Recent Papers

A THEOREM ON EXTERNALLY STABLE SETS

This paper studies cooperative games in reduced 0-1 form and the relation between the core and stable solutions under continuous changes of the characteristic function. It considers a family of games in which coalition values are nondecreasing continuous functions of a parameter, defines a set forme…

ON A CONCAVE \(n\)-PERSON GAME AND ONE MODEL OF PRODUCTION

The paper studies normalized equilibrium points in concave n-person games and develops iterative methods generalizing the conditional-gradient approach for computing them under convexity and regularity assumptions. It proves convergence results for three step-size rules, including subsequential conv…

DUAL MODELS OF PRODUCTION

This paper studies regular positively homogeneous production models in finite-dimensional ordered normed spaces and defines a conjugate, or dual, production model through inequalities between attainable output sets and nonnegative linear functionals. It establishes basic properties of the dual mappi…

A ONE-PRODUCT DYNAMIC MODEL WITH A CONSTRAINED STRUCTURE

This paper studies a one-product dynamic economic model in which fixed assets are distributed by capital structure and new investment reallocates labor from the lowest to the highest structures. Starting from labor and capital balance equations and a differential optimization condition, it derives a…

Connecting Dynamic Models of Production Processes into Schemes

The paper studies how dynamic production models with differing production-cycle durations, reproduction coefficients, and delayed capacity growth can be connected into parallel, sequential, and more complex production schemes. It formulates a differential-inequality model for individual production u…

ON A MATHEMATICAL MODEL OF PRODUCTION

This note studies a general mathematical model of production represented by set-valued mappings between ordered finite-dimensional spaces, where each mapping assigns feasible output sets to input vectors over successive time periods. Under assumptions such as monotonicity, upper semicontinuity, conc…

A One-Product Dynamic Model with Instantaneous Transformability of Capital

This paper develops a one-product dynamic economic model in which output is allocated between consumption and accumulation, with capital assumed to be instantaneously transformable into the form optimal for the current capital to labor ratio. Using a homogeneous concave production function, the auth…

DYNAMIC MODEL OF THE ECONOMY

The paper develops a dynamic macroeconomic model with two products and two departments, in which the first department produces accumulation funds and the second produces consumption goods. Using homogeneous production functions, given labor resources and consumption, and assumptions on nontransferab…

A GENERALIZATION OF A THEOREM OF M. INAGAKI

This note derives an exact optimal growth trajectory for a one-product dynamic economic model with exponentially growing labor, a Cobb-Douglas production relation, and an isoelastic utility function. Under the condition that the production elasticity equals the utility parameter, the author applies …

On One Linear Model of Exchange

This paper analyzes a linear model of economic exchange originally formulated by Schwartz, in which production and inventory dynamics are represented by recurrence relations on an admissible region of the plane. It studies the iterates of the associated linear transformation by classifying its chara…

ASYMPTOTICS OF SOLUTIONS OF LINEAR DYNAMIC MODELS OF ECONOMIC SYSTEMS WITH DISCRETE TIME

This paper studies the asymptotic behavior of trajectories in linear dynamic models of expanding economies with discrete time, with particular attention to dynamic linear programming and closed Gale or von Neumann type models. It formalizes dynamic linear programming problems, constructs equivalent …

Depreciation Payments Under Optimal Equipment Use

This note analyzes optimal acquisition, replacement, and use of equipment under uneven demand, especially alternating normal and peak loads, with costs discounted over an infinite horizon. Using simplified dynamic programming models, it derives optimal stationary policies for purchasing and assignin…

Algorithm for Optimizing the Production and Distribution of Heterogeneous Products

The paper formulates a linear programming model for optimizing production assortment and distribution of heterogeneous products among production sites, consumers, and transport modes under resource, transport capacity, and demand constraints. It derives optimality conditions by representing feasible…

THE 22nd CONGRESS OF THE CPSU AND THE TASKS OF SCIENCE

This article presents the Twenty-Second Congress of the CPSU and the new Party Program as a framework for defining the role of science in the construction of communist society. It argues that scientific research should be directed both toward fundamental theoretical advances and toward closer integr…

Corrections to the Article “The Effect of Anelectrotonus on Inhibited Positive Conditioned Reflexes” (DAN, Vol. 112, No. 6, 1957)

On Methods for Analyzing Certain Extreme Planning and Production Problems

This paper formulates a linear model of production planning in which admissible plans are nonnegative combinations of technological methods producing final and intermediate goods while using bounded production factors. It proves an existence and optimality theorem: under a natural no-free-production…