Abstract Absolute lower bound \(2^{n}\) is established for the length of a full conditional diagnostic test for a Cardot circuit that implements the sum of \(n\) variables.

Abstract An investigation is performed of individual behavioral characteristics of text input that are based on the keystroke dynamics using a virtual keyboard, and their application in the authentication of mobile device users. Key hold time, time between two consecutive keystrokes, and keystroke pressure are used as features to build a user model. A feature vector of a freely typed text is constructed

Abstract The problem of testing real-time constraints for modular computational systems (MCSes) is exemplified by systems of integrated modular avionics. The requirements to the software for testing these constraints are formulated. An approach to modeling MCSes based on the mathematical apparatus of timed automata with suspended timers is described, and a tool system that implements this approach

Abstract Results are presented from developing a parallel code for a joint solution to the nonlinear three-dimensional heat equation and the Poisson equation in creating a multiscale model for phase-change memory based on amorphous carbon nanofilms (a-C). Their numerical convergence is investigated. The parallel effectiveness of the new code is examined on the IBM BlueGene/P supercomputer.

Abstract A model is presented of the financial market with a discrete-time uncertain deterministic evolution of prices in which asset prices evolve under uncertainty described using a priori information on possible price increments; i.e., it is assumed that they lie in given compact sets that depend on the prehistory of prices. Trading constraints depending on the history of prices are assumed to be

Abstract Register machines with counters are arithmetized in class \(\mathcal{E}^{0}\) of the Grzegorczyk hierarchy. As a sequence, we construct a new simple basis via superpositioning in Grzegorczyk class \(\mathcal{E}^{2}\).

Abstract A study is performed of the asymptotic independence of intermediate order statistics and the ‘‘lower’’ and ‘‘upper’’ extreme order statistics as the sample size grows infinitely large. The result is used to refine Rossberg’s theorem.

Abstract Peculiarities of the Toeplitz and polar decompositions of an involutive matrix are described. For instance, it is shown that the unitary factor in both polar decompositions of such a matrix is itself an involution; consequently, it is not only a unitary matrix but a Hermitian matrix as well.

Abstract The class \(\textrm{EP}_{\mathbb{N}}\) of all exponential-polynomial functions that can be obtained from the functions \(0,1,x+y,x\cdot y,\) and \(x^{y}\) by arbitrary superpositions is considered. In \(\textrm{EP}_{\mathbb{N}}\), six precomplete (with respect to the superposition operation) classes are efficiently defined so that a completeness criterion and a recognition algorithm for completeness

Abstract An \(n\)-dimensional economic model is considered that has a Cobb–Douglas production function on the infinite planning horizon such that the utility function is an integral-type functional with a discount and a logarithm-type integrant. It is assumed that all of the model’s amortization factors are equal to one another. The constructed optimum control contains \(n-1\) special segments that

Abstract A study is performed of the main approaches to investigating the stochastic process of population dynamics. Continuous time and space and immovable individuals are used to derive a denumerable system of integrodifferential equations corresponding to the dynamics of the spatial momentum of this process. A way to find an approximate solution using the momentum approach is described.

Abstract A grid analog of the formula of integration by parts is constructed and studied for a two-dimensional case in which one of the grid functions is defined at nodes, and the second function is defined at the midpoints of the sides of cells of a simplicial grid in the Cartesian and cylindrical systems of coordinates. Grid analogs of such first-order differential operators as the gradient, divergence

Abstract Combinations of the cross-products of Bessel functions that arise in oblique derivative boundary-value problems for the Laplace operator in a ring are considered. The behavior of zeros of these functions as the ring thickness tends to zero is studied. It is shown that the zeros are divided into two classes, as in the case of Neumann boundary conditions. Some of them remain finite in the limit

Abstract The problem of synthesizing an asymptotic observer for a linear system with \(l\) measurable outputs \(y=Cx\) and \(m\) unknown inputs \(f(t)\) acting on the system through the matrix \(D\) is considered. A case of hyperoutput systems is examined; such systems have output dimensions larger than that of an unknown input (\(l>m\)). Ways of constructing observers are well-known for such systems

Abstract The problem of constructing a simultaneous confidence tube of the mean value of multiple responses in a multivariate linear normal multiregression model is considered. Simultaneous confidence multivariate ellipsoidal limits for the mean of multiple responses are obtained to solve it. Using a simple bivariate regression model, simultaneous confidence tubes are numerically modeled and analyzed

Abstract The familiar results on ergodicity of priority queueing systems were obtained under the assumption that the input streams of requests of all priorities are Poisson. This assumption is weakened by finding the sufficient conditions of ergodicity of queueing systems with two classes of priorities, where the stream of requests of higher priority is hyperexponential, and the one of lower priority

Abstract An asymptotical approach to the statistical estimation problem is considered under the assumption that the number of observations is a random variable. This leads to distributions with heavy tails and changes in the efficiency of the normally used statistical procedures. Statistical estimates based on random-size and nonrandom-size samples are asymptotically compared against one another. The

Abstract A case is considered in which when the solution to the boundary value problem for a third-order singularly perturbed ordinary differential equation has a strong boundary layer. A difference scheme on piecewise uniform Shishkin meshes is used to solve the problem numerically. It is proved that the solution to the difference problem is reduced to solving the original problem uniformly in a small

Abstract The basics of load tests for a computer cluster with a large number of GPUs (graphics processing units) distributed over the cluster’s nodes are presented and implemented as a program code. Information about the time delays in the transfer of data of different sizes among all GPUs in the system is collected as a result. Two modes of tests, ‘‘all to all’’ and ‘‘one to one,’’ are developed.

A class of schemes of functional elements in the standard basis of conjunction, disjunction, and negation elements is considered. For each scheme Σ from this class, in addition to depth D(Σ), its dimension R(Σ) is determined and found to be equal to the minimum dimension of the unit (Boolean) cube that allows isomorphic embedding Σ. In addition to results obtained earlier, it is proved that within

The problem of the least number of multiplications required to compute the product of a 2 × 2-matrix X and a 2 × m-matrix Y over an arbitrary finite field is considered by assuming that the elements of the matrices are independent variables. No commutativity of elements of matrix X with elements of matrix Y is assumed (i.e., bilinear complexity is considered). Upper bound \(\frac{{7m}}{2}\) for this

The problem of program equivalence, checking whether programs have the same (equivalent) behavior in a given model, is investigated. The considered models of programs with “gateway” procedures were proposed somewhat recently, and almost nothing is known about solving the problem of equivalence for them. An approach is proposed to solving the problem of the consistent halting of programs without procedures

Several families of exact solutions expressed in terms of elementary and special functions are constructed for one nonlinear Sobolev-type equation. The qualitative behavior of these solutions is analyzed.

The problem of stabilizing a mathematical hybrid system with switchings between the operating modes is solved. Each of these modes is associated with nonlinear differential equations that have control parameters. The switching instances (conditions) are control components. A stabilizer must be designed in positional form that allows the trajectory of the entire nonlinear system to reach the target

A single-server queuing system with infinite capacity and a recurrent input flow is considered. Service times of the customer units have an exponential distribution with random parameter. The current value of the parameter is chosen from a finite set with given probabilities at the time the service of a certain customer is completed. Sequential values of the parameters form a special kind of Markov

New upper bound 3n is presented for the cardinality of the definition domain of a universal function for a class of linear Boolean functions in which n is the number of variables.

A finite computational process using only arithmetical operations is called a rational algorithm. Presently, there is no known rational algorithm for checking congruence between arbitrary complex matrices A and B. The situation may be different if A and B belong to a special matrix class. For instance, there exist rational algorithms for the cases where both matrices are Hermitian, unitary, or accretive

A nonclassical queuing-theory problem with calls arising in a space is considered. Stations must be placed to minimize the service time for arising calls. The service time is an increasing function that depends on the distance between a call and a station. The time spent to overcome the same distance frequently depends on the direction of motion. In this case, a metric that considers the nonequivalence

Estimates are obtained for the Shannon function of the length of a diagnostic test with respect to cyclic shifts of scheme inputs, and for the Shannon function of fault detection and length of a diagnostic test with respect to a single stuck-at fault and a cyclic shift of scheme inputs.

The optimum allocation of resources for a Gale problem of supply and demand with uncertain factors is considered. The Dantzig-Wolfe decomposition and the generalized potential method developed earlier by the author for a deterministic version of the problem are used to construct and validate the algorithm for a numerical solution.

The problem of estimating a probability density with a given weight is considered. Probability densities of this type arise in different cases, e.g., analyzing order statistics and studying random-size samples in problems of reliability theory, insurance, and other areas. When constructing an estimator, expansion is used with respect to a wavelet basis based on wavelet functions with bounded spectrum

A way of reconstructing tomographic images based on wavelet-vaguelette decomposition is considered for a model with correlated additive noise. The asymptotic properties of an unbiased estimator are studied for the mean-square risk with stabilized hard thresholding of the coefficients of decomposition. It is shown that under certain conditions, this estimator is strongly consistent and asymptotically

It is proved that in programs of register machines with counters, only the equal-to/not-equal-to relations between registers and counters are essential without loss of computational capabilities.