SovietRxiv · Open Access in English
Rediscovering the Soviet scientific archive, in English
25357 full-text translations 14926 English PDFs 22539 abstracts
Showing 50 of 482 papers
This paper studies a class of two-player differential games in which one player observes the opponent’s phase coordinates only after a fixed delay. It formulates the guaranteed payoff for the delayed-information player and derives a first-order Hamilton-Jacobi type equation with terminal conditions …
The paper presents algorithms for the square assignment problem, seeking one matrix element in each row and column with minimum total sum. It introduces a vector adjustment framework in which selected row bases are maintained as minimal relative to column potentials, and an iteration reduces the num…
This paper studies the computational power of probabilistic Turing machines relative to deterministic machines in problems of enumeration and function computation. It proves that, for sets whose complements are universal in suitable recursion-theoretic senses, probabilistic machines can, with arbitr…
The paper formulates an embedding principle for enumerating labeled graphs by relating a target class to distinguished induced subgraphs inside a larger class, yielding linear recurrence relations for the desired counts. This method is applied to directed graphs with reachability and strong connecte…
The paper develops a multidimensional theory of linear passive systems represented by convolution equations with distributional matrix impedances supported in a causal cone. It characterizes passive operators through the Fourier-Laplace transform as holomorphic matrix functions in a tube domain with…
This paper generalizes Bulgakov’s problem of accumulation of perturbations for nonlinear dynamical systems with bounded initial perturbations and bounded continuously acting perturbations whose derivatives are also constrained. It formulates the maximum deviation from a prescribed trajectory as an e…
The paper studies the computation of all simple eigenvalues of a Fredholm integral operator whose moduli exceed a prescribed threshold, for kernels belonging to specified smoothness classes and under stability and separation assumptions. It develops deterministic approximation and iteration schemes …
This paper studies optimal completion time in a linear differential pursuit problem with convex compact control sets and a linear terminal subspace. Building on Pontryagin’s construction of a guaranteed pursuit time defined by first inclusion in an integral of convex-set differences, the authors ask…
The paper studies the asymptotic stability of nonlinear pulse systems with a single pulse element whose pulse frequency is modulated by the input signal and includes a dead zone. The system is formulated as a nonlinear integral equation with exponentially decaying impulse response, and Popov-type fr…
This paper studies exponential stabilization of finite-dimensional linear control systems with respect to a prescribed positive definite quadratic form and a prescribed decay rate. It formulates algebraic conditions under which feedback matrices can be chosen so that the Lyapunov inequality holds wi…
The paper formulates the design of automatic machines as an optimization problem linking reliability, utilization, productivity, and production cost. It represents unit production cost as a separable nonlinear function of reliability related adjustment durations for machine mechanisms and input mate…
This paper examines periodic motions in a single-loop nonlinear impulse control system containing an ideal impulse element, an integrating element, a static nonlinearity, and a linear dynamic element. By deriving the point transformation over one and multiple impulse periods, the analysis formulates…
The paper studies finite control for discrete linear systems with constant matrices, seeking a scalar control sequence that drives a given initial state to zero after a prescribed number of steps. Using the Z-transform, the problem is reduced to the requirement that a rational transform of the state…
This paper examines how microcontrol can improve program based fault diagnosis in macroprogrammed digital computers, especially where major errors disrupt instruction sequencing and make ordinary diagnostic programs unreliable. The authors define an effectiveness coefficient for diagnostic tests and…
The paper formalizes the syntax and semantics of schematic programming languages, understood as languages for recording algorithms that map objects from a semantic set. It defines schemes as systems of labeled lines generated by a grammar, associates each scheme with a directed dependency graph, and…
This paper studies invariance of the terminal value of a functional for nonlinear dynamic systems subject to external disturbances, generalizing weak invariance in a variational framework. By analyzing large variations of the functional, it derives an exact integral formula for the change in the fun…
The paper addresses the problem of sorting an array of numbers without using an additional working area, beyond a bounded number of cells needed for exchanges. It develops a sequence of in-place procedures for interchanging blocks, merging two ordered subarrays, and arranging zones of fixed size, th…
The paper studies how the complexity, defined as the length of a standard representation, of normal algorithms depends on the size of the alphabet, with particular attention to whether general constructions can be replaced by constructions of only linear complexity. It introduces a uniform coding of…
This note studies two subclasses of Turing machines whose computable predicate truth sets are representable by finite automata: two-way automata and machines operating in a bounded mode. It defines extremal functions measuring the number of states required in the corresponding reduced finite automat…
The paper studies a time-optimal control problem for a class of interconnected linear systems with bounded controls, subject to the additional requirement that the trajectory reach a specified subspace before arriving at the final state and remain there thereafter. The system is rewritten in block-m…
This note studies lower and upper bounds for the complexity of normal algorithms associated with recognizing applicability on bounded words, deciding finite predicates, and computing or minimizing Boolean functions. Using the length of an algorithm representation as the complexity measure, it formul…
The paper addresses computation of optimal controls for discrete systems in cases where the direct discrete analogue of Pontryagin’s maximum principle may fail. It proposes replacing the original problem by auxiliary convexified problems whose solutions satisfy maximum conditions, then constructing …
This paper proposes a general mathematical scheme, called an aggregate, for describing complex systems composed of elements that may not fit standard models such as Boolean functions, finite automata, differential equations, or queueing systems. The authors define aggregates through measurable space…
This note studies numerical integration for systems of nonlinear oscillation type \(du/d\lambda=\varepsilon H(\lambda,u)\) on long intervals of length \(O(1/\varepsilon)\), where standard Taylor methods require prohibitively many small steps. The authors propose an expansion based on transformations…
This paper studies linear automatic-control systems with monotonically varying parameters whose time dependence can be represented by convergent infinite exponential series. Applying the Laplace transform and the shift theorem, the authors reduce the governing differential equation to a one-sided in…
This note studies partial stability of probabilistic automata under arbitrary small perturbations of initial and transition probabilities, asking which portions of behavior may remain invariant when full stability fails. It defines isolated cut points and stability relative to an event, relates stab…
This paper studies the nonuniqueness of extremal solutions in optimal control problems governed by ordinary differential equations and Pontryagin’s maximum principle. It introduces the notion of the relief of a functional, a hypersurface describing the value of an extremal functional over a set of i…
The paper studies numerical regularization of an ill-posed Cauchy problem arising as a model for the inverse problem of ideal gas flow in a Laval nozzle. It formulates the problem as the Cauchy problem for the Cauchy-Riemann equation in an angular domain and establishes conditional well-posedness un…
The paper studies approximation of dynamic characteristics of control objects by models when the input signal has finite support, formulating the output error through Fourier transforms of the object and model transfer functions. It approximates the transfer function on a finite frequency interval u…
The paper studies equivalence of finite automata with a final state relative to a free semigroup with identity and a right zero, viewed as an automaton over its generators together with the zero element. It decomposes the semigroup into two free automata components and derives a criterion expressing…
The paper studies the solution of higher order finite difference Dirichlet problems for the Poisson equation in a rectangle, with schemes of accuracy O(|h|4) and, for equal mesh steps, O(h6). It proposes an alternating direction iterative method using two parameter sets and reduces the minimax choic…
This paper studies controllability for a linear system of differential equations with constant coefficients and controls restricted to a closed domain in a control subspace containing a neighborhood of the origin. It introduces a “general position” condition for the control vectors, requiring the ex…
This paper examines the synthesis of variable-structure automatic control systems when stationary normally distributed noise acts on the logic-forming block and can disrupt the sliding mode. Using statistical linearization, the authors derive approximate equations for the mathematical expectations o…
The paper studies self-correction in gate, contact, and contact-gate circuits subject to open circuits and short circuits of edges, especially when the number of faults grows with the number of variables. It develops two non-coding principles of self-correction: one based on representations by dense…
The paper studies minimum-time transfer to the origin for control systems that are small nonlinear perturbations of linear systems, with controls constrained to a unit cube. Using the maximum principle, it derives an asymptotic construction of extremal triples by perturbing the linear optimal proces…
This paper studies linear stationary controlled systems with unknown inputs of bounded rate of change, focusing on how the greatest accumulated reproduction error is related to the degree of stability and oscillatory character of the system. It derives exact or bounded estimates for first and second…
The paper studies finite difference approximations for first order symmetric systems of partial differential equations with Friedrichs-type boundary conditions. It formulates the continuous boundary-value problem, derives an a priori energy estimate under positivity assumptions on the coefficients a…
This paper extends a formal model of adaptive robots to discrete-time systems with multistep target conditions, where repeated games must eventually be won under unknown parameters of the environment, dynamics, and task. It defines sensor, motor, environment, and brain equations, then formulates suf…
The paper studies completeness of systems of functions in k-valued logic under encodings of arguments and values, generalizing paired-line computation in logical networks. It defines completeness under a fixed encoding and completeness up to encoding, proves the existence of a universal encoding for…
This paper studies Markov chains modeling homogeneous networks of formal neurons with spontaneous activity, where each neuron is activated either by local persistence from neighboring states or by random self-excitation. It develops upper bounds for the probabilities of finite blocks of active neuro…
This note extends operator methods for the stability analysis of difference schemes from real to complex Hilbert spaces. For two-layer schemes with constant operators, it reduces stability in weighted energy spaces to stability of an associated explicit scheme and derives necessary and sufficient, o…
This paper studies a fixed-terminal-time differential game of approach between pursuing and pursued controlled motions with bounded convex control sets, where the payoff is the terminal distance between selected components of the two phase vectors. Under a specified “rough case” involving convex att…
This paper addresses finite-time control of linear systems with lumped parameters, seeking admissible controls that transfer a system from a prescribed initial state to a specified terminal state in a fixed time. Using Fourier transforms and the Wiener-Paley theorem, the problem is reduced to constr…
This paper studies stability of control systems with pulse-width modulation using a general quadratic stability criterion for systems with linear dynamics and nonlinear or time-varying feedback elements. It refines frequency-domain conditions based on quadratic integral inequalities, including versi…
This note proposes a thermodynamic interpretation of learning and adaptation processes in automata, treating transitions under random rewards and punishments as relaxation toward equilibrium in a physical system with discrete energy levels. For an automaton with linear tactics, the final state distr…
This paper studies Kolmogorov-style complexity for programs that decide, up to a bound n, membership in a set of natural numbers, with special attention to recursively enumerable sets. It defines this complexity via a universal partial recursive function and proves that every recursively enumerable …
The paper studies optimal iterative processes for solving nonsingular systems of linear algebraic equations, allowing polynomial corrections in a preconditioned operator with coefficients chosen as functionals of the current residual. It formulates the optimization problem in a weighted norm, reduce…
This paper proposes an iterative principle for constructing multichannel automatic control systems intended to reproduce a prescribed input signal with high accuracy. Each additional channel is driven by the residual error of the preceding channels and contributes a corrective output, leading to rec…
This paper addresses the construction of high-order difference schemes for direct computation of discontinuous solutions of nonlinear hyperbolic systems in divergence form, motivated by the oscillations and smearing associated with lower-order methods. It develops an explicit three-stage, five-point…
This paper studies approximation viscosity in finite-difference schemes for linear hyperbolic systems, focusing on whether numerical dissipation preserves contact discontinuities. Using the first differential approximation of a general difference scheme, the authors define property K and a stronger …
