Feature Of Such Problems Research Articles

Экономикалық контрабанданы саралаудың теориялық және тәжірибелік мәселелері

The article discusses the problems of qualification of economic smuggling. The article analyzes theoretical and practical gaps in the conceptual apparatus of this crime. The author conducted a study in the field of legal regulation of illegal movement of goods and other items across the customs border. The article reveals the main features of such problems of qualification of a crime under Article 234 of the Criminal Code of the Republic of Kazakhstan. At the same time, the article highlights the fact that its correct qualification is ensured not only by the application of criminal law norms but also by strict compliance with the criminal procedure law studying the theory and practice of the qualification of economic smuggling. The article considers some critical remarks concerning this point of view, taking into account the peculiarities of establishing the signs of the composition of economic smuggling and the provisions of the legislation, as well as the established expert, investigative and judicial practice. In conclusion, the authors propose ways to solve the studied problems.

The effect of fiber-matrix interaction on the kinking instability arising in the torsion of stretched fibrous biofilaments

The response of fibrous soft tissues undergoing torsional deformations is a topic of current interest. Such deformations are common in ligaments and tendons and are also of particular interest in cardiac mechanics. The problem of torsion superimposed on extension of incompressible hyperelastic solid circular cylinders is a classic problem of nonlinear elasticity that has been considered by many authors in the context of rubber elasticity particularly for isotropic materials. A striking feature of such problems is the instability that arises with sufficiently large twist where a kink and then a knot suddenly appears. An energy approach to examining this instability when the extension and twist are prescribed was described by Gent and Hua (2004) and illustrated there for a neo-Hookean isotropic elastic material. The theoretical results were compared with experimental observations on natural rubber rods. Murphy (2015) has shown that the approach of Gent and Hua (2004) for isotropic materials can be simplified when the rods are assumed to be thin and this theory was applied to transversely isotropic materials by Horgan and Murphy (2016). In contrast with the case for isotropic materials, it was shown there that the kinking instability occurs even in the absence of stretch, i.e., for the case of pure torsion. Here we are concerned with the implications of this simplified thin rod instability theory for fiber-reinforced transversely isotropic materials that reflect fiber-matrix interaction. It is again shown that the kinking instability occurs even in the absence of stretch, i.e., for the case of pure torsion. The results are illustrated for a specific strain-energy density function that models fiber-matrix interaction. It is shown that the critical twist at which kinking occurs decreases as a measure of fiber-matrix interaction is increased so that the fiber-matrix interaction has a destabilizing effect. The results are illustrated using experimental data of other authors for skeletal muscles and for porcine brain white matter tissue.

Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling

Infinite-dimensional compressed sensing deals with the recovery of analog signals (functions) from linear measurements, often in the form of integral transforms such as the Fourier transform. This framework is well-suited to many real-world inverse problems, which are typically modeled in infinite-dimensional spaces, and where the application of finite-dimensional approaches can lead to noticeable artefacts. Another typical feature of such problems is that the signals are not only sparse in some dictionary, but possess a so-called local sparsity in levels structure. Consequently, the sampling scheme should be designed so as to exploit this additional structure. In this paper, we introduce a series of uniform recovery guarantees for infinite-dimensional compressed sensing based on sparsity in levels and so-called multilevel random subsampling. By using a weighted ℓ 1 -regularizer we derive measurement conditions that are sharp up to log factors, in the sense that they agree with the best known measurement conditions for oracle estimators in which the support is known a priori. These guarantees also apply in finite dimensions, and improve existing results for unweighted ℓ 1 -regularization. To illustrate our results, we consider the problem of binary sampling with the Walsh transform using orthogonal wavelets. Binary sampling is an important mechanism for certain imaging modalities. Through carefully estimating the local coherence between the Walsh and wavelet bases, we derive the first known recovery guarantees for this problem.

State Constrained Control Problems in Banach Lattices and Applications

This paper aims to study a family of deterministic optimal control problems in infinite dimensional spaces. The peculiar feature of such problems is the presence of a positivity state constraint, which often arises in economic applications. To deal with such constraints, we set up the problem in a Banach space with a Riesz space structure (i.e., a Banach lattice) not necessarily reflexive: a typical example is the space of continuous functions on a compact set. In this setting, which seems to be new in this context, we are able to find explicit solutions to the Hamilton-Jacobi-Bellman (HJB) equation associated to a suitable auxiliary problem and to write the corresponding optimal feedback control. Thanks to a type of infinite dimensional Perron-Frobenius Theorem, we use these results to get information about the optimal paths of the original problem. This was not possible in the infinite dimensional setting used in earlier works on this subject, where the state space was an $\mathrm L^2$ space.

The Bitsadze–Samarskii Type Problem for Mixed Type Equation in the Domain with the Deviation from the Characteristics

For a mixed elliptic-hyperbolic type equation in a mixed domain, when the elliptic part is a sector of the circle, and the hyperbolic part consists of two characteristic triangles, the Bitsadze–Samarskii type nonlocal problem is investigated. A feature of such problems is that the boundary conditions in the hyperbolic parts of the boundary are determined by a first-order differential operator and pointwise link the values of the partial derivatives of the desired solution on the characteristics with the partial derivatives on arbitrary monotone curves lying inside the characteristic triangles of the equation. To solve the problem, the methods of the theory of partial differential equations and the theory of singular integral equations as well as the methods of energy integrals and complex analysis were used, with the help of which the existence and uniqueness theorem for the solution of the investigated problem is proved. Also, a method of reducing the investigated problem to an equivalent system of singular integral equations is shown, also, a method for solving this system is proposed, which allows to obtain a solution to the problem in explicit form.

Method of Principal Informative Components in Problems of Statistical Measurements of Signal Parameters (Systematic Review)

The method of Principal Informative Components (PIC) is presented for problems of statistical measurements, where the signal to be measured cannot be directly observed. Such situations include image reconstruction, system identification, communication channel reversal, media tomography, etc. The common feature of such problems, usually, is instability of their solutions to small variations of initial data that generally require the attraction of special methods of regularization. The basic principle of PIC method consists in employing decomposition of signals in special bases that were formed from eigenvectors of Fischer’s information operator. These bases are related to the method of Principal Components Analysis (PCA), which is well known in statistics, however, they have a somewhat different meaning as compared to the PCA method. The review indicates that by using the special procedures for selecting coordinate vectors, it is possible, first, to guarantee the signal estimation stability to unpredictable factors of problem and, second, to ensure a significant reduction of total measurement error as compared to the “direct” signal estimation, i.e., without the use of basis notions. The review presents a substantiation of PIC method application for problems of linear and nonlinear estimation. The composite technique of coordinate basis optimization is also considered that combines advantages of the physical approach (obviousness and effectiveness) with advantages of statistically informative approach (minimization of statistical errors). The specified technique is based on projecting the arbitrary coordinate basis on PIC subspace. As a result, the range of possible fluctuations of signal estimation is reduced and the upper bound of statistical error of signal measurement is lowered. Some numerical estimates of the PIC method efficiency are given using the example of problem of medium acoustic tomography that confirms the general theoretical conclusions. The review includes the analysis of some information technologies, where the ideas of PIC method hold a good promise for practical application. In particular, it is suggested that one of such promising fields can be MIMO systems that play an important part in 5G wireless access systems.

Numerical Solution of Time-Dependent Problems with Different Time Scales

Problems for time-dependent equations in which processes are characterized by different time scales are studied. Parts of the equations describing fast and slow processes are distinguished. The basic features of such problems related to their approximation are taken into account using finer time grids for fast processes. The construction and analysis of inhomogeneous time approximations is based on the theory of additive operator–difference schemes (splitting schemes). To solve time-dependent problems with different time scales, componentwise splitting schemes and vector additive schemes are used. The capabilities of the proposed schemes are illustrated by numerical examples for the time-dependent convection–diffusion problem. If convection is dominant, the convective transfer is computed on a finer time grid.

Linear Inverse Problems for Ultraparabolic Equations: The Case of Unknown Coefficient of Spatial Type

We study the solvability of linear inverse problems for ultraparabolic equations with an unknown coefficient depending only on the spatial variables. The feature of such problems is special overdetermination conditions. We use the method based on reducing the inverse problem to a nonlocal boundary-value problem for ultraparabolic equations.

Optimal dividend and investment problems under Sparre Andersen model

In this paper, we study a class of optimal dividend and investment problems assuming that the underlying reserve process follows the Sparre Andersen model, that is, the claim frequency is a “renewal” process, rather than a standard compound Poisson process. The main feature of such problems is that the underlying reserve dynamics, even in its simplest form, is no longer Markovian. By using the backward Markovization technique, we recast the problem in a Markovian framework with expanded dimension representing the time elapsed after the last claim, with which we investigate the regularity of the value function, and validate the dynamic programming principle. Furthermore, we show that the value function is the unique constrained viscosity solution to the associated HJB equation on a cylindrical domain on which the problem is well defined.

Computational Studies of Connections of Spatial Composite Structures of Space-Rocket Techniques

Objectives: Actuality of the study is determined by a number of technical optimization problems due to singularity of designed objects in creation of large space structures. A characteristic feature of such problems is a combination of requirements for increasing of dimensions and providing sufficient stiffness and reliability in response to minimum mass optimization of load-bearing structure weight. This article discusses the combination of such details of construction as metal bushing and carbon tube by means of a heat-resistant polyurethane adhesive VK-20 modified by carborane compounds. Studies consist of calculation of stress-strain state of adhesive joint to determine the shear and breaking stresses in the contact area between the bonding parts. Assessment of failure-free operation of adhesive joint is also conducted during these studies. Methods: Computational studies of connections for manufacture of spatial composite structures of rocket and space techniques have been conducted by finite element analysis. Findings: Simulation of stress-strain state and assumptions adopted during simulation were described. Improvements: Calculations of stress-strain state have been conducted for model of spatial composite structure of space-rocket techniques.

Necessary Conditions for Adverse Control Problems Expressed by Relaxed Derivatives

This paper provides a framework for deriving a new set of necessary conditions for adverse control problems among two players. The distinguish feature of such problems is that the first player has a priori knowledge on the second player strategy. A subclass of adverse control problems is the one of minimax control problems, which frequently arise in robust dynamic optimization. The conditions derived in this manuscript are expressed in terms of relaxed derivatives: the dual variables and the related functions are limits of computable sequences, obtained by considering a regularized version of the original problem and applying well known necessary condition. This topic was initially treated by J. Warga.

A Survey of Solving Approaches for Multiple Objective Flexible Job Shop Scheduling Problems

Abstract Many real life scheduling problems can be formulated as Flexible Job Shop Scheduling Problems (FJSSPs) which simultaneously optimize several conflicting criteria. A typical feature of such problems is their high computational complexity. The purpose of this paper is to provide a review of the techniques, developed to solve multiple objective FJSSPs during the last decade. These techniques could be classified into two groups: approaches with application of mathematical models and heuristic approaches. Usually hybrid metaheuristic algorithms are proposed for large dimensional real life problems and they outlay the tendency for the future developments of efficient solution approaches for multiple objective FJSSPs.

Index Policies for Shooting Problems

We consider a scenario in which a single Red wishes to shoot at a collection of Blue targets, one at a time, to maximise some measure of return obtained from Blues killed before Red’s own (possible) demise. Such a situation arises in various military contexts, such as the conduct of air defence by Red in the face of Blue SEAD (suppression of enemy air defences). A class of decision processes called multiarmed bandits has been previously deployed to develop optimal policies for Red, in which she attaches a calibrating (Gittins) index to each Blue target and optimally shoots next at the Blue with the largest index value. The current paper seeks to elucidate how a range of developments of index theory are able to accommodate features of such problems, which are of practical military import. Such features include levels of risk to Red that are policy dependent, Red having imperfect information about the Blues she faces, an evolving population of Blue targets, and the possibility of Red disengagement. The paper concludes with a numerical study that both compares the performance of (optimal) index policies to a range of competitors and also demonstrates the value to Red of (optimal) disengagement.

The Pontryagin maximum principle and optimal economic growth problems

This monograph is devoted to the theory of the Pontryagin maximum principle as applied to a special class of optimal control problems that arise in economics when studying economic growth processes. The main distinctive feature of such problems is that the control process is considered on an infinite time interval. In this monograph, we develop a new approximation approach to deriving necessary optimality conditions in the form of the Pontryagin maximum principle for problems with infinite time horizon. The attention is focused on the characterization of the behavior of the adjoint variable and the Hamiltonian of a problem at infinity. The approach proposed is applied to the analysis of the problem of optimal economic growth of a technological follower, a country that absorbs, in its technological sector, part of knowledge produced by a technological leader. By optimizing its growth performance, the technological follower dynamically redistributes available labor resources between the manufacturing and research and development (R&D) sectors of the economy. This problem is of independent interest in the endogenous economic growth theory. Moreover, it serves as an illustration of the approximation approach proposed. The main results presented in this monograph are new. They generalize and strengthen many previous studies in this direction.

Internal boundary layers in a well-mixed equatorial atmosphere/ocean

It is known that a non-viscous homogeneous fluid confined to a rotating spherical shell neither possesses a discrete eigenvalue spectrum nor smooth eigenmodes. Mathematically, the motion of a fluid in a rotating spherical shell is governed by a hyperbolic boundary value problem. Generic features of such problems are singularities in the flow field, referred to as internal boundary layers. Physically, these singularities correspond to wave attractors, that are regions to which all inertial waves in the fluid are inevitably drawn. This focusing results from multiple reflections of the inertial waves at boundaries. Therefore, internal boundary layers typically occur for enclosed fluids. The model studied here is a certain approximation to the equatorial region of a rotating spherical shell. It describes the structure of slow, zonally symmetric inertial waves of a homogeneous fluid in the neighborhood of the equator, enclosed between a flat lower and upper boundary. Exact solutions, computed by a method that can handle hyperbolic boundary value problems, are discussed. Solutions for different frequencies show inertial boundary layers, corresponding with internal wave attractors. The boundary layers consist of alternating shear layers aligned along the wave attractor. They show a self-similar pattern that becomes infinitely thin at the position of the attractor. In addition to the results discussed, the paper is intended to introduce the concept of internal boundary layers and wave attractors to the broader meteorologic and oceanographic community. As in almost all theoretical studies of geophysical flows, strong model simplifications are required to find solutions analytically. Nevertheless, it is believed that this approach is useful to highlight fundamental properties of equatorial internal boundary layers that might be important for atmosphere and ocean.

The direct numerical simulation of two-phase flows with interface capturing methods

Multiphase flows play a central role in problems related to the environment and industry.Common, but significant, features of such problems are complex geometries and topography, transport processes across phase boundaries, and internal interfaces that merge, break, and deform.Requirements to predict fluid motion under such conditions provide significant challenges for computational fluid dynamics, particularly for direct simulation of flows involving internal interfaces.In this paper, we will focus on two models that capture the motion of internal interfaces implicitly and can resolve complex flows down to computational grid sizes. The methods are based on the phase-field approach, which are also applied in its general form to viscoelastic and phase separating polymeric systems—in the latter case using a self-consistent field theoretic approach. For processes occurring over very small length scales, e.g. nucleation and growth, such computations result in finite thickness interfaces and capture the necessary physics.For larger length-scale multiphase structures, the interface becomes a contact discontinuity, and the method smoothly transitions into a level-set-like formulation.However, in this second form the sharp interface is computationally difficult to handle.A variation of the ghost-fluid method in which sharp interfaces can be captured will be presented.Applications will be shown at the two extremes of scales, including early stages of nucleation, growth and coarsening of multiphase structures, as well as macroscopic flows in which length-scales and velocities are large.

A survey on level set methods for inverse problems and optimal design

The aim of this paper is to provide a survey on the recent development in level set methods in inverse problems and optimal design. We give introductions on the general features of such problems involving geometries and on the general framework of the level set method. In subsequent parts we discuss shape sensitivity analysis and its relation to level set methods, various approaches on constructing optimization algorithms based on the level set approach, and special tools needed for the application of level set based optimization methods to ill-posed problems. Furthermore, we provide a review on numerical methods important in this context, and give an overview of applications treated with level set methods. Finally, we provide a discussion of the most challenging and interesting open problems in this field, that might be of interest for scientists who plan to start future research in this field.

ESTIMATING ABUNDANCE FROM REPEATED PRESENCE–ABSENCE DATA OR POINT COUNTS

We describe an approach for estimating occupancy rate or the proportion of area occupied when heterogeneity in detection probability exists as a result of variation in abundance of the organism under study. The key feature of such problems, which we exploit, is that variation in abundance induces variation in detection probability. Thus, heterogeneity in abundance can be modeled as heterogeneity in detection probability. Moreover, this linkage between heterogeneity in abundance and heterogeneity in detection probability allows one to exploit a heterogeneous detection probability model to estimate the underlying distribution of abundances. Therefore, our method allows estimation of abundance from repeated observations of the presence or absence of animals without having to uniquely mark individuals in the population.

A Finite-Difference Method for Nonstationary Convection–Diffusion Problems

Mathematical models of viscous flow problems, in particular, those of hydrodynamic and heat and mass transfer processes, are given by systems of nonlinear second-order partial differential equations that contain terms describing diffusion and transport of a fluid in a moving medium. The convection–diffusion equation can be viewed as a basic equation for such problems. The diffusion of matter is described by second-order terms, and the convection is described by first-order terms. Although the convection is described only by first-order terms, much attention is paid to its approximation. A detailed analysis of numerous finite-difference schemes for hydrodynamic problems can be found in [1–3]. The paper [4] contains a survey of finite-difference methods for stationary and nonstationary convection–diffusion problems, stability estimates, and sufficient conditions for the monotonicity of finite-difference schemes. However, the best finite-difference scheme has not been indicated yet. The present paper deals with the construction of special economical finite-difference schemes that take account of convective and diffusion terms in a unified way. We consider oneand two-dimensional nonstationary convection–diffusion problems, which permit one to take account of the main specific features of such problems and can be used as a basis for the analysis of more complicated equations of hydrodynamics, heat and mass transfer, etc. We present numerical computations for some test problems and give a comparison with the most common finite-difference schemes.

Junctions of singularly degenerating domains with different limit dimensions. II

This paper is aimed at finding asymptotic formulas for solutions to the mixed boundary problem for the Poisson equation in a domain obtained by joining singularly degenerating domains. In this paper, which is the second part of the work (the first part was published in No. 18), the main attention is given to three-dimensional problems in which a thin plate or a periodic family of thin rods is joined to a massive body (the distances between the rods are comparable with the diameters of their cross-sections). The distinctive feature of such problems is that an integral equation arises as one of the limit problems. Bibliography: 48 titles.