查看更多>>摘要：Microneedle systems are compiled by a sufficiently large number of microneedles which are mounted on a flat base and used for drugs injection in modern medicine. Such systems are often made in the form of a patch to which a large number of biosoluble microneedles are attached that significantly simplifies the use of such systems for injecting drugs. As a rule, the patch width is fixed, but the length can be quite long. Therefore, such a patch can be considered as a periodic continuation of the selected fixed fragment. The efficiency of using such systems depends significantly on the size and number of microneedles arranged on such a fragment. The problem of determining such dependences will be considered as the problem of optimizing the interaction of microneedle systems with an elastic surface. Such problems are formulated in the form of classical minimization problems of integral functionals with obstacles supplemented by periodic boundary conditions in one of the coordinates and homogeneous Dirichlet boundary conditions in the other coordinate. The homogenization theory methods are used to obtain homogenized minimization problems for the functionals whose solutions are approximations for solutions of the interaction problem under consideration. The homogenized problems are also formulated in the form of classical minimization problems with an obstacle which have a much simpler form in comparison with the original strongly oscillating obstacles. When obtaining these problems of importance is the fact that the systems considered are formed by a sufficiently large number of microneedles. Conditions are established for the explicit calculation of surface configurations arising from microneedle systems interaction with an elastic surface. Statements justifying the form of such configurations are proved. The condition of "a gap appearance" between the surface and the base of the microneedle system is established and the height of such a "gap" is calculated.
查看更多>>摘要：The paper is devoted to the consideration of a stochastic programming problem where the random factor is homogeneous in a strict sense random field satisfying the strong mixing condition with the appropriate coefficient. The first problem is approximated by the problem of minimization of the empirical function constructed on observations of the homogeneous random field. The conditions under which the empirical estimate is consistent are given, in particular, it is imposed restrictions on the moments of the minimized function. When large deviations are investigated, some theorems from the functional analysis are used. In the theorems, the estimate of large deviations of the empirical function from the former one implies the estimate of large deviations of the minimum point and the minimal value of the empirical function from analogous characteristics of the former problem. In particular, the concept of conditioning function which describes the behavior of the minimized function in a neighborhood of a minimum point is used. The fact that when the second argument is fixed, the function under the expectation sign can be considered as the element of the space of continuous functions, is used. For simplicity, it assumes that the given function belongs to a convex compact subset of the appropriate functional space. The linear operator's theory and the duality relation are used. In particular, the fact that a space of limited signed measures is dual to a space of continuous functions is used. The well-known results from the large deviations theory, in particular, the theorem of a sufficient condition of the upper bound estimate for large deviations are applied. Notions of measurably separated random variables and the first hypermixing hypothesis for a homogeneous field are used. The auxiliary assertion on large deviations of empirical estimates in an abstract space is proved. In the proof, the rectangle on the plane is divided into the subsets separated from each other. Then the homogeneity of the field in a strict sense and the first hypermixing hypothesis imply the existence of the limit which is a sufficient condition for large deviations estimate.
查看更多>>摘要：This work is devoted to the further development of the study of the arms race models, such as Richardson type models. The simplicity and universality of the basic model are analyzed, successful cases of its application are specified. Certain preconditions for the use of such models are discussed. It is noted that previously such models did not take into account the factor of time delay, which is associated with decision-making on the development and implementation of new weapons. In this regard, the authors propose to consider models of these processes in the form of systems of functional-differential equations. There are several separate cases of such models: models with a pure delay, models with the equal claims of the parties, general models. The case of systems with pure delay is considered in detail. Initially, the results are obtained for the general form of systems of functional-differential equations with a time-delay argument. Then these results are reduced to Richardson type systems. Analytical expressions for the solutions of the corresponding Cauchy problems depending on the type of the delayed argument are constructed. The results obtained for systems with a pure delay are quite constructive in sense of practical calculations and can be further extended to the case of general models of the dynamics of the arms race with a deviating argument. This work is devoted to the further development of the study of arms race models in the Richardson-type. The model that takes into account the time delay factor related to decision-making on the development and implementation of new types of weapons is considered. Therefore, the models have the form of systems of differential-difference equations. For systems with pure time delay (general form and Richardson-type), the results are proved, which give analytical expressions for the representation of solutions of the corresponding Cauchy problems.
查看更多>>摘要：To determine the essence of the subject it is used standard information contained in databases. It is a structured set of interconnected data of a specific subject area. To find quickly the required information, this database should be structured, input data should also be modeled accordingly. Today, there are different data models with their advantages and disadvantages, and each has its own scope. The article provides examples of problems of semantics that relate to recognition problems. There are speech recognition, child, female, male voice recognition, the problem of clinical diagnostics, comparison of texts on plagiarism, automatic translation of texts from one language to another, etc. There are two ways of comparing the input information and the standard: by the primary signs that describe the object being sought and by the given object. In the second method, the previous coat by certain signs of the standard and of the object is not conducted. At modeling input data to search for information by the first way the coat of given objects by certain signs takes place. The signs are divided into those that characterize only the given object, by which it is quite simple to define it in the database. In this case, the problem is solvable. If the same signs describe different objects, but using differential analysis one can find the desired object, then this problem is partially solvable. If the same signs characterize different objects and the desired object cannot be identified, then a situation of uncertainty arises. There are problems that do not require the libraries of standards for their recognition. In some recognition problems, which may be semantics problems, the input data is divided into segments, with subsequent determination of the similarity of the resulting parts. In this case, the input data contains both the object to be recognized and the standard with which it is compared. In some problems, it is taken as a standard either an expression that determines the similarity of the input data and standard information, or the conditions are specified by which a given object can be recognized. The library of standards is not used to solve these problems.
查看更多>>摘要：elements, primitive polynomials over fields of order 2~k, where k ≥ 2. The necessary equalities for calculating the coefficients of polynomials are given. This method is relevant in the case of creating subsystems for cryptographic protection of information in modern computer systems that use microcontrollers and microprocessors based on 32 or 64-bit data presentation formats. The indicated method for constructing primitive polynomials over non-simple fields based on the known primitive polynomials over a field of two elements has polynomial complexity. The article provides definitions of the basic concepts, as well as the necessary auxiliary results, which are used to substantiate the algorithm on which the proposed method is based, which can be useful in its implementation, a detailed description of the algorithm is presented and an example of its application is given.
查看更多>>摘要：When solving some types of problems of applied character, nowadays the most efficient are the methods of the theory of approximation of functions. In a modern stage of development of the theory of approximation of functions, one mostly deals with either an approximation of individual functions or whole function classes by preset subsets of functions that turn to be in a certain sense more convenient to deal with in calculations in comparison with the functions that should be approximated. In practice, a set of algebraic polynomials or a set of trigonometric polynomials of a given order often play the role of such a subset. As a result, a new type of problems appeared, that further was called the extremal problems of the theory of approximation. In its turn, among all of the extremal problems of the theory of approximation, the most interesting from the mathematical modeling point of view are the so-called Kolmogorov-Nikol'skii problems. Their essence is the determination of asymptotic equalities for the values of the approximation of functions of certain classes by specific methods of summation of the Fourier series. Here we consider a problem of approximation of 2π-periodic functions of the Lipshitz class by certain singular integrals. The most vivid examples of such integrals are the so-called generalized Poisson integrals. As a result of studying, we wrote down complete asymptotic expansions in powers of 1/δ, δ →∞, of the least upper borders of deviations of functions of the Lipshitz class from their generalized Poisson integrals. The obtained result allows us to write down not only the main term of the asymptotic expansion but also write down its second, third terms, etc., using the Riemann ζ-function, which, respectively, much simplifies the problem of algorithmization when solving the stated applied problem. Moreover, the generalized Poisson integrals are the solutions of partial differential equations, and they are connected directly with the methods of solving integral, difference-differential, and integral-differential games, that are related to the game problems of dynamics.
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