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The paper considers one of the numerical methods to solve problems of scattering electromagnetic waves on the systems formed by parallel-oriented cylindrical elements – two-dimensional photonic crystals. The method is based on the classical partition approach used for solving the wave equation. Тhe method principle is to represent the field as the sum of the primary field and the unknown secondary field scattered on the medium elements. The mathematical expression for the latter is written as the infinite series according to elementary wave functions with unknown coefficients. In particular, the N elements-scattered field is found as the sum of N diffraction series in which one of the series is composed of the wave functions of one body and the wave functions in the remaining series are expressed in terms of the eigenfunctions of the first body using addition theorems. Further, to meet the boundary conditions, on the surface of each element, we obtain systems of linear algebraic equations with the infinite number of unknowns – the required expansion coefficients, which are solved by standard methods. A feature of the method is the use of analytical expressions to describe diffraction on a single element of the system. In contrast to most numerical methods, this approach allows one to obtain information on the amplitude-phase or spectral characteristics of the field only at the local points of the structure. The high efficiency of this method stems from the fact that there is no need to determine the field parameters in the entire area of space occupied by the multi-element system under consideration. The paper compares the calculated results of the transmission spectra of two-dimensional photonic crystals using the considered method with the experimental data and numerical results, obtained by other approaches, and demonstrates their good agreement.

The paper deals with a problem of the obfuscated JavaScript code detection and classification based on Abstract Syntax Trees (AST) coloring. Colors of the AST vertexes and edges are assigned with regard to the types of the AST vertexes specified by the program lexical and syntax structure and the programming language standard. Research involved a few stages. First of the all, a non-obfuscated JavaScript programs dataset was collected by the public repositories evaluation. Secondly, obfuscated samples were created using eight open-source obfuscators. Classifier models were built using an algorithm of gradient boosting on the decision trees (GBDT). We built two types of the classifiers. The first one is the model that classifies the program according to the type of the obfuscator used, i.e. based on what obfuscator created the sample. The second one tries to detect samples obfuscated by the obfuscator whose samples are not observed during training. The quality of the obtained models is on par with the known published results. The feature engineering method proposed in the paper does not require a preliminary analysis of the obfuscators and obfuscating transformations. In the final part of the paper we analyze a quality of models estimated, discussing the certain statistical properties of the obfuscated and non-obfuscated samples obtained and corresponding colored ASTs. Analysis of generated samples of obfuscated programs has shown that the method proposed in the paper has some limitations. In particular, it is difficult to recognize minifiers or other obfuscating programs, which change the lexical structure to a greater extent and the syntax to a lesser extent. To improve the quality of detection of this kind of obscuring transformations, one can built combined classifiers using both the method based on the AST coloring and the additional information about lexemes and punctuation, for example, entropy of identifiers and strings, proportion of characters in upper and lower case, usage frequency of certain characters etc.

When fighting against terrorism in modern armed conflicts, combat vehicles, including tanks, are widely used. To minimise own losses of vehicles and personnel for overthrowing enemy is a relevant task. To solve it, the paper considers certain events in the history of the Great Patriotic War, which are associated with battle of tanks that spring an ambush. A mathematical model of the battle is built. The state graph of the system is given. Using this graph, a probability of tank kills and a ratio of mathematical expectations of losses have been calculated. This mathematical model generalizes the models, previously published in this journal, based on the Markov chain apparatus. The paper gives an example of calculations for this model in the particular case in which experimental data are used as a basis. The ratios of mathematical expectations of losses of the warring parties are obtained. Further, we consider the mathematical models, in which it is assumed that probabilities for tank crews to provide operations of targets detection in firing are known. With technology development and its mathematical support it becomes increasingly more real. The formulas to obtain the probability of tank kills are given according to the graph of states using the known probabilities of transition from one state to another. In each of the three mathematical models under consideration there is a graph of the system state, which allows calculation of the tank kills probability. We have analysed the models to prove a significant dependence of the loss ratio of the warring parties on the number of firing positions used by the tank in ambush in case re-siting is unnoticeable for the enemy. The authors-considered models that use the examples of historical events confirm that the tactics of organising and conducting ambushes in tank battles can be successfully used nowadays, when the technology intensiveness of the opposing forces significantly grows. The obtained results can be applied to organise and conduct tank ambushes in modern armed conflicts and fight against terrorist army.

The paper presents a mathematical model and method for solving a wide class of problems in topological optimization of an adhesive joint to obtain an optimal microstructure and gradient properties in order to reduce the level of stresses arising from both thermal and mechanical loads therein.Adhesive joints have advantages over alternative bonding methods. The paper shows that the introduction of graduating properties in thickness or along the adhesive layer is the most promising strategy to optimize the adhesive. The approach is to modify the material properties or the geometry of the adhesive, varying along the joint.In all the papers known to authors, the shape of the elements to be joined, or the shape and location of the adhesive layer, were subject to optimization. The topological optimization methods to determine the optimal distribution / change of the gradient properties of the adhesive layer itself were not used.In the paper, the stresses arising in the solder joints are analyzed; it is shown that due to the small solder thickness, shear stresses are basic in it. The shear stresses are concentrated near the ends of the solder, and have the lowest values in the middle. The objective of the optimization problem is to reduce the peak values of the shear and peeling stresses in the solder layer. The topological optimization of the solder microstructure is to find the best distribution of a given amount of solder in the region in order to reach minimum peak values of stresses. The advantage of using topological optimization is that the microstructure of the solder should not be known a priori, and, thus, any designs can be optimized without first studying the effect of the original geometric parameters on the strength of the joint.The algorithm is implemented using the finite element method and the method of movable asymptotes. A number of examples are considered in order to obtain the solder microstructure to be optimal for reducing the peak values of shear stresses and delamination in a three-layer package.The results show that optimal microstructures significantly reduce peak stresses compared to a uniform layer. The obtained results reveal the potential of the developed algorithm and show that it can find practical use.

Block ciphers form one of the main classes of cryptographic algorithms. One of the challenges in development of block ciphers, like any other cryptographic algorithms, is the analysis of their cryptographic security. In the course of such analysis, statistical testing of block ciphers is often used. The paper reviews literature on statistical testing of block ciphers.The first section of the paper briefly and informally discusses approaches to the definition of the concept of a random sequence, including the Kolmogorov, von Mises, and Martin-Löf approaches and the unpredictability-related approach. However, all these approaches to the definition of randomness are not directly applicable in practice.The second section describes statistical tests of binary sequences. It provides brief descriptions of the tests included in the DieHard, NIST STS, RaBiGeTe statistical test suites.The third section provides the appropriate information to present further the operation modes of block ciphers.The fourth section deals with techniques for statistical testing of block ciphers. Usually such techniques lie in the fact that based on the block cipher under test, various generators of the pseudorandom sequences are built, with their output sequences being tested using any suite of statistical tests. The approaches to the construction of such generators are given.The paper describes the most known statistical test technique for block ciphers among the submitted for the AES competition. It is a technique the NIST uses for statistical testing of ciphers. In addition, there are other techniques mentioned in the literature.In conclusion the paper states that there is a need to develop new techniques for statistical testing of block ciphers.The paper support was provided from the Russian Foundation for Basic Research in the framework of the research project No. 16-07-00542 supported

There are a large number of examples of using the population-based algorithms (P-algorithms) to have a successful solution for complex practical tasks of global optimization, for instance, problems of computer-aided design, synthesis of complex chemical compounds, optimal control of dynamic systems, etc. P-algorithms are also successfully used in multi-criteria optimization, when a preliminary construction of some Pareto set (front) approximation is required. P-algorithms are numerous and very diverse – over 100 such algorithms are known, and new algorithms continue to appear. In this connection, the problem of systematizing expressive means of P-algorithms is of relevance. We consider one of the components of this problem that is the problem of classification of the search operators of P-algorithms.The paper formulates a global optimization problem and a general scheme of the P-algorithms to solve it. This multilevel classification of the main search operators of P-algorithms at the highest level of the hierarchy identifies the following operators: initialization of the population and the end of the search; coding of individuals; randomization; selection; crossing; population management; local search.These operators at the next hierarchical level are divided into deterministic and stochastic ones. Further, we distinguish static, dynamic program and dynamic adaptive operators. The following classification levels are "operator dependent", that is, generally speaking, different for each operator. We reveal the essence of these operators and give the use cases in various P-algorithms.Although the paper uses the names of operators such as selection, crossing, our orientation is not only to evolutionary algorithms. A description scheme of operators presented in this paper can be used to determine any population-based algorithms.The work development expects extending a set of operators presented, and, above all, using this set and a set of basic essences of population algorithms, the formalization of which was earlier proposed by the author, systematizing the most known algorithms of this class.

The paper considers a problem of difficult accessibility and low quality of data on the reliability parameters of the vehicle system components and the difficulties arising from this problem to estimate the reliability parameters of the systems themselves as statutorily required and in terms of international standards (e.g. ISO 26262). As a problem solution, the paper proposes a method for adjustment of the system reliability estimates based on the field observation of system failures. The method based on a Kalman filter uses non-parametric definition of the failure probability distribution (quantile «folding» of the distribution) with subsequent «unfolding» via Monte Carlo.A mathematical model shows how to use this method. For clarity, the estimates of reliability parameters are given at the time of rollout (100 % of systems are in working order) and upon the failure of 25%, 50%, 75% and 100% of produced systems, respectively. A КК plot shows that the reliability estimates gradually become close to the field reliability data.The method allows, by varying filter parameters, a more conservative estimate of the reliability parameters or an estimate, which is more in accord with the field data. Thus, the results can be used at all stages of the system lifecycle, namely when developing, manufacturing and upon completing production for the aftermarket services.

In this paper, we suggest to use hybrid approach to time series forecasting problem. In first part of paper, we create a literature review of time series forecasting methods based on hybrid neural networks and neuro-fuzzy approaches. Hybrid neural networks especially effective for specific types of applications such as forecasting or classification problem, in contrast to traditional monolithic neural networks. These classes of problems include problems with different characteristics in different modules. The main part of paper create a detailed overview of hybrid networks benefits, its architectures and performance under traditional neural networks. Hybrid neural networks models for time series forecasting are discussed in the paper. Experiments with modular neural networks are given.

So far, there are no efficient algorithms to solve a problem of finding the low degree annihilators for arbitrary Boolean function. In the paper we present a new algorithm to find affine annihilators for an arbitrary Boolean function. We start with considering the identity fg ≡ 0 or the arbitrary Boolean function f and its possible affine annihilator g. We use a special representation of the Boolean function in sum of its sub-functions to reduce degrees of considering functions in previous identity. As a result, we establish equivalence between the identity fg ≡ 0 for Boolean functions of n variables and the system of Boolean equations of n-1 variable.An algorithm for finding the affine annihilators for the arbitrary Boolean function f must find all the affine functions g so that fg ≡ 0. Our algorithm is based on reducing the problem of finding the affine annihilators for the Boolean function f of n to the similar problem for its sub-functions of n-1 variable. The presented algorithm has the following advantages:An input function can be presented in different ways;Output can be also presented in different ways;The algorithm can be effectively parallelized.It should be noted that the result we have obtained is not final and highlights some development directions: first, to study the impact of its input and output on the efficiency of the algorithm of various representations and, second, to use our idea of constructing the algorithm for development of algorithms, which allow finding the 2nd, 3rd, etc. degree annihilators for a specified Boolean function.

To study an arithmetic nature of the values of hyper-geometric functions (and their derivatives including those with respect to parameter), it is common practice to use one either Siegel's method or the method based on the effective construction of the linear approximating form. The main distinction between these methods consists in the mode of construction of the first approximating form. Applying Siegel's method allows us to construct such a form by means of a pigeonhole principle that makes it possible to establish, in certain cases, the algebraic independence of the values of corresponding functions. The Siegel's method can be usually applied just while considering hyper-geometric functions with rational parameters. The effective method has a certain advantage here, for in some cases this method enables us to carry out corresponding investigation also for the functions with irrational parameters. Another advantage of the effective method is that it provides obtaining of high- accuracy quantitative results. By quantitative results one usually implies the estimates of the moduli of the linear forms in the values of corresponding functions. The effective method has made it possible to obtain, in some cases, estimates being precise regarding the height of such forms with calculation of the corresponding constants. A drawback of the effective method is the narrow domain of its applications. The effective construction of the linear approximating form, which initiates reasoning, is always a challenge. So far, an effective construction of the approximating form for the product of powers of hyper-geometric functions (with the rare exceptions) failed.In both aforementioned methods one proves previously linear independence (in Siegel's method, as a rule, algebraic independence,) of the functions under consideration. Such a proof is often considered as an independent result.In this paper, by means of the method especially elaborated for this purpose we establish linear independence of some hyper-geometric functions and their derivatives (including those with respect to parameter) over the field of rational fractions. Subsequently, it will be possible to apply this result to investigate arithmetic properties of the values of such functions. Herewith we mean the application of the effective method to achieve the sufficiently accurate quantitative result.