2018 year, volume 22, issue 3 (PDF)

Molodtsov I.N., Babaeva D.O. Some mathematical models of elastoplastic processes of complex loading

In the framework of the Ilyushin’s theory of elastoplastic processes, in [3] for mathematical modeling of complex loading processes we use special type quasilinear equation with three state functionals. The functionals was calibrated using the experimental results [4] (R.A.Vasin, etc.) for 3D- helical trajectories of deformations. It turned out that the response on a helical trajectory of deformation takes a completely definite loading form, not exactly, but after the exhaustion of some trace of retard. On the helical trajectories of deformations the form of loading is the same: helical trajectory of deformations is becoming to helical trajectory of loading there and back. The used map preserves the geometry of space. This correspondence by Ilyushin is called as isomorphism theorem. All new theories use as the basis the directing vector of stresses and vectors constructed on the base of Frenet basis. For high-dimensional processes, the number of state functionals increases, so and the methods of their identification become more complicated. All models are completly verified. The results are given below.

Keywords: plasticity, plastic deformations, complex loading, state functional, identification of functionals, isomorphism theorem.

Snegova E.A., Aliseychik P.A., Alexeev D.V. The estimation of dependency SSD wear level and write speed on overprovision and block size

This paper is devoted to estimation of SSD write amplification dependency on R — overprovision and N — number of sectors in a block. Garbage collector uses greedy algorithm. More precise formula than in[1] is obtained because it does not depend on N → ∞ assumption. Proved that for fixed overprovisioning the write amplification is monotonic increasing function of N .

Keywords: Write amplivication, overprovision, SSD, garbage collector.

Konovalov A. Yu. The intuitionistic logic is not sound with L-realizability.

An absolute L-realizability of predicate formulas is introduced for all countable extensions L of the language of arithmetic. It is proved that the intuitionistic logic is not sound with this semantics.

Keywords: constructive semantics, realizability, absolute realizability, formal arithmetic, intuitionistic logic.

Perper E.M., Gasanov E.E., Kudryavtsev V.B. On the semantic analysis of juridical documents

The paper considers the task of designing a program which would perform semantic analysis of a juridical document in Russian language. For each entity described in a text, the program must construct a scheme which computes the value of this entity. The paper contains rules which allow to construct such schemes if morphological information about all words of the text is provided.

Keywords: semantic analysis, syntactic analysis, juridical document, logical formula, rule.

Sobyanin P.I. GPU Multiple-Precision Arithmetic Libraries

CUDA libraries supporting multiple-precision integer arithmetic are considered. Features and performance of such open-source libraries are compared.

Keywords: multiple-precision arithmetic, GPU, CUDA.

S. Sh. Adilov An upper bound for the chromatic number of graphs with given thickness and girth

The thickness of a graph G is the minimum number of planar graphs whose union is G. In this paper, we consider an upper bound for the chromatic number of graphs depending on thickness k and girth g, where k ≥ 1 and g ≥ 3. In particular, for biplanar graphs with girth at least 10 we obtain 5-colorability.

Keywords: chromatic number, girth, thickness, planar graph, biplanar graph.

Kalachev G.V., Titova E.E. On the size of the set of motion rules realizable by cellular automata

A model of motion of a dot on the screen is considered. The screen is a semi-infinite one-dimensional cellular automaton. A particular subset of states of the screen is called the image of the dot. A rule of motion is defined by an infinite sequence of zeros and ones, corresponding respectively to the "stop"and "go"commands. For a broad class of motion rules, an algorithm for implementing the given rule is described. A Bernoulli probability measure of realizable motion rules is explored. It is shown that almost all motion rules are realizable. Also it is shown that the set of realizable motion rules is meager with respect to the product topology.

Keywords: cellular automaton, universal screen, motion of the dot, rule of motion, Bernoulli measure, product topology, Baire category.

Konovalov A. Yu. The V-realizability for L-formulas coincides with the classical semantics iff V contains all L-definable functions.

Let L be an extension of the language of arithmetic, V a class of number-theoretical functions. A notion of the V-realizability for Lformulas is defined in such a way that indexes of functions in V are used for interpreting the implication and the universal quantifier. It is proved that the semantics for L based on the V-realizability coincides with the classical semantics iff V contains all L-definable functions.

Keywords: constructive semantics, realizability, generalized realizability, formal arithmetic.

Popkov K.A. Synthesis of easily testable logic networks under one-type stuck-at faults at inputs and outputs of gates

The following assertions are proved: for each natural k and each Boolean constant p, there exists a basis consisting of a Boolean function on max(k + 1; 3) variables and negation of one variable (there exists a basis consisting of a Boolean function on not more than 2,5k + 2 variables and negation of this function), in which one can implement any Boolean function except a Boolean constant p by a logic network which is irredundant and allows a fault detection test (a diagnostic test, respectively) with a length not exceeding 2 under not more than k stuck-at-p faults at inputs and outputs of gates. It is shown that, when considering only stuck-at-p faults at inputs of gates, one can reduce the mentioned bounds on lengths of tests to 1.

Keywords: logic network, one-type stuck-at fault, fault detection test, diagnostic test.

← Back to archive