Numerical Analysis Of Problem Research Articles

Multi-level structural optimization of thin-walled sections in steel/aluminum vehicle body skeletons

A multi-level matching transformation and optimization design method for complex sections of thin-walled structures in steel/aluminum vehicle body skeleton was proposed. The problems of lengthy body performance numerical analysis and low optimization efficiency were solved by the rapid collaborative optimization of simplified cross-sections and performance of the body skeleton. A complex cross-sections shape library of thin-walled structures in steel/aluminum body skeleton and formulas for solving section mechanical properties were established, which overcame the difficulty of translating simplified cross-sections of thin-walled structures in steel/aluminum body skeleton to actual complex sections. A precise optimization method for complex cross-sections of thin-walled structure controlled by proportional vectors was established, which solved the defect that it was difficult to precisely control the arbitrary change of complex cross-section shape, and provided a new way for lightweight optimization design of complex cross-sections. The proposed method achieved the rapid collaborative design of steel/aluminum body thin-walled structure with complex cross-sections and body skeleton performance through multi-level progressive cross-section matching transformation and optimization. A body skeleton model with actual complex cross-sections was established, and compared with the initial simplified structure, the weight reduction ratio of the body skeleton was up to 6.9 %, and the performance indicators of the body skeleton fully met the design requirements, which verified the effectiveness of the proposed method.

Sums of square roots that are close to an integer

Let k∈N and suppose we are given k integers 1≤a1,…,ak≤n. If a1+…+ak is not an integer, how close can it be to one? When k=1, the distance to the nearest integer is ≳n−1/2. Angluin-Eisenstat observed the bound ≳n−3/2 when k=2. We prove there is a universal c>0 such that, for all k≥2, there exists a ck>0 and k integers in {1,2,…,n} with0<‖a1+…+ak‖≤ck⋅n−c⋅k1/3, where ‖⋅‖ denotes the distance to the nearest integer. This is a case of the square-root sum problem in numerical analysis where the usual cancellation constructions do not apply: already for k=3, the problem appears hard.

Optimization analysis of cold extrusion process parameters for valve screws

This study focuses on valve screws and establishes a cold extrusion simulation model using DEFORM-3D software to analyze the deformation characteristics and influencing factors during the extrusion process. Supported by the theory of rigid-plastic finite element, an orthogonal experimental design is conducted to establish a four-factor three-level simulation scheme with general fillet radius, die clearance, extrusion speed, and friction coefficient as the simulation variables, and maximum equivalent stress on the convex die, forming damage of the blank, and maximum wear depth on the concave die as the objective values. The prediction model based on BP neural network algorithm and orthogonal experimental data shows high accuracy. The optimization problem is simplified into a dimensionless numerical analysis problem using GC grey correlation analysis, and the optimal solutions within each variable range are determined using range analysis. The simulation results after optimization show a 20 5% reduction in maximum equivalent stress on the convex die compared to the original scheme, a 4.9% reduction in forming damage of the extruded part, and a 24.24% reduction in maximum wear depth on the concave die compared to before optimization. The actual verification confirms the good forming effect of valve screw extrusion, with well-formed contours and a uniform surface without wrinkles or defects. Finite element simulation provides valuable guidance for practical production.

Effectiveness of MATLAB and Neural Networks for Solving Nonlinear Equations by Repetitive Methods

Finding solutions to nonlinear equations is not only a matter for mathematicians but is essential in many branches such as physics, statistics, and others. However, some of the nonlinear equations in numerical analysis require a lot of complex calculations to achieve convergence. This leads to many arithmetic errors and is consumed a great effort to solve them. Hence, researchers in numerical analysis use computer programs to find approximate solutions. This study used Matlab and Artificial Neural Networks and applied two different numerical analysis methods. The results from training artificial neural networks by utilizing the Backpropagation algorithm and MATLAB have been compared. The importance of this study lies in shedding light on the capabilities of Matlab and its strength in the field of methods for solving mathematical series, and helps students in mathematics in solving complex equations faster and more accurately, also studying the utilization of Artificial Neural Network algorithms in solving these methods, and clarifying the difference between them and programming Ordinary Matlab and comparing them with ordinary mathematical methods. The findings revealed that Traditional methods need more effort. MATLAB helps. On the other hand, solving numerical analysis problems is easier, faster, more accurate, and more effective. Furthermore, in the case of the Matlab application, the Newton method gave faster and less in the number of steps. Additionally, in training, the neural network based on the Newton method gave results faster depending on the Bisection method.

A lower bound for the dimension of tetrahedral splines in large degree

Splines are piecewise polynomial functions which are continuously differentiable to some order r. For a fixed integer d the space of splines of degree at most d is a finite dimensional vector space, and a largely open problem in numerical analysis is to determine its dimension. While considerable attention has been given to this problem in the bivariate setting, the literature on trivariate splines is less conclusive. In particular, the dimension of generic trivariate splines is not known even in large degree when r>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r>1$$\\end{document}. In this paper we use a bound we previously derived for splines on vertex stars to compute a new lower bound on the dimension of trivariate splines in large enough degree. We illustrate in several examples that our formula gives the exact dimension of the spline space in large enough degree if vertex positions are generic. In contrast, for splines continuously differentiable of order r>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r>1$$\\end{document}, every lower bound in the literature diverges (often significantly) in large degree from the dimension of the spline space in these examples. We derive the bound using commutative and homological algebra.

Optimal design of the forced oscillation frequencies of the minimum surface shell on a circular contour consisting of two inclined ellipses under thermal and power loading

The problem of choosing the optimal design solution is a multi-purpose complex task, the solution of which requires taking into account a wide range of requirements for different stages of implementation. There are several levels of solving optimal design problems. The first level deals with general design models, including the main structural elements, taking into account the physical and geometric features of their behavior. This level can be called the "global" level of optimization. Due to the fact that the automated calculation of structures is impossible without the use of finite element models, and at the next "detailed" level, the parameters that make up this model (coordinates of nodes, physical and geometric properties of individual elements, etc.)&#x0D; The choice of a finite element model for optimal design is directly related to the complexity (the possibility of computer implementation) of the optimal design problem. To reduce the computational procedures associated with solving the problem of numerical analysis, an approach based on the approximation of system parameters (displacements, forces, frequencies, waveforms, etc.) can be used.&#x0D; The problem of forced oscillations for shells of minimal surfaces is solved by the finite element method using the Lagrange's variational principle. The potential and kinetic deformation energies of the shell of a minimal surface are defined in matrix form as the sum of the potential and kinetic energies of each finite element.&#x0D; The optimization algorithm for single-criterion parametric optimization is performed as follows: the objective function is the weight of the shell of the minimum surface on a circular contour consisting of two inclined ellipses, the design variables are the thickness of the shell, and the constraints are represented by the first forced vibration frequency. The results of changing the objective function are a decrease in the weight of the shell by 3050 kg of C240 steel, which is a percentage equivalent of 13.4% without loss of strength and stability of the shell of the minimum surface on a circular contour consisting of two inclined ellipses, which proves the effectiveness of the authors' methodology.

Numerical Analysis of a Swelling Poro-Thermoelastic Problem with Second Sound

In this paper, we analyze, from the numerical point of view, a swelling porous thermo-elastic problem. The so-called second-sound effect is introduced and modeled by using the simplest Maxwell–Cattaneo law. This problem leads to a coupled system which is written by using the displacements of the fluid and the solid, the temperature and the heat flux. The numerical analysis of this problem is performed applying the classical finite element method with linear elements for the spatial approximation and the backward Euler scheme for the discretization of the time derivatives. Then, we prove the stability of the discrete solutions and we provide an a priori error analysis. Finally, some numerical simulations are performed to demonstrate the accuracy of the approximations, the exponential decay of the discrete energy and the dependence on a coupling parameter.

Mini-Workshop: Interpolation, Approximation, and Algebra

This report involves two concepts of geometric modeling: multivariate data interpolation by polynomials, and the study of generalized barycentric coordinates. These topics are connected to a wide range of of applications, from computer aided design (CAD) systems for designing airplanes and automobiles to animation in movies to problems in numerical analysis and partial differential equations. Traditionally these topics were studied mostly from an analytic standpoint, but recently advanced algebraic tools have come into the picture. The purpose of the mini-workshop was to bring together a diverse group of researchers with different areas of expertise, drawing from both the approximation theory and algebraic geometry communities, and to explore the connections between the two areas in greater detail.

USING THE GREEN – RVACHEV’S QUASIFUNCTIONS METHOD IN THE NUMERICAL ANALYSIS OF ONE ELECTROSTATIC NANOELECTROMECHANICAL SYSTEM

The problem of numerical analysis of one electrostatic nanoelectromechanical system is considered in the article. Nanoelectromechanical systems are miniature devices that combine electronic and mechanical components of micro and nano sizes. Electrostatic actuation of the mechanical components of such systems is one of the most common types of actuation and that used in accelerometers, switches, micro-mirrors, micro-resonators, etc. The disadvantages of such devices are related to the pull-in instability. This effect occurs when the voltage applied to the moving electrode exceeds a critical value, causing the system to lose its stationary configuration. A semi-linear elliptic equation with the Laplace operator and the first boundary condition was used for mathematical modeling of the process. To construct an approximate solution of the problem, it is suggested to use the methods of nonlinear analysis in semi-ordered spaces, in particular, the results of V. I. Opoitsev on the solvability of nonlinear operator equations with a heterotone operator. The boundary value problem modeling the nanoelectromechanical system is reduced to the integral Urysohn’s equation using the Green – Rvachev’s quasi-function method, which allows us to expand the application of the two-sided approximation method for domains of fairly arbitrary geometry. The article substantiates the possibility of constructing two-sided approximations to a positive solution of the problem, namely: a computational scheme is given, conditions for its convergence to a single positive solution of the problem under consideration are obtained, and an error estimate is obtained. The method is illustrated by computational experiments for a problem considered in a rectangular domain. The results of computational experiments are presented in the form of numerical and graphical information.

Pseudospectral Shattering, the Sign Function, and Diagonalization in Nearly Matrix Multiplication Time

We exhibit a randomized algorithm which, given a square matrix A∈Cn×n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A\\in \\mathbb {C}^{n\ imes n}$$\\end{document} with ‖A‖≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Vert A\\Vert \\le 1$$\\end{document} and δ>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta >0$$\\end{document}, computes with high probability an invertible V and diagonal D such that ‖A-VDV-1‖≤δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\Vert A-VDV^{-1}\\Vert \\le \\delta $$\\end{document} using O(TMM(n)log2(n/δ))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(T_\\mathsf {MM}(n)\\log ^2(n/\\delta ))$$\\end{document} arithmetic operations, in finite arithmetic with O(log4(n/δ)logn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(\\log ^4(n/\\delta )\\log n)$$\\end{document} bits of precision. The computed similarity V additionally satisfies ‖V‖‖V-1‖≤O(n2.5/δ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Vert V\\Vert \\Vert V^{-1}\\Vert \\le O(n^{2.5}/\\delta )$$\\end{document}. Here TMM(n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_\\mathsf {MM}(n)$$\\end{document} is the number of arithmetic operations required to multiply two n×n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\ imes n$$\\end{document} complex matrices numerically stably, known to satisfy TMM(n)=O(nω+η)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_\\mathsf {MM}(n)=O(n^{\\omega +\\eta })$$\\end{document} for every η>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta >0$$\\end{document} where ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} is the exponent of matrix multiplication (Demmel et al. in Numer Math 108(1):59–91, 2007). The algorithm is a variant of the spectral bisection algorithm in numerical linear algebra (Beavers Jr. and Denman in Numer Math 21(1-2):143–169, 1974) with a crucial Gaussian perturbation preprocessing step. Our result significantly improves the previously best-known provable running times of O(n10/δ2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n^{10}/\\delta ^2)$$\\end{document} arithmetic operations for diagonalization of general matrices (Armentano et al. in J Eur Math Soc 20(6):1375–1437, 2018) and (with regard to the dependence on n) O(n3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n^3)$$\\end{document} arithmetic operations for Hermitian matrices (Dekker and Traub in Linear Algebra Appl 4:137–154, 1971). It is the first algorithm to achieve nearly matrix multiplication time for diagonalization in any model of computation (real arithmetic, rational arithmetic, or finite arithmetic), thereby matching the complexity of other dense linear algebra operations such as inversion and QR factorization up to polylogarithmic factors. The proof rests on two new ingredients. (1) We show that adding a small complex Gaussian perturbation to any matrix splits its pseudospectrum into n small well-separated components. In particular, this implies that the eigenvalues of the perturbed matrix have a large minimum gap, a property of independent interest in random matrix theory. (2) We give a rigorous analysis of Roberts’ Newton iteration method (Roberts in Int J Control 32(4):677–687, 1980) for computing the sign function of a matrix in finite arithmetic, itself an open problem in numerical analysis since at least 1986.

Bounds-constrained polynomial approximation using the Bernstein basis

A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In this paper, we consider the problem of constructioning such approximations using polynomials in the Bernstein basis. We consider a family of inequality-constrained quadratic programs. In the univariate case, a quadratic cone constraint allows us to search over all nonnegative polynomials of a given degree. In both the univariate and multivariate cases, we consider approximate problems with linear inequality constraints. Additionally, our method can be modified slightly to include equality constraints such as mass preservation.

Numerical Analysis and Scientific Calculation Considering the Management Mechanism of College Students’ Innovation and Entrepreneurship Education

Purpose. This article aims to study how to analyze and study the numerical value of education management mechanisms based on cloud computing and describe the innovation and entrepreneurship of college students. Methodology. This article addresses the problems of numerical analysis and scientific computing. This problem is based on cloud computing, so it elaborates on the concepts and related algorithms of cloud computing and big data and designs and analyzes cases of numerical analysis and scientific computing of educational management mechanisms. Research Findings. Through the research of different kernel functions, the IG_CDmRMR algorithm can obtain relatively high accuracy results for numerical analysis and scientific computing. The IG_CDmRMR algorithm is the closest to expert evaluation. The maximum difference is 0.002, which is consistent in sample three. The maximum difference of the IG algorithm is 0.005, and the minimum difference is 0.002. The evaluation effect of the IG_CDmRMR algorithm is closer to the evaluation effect of experts. Practical Implications. It analyzes the numerical value of the education management mechanism and finds that the accuracy has a certain height. This has certain evaluation significance for the management mechanism of college students’ innovation and entrepreneurship education.

Classical Computer Assisted Analysis of Small Multiqudit Systems

Quantum computation model is regarded as a model which can overcome barriers in calculations efficiency of problems which appear in modern science. In spite of hardware development, in particular a recent emergence of several different physical installations of the pioneering quantum machines, the contemporary and numerical analysis of problems concerning quantum computing is very important. In the first part of this article, some useful computing techniques for quantum registers processed by a quantum circuits are presented. Applied classical parallel computational techniques are utilised to shorten the whole computational time. New methods of processing state vectors for qudits and density matrices are presented, indicating which operations may be performed in parallel in the context of the implementation of local unitary operations. There is also shown, how to use the reduction operation in parallel implementation of the von Neumann measurement by performing local measurements on a system of qudits. In addition to the purely technical results as described above, the paper includes also a bunch of purely theoretical results which substitute a solid mathematical ground for the computations performed with the help of the computational routines as described in Section III. In particular, a discussion concerning general multi-qudit quantum states through the prism of Entropy and Negativity measures of entanglement included in has been presented. Additionally, the notion of the total entanglement has been introduced. For certain classes of popular multi-qudit states, the introduced deficits of entanglement defined with the use of von Neumann Entropy and Negativity have been discussed. In particular, by the use of Gram matrix technique, the corresponding deficits of entanglement in the analysed states have been computed in an explicite way. Additionally, some new results on AME states for some multiqudit systems are also included in Section V. The last part of the article presents some numerical experiments on multi-qudit entanglement and determination of total entanglement values for convex combinations of GHZ andWstates. Some details concerning technical nature of results are included in the attached Appendix A.

An Ulm-Type Inverse-Free Iterative Scheme for Fredholm Integral Equations of Second Kind

In this paper, we present an iterative method based on the well-known Ulm’s method to numerically solve Fredholm integral equations of the second kind. We support our strategy in the symmetry between two well-known problems in Numerical Analysis: the solution of linear integral equations and the approximation of inverse operators. In this way, we obtain a two-folded algorithm that allows us to approximate, with quadratic order of convergence, the solution of the integral equation as well as the inverses at the solution of the derivative of the operator related to the problem. We have studied the semilocal convergence of the method and we have obtained the expression of the method in a particular case, given by some adequate initial choices. The theoretical results are illustrated with two applications to integral equations, given by symmetric non-separable kernels.

A shooting approach to the scaled boundary finite element equations of elastodynamics in the frequency domain

Dealing with numerical analysis of problems, especially ones with semi-infinite boundaries, scaled boundary finite element method has emerged as one of the efficient tools for the task. Combining the exactness of strong forms with the flexibility of weak formulations makes the method an improvement to its predecessors. Problem with the method arises when the analytical solution of the semi-discretized system is not available, which is the case for numerous problems. In the most recent attempt to solve the issue, a shooting method was proposed for elastostatic problems. Generality of the method removes any concerns regarding the type of governing equations since it no longer needs any analytical solutions. In this study, the method is further developed to deal with elastodynamic problems of viscoelastic media in the frequency domain, for which the closed-form solution is not available. Adopting the shooting method, the two-point boundary value problem of each subdomain is treated as a second-order initial value problem. Boundary conditions of the bounded subdomains are formulated by enforcing equilibrium at both ends. On the other hand, in contrast to linear elasticity, neither forces nor displacements vanish at infinity. As a result, a special treatment is required to deal with the boundary conditions of the unbounded subdomains. A Runge–Kutta–Nyström method, which consists of an embedded pair of adjacent order, is utilized to integrate the strong form of oscillatory equations enabling local error estimation and adaptive step-size control. This guarantees efficiency since the integration proceeds not by equal step-sizes, but by equal user-defined local errors. In the first step, analytical solution of a viscoelastic half-space subjected to a harmonic strip load is used for the verification process. First, the half-space is discretized by Voronoi cells and each truncated edge is defined using an unbounded subdomain. Next, one bounded subdomain is used to define the whole bounded area, and one unbounded subdomain resembles the radiation condition of the far-field boundaries. For the cases involving only bounded subdomains, three other numerical tests, including a perforated plate, an L-shaped panel, and a bi-material specimen are employed, and the effect of discretization method on the results is analyzed. The method is a huge step forward since the size of subdomains are not restricted, far-field boundaries can be arbitrary-shaped, hysteretic damping can be naturally included, no additional unknowns are introduced, no compound matrices are defined, no preconditioning matrices are needed, and a simple unified approach is used for both bounded and unbounded subdomains.

Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks

We perform a comprehensive numerical study of the effect of approximation-theoretical results for neural networks on practical learning problems in the context of numerical analysis. As the underlying model, we study the machine-learning-based solution of parametric partial differential equations. Here, approximation theory for fully-connected neural networks predicts that the performance of the model should depend only very mildly on the dimension of the parameter space and is determined by the intrinsic dimension of the solution manifold of the parametric partial differential equation. We use various methods to establish comparability between test-cases by minimizing the effect of the choice of test-cases on the optimization and sampling aspects of the learning problem. We find strong support for the hypothesis that approximation-theoretical effects heavily influence the practical behavior of learning problems in numerical analysis. Turning to practically more successful and modern architectures, at the end of this study we derive improved error bounds by focusing on convolutional neural networks.

Mathematical methods for optimal synthesis of physical and mechanical structure of composites with required set of properties at extreme conditions

Variational statements of composite structure with the required set of properties synthesis problems are investigated. The study of the limiting capabilities of composites to achieve required set of properties is necessarily associated with development of effective methods for finding global extremum of corresponding functionals. The article deals with problems of numerical analysis and optimal design of composite structure with required set of properties. Mathematical models describing the propagation of wave processes of various physical nature in layered-inhomogeneous structure of composite are investigated. Problems of optimal design for composite structure with required set of properties are formulated in variational formulation. Based on the theory of multi-valued mappings and methods of continuation by parameter, method for studying limiting capabilities of composites to achieve required set of properties is developed. Developed technique allows effective construction of layered composites with complex characteristics. The application of developed method of optimal synthesis for the study of limiting possibilities in reflection of energy of wave action from layered-inhomogeneous coating in given range of spectrum is considered.

Seismic Performance of a Three-Story Reinforced Concrete Building with Masonry Infill Walls and Friction Base Support

The stiffness of masonry infill walls is commonly neglected in design practice of Reinforced Concrete (RC) structures. In fact, the stiffness of masonry infill wall may significantly influence seismic performance and dynamic behavior of RC buildings. In this research, influence of masonry infill walls to the structural performance of a three-story RC frame is investigated. In addition, possible application of friction-based support is also studied. Full 3D non-linear time history analysis is conducted to observe behavior of the structure under two-directional ground motion. In the analysis, any failed elements are removed subsequently from the model to avoid numerical analysis problem. The result shows that the placement of masonry infill walls can significantly influence the structural behavior of RC structure. Inappropriate placement of masonry wall may lead the building undergo soft-story mechanism. It is also found that the use of friction-based support can effectively improve the seismic performance of the building.

Проблемы развития делового климата в депрессивном регионе

The Novgorod region has an exceptionally favorable geographical position, however, during the period of the general recession of the country's economy, the enterprises located in it turned out to be uncompetitive, sharply reducing their production. In modern conditions the most numerous sector of the economy are representatives of small and medium-sized businesses, which are targeted by programs of the Bank of Russia to support and stimulate their development. The Novgorod region created a municipal program for the development of this sector of the economy, which defines a set of various arrangements, the main goal of which is to provide absolute access to financial and other resources. In addition to these events, training activities are carried out, consisting in the provision of information seminars in various forms for representatives of this sector. The article presents an analysis of numerous problems in entrepreneurship development in the region of Novgorod, as well as specifies the theoretical aspects of changing the business climate. The justifications for necessary state support of small and medium-sized business subjects are highlighted. The research emphasizes two main problems of entrepreneurial activity: the socio-economic development of the Novgorod region and the development of small and medium-sized business subjects.

A strength criterion for rocks

A simple strength criterion J2=α+βσ3 is investigated to describe the ultimate stress capacity of rocks. This criterion takes the intermediate principal stress σ2 into consideration. The nonlinear parabolic form on the meridian plane makes the present criterion is more suitable in rock mechanics than the linear Mohr–Coulomb failure criterion. The present criterion has only 3 corners on the π plane, resulting in higher efficiency and reliability in solving the corner problems in numerical analysis than Mohr-Coulomb and Hoek-Brown criteria. Comparison by the experimental results indicates that the proposed strength criterion gives a better agreement with experimental data than Mohr-Coulomb, Hoek-Brown, Drucker-Prager and modified Lade-Duncan criteria.