Geodesic

Sommaire du Fascicule no. 1

On the solution of the Chebyshev approximation problem for an incompatible system of nonlinear equations
p. 3-14
Conditions for the existence of a saddle point in determinate integro-differential games with lag in the presence of parameters
p. 15-25
Differentiation of the maximin function. III
p. 26-38
On the problem of finding a maximum with constraints
p. 39-54
Optimal processes with two groups of control parameters
p. 55-66
A certain numerical scheme for the solution of optimal control problems
p. 67-73
The numerical determination of the solutions that go to zero at infinity for certain two-dimensional nonlinear systems of ordinary differential equations
p. 74-87
The unconditional uniform stability of a certain difference scheme for the equation $u_t+u_x=0$
p. 88-98
Asymptotic expansions of the solutions of problems of the diffraction of waves in angular and wedge-shaped domains
p. 99-113
The method of spherical harmonics in the problem of the solution of the kinetic equation for axisymmetric infinite cylinders
p. 114-123
A certain numerical method for calculating a laminar boundary layer
p. 124-131
Graph schemes with associative calculus
p. 132-145
A certain descent algorithm with constraints
p. 146-157
Certain nonlinear problems of stochastic programming
p. 158-171
Some estimates for the eigenvalues of a matrix
p. 172-177
The efficient use of computations with fixed decimal point in solving systems of linear algebraic equations
p. 177-181
A formula for the polynomial of best approximation, obtained by means of a computer
p. 181-183
Some remarks on the roots of ultraspherical polynomials
p. 183-187
A cubature formula of the seventh degree of accuracy for a hypersphere and a hypercube
p. 187-188
The convergence of a quadrature process for certain singular integrals
p. 189-196
The asymptotic expansion of the Hankel transform of functions that have branch points
p. 196-199
The computation of the probabilities of hitting a circle and a sphere under the normal distribution
p. 199-204
A certain method for the approximate solution of linear ill-posed problems
p. 204-210
On extending the principle of the residual
p. 210-213
A certain approximate method for finding the resolvent
p. 214-215
A method of successive approximations for the solution of linear problems of optimal control
p. 216-223
Sets of accessiblity
p. 224-230
A means of determining the stability of numerical methods of integration for equations with periodic coefficients
p. 230-232
The organization of the double sweep for a certain implicit scheme
p. 233-235
Computation of heat conductivity on a system of rods
p. 236-239
A numerical calculation of detonation
p. 239-243
The asymptotics of the nonstationary transport equation with anisotropic scattering
p. 243-247
An application of a Monte Carlo method to the computation of the risk of exceeding a given dose of protons of solar flashes
p. 247-250
Some solutions of Maxwell's system
p. 250-252
On the structure of the front of non-equilibrium ionization in a gas
p. 252-255
Calculation of laminar boundary layer on sharp elliptic cones in supersonic flow at the angle of attack equal to zero
p. 255-259
The numerical solution of a mixed boundary value problem for the bending of rectangular plates of constant thickness
p. 259-262
The simulation of random variables by the method of superposition
p. 262-266
First IFAC/IFIP International Symposium on Traffic Control
A remark on “Tables for solutions of the Laplace equation in elliptic domains” (letter to the editors)
p. 267-268
A note on the paper “On the Cauchy problem in the theory of pursuing” (letter to the editors)
М. R. Hestenes. Calculus of variations and optimal control theory. New York–London–Sydney, John Wiley and Sons, 1966, XII+405 pp., 100 sh. (Book review)
p. 269-270
J. Clegg. Calculus of variations. Edinburgh, Oliver and Boyd, 1968, IX+190 pp., 27 sh.. 6 d. (Book review)
W. Magnus, S. Winkler. Hill's equation. New York–London–Sydney, Intersci. Publs, a div. of John. Wiley and Sons, 1966, VIII+127 pp., 68 sh. (Book review)

Sommaire du Fascicule no. 2

The Lenin centenary
p. 283-285
The method of stationary phase in the multidimensional case. Contribution from the boundary of the domain
p. 286-299
The method of stationary phase for an integral in finite limits with an arbitrarily located stationary point
p. 300-312
Computation of the incomplete cylindrical functions
p. 313-325
The rate of convergence of the Bazley-Fox method of intermediate problems in a generalized eigenvalue problem of form $Au=\lambda Cu$
p. 326-339
Asymptotic properties of the solutions of integral equations with kernels $K(x,s)$ that are equal to zero when $x-s\ge a$
p. 340-351
The uniqueness of the solution of an inverse problem of potential theory
p. 352-361
Eigenfunctions with a given caustic
p. 362-373
Asymptotic expansions of the solution of the problem of the radiation of waves by the vibrating edges of an arbitrary wedge
p. 374-382
Convergence of expansions with respect to a small parameter, introduced into the boundary conditions, for the solutions of a boundary value problem for the Navier–Stokes equations
p. 383-400
Numerical solution of certain problems in gas dynamics
p. 401-416
Report on a monitoring system of programming automation and a translator from FORTRAN for the MINSK-22 computer
p. 417-428
An application of orthogonal transformations to the numerical realization of linear algebraic problems on perturbation
p. 429-433
Differentiation of a tabular function by the method of interpolating conjugacy
p. 433-437
Interpolational quadrature formulae containing derivatives, for certain Cauchy type integrals and their principal values
p. 438-444
On the article “Cubature formulae and orthogonal polynomials”
p. 444-447
An analysis of the accuracy of computational algorithms
p. 447-453
A special A. N. Tihonov regularizer for integral equations of the first kind
p. 453-461
Discrete maximum principle in maximin determination problems
p. 461-465
The choice of optimal nets in the numerical solution of the Cauchy problem for a system of ordinary differential equations
p. 465-474
An algorithm for the solution of difference problems on graphs
p. 474-477
The stability of the double sweep method in the realization of difference schemes for the heat conductivity and oscillation equations
p. 478-481
Schemes of an improved order of accuracy for systems of elliptic and parabolic equations
p. 482-490
Computation of corrections for geometric optics. II. The electromagnetic problem
p. 490-498
The numerical solution of the stationary equations of hydrodynamics with tangential discontinuities
p. 499-505
The numerical solution of problems on unsteady filtering with free surfaces for the liquid
p. 505-514
On explicit schemes of method of establishment in a problem of supersonic flow about blunted body
p. 514-520
On the “interior” shock waves stipulated by non-equilibrium of chemical reactions
p. 521-526
On the use of Ithe language ALGOL 60 in solution of logical problems
p. 527-530
On the concept of function in the language ALGOL 60
p. 530-532
Cycling in linear programming
p. 532-540
Information about IFIP Congress 71
p. 541-543
Funktionalanalytische Methoden der numerischen Mathematik. Ed. L. Collatz, H. Unger. Basel–Stuttgart, Birkhäuser Verlag, 1969, 144 S. (Book review)
p. 543-544
Н. Neill, A. J. Moakes. Vectors, matrices and linear equations. London, Oliver and Boyd Ltd, 1967, VIII+216 pp. (Book review)
D. Martin. Solving problems in complex numbers; R. R. S. Cox. Solving problems in dinamics. I. Edinburgh–London, Oliver and Boyd, 1968; 90 pp., 15 S.; VIII+109 pp., 15 S. (Book review)
p. 544-545

Sommaire du Fascicule no. 3

The properties of optimal methods of solving problems in mathematical physics
p. 555-568
Regularizing algorithms for finding a stable normal solution of an equation of the second kind on the spectrum
p. 569-574
The best uniform approximation of functions of several arguments
p. 575-586
On the solution of minimaximin problems
p. 587-596
The properties of the maximum function with constraints
p. 597-606
The theory of optimal control by discrete processes
p. 607-620
A certain method of solving linear and convex programming problems
p. 621-629
Difference approximations for differential games
p. 630-643
Some economical additive schemes for solving boundary value problems for a multidimensional equation of parabolic type
p. 644-653
A numerical solution of the Boltzmann kinetic equation for one-dimensional stationary motions of a gas
p. 654-665
A certain successive approximation method for solving a nonlinear Volterra integral equation of the second kind
p. 666-672
A solution of the problem of the diffraction of a plane wave by a periodic lattice
p. 673-684
On the question of the choice of optimal parameters in the solution of the difference analogue of the Dirichlet problem in cylindric geometry
p. 685-692
A rigorous solution of the problem of the diffraction of electromagnetic waves on a certain arrangement of strips
p. 693-715
Solution of problems on computer models
p. 716-733
Optimization of the estimate of functional dependencies by the Monte Carlo method
p. 734-740
The representation by a trigonometric polynomial of a function that is given at equidistant nodes
p. 741-744
The smoothing of the optimal solution in a certain control problem
p. 744-748
A double layer scheme of an improved order of accuracy for systems of parabolic equations with constant coefficients
p. 748-753
Certain properties of a linear-fractional operator which has applications in the theory of difference schemes
p. 753-759
On the solution of the inverse one-dimensional problem of electromagnetic sounding theory
p. 759-762
On a boundary value problem for Schrödinger's equation
p. 763-766
Solution of the single-velocity kinetic equation of neutron transport in spherical geometry with scatter indicatrix linearly dependent on the angle
p. 767-773
Completely conservative difference schemes for the equations of gas dynamics in Euler's variables
p. 773-779
The uniqueness of the solution of a certain inverse problem for the dynamical equations of elasticity theory
p. 779-784
The convergence of the method of successive approximations with decomposition of the boundary conditions in the solution of a boundary value problem for the Navier–Stokes equations
p. 785-788
Numerical computation of the relaxation of a reacting gas with a particle sink
p. 789-794
A matrix method for the determination of the ranks and the realization of a regular enumeration of the vertices of a directed graph
p. 794-797
The second all-union conference on Monte Carlo methods (Sukhumi, 20–25 October 1969)
p. 798-799
P. W. Melentjew, Н. Grabowski. Näherungsmethoden. Leipzig, VEB Fachbuchverlag, 1967, 248 S. (Book review)
К. Göldner. Mathematische Grundlagen fur Regelungstechniker. Leipzig, VEB Fachbuchverliag, 1968, 364 S. (Book review)
p. 799-800
J. Watters. FORTRAN programming. A complete course in writing FORTRAN programs. London, Heinemann, 1968, 354 pp. (Book review)
p. 800-801
М. Beckmann. Dynamic programming of economics decisions. Berlin, Springer, 1968, XII+143pp. (Book review)

Sommaire du Fascicule no. 4

Asymptotic computation of a double integral in the case of a stationary curve
p. 811-817
The optimal regularization of operator equations
p. 818-829
On the error of the solution of a linear operator equation
p. 830-839
Stability of the Ritz method for a certain nonlinear equation
p. 840-847
The sets of attainability, and the controllability of a linear set
p. 848-856
Singular controls in discrete systems
p. 857-867
Difference approximations for differential games with phase constraints
p. 868-884
An iterative method for solving optimal problems with phase constraints
p. 885-894
Iterative solution of linear programming problems
p. 895-907
Application of optimal control theory to a scheduling theory problem using penalty functions
p. 908-921
Optimal search for the extremum of unimodal functions
p. 922-933
A numerical method of solving multistage games for equations of Lanchester type
p. 934-941
Iterative methods of solving time-optimal problems that are connected with parabolic equations
p. 942-957
The two-point problem for a certain class of ordinary differential
p. 958-968
The existence in the large of a regular solution of a quasilinear hyperbolic system
p. 969-980
Conditions for the correctness of nonlinear integral equations with a kernel that depends on the difference of variables
p. 981-989
Completely conservative difference schemes for the equations of magneto-hydrodynamics
p. 990-998
Importance sampling in transport theory
p. 999-1005
Stationary three-dimensional irrotational motion of a gas at supersonic velocity
p. 1006-1015
An adaptive method for separating real roots of algebraic and transcendental equations
p. 1016-1021
A numerical method for locating the zeros of quasi-polynomials
p. 1022-1024
The solution of systems with several right hand sides
p. 1025-1027
The numerical solution of matrix equations of the form $WX=Y$, which are compatible for any right-hand side
p. 1027-1029
Symmetric cubature formulae for the computation of integrals in a hyperball
p. 1029-1031
A certain method of solving boundary value problems
p. 1031-1036
The behavior of the energy of a solution of the wave equation at large values of the time
p. 1037-1041
The method of incomplete factorization for solving two-dimensional and three-dimensional equations of the diffusion type
p. 1042-1044
The interaction of solid particles dragged by a viscous incompressible liquid
p. 1044-1049
Effective algorithms for the solution of problems for flow graphs
p. 1049-1054
L. J. Slater. Generalized hyper geometric functions. London, Cambridge Univ. Press, 1966, XIII+273 pp., 70 sh. (Book review)
A. Halanay, D. Wexler. Teoria calitativa a sistemelor du impulsuri. Bucuresti, Ed. Acad. RSR, 1968, 315 p. (Book review)
L. Sachs. Statistische Auswertungsmethoden. Zweite, neubearbeitete und erweiterte Auflage. Berlin–Heidelberg–New York, Springer, 1969, XXXII+677 S. (Book review)
p. 1056-1057

Sommaire du Fascicule no. 5

Minimization methods that are based on the approximations of the initial functional by convex ones
p. 1067-1080
Error estimates of the solution of ill-posed problems with linear unbounded operators
p. 1081-1091
Certain criteria for the regularity of matrices and the localization of their spectrum
p. 1092-1097
Iteration methods that utilize Lagrange multipliers for the solution of extremal problems with equality type constraints
p. 1098-1106
Sufficient conditions for a local minimax
p. 1107-1115
A certain class of differential pursuit games
p. 1116-1123
The approximate solution of the time-optimal problem with lag
p. 1124-1140
An application of the second order method to the solution of optimal control problems
p. 1141-1149
On the solution of boundary value problems on an infinite interval for certain nonlinear systems of ordinary differential equations with a singularity
p. 1150-1163
The method of finite differences for a degenerate equation
p. 1164-1171
The solution of systems of mixed type equations
p. 1172-1179
An application of the method of minimal iterations for the computation of eigenvalues of elliptic operators
p. 1180-1190
The solution of a certain boundary value problem for a mixed type equation by the finite difference method
p. 1191-1198
A method of solving boundary value problems for non-linear differential equations that describe the motion of charged particles in magnetic accelerator fields
p. 1199-1209
Diffraction of a plane acoustic wave on a thin semi-infinite elastic plate
p. 1210-1227
Blunt body flow of a viscous radiating gas
p. 1228-1237
Calculation of the magnetohydrodynamic shock waves ionizing gas
p. 1238-1246
The construction of a set of modes of values in algorithmic languages
p. 1247-1268
A single class of estimators for the Monte Carlo calculation of functionals of the solution of an integral equation of the second kind
p. 1269-1280
The block variant of the reflection method in the solution of linear algebraic systems
p. 1281-1285
A regularized computational process for the analysis of exponential dependence
p. 1285-1287
The tabulation of a function that is defined by Fourier coefficients
p. 1287-1289
A certain method of the simultaneous solution of the energy equation and the heat transfer equation
p. 1290-1292
The renewal of the depth and form of a contact surface on the basis of regularization
p. 1292-1297
Motions, close to the selfsimilar flows of a radiative gas
p. 1297-1301
The calculation of shock waves which absorb radiation
p. 1301-1305
Determination of the distribution function at the beginning of a chemical reaction
p. 1306-1311
The plane problem of the circular flow of a viscous heat-conducting gas between coaxial cylinders
p. 1312-1318
The utilization of supplementation in solving integer programming problems
p. 1318-1326
С. Lanczos. Numbers without end. Edinburgh, Oliver Boyd, 1968, X+164 pp. (Book review)
A. Jaeger, К. Wenke. Lineare Wirtschaftsalgebra. Stuttgart, Teubner, 1969, X+334S. (Book review)
p. 1327-1328
L. Fox, D. Mayers. Computing methods for scientists and engineers. Oxford, Clarendon Press, 1968, XII+255 pp. (Book review)
p. 1328-1329

Sommaire du Fascicule no. 6

Mikhail Alekseevich Lavrent'ev is 70 years old
p. 1339-1340
On methods of minimization with accelerated convergence
p. 1341-1354
The optimal search for the minimum of convex functions
p. 1355-1366
An averaging method for integral equations and an extension of Bogolyubov's method
p. 1367-1374
On a Monte Carlo method algorithm for computing functionals defined by the paths of a non-linear set of stochastic differential equations
p. 1375-1384
A maximum principle for differential inclusions
p. 1385-1393
The connection of the spectral theory of differential equations on the halfaxis with the theory of orthogonal polynomials
p. 1394-1408
Numerical solution of the interior stationary problems of electrodynamics
p. 1409-1418
Diffraction of electromagnetic waves by multielement and multilayer gratings
p. 1419-1446
The self-modelling problem of a heavy current discharge in a plasma
p. 1447-1457
A method for solving problems on the electrodynamics of inhomogeneous media
p. 1458-1464
The uniqueness of the solution of certain inverse problems of seismology
p. 1465-1480
A difference scheme for the solution of the second boundary value problem of a static problem of elasticity theory
p. 1481-1490
Numerical integration of the equations of the three-dimensional laminar boundary layer on lines of divergence
p. 1491-1502
Study of the non-viscous flows of a radiating gas by means of differential approximations
p. 1503-1511
Methods of the Runge-Kutta type for gas dynamics
p. 1512-1519
Pattern recognition as a method of automatic choice of procedure in computational methods
p. 1520-1525
A problem of the theory of graphs, connected with random fields
p. 1526-1532
The iteration methods of the solution of nonlinear systems
p. 1533-1536
The collocation method for integro-differential equations with a biharmonic principle part
p. 1537-1541
Numerical solution of one optimal problem
p. 1541-1547
On the decrease of the dispersion of a probability estimate by the Monte Carlo method
p. 1547-1549
The ALGOL 60 translator–“Razdan-3”
p. 1549-1552
G. С. Shephard. Vector spaces of finite dimension. Edinburgh–London, Oliver and Boyd /LTD; New York, Intersci. Publs, Inc., a div. of John Wiley and Sons, Inc., 1966, VIII+200 pp., 17 sh. 6 d. (Book review)
Book reviews
p. 1553-1554