Neural network-based models of binomial time series in data analysis problems

This article is devoted to constructing neural network-based models for discrete-valued time series and their use in computer data analysis. A new family of binomial time series based on neural networks is presented, which makes it possible to approximate the arbitrary-type stochastic dependence in time series. Ergodicity conditions and an equivalence relation for these models are determined. Consistent statistical estimators for model parameters and algorithms for computer data analysis (including forecasting and pattern recognition) are developed.

Arbitrary stability for a Hopfield neural network problem with discrete and distributed delays

We consider a Hopfield neural network system containing discrete as well as distributed delays. A stability result of arbitrary type is proved under weaker assumptions than the used ones so far. This result includes exponential and polynomial (or power type) stability as special cases. Our proof relies on a judicious choice of Lyapunov-type functionals and some appropriate manipulations.

The Limits of Computation

This article provides a survey of key papers that characterise computable functions, but also provides some novel insights as follows. It is argued that the power of algorithms is at least as strong as functions that can be proved to be totally computable in type-theoretic translations of subsystems of second-order Zermelo Fraenkel set theory. Moreover, it is claimed that typed systems of the lambda calculus give rise naturally to a functional interpretation of rich systems of types and to a hierarchy of ordinal recursive functionals of arbitrary type that can be reduced by substitution to natural number functions.

A FEATURE OF THE CONCEPTION INHERITANCE IN THE ELEATIC SCHOOL OF PHILOSOPHY

The purpose of the paper is to identify common theses supposedly shared by Parmenides and Zeno of Elea. In order to achieve this goal, we show that an alternative interpretation of the aporia from 29 B 1 DK is possible, in which we don’t deal with an infinite division of an extended being, but we deal with a regression of relations of an arbitrary type. These relations are connecting an arbitrary type of constituents of a complex object. In this case, the aporia proves the impossibility of a complex object of any type, not just the impossibility of an extended object. Finally, we show that interpreted in this way Zeno’s reasoning from 29 B 1 DK, and appropriately interpreted Parmenides’ proofs of the unity of being in 28 B 8 DK can be treated as based on a holistic assumption. This enables us to assert that Zeno was the successor of Parmenides, not only in the sense that he was indirectly proving Parmenides’ thesis of the unity of being, but also in the sense that he was using a statement that Parmenides could imply.

Электродинамическая модель системы «излучатель-корпус объекта»

В целях выработки единого подхода к оценке роли корпуса подвижного объекта (грунтового, воздушного, корабельного, железнодорожного), на котором установлен малогабаритный излучатель произвольного типа, предложен единый энергетический подход с использованием понятия добротности. Показано, что добротность системы в широких пределах изменяется в зависимости от места установки малогабаритного излучателя. Для оценки вклада корпуса объекта в общую эффективность системы предложен параметр коэффициент возбуждения корпуса объекта, определяемый соотношением идеальной добротности малогабаритного излучателя в свободном пространстве к идеальной добротности излучателя, размещенного на корпусе подвижного объекта. Проанализированы пределы изменения данного коэффициента в зависимости от координат места установки излучателя и его типа (электрического или магнитного). Указанный подход позволяет численно оценить коэффициент полезного действия системы излучатель-корпус объекта при рассмотрении антенны произвольного типа, расположенной в произвольном месте корпуса.In order to develop a unified approach to assessing the role of the body of a moving object (ground, air, ship, or rail) equipped with a small-sized radiator of an arbitrary type, a unified energy approach is proposed using the concept of quality factor. It is shown that the quality factor of the system varies widely depending on the installation location of a small-sized radiator. To assess the contribution of the objects body to the overall system efficiency, a parameter is proposed - the excitation coefficient of the objects body, which is determined by the ratio of the ideal quality factor of a small-sized radiator in free space to the ideal quality factor of a radiator mounted on the body of a moving object. The range of this coefficient is analyzed depending on the location coordinates of the installed radiator and its type (electric or magnetic). This approach allows the numerical evaluation of the efficiency of the radiator objects body system when considering an antenna of an arbitrary type located in an arbitrary location on the body.

VERIFICATION OF A PREDICATE HEAPSORT PROGRAM USING INVERSE TRANSFORMATIONS

Deductive verification of the classical J.Williams heapsort algorithm for objects of an arbitrary type was conducted. In order to simplify verification, non-trivial transformations, replacing pointer arithmetic operators by an array element constructs, were applied. The program was translated to the predicate programming language. Deductive verification of the program in the tools Why3 and Coq appears to be complicated and time consuming.

Mathematical model of nonlinear deformation of three-layer shells

The article presents the study results of geometrically nonlinear deformation of elastic shells of arbitrary type with consideration of transverse shifts. There is constructed a new mathematical model of nonlinear deformation of thin-walled elastic isotropic three-layer shells. Each layer of the shell is made of different materials, but with similar shear modules. The thickness of the layers can be different. Averaging of all three layers becomes possible, and deformation of a three-layer shell as a single-layer shell with the given characteristics of the modulus of elasticity and the Poisson's ratio can be considered.