# No 2 (2012)

**Year:**2012**Articles:**15**URL:**https://journals.rudn.ru/miph/issue/view/525

## Articles

### The Number of Fixed Length Cycles in Undirected Graph Explicit Formula in Case of Small Lengths

#### Abstract

Modifications of Ross and Harary algorithm to express the number ck of cycles of length k in an undirected graph in terms of its adjacency matrix are developed. The general undirected graphs as well as bipartite graphs were considered. Computer algebra implementations of the algorithms enable us to construct the formulae at least for k ≤ 12 in general case and for k ≤ 14 in case of bipartite graph. It was shown that, for any fixed value of k ≥ 8 and space complexity quadratic in order n of a graph, the time complexity of computing ck is O(n[k/2] logn). In case of bipartite graph, for k = 8,10,14 better estimations are obtained: O(n3 log2n), O(n4 log2n), O(n6 log2n).

**Discrete and Continuous Models and Applied Computational Science**. 2012;(2):6-12

6-12

13-18

### Necessary Optimality Conditions for Stationary Nonlinear Hydrodynamic Disrupted Problems in a Bounded Domain

#### Abstract

In the paper we establish the optimal necessary conditions for guaranteeing uniquely the resolution of boundary hydrodynamic problems in a bounded domain so that they could accurately describe the studied hydrodynamic phenomenon.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(2):19-32

19-32

### On Estimation of Convergence Rate of Statistics Expectancy LN to Linear Functional of Spectral Density L(f) of Stationary Gaussian Process

#### Abstract

For the real-valued stationary Gaussian centered process X(t),t = 0,±1,±2…, with a spectral density f(λ), a problem is considered of estimating the convergence rate of expectancy of statistics LN = ∫ φ(λ)IN(λ)dλ,λ ∈ [−π;π], where IN(λ) is a periodogram of a process X(t), t = 0,±1,±2…, to a linear functional of the spectral density L(f) = ∫ φ(λ)f(λ)dλ of the stationary Gaussian process based on the sample {X(1), X(2),…,X(N)}.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(2):33-42

33-42

### The Operational Model of Quantum Measurement of Kuryshkin-Wodkiewicz

#### Abstract

K. Wodkiewicz describes Holevo-Helstrom method, and proposes his own operational model of quantum measurements as an example of using this method. It involves the quantum probability distribution function P q,p = Wψ * Wφ q,p. Here Wφ is the Wigner distribution function of the quantum state of a quantum system before measurement, Wψ is the quantum Wigner distribution function of the quantum ﬁlter before the measurement procedure. It is known that the convolution of two quantum Wigner distribution functions is positive-deﬁnite probability distribution function in phase space of a quantum system.
Quantum Wigner distribution function is uniquely related to Weyl quantization rule, which says that a classical observable A q,p corresponds to a (pseudo) differential operator OW A, whose symbol is the function A q,p. The paper states that Kuryshkin quantization rule is associated with the quantum distribution Kuryshkin-Wodkiewicz function. This quantization rule corresponds to a classical observable A q,p the operator of the observable Oψ A with the symbol AG q,p = A * Φ q,p. Here Φ q,p = 2πℏ −3 2 e−ipq ℏ ψ q ˜ ψ p, where ˜ψ p is the Fourier transform of the state function ψ q of the quantum ﬁlter.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(2):43-55

43-55

### Mathematical Modeling of Mouthpiece Type Waveguide

#### Abstract

In the paper is shown the difference in description of the mouthpiece type waveguide by the method of adiabatic waveguide modes and by the method of comparative waveguides. The difference is demonstrated by the results of numerical calculations.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(2):56-65

56-65

### A Variant of Gerdts Algorithm for Computing Involutive Bases

#### Abstract

In , the fist author presented an efficient algorithm for computing involutive (and reduced Gr̈obner) bases. In this paper, we consider a modiﬁcation of the algorithm which simpliﬁes matters to understand it and to implement. We prove correctness and termination of the modiﬁed algorithm and also correctness of the used criteria. The proposed algorithm has been implemented in Maple. We present experimental comparison, via some examples, of performance of the modiﬁed algorithm with its original form described in and implemented in Maple too. In doing so, we have taken care to provide uniform implementation details for the both algorithms.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(2):66-77

66-77

### Properties of Wigner Distribution Functions Applied to Quantum Mechanics

#### Abstract

An operational model of quantum measurements was presented befor. In order to obtain constructive theoretical results from this model there is a need to deﬁne previously not described properties of Wigner distribution functions. The report contains the proof of these properties. Multidimensional generalization and relationships with diﬀerent conventions of the Fourier transform were described.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(2):78-86

78-86

### Numerical Stability of an Integral Equation Applied for High-Temperature Plasma Diagnostics

#### Abstract

The steady numerical solution using Tikhonov functional with a stabilizer of the second order was obtained for the integral equation of the ﬁrst kind, which occurs for deconvolution of thin-target bremsstrahlung spectra to determine electron energy distributions function (EEDF)

**Discrete and Continuous Models and Applied Computational Science**. 2012;(2):87-89

87-89

90-96

### About Interaction of the Spinor and Scalar Fields, Removing Contribution of the Scalar Field in the Geometry of the Space-Time

#### Abstract

In the static cylindrically symmetric metric and cosmological metric Bianchi I we consider the interacting scalar and spinor ﬁelds with the Lagrangian of the interaction Lint = V (φ)S2, where V (φ) is arbitrary function of scalar ﬁeld φ, S = ψ¯ψ is an invariant of the spinor ﬁeld ψ. We obtain exact solutions of the Einstein, spinor and scalar equations and one exhibited that function V (φ) is absent in the components of the energy-momentum tensor for the interacting ﬁelds. It means that the considered type of the interaction removes the contribution of the scalar ﬁeld in the geometry of the space-time.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(2):97-103

97-103

### Development of Relational Model of Data on the Inhabitants of the Russian Empire based on the Digitized Russian Census Documents

#### Abstract

A technique of a database constructing which contains materials of the Russian Empire censuses, by the example of census returns of XVIII-XIX centuries is considered. The database is based on the digitization of archival materials census made in Excel-format. An algorithm for recognition of semantic structures in the records of census documents, the detection of attributes and rules for ﬁlling the relational tables are described. The algorithm is given for the speciﬁc census (4 and 5 revisions), but these algorithms can be also developed for other revisions and it will make possible to build a continuous chain of historical census lists, translated into a single database format. Such a chain can provide meaningful assistance in genealogical research.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(2):104-115

104-115

### The Modern Level and Development Trends of Network Security for Cloud Computing System

#### Abstract

The article considers the modern level of researches in the ﬁeld of cloud computing network security. The structure and functioning principles of cloud computing security systems, as well as cloud-based security system were analyzed. The modern trends in this ﬁeld were studied.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(2):116-126

116-126

### About Language of Distorted Text Identiﬁcation Using Support Vector Machines

#### Abstract

In this article we consider a problem of language identiﬁcation in a text message in case where the message is under stochastic distortion called symbol change with diﬀerent probabilities. We provide experimental results in language identiﬁcation using support vector machines.

**Discrete and Continuous Models and Applied Computational Science**. 2012;(2):127-131

127-131

### Nashi avtory

**Discrete and Continuous Models and Applied Computational Science**. 2012;(2):132-133

132-133