SCIENTIFIC ABSTRACT GANTMAKHER, F.R. - GANTMAN, V.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000614230003-2
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: September 17, 2001
• Sequence Number: 3
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

AUTHOR3; Ayzerman, 14. A., Gantmakher. F. R.(Mo.acor,) 1o3-19-06-9/13
TITLE: On the Stability of Periodic Methods of Oi;eration in Non-
linear Systems With Piece-Wise Linear Charocteristics (0b
uutoychivosti periodicheskikh rezhimov v nolinoynykh sistemakh
s kkusocbno -lineynoy kharakteriatikoy)
PERIODICAL: Avtomatika i talemekhanika, 1958, Vol 19, Nr 6,
pp 6o6 - 6oS (USSR)
ABSTRACT: A method is described here by means of which the equations
of a linear approximation for solving problems concerning
the stability of a periodic solution in a system with piece-
wise linear characteristics can be found. As in references
I and 2 the automatic control system is here expressed by equa-
tion (1). At first the more general equation (2) is investi-
gated and beside it also the linear equations (3) which,
supplemented by linear relations, yields equation (4). Formulae
(3) and (t~) toj;ether determine the discontirmuri into~;ral curves.
The totality of (3) arid (4) is deaienated an linear approxi-
mation of (2 )for the periodic solution of (2)zi - z i(t). (f(zj)
Card 1/2 is given function which is piecewise linear). By additional

On the Stability of Periodic Methods of Operation 103-19-6-9113
in Nonlinear Systems With Piece-Wise Linear Characteristics
limitations the following theorem is obtained:(reference 1).
When the zero-solution x i - 0 of a system of linear approxi-
mation (3) + (4) is asymptotically stable, the periodic so-
lution z T.(t) of the set of equations (2) also is asympto-
tically stable. Going back to the set of equation (1) the
equations (31) and (4') are obtained for it. Linear relations
are found and written down in matrix form: x(t 0+,r). ux(t 0)3P
where U denotes the constant transformation matrix. For the
stability of the periodic solution of syster, (1) it is
sufficient when the roots of the characteristic equation
det(U-X E)-O lie on the circle of unit radiua. The problem
concerning the stability of the periodio solution of system
(1) can also be solved by direct alignment. There are 4 refer-
encesp 4 of which are Soviet.
SUBMITTED: May 159 1957
Card 2/2 1. Servomechaiiisms--Mathematical analysis

: I I I ~~ . I .-
AYZERMAN, M.A.; G&WHARM, F.R. (Xookva)
I ... I
Stability of periodic motions. Prikl.uat. i makh. 22 no.6:
750-758 N-D '58. (MM 11:12)
1., Noskovskiy fisiko-takhnicheakiy inatitut.
(Notion)

13(1) HASE J. BOOK alWITATION SQV/3113
Gantmakher, Feliks Ruvimovich and Lev MiVia,r1c;vi,:_n Levin
Teoriya ppleta neupravlyayemykh raket (Theory of Unguided Rocket Flight) Moscow,
Fizmatgiz, 1959. 360 p~ 8,000 copies printed.
Ed.: G. I. Felldman; Tech. Ed.: N. Ya. Murashova.
PURPOSE: This book ia intended for studento of exterior bnlliatics. It will be
of interest to military, scientific, and technical Wroonnel concerned uith
unguided rocket flight.
COVERAGE: This book constitutes a systematic course in the theory of exterior
ballistics of unguided rockets nnd presupposes a knowledge of mathematics and
theoreAcal mechanics at the vtiz level. The book considers -hio major
prob.Lem3: rocket trajectory and rocket dispersion factors, Approach to the
problem and actual execution are the result of Soviet thinxing and do not re-
flect work of western scientists. Rocket trajectory, the "soldd state
principle", vertical and distance dispersion, antitank rockets, finned and
rotating rockets, effect ok wind and Coriolis foree, and aerodynamics are
discussed. Examples of computations are given. The authors thank Yu. 1.
C ard IAO

Theory (Cont.)
SOV/3115
Korostelev. There are 12 references: 8 Soviet, 2 English, and 2 French.
TABLE OF CONTENTS:
Foreword 7
Basic Definitions and Symbols 9
Ch. I. Equations of Rocket Motion 1-1
1. The rocket as a system of variable composition 11
2. Theorems on the chAnge of mementum and of kinetic moment for a
system of variable composition 12
3. Systems of variable composition with a rigid shell. Rockets 16
4. "Solid-system principle" ("equivalent shell") for a rocket 19
5. Equations of motion of the.center of mass of a rocket 20
6. Equations of the rotary motion of a rocket 21
Ch. II. Calculating the Trajectory of a Rocket 24
7. Statement of the problem 24
8. Reactive force 25
Card 2/J_0

Theory (Cont.)
SOV15113
9. Equations of motion of the center o" gravity of a rocket on the
powered section of the trajectory 28
10. Tsiolkovskiy's fonmla, 30
11. Change in the speed of the rocket on the powered section of the
trajectory. Determining the arc of the trajectory 34
12. Direction of the rocket speed on the powered section of the
trajectory. 39
13. Consideration of the effect of drag and of weight force on the
speed 42
14. Calculation of the trajectory of a rocket 61
Problems 62
Ch. III. Fundamentals of the Theory of Dispersion of Rockets 67
15. Introduction 67
16. Factors causing lateral dispersion 68
17. Continuous random quantities 70
18. Role of the powered and unpowered sections of the trajectory
in the lateral dispersion of rockets 75
19. Angular deviation at the end of the powered section of the
trajectory and its horizontal and vertical projections 77
Card 3/10

Theory (Cont.) SOV/3113
20. Random vectors 81
21. Angular dispersion and its relationship to lateral dispersion 83
22. Distance dispersion 84
Ch. IV. Dispersion of Finned Rockets 87
23. Introduction 87
24. Statement of the problem 87
25. Equations of motion 89
26. Integrating equations of motion 92
27. Integrating equations of motion In the case of an incomplete
system of forces and moments 94
28. Dominant role of asymeti.7 af the reacti-Te force in the angular
dispersion of Linned vockets 98
29. Calculating the dispersion of specific types of rockets 99
30. Simplification of the basic formulas 103
31. Critical section of the trajectory 105
32. Formulas for the attack anglecr and the angular displacement 107
33. Graphic method of calcu.3ation. Cormils spiral 110
34. Basic calculation for=Lla 1-14
35. Dependence of the angular dispersion on the design parameters
of the rocket and the length of the launcher U7
Card 4/10

Theory (Cont.)
GOV/5113
36. Effective length of the launcher 120
37. Stepped diagram of reactive acceleration. "Active-reactive
mines". Multistage rocket 122
38. Firing rockets from an eircraft 126
39. Angular dispersion caused by initial perturbations 127
40. Methods for reducing the dispersion of finned rockets 130
41. Integrating the basic differential equation in the case of a
complete system of forces and moments 130
42. Formulas for the anglescP and Y(in the case of' a complete
system of forces and moments 132
43. Investigation of the formulas obtained. Primary and secondary
forces and moments 134
44. Coriolis force and Coriolis moment 139
45. Effect of the Coriolis force and Coriolis moment on the lateral
displacement of a finned rocket 143
Problems 145
Ch. V. Dispersion of Rotated Finned Rockets 151
46. Introduction 151
47. Statement of the problem 153
Card 54.0

Theory (Cont.)
SOV/5113
48. Rotational reactive moments 155
49. Equation of rotary motion 159
50. Integrating the equation of rotation l6o
51.' Analysis of the character of rotation 165
52. Determination of the angular deflection of rotated finned
rockets 168
53. Calculation of the angular deflection vith the aid of the
kernel R(sJQ5) 170
54. knalysis of tbe angular deflection of rotated finned rockets 175
55. Role of the eccentricity of the reactive force in the lateral
dispersion of finned rockets 178
56. Case of arbitrary motion along the launcher. Firing from an
aircraft -182
Ch. VI. Dispersion of Antitank Finned Rockets 184
57. Introduction 184
58. Basic characteristics of the ballistics of antitank rockets 185
59. Effect of the aerodynamic forces and moments on -the angular de -
flection of antitank rockets 188
60. Integrating the equations of motion 191
Card 6/
.Lo

Theory (Cont-)
SOV131-13
61. Calculation of the angular deflectirin 194
62. Range of a straight shot 198
63. Analysis of angular and lateral dispersion of' antitank rockets 199
64. Vertical dispersion of antitank rockets 204
65. Calculation of -the anbl.ar deflection for certain forms of the
a(t) diagram 206
66. Effect of the Coriolis force and the Coriolis momen' on the
dispersion of antitank rockets 211
Ch. VII. General (Three-dimensional) Problem of the Motion of Rockets 215
67. Introduction 215
68. Equations of motion of the center of grivity of a rocket 215
69. Equations of the iotary motion of a rocket 218
70. Forces and moments acting on a rocket 221
71. Linearization of the equations of motion 223
72. Integration of the equations of motion 228
73. Spinning rockets 232
74. Non-spinning finned rockets 233
75. Rotated firined rockets 234
Card 7/10

Theory (Cont.)
SOvI5113
Ch. VIII. Spinning Rockets 237
76. Acc-aracy criteria for the flight of spinning rockets on the
unpc~wered section of the trajectory 237
77. Condition of flight stability on the powered section of the
trajectory 245
78. Calculation of the angular deflection of spinning rocla ts on
the powered section of the trajectory 246
Ch. TX. On the Effect of Wind on Rocket Flight 254
79. Introduction 254
80. Physical picture of the phenomenon 255
81. Angular deflection of a finned rocket on the porwered section
of the trajectory 257
82. Corrections. due to the vind,, to the coordinates of the impact
point of a finned rocket 261
83. On the possible effect of wind on the dispersion of rockets 263
84. General case of motion of a rocket on the powered seetion of
the trajectory in the presence of wind 265
85. Non-spinning finned rockets 271
86. Rotated finned rockets 273
Card 8/10

Theory (Cont..)
87. Spinning rockets 274
Appendix I. Formulas for Auxiliary Forces in the Equations of Rocket
Motion 277
1. Second form of the equations of the momentum wid of the kinetic
moment for a body S 277
2. Formulas for momentum., Coriolis force, and Coriolis moment 281
3. On the displacement of the center of mass with respect to the
body of the rocket 284
Appendix II. Brief Data on the Aerodynamics of a Missile 285
1. Introduction 285
2. Elements of the tbeory of similar phenomena 286
3. Methods for describing aerodynamic forces and moments 289
4. Drag 292
5. Lift 296
6. Equa;ltorial aerodynamic moment 299
7. Equatorial dAmping moment 304
8. Axial aero-i'vnFunic. moments 3o6
9. On the effect of ae-rodynamic characteristics on the flight of
a missile 309
Card 9/10

Theo.r7 (CC-Tit.) Solt/31.13
TABLES
I. Table of ~ (M) functions for Siaccils drag laws, 1930 and 1943 313
Ii. Tdble of tKe H(Y) function 314
Ma. Table of K( f'unctions 315
IIIb. Table of Y-1 ) f~anctlons and K function s 316
17. Vable of tHe fun-etions F(v): L,(v~, L2(y), L3(v), L4(v),
L 5(v), M(v).. N(v) for the drag law of 1930 317
V. Table of the functions z
), 1~(z
(z
), ~r(z
) 325
o
cr
0
.
VI. Table of Bessel functions and Fresnal integrals
' 327
VII. Table of the functions.I(x), I (
x), I W, H(x) 349
VIIIa.- Table of fun-etions for a recti;~;iar diagram 353
VIIIb. Table cf f%metions for a trian
,gular diagram
354
VIIIc. Table of ( Aoc, functions 355
Bibliography 357
Subject Tndex 358
AVAILABLE: Library of Congress
Card 10/10 AC/os
2/2/6o

Af A~L,
66 .4
a m
i 3i
143 Oili, 19

GOTHADUR, Felike Ruvimovich; ILOICHETA. GA. red..- YMWOTA, Ye-A.,p
tekhn.red.
(Lectures on analytic mechanics] Lektaii po analiticheskoi
mekhaniks. Moskva, Gos,,Izd-vo fixiko-mtem.lit-ry 1960
296 p. imlu i4:4)
(Mechanics. Analytic)

S/194/61/000/006/021/077
too 0 D201/D302
A.UTHORS: Llyzerman, M.A. and Gantmakher, F.,R.
TITLE: Fundamentals of the theory of non-lincar automatic
control systems with diSCOntinUOLIS ch,:ir --c teris tics
PERIODICAL: Referativ-nyy zhurnal. Avtomatik~a i redioelektroni-ka,
no. 6. 1961, 33-34, abstract 6 V242 (V sb, Vses,
Mezlivuz. konferentsiya po teorii i metodam rascheta
nelineyn. elehtr. tsepey, no. 1, Tasbhent, 1960,
30-44)
TEXT: The analysis of systems is given which differ from the
linear ones by the presence of one or several cleriients Nrith str.-dght
line segmented characteristics. The peculiarities are explained in
the notation of equations of motion in discontimous systems and of
the Drocesses occuring during the transition over the discontinuity
surface (slip states). An exact method is suggested for determin-
ing the periodic states and an analysis of their stability is given
Card 1/2

S/194/61/000/006/021/077
Fundamentals of the theory ... D201/D302
for the general case. The idea of a linear appro-1-imatiou is intro.-
duced. It is shown that in discontinuous systems equilibrium states
may occur an analysis of which is given. 6 fignxes, 18 refer-
ences. 2~zstracter's note: Complete translation-7
V
9
Card 2/2

L) L) 0 L) 80248
S/040/60/024/02/12/032
AUTHORS: Ayzerman, M. A., Gantmakher, F. R. (Moscow)
TITLE: On the Stabilit f 'Position of Equilibrium in
Discontinuous Systems
PERIODICALt Prikladnays, matematika i mekhanika, 1960, Vol. 21t, No. 2
pp. 283-293
TEXT: Let a discontinuous motion be described above or below the sur-
face
(2) F(x) = 0
by the systems of equations
(+1) Lx f * (X)
or
Lx (X)
at-
Both systems "re assumed to possess unique solutions for given initial
conditions and to be without singular points on the surface (2). The
motion of the image point on (2) is not defined by (�1) and must be
additionally determined. Thereby positions of equilibrium can arise
Card 1/2

80248
S/040/60/024/02/12/032
On the Stability of the Position of Equilibrium in Discontinuous
Systems
on (2), the stability investigation of which has to be car--r-ied out
either by considering the additional conditions or by considering the
systems (�1). The last case is investigated in the present paper. Let
(2) be the plane x, =O, in the semiplane xr, = 0, x1, > 0 the
trajectories of (+1) are assumed to proceed downwards and in the
semiplane xi, = 0, x-1 < 0 to proceed upwards. Then (t1) describes
a point transformation G, of the semiplane x h = 0, X, ;;- O-into the
semiplane x. = 0, x1l< 0 and (-1) describes a point transformation G
of. x = 0, x 0 into x , = 0, x, > 0. The limit x, = 0, x. = 0
consists of fixed points of the transformations G,, G~., G = G~G,. The
stability of the fixed'~oint x = 0 of G is equivalent to the stability
Of the Dosition of equilibrium in the orisin (see (Ref.8,9)). It is
shown that, if f4 (0) and f- (0) are not collinear vectors, the P'Osi-
tion of equilibrium x = 0 is unstable. In the 6ase where f4 (0) and
f- (0) are collinear the authors give sufficient conditions for the
stability and instability of the fixed point x = 0 (generalization of
the results'of Yu. J. Neyma:rk (Ref.8),(Ref,5)).
There are 3 figures, and 10 references: 8 Soviet, 1 ("':eririan and 1 Italian.
SUBMITTED: November 3, 1959
Card 2/2

31~33
S/569 61/001/000/018/019
D274 D004
IWo (no PL
14 f
AUTHORS: Ayzermanp M. A., and Gantimakher, V., R. (USSR)
TITIAt Some problems in the theory of nonlinear control systems
with discontinuous characteristics
SOURCE s International Federation of Automatic Control* let
Congress, Moscovp 1960. Teoriya, nopreryvnykh sistem.
Spetsiallnyye matematicheskiye problemy. Moscovq
Izd-vo AN SSSRp 1961. Trudyp v. 19 679-690
TEXTs A system with one nonlinear element in described by
n
&,Jxj + (i - 112t ... qn) 9 W
J-1
where f(xl) in a piec*viso linear function. If the phase space of
the system in divided by the discontinuity surfaces
Card 1/7

31 3
S156 61/001/000/018/019
Some problems in... D274 B304
F,,( (Xl9X29 ... 9X 0 192900ot1m) (2)
a
into parts, then the process In each part Is described by
i1 0 fi(xj1x2V---1Xn) ; (I - 199YOU090) 9 (3)
where the right-hand sides are continuous. Certain aspects of the pro-
ceases are discussed which &rise on passing from one system (3) to anotherp
through (2)., An exact method In proposed for deteruining the periodic
solutions in systems of type (I)* 'Stability of the periodic solutions is
analyzed. The systems of Eqn. (1) or (3) do not completely detemine the
motiong an the passage of the representative point in phase apse* through
the discontinuity surface is not taken into account, nor is the motion
of that point along the surface. For that Furposeq the discontinuity
surface is dividedg by means of the manifolds r, + and r - p into slip
regions C and regular regions Po The motion of the representative
point is determined by means of theme regions. Furtherp the response
equation is defined as that obtained from system (1) by eliminating all
Card 2/7

31133
S/50 9;~'Oijo 01'/000/018/019
Some problems in... D274/11304
X, , except X, W X 0 If f(xl) is continuous and sufficiently smoothp
the response equation for system (1) in written
1D(p)z - 11(p)y (4)
whore
y Ax) 9 p x - X,
dt
But in the present case,, Eq. (4) has to be supplemented by the conditions
(jumps) at the discontinuity surfaces
Card 3/7

Some problems in..,,
31333
3/569/01/001/000/018/019
D274/WO4
0 t eu b ".10
~o 0
~1-
- b
s
+ a
~ I
b
~

11
o
,
0
o
I
t 0
,
U 0 a 0 0 a 4 0 j a U -D 0 0 0 a a (5)
Ao U-1 + a, D_2 + + , A_l 0 - b4) Ilk_, + b
,'nn_2 + + bn-l 10
0
.
'whe re and ^r, are the discontinuities of x and y respectively
and
D(p) = so? + e o o + a
n
K(p) = b + + b
0 n
Further, the concep t of "response equationfl is discussed. The conditions
of transition from one branch of the characteristic to another in systems
Card 4/7

31333
S/669/61/001/000/028/029
Some problems in... D274,71~04
of type (1) involve 5 possible cases. Two of these cases correspond to
special switching conditions and were apparently discovered by the authors;
they are called "pseudoregular" and "pseudoslip* respectively. In all
systems of type (1), as well as in systems vhich differ from (1) by the
presence of a given periodic disturbance,, the periodic solutiens can be
found exactlyg i.e.9 without neglecting the harmonics. For this purposeq
the authors used a method proposed by Ye,, N* ROZeDVSN8Orj vheroby System
(1) is replaced (4) and (5); in (4), x and y are replaced by
+00
x .5 i r :..) t
r oc)
in expressed in terms of inI and Ii.
tem of transcendental equatione in t,,
periods. Stability of periodic solutions~
irwt
r 00
These equations lead to a sys-
to the equation of the
System (3) is considered.
Card 5/7

31333
S/f569161/001/000/018/019
Some problems in... D2-14/D304
Let t m t i be the time moments when the trajectory which corresponds to
the periodic solution cuts the discontinuity surface. In order to apply
Lyapunov~s theorem, the equations of linear approximation are set ups
.7 'a fi "
A
ii 6 x (i 112soqn) 9 (7)
-J Nk ;,.
[C 2(t)
supplemented by the linear "discontinuity conditions"s
+ 1" +
h~ ~x
~k
k k
where
Card 6/7

Some problems in*..
ar
.4
hi 3 t
31333
S/ti69/61/0,01/000/018/019
B274/D304
The authors studied the appearance of atable-equilibrium points on the
discontinuity surface for system (3). Three theorems are formulated for
the special case when the manifolds r+ and r- coincide vithout being
contigmous to the slip region. These theorems involve the stability con-
ditions for the special case. A discussion follovede There are 6 figures
and 20 referencess 19 Soviet-bloc and I non-Soviet-bloc.
Card ",r/7

F-VI /L
AIMRMAN M A. and GAMAKUR
"Problem of absolute stability of controlled systems in the list of vorY.5"
Report presented at the Conference on App7Aed Stability-of-Motion 7heory and
Analytical Yechwics, Kazan Aviation Institute, 6-8 December lq52

AM4016855 BOOK EXPIDITATICN S/
Ayzerman, Mark Arcnovich; GantmAher, Feliks Ruvimovich
Absolute stability of control systems (Absolyutnk7i'V~viostl reguliruyemy'VA i
sistem) Moscow, Izd-vo AN SSSRj 63, 0136 ps illusso biblio., 6000 copies
printed. (At head of title: Akademiya nauk SSSR. Institut avtanatiki i
telemewmiki.)
TOPIC TAGS: automatic control, absolute stability, ccntrol system absolute
stability, frequerx,.y analysis of control, Lyapunov method, direct method, Popov
criterion, Wrlye resolvent equation method',
PURPOSE AND COVERAGE: This book is devoted to a new approach to the theory of
autanatic control and its absolute stabilitys initiated by the Ruvanian
scientist V. M. Popov, and cenuins a systematic exposition of the main results*
along with the point of view of the authoirs themselves regarding the present
status of the preblem. 7he book is intended fcv a large group of specialists
interested in stability, and the mathusatica3
approach is tw4iftL-e somewhat
r
implified.

L~11598-63,- EIWT(d)/BDS AFFTC/APGC/ASD Pg-4/Pk-4/P.,'1-4 ~"I/Pq_4
inc(C)AC
ACCESSION NR: AP3001082
S/0103/63/024/006/073210737
r
AUTHOR: Ayzerman, M.'A. (Moscow); Gantmakher, 1'. R. (Moscow),
On critical caBes'-in the theory of absolute stabilitY f co tvoi d
SOURCE: Avtomat-i~a i ielemekhanika, v. 24, no.,6, 1963, :732.ri 7
TOPIC TAGS: control,system, absolute stabilityt critical casejl limiting stability,'Z~-
control system stability
ABSTRACT: -Popov's criteria of absolute (global) stability are~,'applied to a control'
system described by the equation
dx
Ax + bya.:
dt
where y are column:vectorg and cl is a:row voctor; A is a cbnstaTit:!squmrc
matrix, all the digen-values of which are locatod on the left hand a i the::
imaginary axes; and Y(C;) is a continuous scalar:function satisrying1the conditiOn
0 cp (Cr) cr< k, wbere k is a finite number. These criteri4j: pr6viously apOlied,
Card Y

-63
11598
ACCESSION N~: AP3001082
arrowLn own
'to noncritical cases, are realized here for all critical case's by im
the class of characteristic functi6na y (p (0 by inequality
o k,
(2)
g ra;l criie~rion ibsolute
:where Z is an arbitrarily small positive number. :,The, ene of
;stability is formulated in'the following theorem: For the Asoiutle stability :,of
;system (1) in any critical case when Qr) satisfies inequality (2!),* it is sufficient
:to satisfy the Popov inequality
-Re(I + NO w4w) + llx,~ 0
,for any finite real q and for all real W and to satisfy them condition of "limiting'
stability," i.e to make stable "the 'linear system+ derived from (1) at, y E;Olfor
'any small E; Necessary.*4nd sufficient conditiaiis which:~the f ie4ue),Lty ...I,
-characteristic- W(iW) must satisfy to secure the I'limiting si~b'ilityW of' t lineiari
a e a.
r MA k (k+e ark robv
a
Card

GANTMAKIIER, V.F.-;.. KANER, E.A.
Dimensional effect in the presence of a drift of electrons
inside a metal. Zhur. eksp. i teor. fiz. 45 no.5:1430-1444
N 163. (MIRA 17t1)
1. Institut fizicheskikh problem AN SSSR i Institut radiofiziki
i elektroniki AN UkrSSR.

:A ETTER, I" ..R . (i,IOSCO!.:) ; YA I, V, .,*I. ~ Lei I-` zIL-rnd ) :
TIAbsolute stability of non-linear controls."
report presented at the 2nd All-Union Congress on Thect-etical and Applied
I
M
echanics, Moscow, 29 Jan - 5 Feb 64.

GANTMAK-TMER,-V.-.-F.; SHARVIN, Yu. V.
"Temperature dependence of the electron mean free path in tin at liquid helium
temperature."
1
report presented at the gth Intl Conf on Low Temperature PhIj-sics, Columbus,
Ohio, 31 Aug-4 Sep 64.
Inst for Physical Problems, AS USSR.

VASILIYEV, A.N., starshiy nauchnyy sotrudnik; Priniml uchastiyot
GANTMAKHER, M.I.) mladahiy naucbW sotrudnik
Economic efficiency of the use of the newest loom types in the
linen industry. Tekst.prom. 22 no.11:43-46 N 162.
(MIRA 15:11)
1. TSentrallnyy nauchno-issladovatellskiy inatitut lubyanykh
iolokon (TSKIILV) (for Vasillyev).
(Loons)

83582
S/056/60/0313/005/015/050
140 v#3 B006/BO70
AUTHORS: Sharvin, Yu. ., Gantmakher, V. F.
TITLEt Anisotropy of Surface TensionAat the Interface Between the
~X Superconductin6 and the Normal Phases of Tin
PERIODICAL: Zhurnal eksperimen,,allnoy i teoreticheskoy fizikl., 1960,
Vol. 38, No. 5, PP- 1456-1470
TEXT: The present paper is a detailed report on the determination of the
anisotropy ib of surface tension at the interface between the super-
conducting (s) and the normal (n) phases of tin, using two methods that
give directly independent values for A. 6 has the dimension of a length,
and is related to the free surface energy 6' no by the relation
d, 'AH2 /8tr. The difficulties in the experimental determination ofj~
ns 0
are discussed in the introduction. Then, the first method is described.
It is based on an analysis of the structure of the intermediate state on
samples with different brystalline orientations, the analysis being made
with the help of ferromagnetic powder. The apparatus used is schematically
Card 1/3

83582
Anisotropy of Surface Tension at the Interface 8/056/60/038/005/015/050
Between the Superconducting and the Normal B006/BO70
Phases of Tin
shown in Fig. 1. The results of the method, called "the method of frozen
flux" and described in detail, are separately discussed for the individual
samples. Figs- 4-7 reproduce photographs of the structures of the inter-
mediate stage in a field of view 1.4 cm in diameter; the white regions
are superconducting, the arrows show the projection of the crystallo-
graphic axis onto the surface of the sample. The numbers of the samples
and the temperatures are also given. Figs. 8-10 and '13-15 give the cor-
responding polar diagrams. The second method is based on the measurement
of the moments of force acting on spherical samples in a magnetic field.
This method is called the "method of torsion balance", and is also
described in detail. Due to the anisotropy, the free energy of the sample
depends on the orientation of the magnetic field relative to the crystal-
lographic axes of the sample. The sample is suspended by an elastic thread
in such a way that in the state of equilibrium the moment tit - -aF/11111L may
be determined from the angle of rotationo4 in a horizontal magnetic field;
A is calculated from M. Densities, impurity concentrations, and the
momentYA of nine samples are given in Table 1.. Figs,. 18-21 show the angular
dependence of the moments m (m - 8,TM,/H2V, V - sample volume) for different
Card 2/3

83582
Anisotropy of Surface Tension at the Interface S/'056/60/038/005/015/050
Between the Superconducting and the Normal B006/BO70
Phases of Tin
axes of suspension (axes of rotation). The f-values measured in the
various positions (f is the free energy divided by VH2/81r),j ml and
c max
,&m are given in Table 2. The results relating to the dependence of
surface tension on the direction of the normal to the interface, the
order of absolute magnitude of this affect, and its temperature dependence
are discussed in detail. Finallyq VAI
the results of the two methods are
compared with each other as well as with the results of the theory.
P. A. Bezuglyy, X. N. Bogolyubov, V. L. Ginzburg, and L. D. Landau are
mentionea7ffi-this connection. The authors thank Academician P.L.Kapitsa
for his interest, and A.-I. Shallnikov for discussions. There are 21
figures, 2 tables, and 21 refer~n-cesz 15 Soviet, 3 US, and 3 British.
ASSOCIATION: InStitUt f12icheskikh problem Akademii nauk SSSR (Institute
;r ---
of Physical Problems of the Academy of Sciences U SR)
SUBMITTED: December 31, 1959
Card 3/3

GANTWMM, v.r.; suRviN, Yuev-
C,
Nonmonotonous dependency of the surface impedance of tin on the
magnetic field at a frequency of 1.9 me. Zhur. eksp. i teor.
fiz. 39 no.2:512-513 Ag 16o., (MIRA 13:9)
1. Institut fizicheskikh problem Akademii nauk SSSR.
(Tin) (Metals at low temperatures-Xlectric properties)

86896
4- 10 (11!~gl Ile- 0//,/.9 S)
S/056/60/039/005/012/051
B029/BO77
AUTHORS: Sharvin, Yu. V., Gantmakher. V. F-
TITLEi The Depth of Penetration of a Magnetic Field Into a
Superconductor as a Function of the Magnetic Field Strength
PERIODICAL: Zhurnal eksperimentallnoy'i teoretioheskoy fiziki, 1960,
Vol. 39, No- 501), pp. 1242-1250
TEXT: So far, the intensity and characteristic of nonlinear effects in
real superconductors has not been clarified by experimest and theory.
The theory of V. L. Ginzburg and L. D. Landau furnishes the following
expressions for a temperature range close to T
X(?, + 2 F2 I f2 / eef f 2
8(X+ y-2)2 P W ~ c (0)'; Abb rRing to
L. P. Gorlkov (Ref. 2), e eff has to be twic6 the charge of electrons in
order to agree with modern superconductor theories, and the range of
application of the above relations has to be limited, too.. Evidently,
Card 1/4

86896
The Depth of Penetration of a Magnetic Field Into S/056/60/039/005/012/051
a Superconductor as a Function of the Magnetic B029/BO77
Field Strength
no investigations have been made so far for ranges where the theories of
Ginzburg and Landau do not apply. To clarify several discrepancies, the
authors studied many specimens, employing.*,jke more accurate radar-
frequency method. A. A. Abrikosov, L. P.GcllWov, and I, M. Khalatnikov
(Ref. 12) developed a method for a theorJiTal estimation at limited
frequencies. On the basis of the experimental data, the authors selected
an operating frequency of 2 megacycles. The following part of this paper
deals with the measuring methods, the measuring instruments and their
calibration, the necessary control tests, and the evaluation of the
results. Superconductivity vanishes at the sharp bend of the curve
Afj(H); Af, denotes the frequency shift of the signal of the first
generator. Sometimes this superconductivity vanishes at a field strength
greater than H In another specimen the dependence of the effective
increment Aeff - (dr/dfl)bf, of h - Ho/Hc was' nearly parabolic. The
rapid increase of o( at T-4Tcseems to be caused by secondary effects,
The following expression was found for the transverse f~eldi
Card 2/4

86896
The Depth of Penetration of a Magnetic Field Into S/056/60/039/005/012/051,
a Superconductor as a Function of the.Magnetic B029/BO77
Tield Strength
h 2 h4 );. h
i + a P 1 .1 denotes the ratio of the strength of the
external field to that where the specimen is no longer superconducting,
Other specimens showed considerable deviations of the curves A (h2) from
2 eff I
linearity at small values of h 1 T C
found in this investigation are smaller than the values calculated by
Ginzburg and Landau from the penetration depth, The theoretical value of
F, 4-5-lo-4, agrees with the experimental value. The values for ae are
two to three times greater than the one determined by M1. Spiewak (Ref.19)n
It would be interesting to study the surface impedance of superconductors
as a function of field strength at relatively low frequencies (106-109cyclE).
Academician P., L. Kapitsa and A. I. Shallnikov are thanked for their
Card 3/4

The Depth of Penetration of a Magnetic Field Into S/1056/60/039/005/0'2/051
a Superconductor as a Function of the Magnetic B029/,aO77
Field Strength
interest and for discussing the resultq. There are 6 figures, 1 table, and
19 references: 11 Soviet, 3 US, and 5 British.,
. ASSOCIATION: Institut fizicheakikh problem Akademii nauk SSSR (Institute
of Physical Problems, Academy of Sciences USSR)
SUBMITTEDs July 15, 1960
Card 4/4

S/056/62/042/005/046/050
B108/B136
AUTHOA: Gantmakher V. P.
TITL-'-': A method of measuring the momentum of electrons in a metal
Zhurnal eksperimentallnoy i teoretichoskoy.fiziki, Y. 42,
no. 5, 19062, 1416-1418
TZ',,"'T: A constant magnetic field causes t'he electrons on a spiral path
to penetrate into the metal beyond the skin depth. If the size of the
soeci.men is equal to the diameter of the electron orbit, this will cause
scat'-erin '- of the electrons from the crystal boundaries. The diameter
depends on the field strength. This kind of effect becomes evident in
the behavior of the impedance. Experiments were made with single-crystal
tin plates with an electron free path of 1- 3-10- 1 om at helium
temperatures. The variation in frequency (,./10 6 cps) with variation in
ma6netic field strength owing to the specimen-induced variation in the
reactance of the oscillatory circuit was measured by a modulation
method. 5.7-10
20 g-cm/sec was the value obtained for the orbit
Card 1/2

S/056/62/042/005/046/050
A method of meazuring the momentum ... B106/B138
diameter in momentum space. This method can also be used to study the
Ferm.i surfaces of -metals. . There is 1 figure . J,
ASSOCIATION: Institut fizicheskikh problem Akademii nauk SSSR
(Institute of Physical Problems of the Academy of
Sciences USSR)
SUB,i!,1TTED:' March 12, 1962
Card 2/2

3 96-f 8
S/056/62/043/001/052/056.
B102/B104
AIMOR: -Gantmakhdr, V. P.
TITLE: A size effect in metal with multiple magnetic fields.
X,Z'.-UODICAL: Zhurnal eksperimentallnoy i teoreticheakoy fiziki, v. 43,
no. 1M, 1962, 345-347
Anew type of size effect was observed when measuring the field
dependence of the surface i-;pedance of tin at helium~temparaturen, using .7
frequencies of 1-5 i4c. The measurements were made with a highly pure V
single crystal (,-10-4tA impurities) cut as a plate perpendicular to the
10dI a~:is, thickness d - 0.39 mm; the electron mean free path was
(1-3)-10-lcm, the skin depth at 1-5 Mc was 10-4 cm. At a field 11 0 - 2cp/ed
half width of extreme electron orbit in the momentum spacep
perpendicular to the -2 direction and normal to the surface) the curve X(H)
has a singularity (Gantmakher, ZhETF, 42, 1416, 1962). Such
sin-ul~rities were now found to arise also at nH (measured up to n-5)
0 0
Card 1/2 V
/ f

S/056/62/043/001/052/056
A size effect in metal with multiple ... B102/B104
%vhen the plate thickness equals 2np. This is ascribed to the fact, that
n.ear the extreme cross sections of the Fermi surface (i. e. for extreme
widths of the electron trajectories in the plate) the electron
concentration is greatly increased, and likewise the current density at
this depth (2p). There are 2 figures.
ASSOCIATION: Institut fizicheskikh problem Akademii nauk SSSR
(Institute of Physical Problems of the Academy of Sciences
USSR)
SUB'-IiITT.i~D:
May 18, 1962
Card 2/2

SHARVIN, Yu.V.;,GANTMAKHERp V.F.
Growing metal Ringle cryBtals in optically polished molds.
Prib. i tekh. eksp. 8 no.6tl65-167 N-D 163. (MIRA 17:6)
1. Institut fizicheskikh problem AN SSSR.

L 17610-63 EW(1)IEPF(n)-21EWP(q)IEWr(m)IFCC(v)IBD51bli.5(s).~- AFFTC/ASD/
f~~ Ptf-4/Pt-4 WW1JD S/056/6.3/04-4/003/0~6/053
AMOE:
TITIZ: Investigation of the Parml surface of tin byj~the m"tza effect.
PBRIODICAL: Zhurnal elmperimentallnoy I tekhnieheskoy f#11ci, v. 44, no. 1~
1963, 811-822
TEXT: The size effect during measurements of surface resistance ~Z R + ix of a!
metal in a magnetic field at not too high radio frequenciesl is a ~:rwv conveniorit
method for the study of Fermi surfaces described by the aut)ior in. an earlier,
papor
(Ref. 1: ZhETFI? 42, 1416,, 1962). This paper contains restate of the observsd
size effect during surface resistance m9aeuremont. In tin at'helikin temperatures Sad
friquencies between I and 5 Mo/s, and presents detailed date. about the sizea:of ',
extremal electron orbits in moment= space with magnetic f Ilolds 3,y1x1g in the 1 [100-1
and IhOj7 planes. The article concludes with a thorough ova''luati-on of the results,
their comparison with the results of other authors, and witl~ the Incdel of aaost!
free electrons. However, more information Is still needed beforo: final con~lusldns
can! be reached. There are 13 figures and 1 table.
Card 1/2

GANTXAMR,, VSF.
Studying the Fermi surface of tin with the aid of the dimensional
effect. Zhur. eksp. i teor. fiz. 41f no.3%811422 Mz '63. (HIPA 16:3)
I* Institut fizicheskikh problem AN SSSR. -
(Fermi surfaces) (Tin)

ACCESSION NR: AP4042563 S/'0056A4/04G/006/2028/2034
AUTHOR:- dantmakher, V. F.
TITLE: Concerning the Fermi surface of tin
SOURCE: Zh. eksper. i teor. fiz., v. 46, no. 6, 1964, 2028-2034
TOPIC TAGS: tin, Fermi surface, free electron, electron orbit
ABSTRACT: Continuing an earlier investigation (ZhETF, v. 44, 811,
1963), the dimensional effect is used to study the extremal electron-
ic orbits of a tin specimen in the (001) plane, with the magnetic
field lying in the (001) plane. The installation used was the same
as in the earlier investigation. The results show the following to,
exist in tin: an open surface very similar to the almost free elec-
..tron model, a closed surface*whose dimensions provide a basis for
assuming it to correspond to the surface of zone Q of the model, a
surface corresponding to the closed surface'obtained in the.earlier
Caid 1/2

'ACCESSION NR; AP4042563
:investigation, and a complicated open surface whose*det.ailed struc-
has not yet been ascertained. It is pointed out that the data
admit of ambiguous interpretations and that information on the-ex-
tremal orbits of the three principal crystallographic planes is in-
addquate for the complete determination of all the Fermi surfaces.
"Thb author thanks Yu. Shavrin for a detailed description of the
results." Orig. art. has: 5 figures.
ASSOCIATION: Institut fizicheskikh probiem Akademii nauk SSSR (In--;
stitute of Physics Problems, Academy of Sciences SSSR)
SUBMITTED: 22Jan62 DATE ACQ: ENCL: -00
SUB CODE: UP, SS NR REF SOV: 008 OTHER: 003
Car~ 2/2

I 'Y" .. 1- . i
ki ti~ I%: n K-;* ~;l ,
jj,.j lr~ i
F~rinL (if t'rl- " . 1. .
ip Q'I_
1. lnstivot fizlchf-,-7~!kh problem AN "T:SR.
(111 RA 17;

L 22574-65
ACCESSION VR: AP5001835 s/0 AV64 L/2LIL5
P.
AUTHOR: -Gantmakher, V. F.; Kryl2v
~tlined m84 i!tici
TITLE- Size effect in indium on helical trajectories~Ab im 14 n
effect
8(7jRCEt Murnal eksparimentallnoy I taormtic~mxxo~ ri 4~9 ii, Ij-7; ho.
2111-2115
single crystals skin effect., Fermi I Airf :e' elec
TOPIC TAGS: indium tr6Wtra;,-
jectory
ABSTRACT: The size eftect at radio frequencies Wu~ obicil rved
indium single crystals~'~ih the experimental-tet- ibe 'Abyi"4t,6tn=~'-1 ~!r
earlier (ZhLU,v. 44, 811, 1963). The measurei~ent wer...~'xaadq 1A~6 1-3K app~rox-
fdiiks
imatelY 3 Mcpa The s=ples were in the form.o "Ama I i li~iameter 1~ 'ad d,.4-.
0.5 = thick. The angle between the direction of the Vul I Vibld arvi itbe !Sur-
Oeti
face of the sa=.le was reguUted by.tilting the Devar. ra 14tki~, +o! the I ~,'trdl-
magnet. The size effect itself, and the splitting of t~t~ miz6l-ei.Vect, 1~12s` lc~re
observed for several samples with different orientutioiali.' Thii iplitting' ~of the
Card 1/2

L 22574-i-6,9
!:,ACCESSION NR,: -AP5061835
liries-Vhen the-field i9 -inclined ieviral 44g~e ~sl' to~ !U41 i
plained as being due to the drifting, of eli~irobi im 4
c:ross sections of the Fermi surf e 'in'a.direction
ac
of the sample, thus allowing theseelectron a to. ~ pen~.6ii-
skin layer on one side of the sample to the 'skin layer'61
splitting of the size-effect linisby inclinati6n of.th4
possible to estimate the mean free path of the indi~idujiJ
same manner as for the electrons near the limiting ~oibts.
Kimer, ZbETF v. 45, 1430* 1963), and to differentjate,bql
central orbits; thus allowing the shape of the Fermi suid
r
The autho a thank Academician P. L.1,qi~itsa for affordir
the work at the Institute of PhysicLal Problems, Ac~41 1C
so Yu. V. Shavrin for a detailed diSCUSsion of the tesWA
4.:figures am 3 formul".
AS=IATION: Institut fizicheakikh problez Akademii n"I
P~Meical Problems, Ac~Ld~ of Sciences, S5SRjj_X astitut1i
A'Aademii nauk SSSR (Institute of Adi
-.SUMWXTED: 28ju164 EML.- , 00
NO M? SOV:
40rj=;~4, Oa
Card 2/2
1;: SS NP!:
31721 1

529-5k W/EP
-65 MT(d)/9WT(l)/EWT(m)/9NP FW
Pr-4/Pu.4 IJ,P(,c;) 0'/
ACCESSION Mt AP5010501 6/611
AMOR3 intmakher, V#
TITIZ I
Tex erature dependence of the mean tro's *1~~ "of eledt. ws:~ b~ltjja!:
t!Reraturas: ~j 1 ii
TI
48
SMW.Es Murnal eksperimental'aar i td"etlch4ikadr MAki io:! I
~pb
1 1080
077-
et, i~t 1!3;00t, a'
TOPIC TAGSt tin, electron mean free pathp Feriai OUT
phon-on scattering,, low temperature researeb
ABSTRAM 7be temperature dependence of-tte amplitude ~or it 441 i Off~ot vt!is imealw:
ured, at the limiting points in 'tin for the purpos.t ~ot t N ts Ot ~Oiljtd dat)'sj 6%i
the mean free path of the electrons at, low temper4urei. pl~.' 1 pr6 eitursi,useA Its,
that, proposed by one of the authors earlier (GaA*&khe4.,.- iftil 1 E. KiMr, 2;' Mr If*-
:45p 1430, 1963) and based on the measurement of the relatil-01', i~tonslty i :1
Uno
sizt! effect, as described in another paper, (GoatmaAerp VOM F: V. oil., 1J63).
The measured size-effect Nas found to incroaae l1ke the 3..44~!Ip4wei;~r the teurpera-'
ture., vhich is close to the cubic dependeuce e'xvodted fro1w ~11~e Bi JcOx Ueoryi, Thd
effective mean free path betweea two elementary acts of lutil-rtetil'in! vith jbt~001%
1/12
!d.

jBit MR VOUH=Ma~dki
r-L 520,54-6.5
ACCEMION RR: AP5010561
V.
for,electrons lw,~ I no'
vas determined from the experimental data
gated point on the Fermi surface, and folindto'bt of thl6'6rA1' ii i-if e0ereJ.' ejit~'-
meters at 2K. 7be results show that in tdation: t9, the I U!iels iihosii 1 j,'kelisiti
changes by one order of magnitude ia thelavest"igated ra,44;0 .~Ite~jj i:jla~lwia
b Ott
-temperature-indepen
is also a line whoge amplitude in dept 0 n u r
perimental error. This line corresponds to tho extremal U,~J.-4!tozj: !'16vi#AOP;jj Hiol"
- 1. u -16
1 cylinder in the fourth zone of the Fermi surface' or: the ! tliii i E ~,P,6 14 the - (10. Y
plane. This absence of temperat-are dependence is MtrUvttiii 1~ ~4 t~e;: nario' L
shape of the Investigated part of the Feml.avxfta*'~ but, wt iq ALaiit.' 'i"I'vo ~'-Xplon~xtla 2~
4 1,
is found for this connection. "The siftors thwk L FA 4 f6l iatoxest -b
vork, and M. Ya. Azbell and A. X# ShWnikov for a
ego
Orig._ art. Fmot
;titixte or-001io,
ASSOCUTIONs Institut fiziki tvardogo, tela, Akideali. nauklOOR
State Physics, Acaderg of Science
SWO
SUBX=t 25ituw64 as
EXCLs 00
NR Ra SOV: 006 OMORt 001
I Card ?/2

L60349-65 EW
a
ACMION WR: AP50165hi 3D XT
AUMR: Gantuakhers V. F. ~~er~ gill, *I
TrMt Radio-frequeney size effectln a am& 1e
face of a metal
SOUPOE: Zhurnal eksperimentallnoy i teoreticheskoy:fW
1572-1582
TOPIC TAGS. size effectp Fermi ourfacej tihp -4lectron 1
lation;- cyclotron frequency
ABSTRACT: 7be authors investlgated.expej~_
feet, due to the motion of ineffec
_tAy
field perpendicular to the surface, of the4mmpile. lo
oscillations observed in the static conduidti-wity~ ot wq~~
is varied. The theoretical analysis Is based on a ideitdi
tion of an electramngnetic field in the a! e'occu~ied.;l
pac
ssumptions concerning the nature of the Femi ffurface"
based oh a ariWation procedure for meoisuringUe deiiiiil~l
of the sdrface impedance of the tallic ida~uple on the 'in
me
the authors earlier (MMF 45) 14-30 1963) Tha risuliii
1/3
A:
~T
-A
ie/bw I
1. tol _F
~p V;t! 48,! tho. 6i, 1961~f
lojeci oi~,. vemg;ee Iscil-
I I v ia
x1ly a no. It., 81 ;e- e
etic
;61 ttlated in I me~oi
Teat.- U 4W~oii t. to 1:the ~ 1-J
lic ~ ijit44 whenj the ffeld
d.natJ h
o# qi~ t e ' strLbu-
~.thd :und'jaa *: -ce.-tal
he Mtet"L stuly wa
le.~nt~
Mae I -tii",him,ir4gLkary,partl3.,i
0 4
4,,Mn e t i)ed**
M; the
ohaiii It 1~ ion! of-

A.
the ineffective electrons proftcoo 4mewdy doxw 11i
wid this in -turn produces bVedence: osoilUtions M
oscillations are periodic In a straight fIe1d4 'This peiH
i
extrP-1 values of the electron d1splacem#nt 4aong,tho~ji
cyclotron period. Two types of eleictron tra iem 1i
Jector
limiting po:Lmta aM helical trajectoriesp Jare;: msideiiyl
WCAre, er
oscillations. The experInants p foLited. i6n tin 01i
I or at
field directions close to thmt of the [1W
WIN
Wet the oscillations were periodle i"h*lstimi ft
pendent of the temperature and frequanarp,but'Am 1 41
SmreL types. a a
thielmeas of the oad i0m
ample.
Jmterpreted on the baais of the propoized thear, Altkm
gives ia principle the am tuftwtion m% tbe; eleotrtrA
i the Static COOdUCtiVity' 1A 4 nOXTAM.1, MPdUO lield;] tho
Is considered by the authors -to I* V"fereibls~ ~ 0*6. it 0
tions of tbstl alltle cocdm*tWty~ sbouU Ocrm4e r*pi
flado "The authord tbank P61LO., I
....... Milpitas, tor
experimental, pert he "rk at institut twel
jig the
ftelas Problew)'AN 6892# sjA 11g, V, Marvin 6V 46 4
of
t j~laiI4 -it 0: m tal
!;i!'fiu,!Ld
I:n
Wlt:
17-
rhe-
the'~~
the
Log
;J:
Llar
tbtai 2-10
nde-
40,the il:, ~i
- b61rg
h
ITect
Littlims of 1,
le
Otte
N4
pa rans- o%
~81 Lute,
I-. j

: I I I; II : !, . ~ti-: 1,1j:
L 8875-66 E'dr (m)/E'dP W/MiNt _1JP(0 JD
ACC NRi AP5026594 SOURCE CODE: _6R-/oo.,)6/-6-5/6 qprd /1054/1061,.
W
AUTHOR: Gantmakher, V. F.; Krylov, P.
3:
ORG: Institute of Solid State Physics. Academy of Sciences.SSSR (Institut Piziti
tverdogo tela Akademii nauk SSSR); Lnstitute of Physical Proble . c~Ld f Sciences
-.!LILL _~W
SSSR (Institut fizicheskikh problem Akademii nauk SSSR)
TITLE: Radio-frequency size effect in indium
SOURCE: Zhurnal eksperimentallnoy I teoreticheskoy fiziki, V. 49, no. 4, i965,~
1054-1o67
TOPIC TAGS: semiconductor, Fermi surface, indium, free electron model 44A41-j
ABSTRACT: The Fermi surface in In Is investigated by the radio-frequency size effect
technique at a frequency of 3 Mc/s. Identification of th6experimental cr~oqs sec-
tions was made using the dependence of the size effect lines on'the inclination of
the magnetic field relative to the sample's surface. The compllix~shape of! the Isoen-
ergetic surface in the second band resulted in the appearance at a number at sike
effect lines due to the presence of breaks in the electron trajdciories in 4 magnetic
field. These lines are not related to the electromagnetic field bursts within the
metal but to less notable features of the field distribution between the Vursta4 The
set of linen associated with the Fermi surface of thelsecond band confirms the fact
that this gurface is very similar to that predicted by the almost free electron model.
-Card,
F111

L 8875-66
ACC NRt AP5026594
No lines have been observed which would indicate that the Fermi~surface may'be open.
It also follows from the experimental data that the Fermi 4urface in the third ienergy
band consists of tubes connected into rings, the axes of*ilie tubet; being oriented
along (110). The shape.of the central cross section of th6b tube-produced * inter-.-
section with a plane perpendicular to the tube axis was de termined by USiUg!Beveral
s;%mples with different directions of the normals. No lines have been observed which
would indicate the existence of tubes with axes parallel.tb (101). Orig. art. has:
[CS)
14 figures.
SUB COM A01 MMM DATE: 21may65/ ORIG REF: On/ Gq~: nEF.- oW ATD PPXSS:
Cmd 2 /2 A-4

GANIIIAMER, V. F.
"Free" electrons in metals. Pr--roda 54 no.7.-11-23 J2 16'j.
01111RA 18:7)
1. Institut fiziki tverdogo tela Ali SSSR, Moskva.

GANIW,J~HERJO V.F.
Surface impedance in Bi at frequencies of I - 10 14c in weak
magnetic fields. Pis'. v red. Zhur. eksper. i teoret. fiz. 2
no.12:557-562 D 165. (MIFLA 19: 1)
1. Institut fiziki tverdogo tela AN SSSR i Inistitut fizicheakikh
problem AN BSSR. Submitted Nov. 9, 1965.

L 02194-67 - E-,NT(-.n)AwPC0/E.T1. _ TJ-P(.CJ'" _JD
',cc NR: AP6032469 SOURCE CODE., IJR/0056/66/051/003/0740/0745 4?
AUTHOR.-' Krylov, 1. P.; Gantmakher, V. F.
ORG: Institute of Physical Problems, Academy of Sciences SSSR Onstitut
fizicheskikh problem Akademil nauk SSSR); Institute of Solid State Physics,
Academy of Sciences SSSR.(InBtitut fiziki tverdogo tela Akademfi naulk SSSR)
TITLE : Radio-frequency size effect at the limiting point In Indium
SOURCE: Zhurnal eksperimentaltnoy I teoretichesitoy nziki, v. 51, no. 3, 1966,
740-745
TOPIC TAGS- Indium, magnetic field, frequency size effect, Fermi surface
curvature, e;eetron model, almost free electron, electron mean free path
ABSTRACT: The curvature of the Fermi surface of indlum near the [111] direc-
tion was measured by mearm of the radio frequency size effect at the limiting point
in an Inclined magnetic field. The experimental value of the curvature is identical
with that yielded by the almost-free electron model. A study of amplitude depend-
ence of the size effect lines showed the electron mean free path to be a function
Card 1/ 2

M
L 02194-67
of temperature. The thickness of the skin layer was determined on the basis of
size effect line width, and on Its dependence upon the frequency. The authors
thank Academician P. L~ Kapitsa for making their work possible, and Yu. V.
Sharvin for discussing results of their research. Orig. art. has: 5 figures,. and 2
formulas. [Based on authors' abstract)
SUB CODE: 20/ SUBM DATE: 23M&r66/ ORIG REF: 009/ OTHREF; 003/
Card ~ 2/2-

ACC Ma A?7003535 SOURCE CODE: UR/0,746/6 7/00 5/0o 1/0017/0020
AUMOR: Gantmakher, V.,F.; Doleopolovi V. T.
ORUI: institute of Physics Problems, Acadeow of Sciences SSSR (Institut fizicheskikh
problem Akademii nauk SSSR)
T'ITU:: Excitation of standing sound waves in Bi by an electromagnetic method
SOURICE: Zhurnal eksperimertallnoy i'teoreticheskoy fiziki. Pis'ma v redaktsiyu.
Prilozheniye, v. 5,. no. 1, 1967, 17-20
TOPIC TAGS: bismuth, sound propagation, low temperature research, surface property,
skin effect
ABSTRACT: The authors report here the results of preliminary experiments in which
they observed excitation of sound in Bi by an electromagnetic wave incident on its
surf-ace. Single-crystal BI samples in the form of discs mere placed inside an in-
ductance coil, with which they were cooled to helium temperatures. The coil together
with the sample served as the inductance of the tank circuit of an rf oscillator,
which included a blocked semiconductor diode. The dependence of the barrier capaci-
tance of its p-n junction on the blocking voltage made it possible tovary smoothly
the oscillation frequency, and also to modulate it sinusoidall~y at a frequency (P - 19
cps. The oscillator output was detected and fed to a narrow-band amplifier with syn-
chrcnous detector, tuned to double the moduletion frequency 2cp. As a rtsult, the
2p/af2
out;ut signal was proportional to a (H - real part of Bi swVle surface imped-
1/2

ACC NRz AP7003535
ance). 71he dependence of Z'Wa& on f uas investigated in the interval 1 - 10 Yjiz.
In magnetic fields on the Cirder of 10 - 100 Oe and parallel to the coil axis, a group
of equidistant peaks appeared on the a2)Vaf2 curves, separated by frequency intervals
larger by one order of magrLitude than the width of each individual group. The mag-
nitude and direction of thc! magnetic field affected only the amplitudes of the peaks,
tl.e positions of which reme.ined; unchanged. Arguments are presented to show that the
observed excitation of sound in Bi is due to some specific mechanism, connected with
emission of sound as a resUt of large electron drift velocity. It is concluded,
however, that further experiments are needed to clarify the sound-excitation mecha-
nism. The authors thank Academician P. L. Kapitsa for the opportunity to perform
the experiments at the Institute of Mysics Problems, and Yu. V. Sharvin for interest
in-the work. Orig. art. has: 2 figurea.
SUB CODE: 20/ SUM DAM 100et66/ ORIG IREF: 001/ OTH FV: 003
Card 2/2

L 12071-66
ACC Ul; -'Ap6oo2661 SOVRCE CODE: UR/6366/65/00?1012/05~716 .562
AUTHOR: Gantmakher, V.
ORG: Institute of Solid-State PlVrsics, Academy of Sciencem SSSR (Institut fizWn
tverdl)go tela Akademii-&~t SSSIQ 611-tute -6-f Academy of Sei-
ences SSSR (Institut fiticheskilils problem Akademii nauk S011R)
TITIZ: Surface impedance of Bi at 1-1) Me in weak !Aeetic f ie Ids
SOURCF.: Zhurnal eksperimeiTtallnoy i teoreticheskoy fiziklio' Pio,lxa v redakbsiyU.
Prilozheniyep Y. 20 no. 12., 1,965o 571-552
.TOPIC TAGS: blmnuthp electric impedance, surface property skiri effecti, weak ms -
0
netic field
ABSTRACT: In a search f2r I Convincing explanation of the ~~ijtror0g:nonmonot6blc yarl-
ation is of the surface Z of a metal with varying magneCic field H1, ~esr:
rH - 0, the author ciarried out. experiments on the behavior gif bisIorth single!'crys-
talB in weak fields. Bismath discs 18 mm in diameter contmining
purities were placed in the coil of a radio-frequency tankcircuit. and vere~~cooled
together with the coil to helium temperatures. The experiments -consisted of record-
ing 21f/i)H (f - frequency) as a function of H with an autoolktic two-coordin~te plot-
,ter in the maimetic-field renge fr---A 0 to 5 oe. The measuring apiwatus vat de-
Ic
Ord -1/3

L 12071-66
2661
mc NR: Af6w A k
Iscribed by the author earlier (ZbETF V. 44A
Z11j, 1!)63). The measures Uken to eliminate 1 oe:,
k
:the Imfluence of extraneous factors are de-
scribed. The results of th-t experiments
Aive g,,rounds for assuming that the observed
,nonmonotonicity and the relixted dependence
;on the amplitude of the hf tield are con-
:nected with the quasistatic distribution of
,:the mognetic field inside the skin layer.
'The inhomogeneity of the mo4gnetic field in
Ahe skin layer greatly complicates the in-
itegral relation between the current and the
;electric field in the skin layer. Applica-
ition of a sn-11 constant filald shifts the
ipicturts of the instantaneous field distri-
'bution in the skin layer, amd this naturally"
!should lead to a decrease ia the impedamee.
Jf the proposed explanation of the Observed Fig. 1. Depenaence, of the osc4la-tilon
correct inprinciple, then frequency on the canwtant. maglittic!
similax investigations can yield inform-tion field at diffiorent '"9111tild"S: of tile
hf field
Card
- #3

L 12071-66
ACC NR: AP6002661
ture of the fiel.d in the skin layer. Author istraterul to Aca4einic~
qjj,~he st!rue
~/P.JL. J~Ritza for affording the opportunity to work at the Institute of PhvikB/""'
:Problems of the Academy of ;ciqnrcA-WH and to Yu. V. Shai4rn-for a d1scussibn of
reaultas Orig, art* han 1 figure.
CODIS 20/ MM DATS i OgNov65/

Ub
17 U."37),
C, ojz~bo,
lo:
USSR: 1
A u~

SUBJECT USSR/IWMEMATICS/Differential equations CARD 1/1 PG - 51
AUTHOR GANTMACIMR E.R. AMMAN M.Ae
TITLE On an algebraic problem in the theory of automatic control.
PERIODICAL Uspeohi mat. Nauk.2L No.19 136-138 (1954)
reviewed 511956
The following problem is considereds two real polynomials D1(p) and D2(p)
are given. The number of their zeros in each of the four quadrants, on the
positive and on the negative semiaxia and in the origin of the coordinated*
is known. It is asked for necessary and sufficient conditions for this
distribution of zeros such that the polynomial D,(p) + D2(p) satisfies the
Hurivitz conditions of stability.
Necessary and sufficient conditions are given for a series of special canes.
For the general case there are presented only four necessary (but not
sufficient) conditions.

J~p
Ps,-4/P"-.-7,/Pz. 6/Peb TTVAT
ACCESSION NR: AP50.16779
tit,
OR Abramoviph,, R. B.; Arinushit n
MH
A
Golod.ovskty I A. Ye.; Zas3.a-Tskiy,, Zhukqv: :Tq, K
TITI-v! Aircraft turbodrive. Class 47 Ito 1~1712~h
OU,('.E, Byulleten' izbbreteniy -tov~ i ri
S R I ray kh 10, 1.1
VOPIC: TAGS: aircraft turbodrive. constant"
T.A.BarRNM An Author Certificate h as beeri Osuoa' for!
i the aLr-t.urbLineL:.-st art ing of engineo and toridrivi~g j~ eop!
uniL contains an air turbine, m a- C generatbr, Wlitaj7tei~l
land m a unguided -Erae-wheeling.cl utel I., F ~c
or n reased' cewil
'decrease weight, and to shorten. starting tirie ~'Ale uilit A.I
toi-iis drive in the form of two driver torus'dialis in into~L
01
driveo torus disk3 mounted on a fixed ohaft- dild 13 epaj, at6jL
unit Is also equipped vith intermediaLe roIlera';vbich
~Sard 1/3

-65
L 57795
I ACCI.;1ISSIoIN AR. A-P5016779
a control de%ict~ these provide interuci. Lori baturevil W1 Mldt~ toruo 1.
in transtrif 'Ang rotation frovi the en&-,c~ to Lhe (-611:.Aazj-4
ea~.- traiiii:
a differential control macbanism and the geirierattor i4g.:I,
Orig. art. han: I :ti [LB
igure -
ASSOCIAT lid "i!"
-i0ii- Organizatsiyo . audarstvainiogo JtcrnLtcta pi
90 A~
T,
-te Committee on AvIEtAori Technalogy'll 13
(Organization of th~-, Sta
v B
SITIMITT'VED: 05may64 ENCII: 01
'000 11111DV
1.N0 M. FSOV: OTHER: 000
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GAITKAM L.V. inshener; SHVMDOV,Ye.P., inzhener
~.-
IndustrW production of reactivs hydrochloric acid. Khim.prom.
no.4:115-117 Ap 147. (MMU 8:12)
(Hydrochloric acid)

GANTRO. lr.V. ,
I
Designing multieffect evaporators. Xhim.prom. no.3:169-170
Ap-M47 '57. (KW 10: 7)
(Braporating appliances)

AUTHOR: Gantman, L. V. S07/64-58-5-11/21
TITLE: The Intensification of the Working Plants for the Concentration
of Electrolytic Caustic Potash (Intensifikatsiya deystvuyushchikh
ustanovok kontsentrirovaniya elektroliticheskogo kaustika)
PERIODICAL: Khimicheskaya promyshlennost', 1958, Nr 5, PP- 309 -- 311 (USSR)
ABSTRACT: The three-membered evaporation apparatus of the system GNIIKhM
is the one most often used in the Soviet factories. Since this
apparatus has some deficiencies, and the production of
caustics has increased, a new apparatus was constructed in one
of the chemical plants which has a much greater output and
better economic properties. Besides the author of this article
F.T.Bonyuk, L.S.Genin, V.S.Yevdokimova, S.M.Krugly-y, G~V-,
Seleznev, I.E.Spektor, P.G.Khain and Sh.S.Shchagoll also partici-,
pated in this construction. The paper gives a diagram of this
new evaporation apparatus, and from its description it may be seen
that in the second stage new apparatus with forced circulation
of the solution (after the construction by the NIIkhimmash)
were employed. Some changes in the dimensions were made. The
Card 1/2 heat transfer coefficient was increased 2-3-fold in the first

The Intea-,sification of the Working Plants for the Sov/64-5/8-5-11/21
Concentration of Electrolytic Caustic Potash
stage by a proper use of the function of the heat transfer
coefficient vs. the temperature difference, while in the second
stage it increased 3-4-fold by the above mentioned change. For
separating the salt from the liquid mustic potash automatic
horizontal centrifuges of the type AGwere used. These centri-
0
fuges were manufactured by the Suuy Factory imeni TJ.V.Frunze
(Sumskiy zavod im.I.I.V.Prunze). The --heme elaborated for the
plant is automatic in almost all operations, and the author
hopes that it will become completely automntic. There are
1 figure, 2 tables, and 5 reference aU of v1d,ch we Sarie4t,
1. Potassiwn carborates-11-1roduction 2. Fvaporat-ors--ConBtr-..~~!t4;-C~~I
3. Evaporators-Applications 4. E%,aporatws--Ope::,et--'on
Card 2/2

GANTWT, M.N.
Ion-aftlectIve membranes and methods for tnutirw then, 18"1.P0
vodopodg. no.3:210-217 0 59" (MIRA 12:9)
(Ion exchange)

USKORIN, B.N.; WIRPOVA., N.M.; GANTMAN, M.11,; VOA0110VA, A.I.., red.;
VLASOVA, N.A.., tekhn. red-.- -
(Ion-exchange membranes and their use] Ionoobmennye membrany ikh
primenenie. Moskva, Gos.izd.-vo lit-ry v oblasti atomnoi nauki i
tekhnikiy 1961. 162 p. NIRA 14:12)
(Ion exchange)

8(l) SOV/107-58-12-42/55
AUTHOR: Gantman,_a.-..
TITLE: VDZh-400 Ferrocarbon Elements (Zhelezo-
ugollnyye elementy VDZh-400)
PERIODICAL: Radio, 1958, Nr 12, pp 45-46 (USSR)
ABSTRACT: The author states that as a result of work
carried out by the Vsesoyuznyy nauchno-
issledovatellskiy institut istochnikov toka.
(All-Union Scientific Research Institute for
Sources of Current), a ferrocarbon element
has been produced having an alkaline electro-
lyte and electrodes made of activated carbon
and porous iron which serve a similar pur-
pose to cupric oxide elements (MOE) and ele-
ments with manganese-air depolarization (MVD),
but which do not use non-ferrous metals and
other scarce materials. They cLn be used for
the filament power supply of the "Rodina",
Card 1/4 "Iskra" and "Nov'" battery radio receivers,

VDZh-.400 Ferrocarbon Elements
SOv/lC7-58-12-42/55
railroad si7,nalling and automatic block sys-
tems,telephone lines, lighting etc. The
electrical power is produced by the reaction
of active porous iron oxidation by the oxygen
in the air. The negative electrode of the
element is the porous iron (porosity of ?5-..
80%), the positive one is the air polariza-
tion carbon electrode. The composition of
this electrode is fully described. The ele-
ment is contained in a steel cylindrical con-
tainer: its inner construction, main feature
of which is the horizontal positioning of the
electrodes, is described and illustrated in
Figure 1. The horizontal positioning of the
electrodes improves the working conditions of
the carbon electrode, makes it possible to
use pieces of porous iron which have not been
specially processed mechanically, and simpli-
fies the design. An element ready for work
Card 2/4 is shown in Figure 2a and two elements mounted

VDZh--400 Perrocarbon Elements
SOV/107-58-12-42/55
on top of each other in Figure 2b. The
basic features of the element are as follows;
diameter 221 mm, height 75 min, weight 5 kgj
emf 0.9-1.0 v. normal discharge current 0.5
amps, maximum permissible current 0.8-1.0
amp, capacity with a continuous discharge in-
to a resistance of 1.25 ohms u-P to a voltage
of 0.5 V is not less than 500 amp-hrs, capa-
city with discharges of a lengthy, inter-
rupted nature is about 400 amp-hrs. The dis-
charge curves of the element when it is under
continuous discharge against resistances of
1.25 and 0.8 ohms are shown in Figure 3a and
comparative discharge curves of the element
with that of the MOE-500 cupric oxide element
(curve 2) in Figure 3b. The basic character-
istics of the VDZh-400 end RME-500 elements
and the IvTVD "Ek-ran" and "Deviz" batteries are
Card 3/4 given in the table. The final. conclusions of

VDZh-400 Ferrocarbon Elements
SOV/107-58-12-42/55
the author are that the VDZh-400 element
has the following advantages; it does not
use up scarce non-ferrous metals, has a
simple desi-n and is very suitable for mass
U
production. There are 1 schematic diagram,
2 drawings, 2 gra-Dhs and 1 table.
Card 4/4

Translation from: Referativnyy zhurnal, Mekhanika, 1957, Nr 1, p 167 (USSR)
AUTHOR: Gantman, S . A
TITLE: Determination of the Rigidity of the System "Lathe - Product -
Instrument" in an Automatic Longitudinal- profile Lathe
(Opredeleniye zhestkosti sistemy "stanok - detal' - instrument"
avtornata prodol'no-fasonnogo tocheniva)
PERIODICAL: Tr. Penzensk. industr. in-ta, 1955, Nr 3, pp 49-60
ABSTRACT: Bibliographic entry
1. Lathes--Stability--Bibliogi-aphy 2. Lathes-Performance
Card 1/1

GANTMAN, S.A.; KUZNETSOV, K.A.
Selecting the method of machining on automatic turret latnes.
Priborostroenie no.10:28-30 0 '57. (MIRA 10:11)
(Turning)

GANVW, S.A., kand. tekhn. nauk, dotsent
Gheqking the precision of adjustment of automatic machine tools.
Izv. vys. ucheb. zav.; mashinostr. no-3/4-.155-164 '58.
(MIRA 12:5)
1.Penzenskiy industriallny7 inatitut.
(Machine tools)

28(5)
AUTHORS: -aantman,,-S. A., Candidate of 307/119-59-1-12/20
-
-
Technic~
I
s-clbnoes, Kuznetsov, K. A., Engineer
TE,ILE: More Exact Shapes of Turned PartB (Povysheniye tochnosti formy
obtachivayemykh detaley)
PERIODICAL- Priborostroyaniye, 1959, Nr 1, pp 22-2.3 (USSR)
ABSTRACT: The degree of exactitude of the shape of turned parts depends on
many factors, above all, however, on the goumetrical accuracy of
thelathe. The error of non-parallelil3M Of the axis of the
spindle and the axis of the shell of a turret lathe may be
reduced for example by applying the cut.ting tool under a certain
angle~,~ to tho horizontal. The angle a< can be computed from the
1
�
-
equationc-(=ar,-tg
. are the deviation in the horizontal
4~1 4
2
A2
and vertical plane. In case that the piece to be worked is
easily deformable the effect of elastic deformation of the lathe
piece*may be eliminated when the tool is applied to an angle c<
opposite to the horizontal direction. A corresponding formula
is derived for the determination of the angle o