ornas t1tef.el.
ASSOCIATIONt MOBCOW State University " X.Vo Lomonosoy (Moskovskiy goandarstvanW
universitat ix4 M,V. lomonosova)
PPMUM BTA, N.,Xolmogorov,, Aaadsmici&ns APrII 10s 1957
SUBMITTEN YebrWary 28p T957'
AVAILABLZi Library of Coagross
Card 2/2

KACHKA2H. S. [Kaosmarz, Stefan]; WHINGAUZ. G.; GIJTFAR, R.S. [translator);
ULIYANOV, P.L. (translator]; VILENKIN, N.Ya., red.
(Theory of orthogonal series] Teoriia ortogonalIny)-ch riadov.
Pod red. i a dop. R.IA.Vilenkina. Koskva, Gos.izd-vo fiziko-
matem.lit-ry, 1958. 507 P. (MUIA 12:11)
(Series, Orthogonal)

NIKTAISKITO S,K., otv,red,; ABRMOV, A.A,o red.; BOLTYANSKIY, T.G., red,;
VASILOYBY, A.M., red.; MEDYMM, B.T., red.; MYSHKIS, I.D., red.,-,
POSMIKOY, A.G., red.; PROKHOROV, Yu.Y.. red.; MBIJWT, K.A.,
red.; ULITAK L.. red.; USPSKSKIT, T.A..'red.; CENAM, N*Geg
r-ade-, UZZ. I FIG#14e. * $red.; SHIRSHOV,'A.1.0 red.; GUMffA, I,N*~
takhn.red.
(PrAceadings of thot Third All-Union HathematIcal Cengrems) Trudy
$retlego Veasolusnege matematicheskogo swesda. Vel-3 LOYmoptic
papers] Obzornya doklady. Moskva, Izd-vo Aked.nauk SSSR. 1958. ~96 p.
(XIBA 12:2)
1. Teencyazu" matematichaskly s'"yezd. .3do Moscowo 1956,
(Nothematics-Gougresses)

AUTEOM Skoryy. I.A., University Lecturer. and COT/55.5a.2-33/35
Kopytov, V.D.. Scientific Assistant
TITLZ& Lomotasov - Lectures 1957 at the Usch"ical-rAttazatical
Faculty of Moscow State University (Lowaoso,skiyo
ahteniya 1957 &ad& me zekhanLko-catematlebeakost fakulltete
NGV)
PFAXODICLLs Tentnlk Vookovskogo Univoreltety. wateaatlM, ve-afki,
eatzaacall, flow, khWI, 1958 Jr ~,,pp 241-246 (VOU)
"STBACTs The Lomonomov leeturas 1957 took place from October 17 -
October 31 j 1957 and were 40,11cated the 40-th anniversary
of the October r670jUtIQft.
16. A.D. Corbinow. Lecturer and B.M. budak, Lecturer s
I)IffMn,o method@ for the sol.Ma or syperboila
Squations.
11. 9.3. Itakbalav t Number of Calculation Oldr-ticAs fQv
the d'aTution of Zlliptlo Equations.
Is. V.I. loji.aaw, asgrant , Dirter.n.. Method for the
soloi on or the sobolov-systes.
19, Professor U.B. byzkLA a Karkov Proeaes.s &A1 Swalgroups.
Kostyumb#nka~-Cao4idat# of
20. A
C
3 A ol-so Decosposition cf Differential Operator@ With
;n
;
Respect to comralixot Estafunatious.
Y.Ajarsain, Candid&-,. of Physical-Ysth.astlftl Scion.aa.
Youndstions, of the Theory of Spherical Rarmaclas an Real.
folds. r
22. T.M. Borok# Aspirant v General Proportion of Partial
Zvor"Imn System.
23. V.A. VIjAnskly. Candidate of PhysIcal-Ksthsatical
3cleaces 6 Om Construct1we vathwastIcal Analysis.
24.-P.L. .011 Yana . Lecturer i Uver-I of Terms in Tr1gooo-
- ------ Astrid, Secier.--
25- I.Q. PUrovskly. Academicism and To.l. &!,main. Senior
Scientific Assistant I On the Nuabor of Boundary Cycles
or a Differential 2quation of first Order With a UtLonal
light Side.
The coAtonts of all the lectures have alre"y beft published,
card 5/5

0 0 S
AUTHOR: Ullyanov, P.L. OV/155-58-4-11/34
TITLES on the Divergence of Orthogonal Series to + ciD (0 raskhodi-
mosti orto&nallnykh ryadov; k + cD
PERIODICAL: Nauchnyye doklady vysshey shkoly, Fiziko-matematicheskiye
naukil* 1958, Nr 4, pp 63 - 68 (USSR)
ABSTRACTS Let an>0 and a 2 = 00 . Then there exists a system
n
nol
ftf (x)j of bounded functions orthogonally normed on
n 10
so that the orthogonal series f bk ifk(x) for every order
k=1
of the terms diverges everywhere on 10til to + oD, if b0 ak
Theorem : CD
It exists, an, -orthogpwb1 B&T1*9 -2 an'LPn (x) , which for an
n-;
arbitrary sequence of the terms divorges everywhere on 1011
Card 1/2

On the Divergence of Orthogonal Series to + cD SOV/155-58-4-11/34
00 2+ F_
to + oo p while cn 0
(D
Theorem : On 100] there exists an orthogonal series cn ?n (X)
with the 1.) it diverges to + (3D everywhere on
bj C (pro5erties:
a. Otl for arbitrary reversal of the terms 2.) the
E
orthogonally normed system ~(F'(X)~ is bounded on [0,11
The author mentions D.Ye. Men'shov.
There are 3 references, 2 of which are Soviet, and I French.
ASSOCIATION: Moskovskiy.gosudarstvennyy univeraiiet imeni M.V.Lomonosova
(Moscow state University imeni M.V. Lomonosov)
SUBMITTED. - June 4p 1958
Card 2/2

AUTHORt UllyaAm-F.L. SOV/38-22-4-4/6
TITLE% On the Series With Respect to a Transposed Trigonometric
System 0 ryadakh po perestavlennoy trigonometricheskoy
sisteme
PERIODICALt Izvestiya Akademii nauk SSSRtSeriya matematichoskaya,19589
Vol 22pNr 4oPP 515-542 (USSR)
ABSTRACTs 1. Theorems Lot f(x)6 L 2 (0,21) and for an F-> 0 let be
(ininn) 1411 lnn (2)( f) < oo, where E (2)(f) in the beat
n n n
n=10 f
approximation of f(x) in the metric L 2 by trigonometric polyp
nomialB of order 4 n - 1 .. Then the Fourier series of f(x)
converges absolutely almost everywhere on LO,27](i.e. under
arbitrary transposition of the terms). Theorems If
f(x)(=-L 2(0,21& and if for an 6 > 0 it holds
Card 1/ 4

On the Series With Respect to a Transposed Trigonometric SOV/38-22-4-4/6
System
Iln tlflnlln t111+E dt dx 1 then
OD
(24) 2: 1 a n[ OD
n=1
i.e. the series (22) convergent absolutely on Fool From
Card 3/4

67508
Unconditional Convereence With Respect to + co SOV/155-59-1-11/30
15
this theorem there results as a special case a theorem of
Privalov Z-Ref 4 -/*7
Theorem 4 j if I Tn jx)~ is a bounded orthogonally normed system
00
on [0,11, then there exists no series a (x) which on
nfn
a set E~--. 0,11 with m E - 1 is unconditionally convergent
with respect to + 00.
Theorem 61 : There exists no trigonometric series
OD
2 (an cos 27 nx + b n sin 2-,t nx) which on E with m E >0 is
L
unconditionally convergent with respect to + co
The author mentions Z.N. Kazhdan.
There are 5 references, 3 of which are Soviet, 1 Polish and
I American.
ASSOCIATION: Moskovskiy gosudarstvennyy universitet imeni jY.V. Lomonosova
(Moscow state University imeni T-V. Lomonosov)
SUBMITTED: January -1~)q
Card 4/4

ULI UMV, P4L.
Local properties of convergent Fourier series, UchozapsMoske
un. no.186[&]:71-82 159. (MM 13:6)
(Yourierts series)

6902
)~.q5t 00 S/055/59/000/05/004/020
AUTHOR: -Ullyanov, P. L.
TITLE: Singular Integra s and Fourier Serie80
PERIODICAL: Vestnik Moskovskogo universiteta. Seriya matematiki,
mekhaniki, astronomii, fiziki, khimii, 1959, No- 5,
pp. 33-42 W1-1q
TEXT: The author constructs a continuous function f(x) for which
the limit
(5) 4 +0 (.x - +,) - 2 4 (x)
t
h
exists for no x. The Fourier series of this function, however, is
uniformly convergent. Moreover it is shown that the functions f(x)
with-these properties form a set of first category in the set of
the'continuous 2*irm;periodical functions. Furthermore it is proved:
Theorem 2: There exist two conjugate continuous periodical functions
Fl(x) and F2(x) with the properties:
00 for all x; i = 1,2
Card 1/2 0 ilk

69472
Singular In~tegrals and Fourier Series S/055/59/000/05/004/020
2~ lim 4t exists for all x; 1 1,2
41
3.) The Fourier series of F,(X) and F2(x) converge uniformly on
10,2~Tl.
The author mentions N. N. Luzin and Kolmogorov.
There are 6 references; 2 Soviet, 3 Polish and 1 English
SUBMITTED: October 12, 1956
Card 2/2

,6(,) 16.26oo 05704
AUTHORt Ullyanov, P.L. SOV/38-23-5-8/8

TITLEs Unoondlti6nal Summability
PERIODICALs Izvestiya Akademii nauk SSSR9 Seriya matematicheskaya, 1959,
Vol 239 Hr 5; PP 781 - 808 (USSR)
ABSTRACTs The:pa-per-aontaims-proofw an&- Erome-generalizations of the
q,meartions -already treated by the - author in Z'Ref 4,5,6
7
-
cancerni g the unconditional summ-ability of function and
numerical series, whereby the notion of summability is some-
what-ext'anded.-Al-toge-ther the author gives eight theorems,
eleve-n--cancluslons and ten lemmata-,s He memtions I.I. Volkov
and-.A.M. Olevskiy.
There are 12 references, 6 of which are Soviet, 3 Polishq
2 English, and 1 American.
~'PRESENTED:~ -by A. N. Kolmogorov, Academician
SURKWED: December 7, 1958
Card 1/1
a

S/044/162/OC;~-,!/CG-2/C;06/"C);-:2
C 11 1/C222
P.UTHOR; Ullyanov, P. L.
TITLE: ConverGence and summability
PERIODICALL: aeferativny-y zhurnall n1atematika, no. 2, 1962, 12-13,
aabsty.%--ct 2B59- ("Tr. Mosk. matem. o-va,11 1960,
3 7 3 - -5, ~,. -;'; )
TEXT; This paper is a continuation of the author's examin;.Ltion
of unconditionally surimable (in one sense or another) function series
(Rzh. 1",at., 1960, 73906). By B B li linear regulz~r summation methods
nm
with the aid of factors ~:Lre denoted. B~`- B denotes methods
nm,
which satisfy the conditions
lim B nm ~ 1 0,1,2,...)l
n -~ co M
lim B nm = ~'n' "m 0
m -> 00 n .. ~ co
B'"' denotes methods having matrices which satisfy (1). By T Ila nmh
Card 111G
7-f
3-61 PANN

S/04 62/000/002/008/092
Convergence and summability C1 1 1YC222
linear Toeplitz methods are denoted for which
1-im anm 0 (M ~ 0,11 ... lim Ya nm = 1
n -1 CD n -4 co
Function series
00
757 fn(x) (x (,=- E) (2)
n=0
are considered, where t1he f n(:c) may not be measurLble. 111he series
00
C5 fnk(X)
k=0
is called z-. partial series of the first kind of (2), and the series
00
rf W 0, or 1
On n Pn
Card 2/G n=0

S104Y621000100
Convergence and su,.wn.L,bility C111 C222
is z~ partial series o~ t~fc second kind of (2). The scries
f . (X)
"k
resultin- by rearran,inj the terms of (2) is called i~ wea"I.- rearranje-
ment of (2) if tne sequence ~V splits into finitely Man. increa-
s:~ne sequences. If for every wok rearran-ement of (2)"the B-means
Q
Ci~(x) of the reaultinL7 sories (x) is understood in the sense of
convergqnce with respect to the outer raeasure) converge for N --~ oo
on E alraost everywhere on E) vith respect to the outer neasure,
then ~2) is weakly, unconditionally B-sum:-,utble with respect to the
outer measure on E (al--most everywhere on E). The weak unconditional
11 '"-, B and T summability with respoct to the outer mea~-ure
on E', or almost everywhere on E, are defined in analogy.
Theorem 1: If the series
c0
(x) (x E)
n
n=0 )~~; summable (T!~-- summable) on -!-' -wi
is weakly, unconditionally B th
Card 3/c
21000109 2

S/044/62/000/002/008/092
ConverCence and uummability Clll/C222
respect to the outer measure, 11hen
T n(X) = f(x) + n(X), x e E
where f(x) is --, finite fiinction on i4', and the series
CD
~n(x)
converges unconditionally on E according to the outer measure. If the
method B* (method T*) docs not sum-up the series
OD
T 1 (3)
n=O
then
f 0, x F-- E
Theorem 5: If the series
Card 4/6-

S/044/62/000/002/000/092
COX1VL1,'% urlC(~ LIM bum,~.1abil-jit.- C111/C222
~Pn(x) (x 0' 1
n=O
it; ouela *,.i-,Ltt each of its ',)artiLl series of the firut kind on [ 0, 1
is B summziblu with rez;pcet to the outor measurl~', thL-n
41n(x) - f(x) + '-Y-n(x)
00
Where f(x) is a lriniLe function, and the series I?n(x) converces
n=O
on C O'l ] unconditionully'yvith respect to the outer -qea~:ure. Here
f(x) = 0 if (7) i* not B"' - summable.
Theorem 7: If the series
00
'> fi(x), x6 E (4)
i-O
is such that each of its partial series of the second kind is B*
summabl on E With respect to the outer measure, then (4) is uncondi-
Card V6

S/044/62/000/002/008/092
Conver-,--Encla Lrld :E:U-I--,ZI-C~I CillIC222
tion4lly convereent on with renpect to the outer mea,.,;urL'.
% few conclm;iorio ('Ir;~vin from the stated 'heorems. "'he unconditional
sui,.miability aii;io~,L uvor,' 'L'-Id tho caso of numerical ,3erios are
considered. Applications o-f th; obtained results are given regarding
orthor~onal series and -eries of the type
00
_Iz- r., )
a 7. +
n ~jj i Jh
n=0
where Y(x) is a periodic function, the integral of which is 0.
- bstructers note: Complete trarslation.]
Card 6/1

30005
S/550/60/009./-000/004/008
D251/DJ05
AUTHOR: Ullyanov, P&L~
TITLE: Convergence and siimmability
SOURCE: Moskovskoye matematicheskoye obshchestv~%Trudy,
Ve 9p 1960P 373 - 399
TEXT: The results of this article were reported to the Moscow
Mathematical Association on November 24, 1959. The author defines
B = //Bnpm// as the methods satisfying
lim B = 1 (m = 0, 1, 0..)
n--* oD ' P m
and lim Bn,m = YnV lim Tn = 0. (2)
n-~, oo n---). -00
If only (1) is satisfied, the method is denoted by B T an,m
denotes the linear methods of Tepiits
lim anpm = 0 (m = 0, 19 (3)
Card 1/14 n--* oo

30005
S/550/'60/009/000/004/008
Convergence and silmmability D251/D305
OD
lim an,m ~~ 1. (4)
OD "
M=O
The author then states and proves the following theorems-~ Theorem L/
1: If the series
OD
El Vn(x) E) (19)
n=0
is weakly absolutely B** - summable (T* summable) on E accorling
to the lower measure that
Vn(x) = f (x) + ln(x) (x (20)
where f(x) is a finite function on E and
OD
(21)
n
Card 2/14 n=O

30005
S/550/60/009/000/004/008
Convergence and silmmability D251/D305
is absolutely convergent on 2 according to the lower measure. Also,
if the method B** (T*) does not slim the series
00
7 1 (21S)
Z__j
n=O
then f(x) 0 for x G Theorem 2: If series (19) consists Of
metric functions and is weakly absolutely B**-silmmable (T*-summa-
ble) on E according to the measure (20), then series (214-is abso-
lutely convergent on E according to the measure and
Ica
E ~ 2 (x 00 (29)
n
n=O
almost everywhere on E. Alsop if B** (T*) does not sum the series
(22) then f(x) = 0 on E. Theorem 3: If near the telp of the se-
ries
Card 3/14

30005
B/550/60/009/000/004./008
Convergence and summability D251/D305
OD
V (X) (xE[O9 11) (30)
n
n=0
there are infinitely many metric functions and the series (30) is
weakl 'absolutely B*-silmmable (T*-summable) almost everywhere on
[0, A then Vn (x) = f (x) + Tn (x) 9 (x E L 0 9 11) (31)
where f(x) is a metric finite function or, [09 it and the series
00
q"(X) 2
n=;
is weakly absolutely convergent almost everywhere on [0, 1]. If
B*1 (T*) does not sum (22) then f(x) E 0. The result of AeMo Olevs-
kiy (Ref. 15: DAN 125p No. 2, 1959; 269-272) is mentioned in the
discussion%Dn this theorem. Theorem 4: There exists a regular me-
Card 4/14

00
8/5555 60 009/000/004/008
Convergence and summability D29/D305
thod B - //Brl,m// and an orthogonal series
00
7-1 (33)
/ , %cfn(x) (anfn(x) ---> 0 on 109 11)
n=0
which diverges everywhere on [09 1] and which neverthelel* is ab-
solutely B-sinnnable almost everywhere on L09, 1]. The orthogonal
series of Men'shov is used in the proPr (Ref. 14: Kaohmazh S.9 and
G Shteyngauz, Teoriya orto onallnykh ryadov (Theory of Orthogonal
S;ries) M.p Fizmatgizv 19581. Theorem St If the series
00
7-1 In (x) (XEEOP 11) (48)
Z.L -4
n=O
is such that any of its partial series of the first kind are B**-
summable on CO, 11 according to the lower measure
'Pn(x) = f(x) + Tn(x)
Card 5/14

3WJ5
B/550/60/009/000/004/008
Convergence and summability D251/D305
where f(x) is a finite function and the series
00 VK
71 ln(x)
n--d
L
'L
isx~bsolutely convergent on [Op lj according to the lower measure.
f( 0 if (22) is not B**-summable. Theorem 6: There exists an
orthogonal series
00
off (x) (enTn(x) 0 on (09 1]), (56)
n n
n=t
L
and which nevertheless is such that any one of its partial series
of the first kind is 09 l)-summable almost everyw4ere on (09 1]
(Abstrao'torts note: (0, 1) summability not definedj. Theorem 7~ If
the series
Card 6/14
Convergence and summability
OD
7-1 fi(x)
L-4
i=O
300111/55%60/009/000/004/008
S
D251 D305
(X
(70)
is such that any of its partial series of the second kind is B**-
silmmable on E according to the lower measure, then (70) is abso-
lutely convergent on E to the lower measure. Theorem 83 If series
(70) consists of metric functions on [09 ij and anloof its Par-
tial series of the second kind j.~ B**-~summable on 9 1J9 then this
series is absolutely convergent on [0, 1] according to the measu-
re, and
00
f2 cD
(x)
ZL-j i
i=0
Theorem 9: If the series
00
Card 7/14 i=0
for almost all x (72)
10, A
f (x) (x 6 E)
i
(75)