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Showing 50 of 15077 papers
DIFFERENTIAL GAMES WITH INCOMPLETE INFORMATION
MATHEMATICS
1970-01-01<br>SovietRxiv: ru-197001.82500
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This paper studies zero-sum differential games of fixed duration in which one player observes the current state while the minimizing player receives state information only after a fixed lag. A discrete-time approximation is introduced to define information sets, pure, mixed, and behavioral strategie…
A REFLECTED ONE-DIMENSIONAL RAREFACTION WAVE IN A CONSTANT GRAVITATIONAL FIELD
HYDROMECHANICS
1970-01-01<br>SovietRxiv: ru-197001.83470
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This paper studies the one-dimensional reflection of a rarefaction wave from a rigid wall in the products of an instantaneous explosion in a constant gravitational field, for a gas obeying a polytropic equation of state. Starting from the general solution of the gas-dynamic equations for discrete ad…
On a Differential Game of Approach
MATHEMATICS
1970-01-01<br>SovietRxiv: ru-197001.16740
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This paper studies a differential game of approach in which two players choose constrained controls entering jointly, rather than separately, in the system dynamics. It formulates the problem in the class of mixed approximating strategies, introduces extremal strategies and a modified notion of posi…
Mappings of Families of Sets
ft(M)=t'f(M),
1970-01-01<br>SovietRxiv: ru-197001.67797
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The paper studies one-to-one mappings between affine spaces that send every translate of a fixed bounded set onto a translate of its image, and asks when such mappings must be affine. It introduces shifts preserving a generator and the associated class of quasicylinders, then proves that every conti…
On the Divergence of Fourier Series
MATHEMATICS
1970-01-01<br>SovietRxiv: ru-197001.16323
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This paper examines borderline conditions for convergence in the L metric of trigonometric Fourier series and their conjugate series. It constructs a summable periodic function whose integral modulus of continuity, and that of its conjugate function, are both of order 1 divided by log 1 over delta, …
ON THE NONLINEAR INTERACTION OF RESONATING OSCILLATORS
PHYSICS
1970-01-01<br>SovietRxiv: ru-197001.84067
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This paper studies nonlinear interaction in resonant conservative Hamiltonian systems with multiple degrees of freedom, assuming a single resonance relation among distinct linear frequencies. Using a polynomial canonical transformation, the authors reduce the Hamiltonian to a resonant normal form up…
INFORMATION ASPECTS OF THE REGULARIZATION PROBLEM
MATHEMATICS
1970-01-01<br>SovietRxiv: ru-197001.83458
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This note interprets Tikhonov regularization for ill-posed statistical optimization problems in control systems from an information-theoretic viewpoint. For a Gaussian signal corrupted by additive Gaussian noise, the authors formulate a regularized mean-square filtering problem and show that the res…
REPEATED TWO-PERSON GAMES OVER LARGE TIME INTERVALS
MATHEMATICS
1970-01-01<br>SovietRxiv: ru-197001.82856
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This paper studies repeated two-person zero-sum matrix games in which each pair of pure strategies has both a payoff and a mean duration, and the total encounter time is large but finite or random. It argues that ordinary optimal strategies for the payoff matrix, and generally also those for payoff …
ON SCALES OF GROWTH OF ENTIRE FUNCTIONS OF SEVERAL VARIABLES
MATHEMATICS
1970-01-01<br>SovietRxiv: ru-197001.83733
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The paper studies growth scales for entire functions of several complex variables through the majorant of the function and the geometry of associated convex or quasiconvex functions. It analyzes Goldberg-type orders and shows how they correspond to scales built from homogeneous logarithmically conve…
ON THE EXPANSION OF FUNCTIONS OF THE CLASS \(B^\alpha_{p,\theta}\) IN A FOURIER SERIES WITH RESPECT TO AN ARBITRARY FUNDAMENTAL SYSTEM OF FUNCTIONS OF THE LAPLACE OPERATOR
MATHEMATICS
1970-01-01<br>SovietRxiv: ru-197001.88059
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The paper studies Fourier expansions of functions in Besov classes with respect to an arbitrary complete orthonormal system of...