Solution Of Variational Problem Research Articles

Multi-CPU Parallel Computing System with Mixed Modes

Multi-CPU[1] parallel computing system [2] with mixed modes is the product of parallel computing idea. Control system cannot guarantee real-time control performance due to limitation of computing speed while utilizing complex control algorithms, so operating efficiency of the system needs to be solved. High-speed computing [3] system is needed. Parallel algorithm [4][5] is an effective way to improve computing speed. Mixed-mode parallel computing system is a hardware platform with multiple parallel computing modes. Users can directly change the connecting mode between computing modules through jumper, and the diversity of communication modes provides solutions for various problems.

On- and off-resonance radiation-atom-coupling matrix elements involving extended atomic wave functions

In continuation of our earlier works, we present results concerning the computation of matrix elements of the multipolar Hamiltonian (MPH) between extended wave functions that are obtained numerically. The choice of the MPH is discussed in connection with the broader issue of the form of radiation-atom (or -molecule) interaction that is appropriate for the systematic solution of various problems of matter-radiation interaction. We derive analytic formulas, in terms of the sine-integral function and spherical Bessel functions of various orders, for the cumulative radial integrals that were obtained and calculated by Komninos, Mercouris, and Nicolaides [Phys. Rev. A 71, 023410 (2005)]. This development allows the much faster and more accurate computation of such matrix elements, a fact that enhances the efficiency with which the time-dependent Schr\odinger equation is solved nonperturbatively, in the framework of the state-specific expansion approach. The formulas are applicable to the general case where a pair of orbitals with angular parts $|{\ensuremath{\ell}}_{1},\phantom{\rule{1.0pt}{0ex}}\phantom{\rule{1.0pt}{0ex}}{m}_{1}\ensuremath{\rangle}$ and $|{\ensuremath{\ell}}_{2},\phantom{\rule{1.0pt}{0ex}}\phantom{\rule{1.0pt}{0ex}}{m}_{2}\ensuremath{\rangle}$ are coupled radiatively. As a test case, we calculate the matrix elements of the electric field and of the paramagnetic operators for on- and off-resonance transitions, between hydrogenic circular states of high angular momentum, whose quantum numbers are chosen so as to satisfy electric dipole and electric quadrupole selection rules. Because of the nature of their wave function (they are nodeless and the large centrifugal barrier keeps their overwhelming part at large distances from the nucleus), the validity of the electric dipole approximation in various applications where the off-resonance couplings must be considered becomes precarious. For example, for the transition from the circular state with $n$ = 20 to that with $n$ = 21, for which $\ensuremath{\langle}r\ensuremath{\rangle}\ensuremath{\approx}400$ a.u., the dipole approximation starts to fail already at XUV wavelengths ($\ensuremath{\lambda}l125\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$).

An algorithm for finding common solutions of various problems in nonlinear operator theory

Abstract In this paper, it is our aim to prove strong convergence of a new iterative algorithm to a common element of the set of solutions of a finite family of classical equilibrium problems; a common set of zeros of a finite family of inverse strongly monotone operators; the set of common fixed points of a finite family of quasi-nonexpansive mappings; and the set of common fixed points of a finite family of continuous pseudocontractive mappings in Hilbert spaces on assumption that the intersection of the aforementioned sets is not empty. Moreover, the common element is shown to be the metric projection of the initial guess on the intersection of these sets. MSC:47H06, 47H09, 47J05, 47J25.

Convergence theorems for common solutions of various problems with nonlinear mapping

In this paper, motivated and inspired by Zegeye and Shahzad (Nonlinear Anal. 70:2707-2716, 2009), Qin et al. (J. Comput. Appl. Math. 225(1):20-30, 2009) and Kimura and Takahashi (J. Math. Anal. Appl. 357:356-363, 2009), we introduce a new hybrid projection iterative scheme that converges strongly to a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of common fixed points for a family of hemi-relatively nonexpansive mappings in a Banach space.MSC:47H10, 47J20, 49J40.

A Study on Imposing Exact Solutions as Internal Boundary Conditions in Simulating Shallow-water Flows over a Step

이 연구에서는 계단과 같이 불연속 횡단 구조물을 지나는 천수 흐름에 대해 내부 경계조건으로서 정확해를 부여하는 기법을 제안하였다. 제안된 기법의 검토를 위해 MUSCL이 적용된 HLLL 근사 Riemann 해법을 이용하였다. 계단을 지나는 천수 흐름에 대한 다양한 문제에서 모의 결과는 정확해와 잘 일치하였다. 또한, 계단에서 댐 붕괴 실험 및 급경사 수로 실험의 결과와 부합되었다. 개발된 모형으로 낙차공과 같이 불연속 바닥을 지나는 천수 흐름에 대해 별도의 수위-유량 관계나 지형의 완화 없이 모의가 가능하다. 향후, 계단에 의한 흐름 저항과 수맥에 의한 에너지 손실에 대해 적절한 평가가 이루어진다면, 보나 옹벽(강변 도로)과 같은 불연속 지형을 넘나드는 천수 흐름에 대한 수치모의가 가능할 것으로 기대된다. In this study, was proposed a numerical scheme imposing exact solutions as the internal boundary conditions for the shallow-water flows over a discontinuous transverse structure such as a step. The HLLL approximate Riemann solver with the MUSCL was used for the test of the proposed scheme. Very good agreement was obtained between simulations and exact solutions for various problems of the shallow-water flows over a step. In addition, results by the numerical model showed good agreement with those of dam-break experiments over a step and stepped chute one. Developed model can simulate the shallow-water flows over discontinuous bottom such as a drop structure without additional rating curve or topography smoothing. Given the proper evaluations for the flow resistance by a step and the energy loss by the nappe flow in the future, could be simulated flooding and drying of the shallow-water flows over discontinuous topography such as a weir or the river road with retaining wall.

Natural Language Processing and its Use in Education

Natural Language Processing (NLP) is an effective approach for bringing improvement in educational setting. Implementing NLP involves initiating the process of learning through the natural acquisition in the educational systems. It is based on effective approaches for providing a solution for various problems and issues in education. Natural Language Processing provides solution in a variety of different fields associated with the social and cultural context of language learning. It is an effective approach for teachers, students, authors and educators for providing assistance for writing, analysis, and assessment procedures. Natural Language Processing is widely integrated with the large number of educational contexts such as research, science, linguistics, e-learning, evaluations system, and contributes resulting positive outcomes in other educational settings such as schools, higher education system, and universities. The paper aims to address the process of natural language learning and its implication in the educational settings. The study also highlights how NLP can be utilized with scientific computer programs to enhance the process of education. The study follows qualitative approach. Data is collected from the secondary resources in order to identify problems faced by the teachers and students for understanding the context due to obstacles of language. Results provide effectiveness of linguistic tools such as grammar, syntax, and textual patterns that are fairly productive in educational context for learning and assessment.

Современное состояние исследований в области обфускации программ: определения стойкости обфускации

Program obfuscation is a semantic-preserving transformation aimed at bringing a program into such a form, which impedes the understanding of its algorithm and data structures or prevents extracting of some valuable information from the text of a program. Since obfuscation could find wide use in computer security, information hiding and cryptography, security requirements to program obfuscators became a major focus of interests for pioneers of theory of software obfuscation. In this paper we give a survey of various definitions of obfuscation security and main results that establish possibility or impossibility of secure program obfuscation under certain cryptographic assumptions. We begin with a short retrospective survey on the origin and development of program obfuscation concept in software engineering and mathematical cryptography. In the introduction we also point out on the main difficulties in the development of practical and secure obfuscation techniques. In the next section we discuss the main line of research in the application of program obfuscation to the solution of various problems in system programming and software security. Finally, in section 3 we present and discuss a compendium of formal definitions of the program obfuscation concept developed so far in mathematical cryptography - black-box obfuscation, gray-box obfuscation, the best possible obfuscation, obfuscation with auxiliary inputs, etc.. We also make a comparative analysis of these definitions and present the main results on the (im)possibility of secure program obfuscation w.r.t. every such definition.

Plough body breast surface plotting by means of variational problem solution

The work minimization problem of soil motion on plough body breast surface was solved by the variational method.

BIOCAT: a pattern recognition platform for customizable biological image classification and annotation

BackgroundPattern recognition algorithms are useful in bioimage informatics applications such as quantifying cellular and subcellular objects, annotating gene expressions, and classifying phenotypes. To provide effective and efficient image classification and annotation for the ever-increasing microscopic images, it is desirable to have tools that can combine and compare various algorithms, and build customizable solution for different biological problems. However, current tools often offer a limited solution in generating user-friendly and extensible tools for annotating higher dimensional images that correspond to multiple complicated categories.ResultsWe develop the BIOimage Classification and Annotation Tool (BIOCAT). It is able to apply pattern recognition algorithms to two- and three-dimensional biological image sets as well as regions of interest (ROIs) in individual images for automatic classification and annotation. We also propose a 3D anisotropic wavelet feature extractor for extracting textural features from 3D images with xy-z resolution disparity. The extractor is one of the about 20 built-in algorithms of feature extractors, selectors and classifiers in BIOCAT. The algorithms are modularized so that they can be “chained” in a customizable way to form adaptive solution for various problems, and the plugin-based extensibility gives the tool an open architecture to incorporate future algorithms. We have applied BIOCAT to classification and annotation of images and ROIs of different properties with applications in cell biology and neuroscience.ConclusionsBIOCAT provides a user-friendly, portable platform for pattern recognition based biological image classification of two- and three- dimensional images and ROIs. We show, via diverse case studies, that different algorithms and their combinations have different suitability for various problems. The customizability of BIOCAT is thus expected to be useful for providing effective and efficient solutions for a variety of biological problems involving image classification and annotation. We also demonstrate the effectiveness of 3D anisotropic wavelet in classifying both 3D image sets and ROIs.

Research on Optimization of Renewal Project Planning System of the Industrial Cities

The urban renewal is not a simple reconstruction by demolition for the urban material substances, but its a kind of the artificial behavior to promote solution of various problems which can affect and hinder the urban development and obtain sustainable development. The renewal project planning of the industrial cities is a continuous, dynamic, long-term development process, in this process, emphasizing the application of the optimization of the forward-looking, dynamic and comprehensive renewal planning system has an important guiding significance on the sustainable development of the cities.

Adaptive meshless local maximum-entropy finite element method for convection–diffusion problems

In this paper, a meshless local maximum-entropy finite element method (LME-FEM) is proposed to solve 1D Poisson equation and steady state convection---diffusion problems at various Peclet numbers in both 1D and 2D. By using local maximum-entropy (LME) approximation scheme to construct the element shape functions in the formulation of finite element method (FEM), additional nodes can be introduced within element without any mesh refinement to increase the accuracy of numerical approximation of unknown function, which procedure is similar to conventional p-refinement but without increasing the element connectivity to avoid the high conditioning matrix. The resulted LME-FEM preserves several significant characteristics of conventional FEM such as Kronecker-delta property on element vertices, partition of unity of shape function and exact reproduction of constant and linear functions. Furthermore, according to the essential properties of LME approximation scheme, nodes can be introduced in an arbitrary way and the $$C^0$$ C 0 continuity of the shape function along element edge is kept at the same time. No transition element is needed to connect elements of different orders. The property of arbitrary local refinement makes LME-FEM be a numerical method that can adaptively solve the numerical solutions of various problems where troublesome local mesh refinement is in general necessary to obtain reasonable solutions. Several numerical examples with dramatically varying solutions are presented to test the capability of the current method. The numerical results show that LME-FEM can obtain much better and stable solutions than conventional FEM with linear element.

ASSESSING CONCEPTUAL UNDERSTANDING IN MATHEMATICS: Using Derivative Function to Solve Connected Problems

Open and distance education plays an important role in the actualization of cultural goals as well as in societal developments. This is an independent teaching and learning method for mathematics which forms the dynamic of scientific thinking. Distance education is an important alternative to traditional teaching applications. These contributions brought by technology enable students to participate actively in having access to information and questioning it. Such an application increases students’ motivation and teaches how mathematics can be used in daily life. Derivative is a mathematical concept which can be used in many areas of daily life. The aim of this study is to enable the concept of derivatives to be understood well by using the derivative function in the solution of various problems. It also aims at interpreting difficulties theoretically in the solution of problems and determining mistakes in terms of teaching methods. In this study, how various aspects of derivatives are understood is emphasized. These aspects concern the explanation of concepts and process, and also their application to certain concepts in physics. Students’ depth of understanding of derivatives was analyzed based on two aspects of understanding; theoretical analysis and contextual application. Follow-up interviews were conducted with five students. The results show that the students preferred to apply an algebraic symbolic aspect instead of using logical meanings of function and its derivative. In addition, in relation to how the graph of the derivative function affects the aspect of function, it was determined that the students displayed low performance.

Los valores en la evaluación del aprendizaje en la formación de las disciplinas de los negocios

El aprendizaje se puede definir como el cambio de conducta que tiene un alumno, más o menos permanente, por tanto, su evaluación es indispensable para comprobar la capacidad para la toma de decisiones orientadas a la solución de diversas problemáticas que se le presentarán al profesionista, es decir, para modificar y mejorar el aprendizaje durante el período de enseñanza desde la formación básica, la función de la evaluación es eminentemente pedagógica ya que se realiza para obtener la información necesaria para dimensionar el proceso de cambio, en el llamado “proceso formativo”, ello constituye lo que en las sociedades del conocimiento, se denomina “el saber”, es en este momento en el que juega un rol trascendente un ingrediente especial, la capitalización de los “valores de la persona” como elemento imprescindible para lograr una formación integral y continuar por la derecha en la vida.

A General Approximation Scheme for Solutions of Various Problems in Fixed Point Theory

It is our aim to prove strong convergence of a new iterative sequence to a common element of the solution set of a generalized mixed equilibrium problem; the null space of an inverse strongly monotone operator; the set of common fixed points of a countable infinite family of nonexpansive mappings; and the set of fixed points of a continuous pseudocontractive mapping. Moreover, the common element is also a unique solution of a variational inequality problem and optimality condition for a certain minimization problem. Our theorems generalize, improve, and unify several recently announced results.

浅析我国大型超市的服务竞争策略

随着我国改革开放的不断深化以及全球经济一体化发展的趋势，我国的大型超市面临着国内和国际企业的双重竞争。科技的迅猛发展使得产品的差距越来越小，传统的营销策略实践活动越来越难以维护顾客忠诚，实现企业预期的营销目标。我国的大型超市如何在众多的竞争对手当中脱颖而出，服务就成为企业制胜的有力武器。当代的消费者追求的不仅仅是买到东西，更重要的是一种购物体验。超市如何通过提供各种个性化的服务来提高顾客满意程度实现顾客忠诚，从而巩固企业的市场份额，提高企业的核心竞争力就显得尤为重要。本文通过分析影响大型超市消费者满意程度的因素，着重分析了超市服务对消费者满意的影响，系统分析了我国大型超市在服务方面存在的问题，并结合我国消费者的特点针对我国大型超市在服务方面存在的各种问题提出了一套完整的，具有针对性的可行性的解决方案。 With the deepening of China’s opening-up and global economic integration, China’s large supermarkets are faced with competition from both internal and external companies. What’s more, rapid development of science and technology makes smaller product differentiation. As a result, traditional marketing strategies and practice activities have more difficulties in maintaining customer loyalty and achieving the expected business marketing goals. How do China’s large supermarkets stand out among competitors? Consumer service has become a powerful weapon for winning business. Contemporary consumers expect not only to buy something, more important, but to seek a shopping satisfaction. Therefore, in order to enhance customer satisfaction, achieve customer loyalty, consolidate market share and improve the core competitiveness of enterprises, a variety of personalized services offered by China’s large supermarkets are particularly important. By analyzing impact factors on consumer satisfaction, especially supermarkets’ services on consumer satisfaction, exploring the existing problems of large supermarkets’ services, and integrating the consumer’s characteristics, this paper proposes targeted and practical solutions for various problems which existed on China’s large supermarket services.

The finite element method enriched by interpolation covers

In this paper, we focus on an enriched finite element solution procedure for low-order elements based on the use of interpolation cover functions. We consider the 3-node triangular and 4-node tetrahedral displacement-based elements for two- and three-dimensional analyses, respectively. The standard finite element shape functions are used with interpolation cover functions over patches of elements to increase the convergence of the finite element scheme. The cover functions not only capture higher gradients of a field variable but also smooth out inter-element stress jumps. Since the order of the interpolations in the covers can vary, the method provides flexibility to use different covers for different patches and increases the solution accuracy without any local mesh refinement. As pointed out, the procedure can be derived from various general theoretical approaches and the basic theory has been presented earlier. We evaluate the effectiveness of the method, and illustrate the power of the scheme through the solution of various problems. The method also has potential for the development of error measures.

Convergence to common solutions of various problems for nonexpansive mappings in Hilbert spaces

In this paper, motivated and inspired by Ceng and Yao (J. Comput. Appl. Math. 214(1):186-201, 2008), Iiduka and Takahashi (Nonlinear Anal. 61(3):341-350, 2005), Jaiboon and Kumam (Nonlinear Anal. 73(5):1180-1202, 2010), Kim (Nonlinear Anal. 73:3413-3419, 2010), Marino and Xu (J. Math. Anal. Appl. 318:43-52, 2006) and Saeidi (Nonlinear Anal. 70:4195-4208, 2009), we introduce a new iterative scheme for finding a common element of the set of solutions of a mixed equilibrium problem for an equilibrium bifunction, the set of fixed points of an infinite family of nonexpansive mappings, the set of solutions of some variational inequality problem, and the set of fixed points of a left amenable semigroup of nonexpansive mappings with respect to W-mappings and a left regular sequence of means defined on an appropriate space of bounded real-valued functions of the semigroup S. Furthermore, we prove that the iterative scheme converges strongly to a common element of the above four sets. Our results extend and improve the corresponding results of many others. MSC:43A65, 47H05, 47H09, 47H10, 47J20, 47J25, 74G40.

Ant Colony Optimization in Different Engineering Applications: An Overview

Ant Colony Optimization (ACO) is a technique that was introduced in the early 1990’s and it is inspired by the foraging behavior of ant colonies. ACO algorithms have long been thought as generating high quality solutions for various problems in different Engineering Applications. This survey provides an overview of past and on-going research of ACO in diverse engineering applications pertaining to computer science fields such as mobile and wireless networks, sensor networks, grid computing, P2P Computing, Pervasive computing, Data mining, Software engineering, Database systems, Multicore Processing, Artificial intelligence, Image processing, Biomedical applications and also other domains relevant to Electronics and Electrical Engineering fields. We finally summarize the comprehensive study of applications in all these fields deployed ACO.

Artificial Neural Networks: Theoretical Background and Pharmaceutical Applications: A Review

In recent times, there has been a growing interest in artificial neural networks, which are a rough simulation of the information processing ability of the human brain, as modern and vastly sophisticated computational techniques. This interest has also been reflected in the pharmaceutical sciences. This paper presents a review of articles on the subject of the application of neural networks as effective tools assisting the solution of various problems in science and the pharmaceutical industry, especially those characterized by multivariate and nonlinear dependencies. After a short description of theoretical background and practical basics concerning the computations performed by means of neural networks, the most important pharmaceutical applications of neural networks, with suitable references, are demonstrated. The huge role played by neural networks in pharmaceutical analysis, pharmaceutical technology, and searching for the relationships between the chemical structure and the properties of newly synthesized compounds as candidates for drugs is discussed.

On the Homotopy Analysis Method and Optimal Value of the Convergence Control Parameter: Solution of Euler-Lagrange Equation

This paper presents, an efficient approach for solving Euler-Lagrange Equation which arises from calculus of variations. Homotopy analysis method to find an approximate solution of variational problems is proposed. An optimal value of the convergence control parameter is given through the square residual error. By minimizing the the square residual error, the optimal convergence-control parameters can be obtained. It is showed that the homotopy analysis method was valid and feasible to the study of variational problems.