应用和计算数学考虑发表关于计算和应用数学广泛主题的高质量论文。涵盖的领域和学科包括控制理论、博弈论、网络、优化、计算科学、信息技术、机电一体化以及经济和能源系统。这些和相关领域的原始研究成果，使用最先进的数学工具，在本期刊中找到，一个自然的家，一个更广泛的科学界的出路。应用和计算数学也考虑调查论文、简短的交流和对论文的评论。从事应用数学和计算数学的任何方面工作并希望了解最新进展的读者都可以轻松访问这些论文。

The journal "Applied and Computational Mathematics" is dedicated to publishing high-quality papers on a wide range of topics in computational and applied mathematics. The fields covered include control theory, game theory, networks, optimization, computational science, information technology, mechatronics, as well as economic and energy systems. Original research findings in these areas, utilizing state-of-the-art mathematical tools, find a natural home in this journal, providing an outlet for the broader scientific community. "Applied and Computational Mathematics" also considers survey papers, brief communications, and comments on papers. Readers engaged in any aspect of applied and computational mathematics can easily access these latest developments.

《Applied and Computational Mathematics》期刊致力于发表关于计算和应用数学的高质量论文，涵盖控制理论、博弈论、网络、优化、计算科学、信息技术、机电一体化以及经济和能源系统等广泛领域。这些领域的原创研究成果运用最先进的数学工具，旨在为更广泛的科学界提供一个自然的交流平台。《Applied and Computational Mathematics》也欢迎调查论文、简短交流和对论文的评论。所有从事应用数学和计算数学研究的读者都可以轻松获取这些最新进展。

Applied and Computational Mathematics

The NP-Completeness theory states that exact and efficient algorithms are unlikely to exist for the class of NP-difficult problems. One way to deal with NP hardness is to relax the optimality requirement and look for solutions instead that are close to the optimum. This is the main idea behind the approximation algorithms, which are called heuristic or metaheuristic. The problem of motion estimation is a process with a high degree of computational complexity, it requires sufficient memory space and execution time. It represents the cost of static, dynamic and video image sequence coding. The main task is to minimize the distortion rate and improve visual quality. This makes research in the field of coding, image compression and video focus on finding efficient algorithms to carry out the estimation of movement in a reasonable time. If a list of images of n elements is analyzed, there are feasible solutions. So, an exhaustive search is too slow, even for small values of the solution space. Therefore, from a practical point of view, it is crucial to have efficient and fast heuristic algorithms that avoid thorough search. In this investigation we design and implement heuristic algorithms, based on the frequency domain, which are applied on the coefficients of the discrete transform of the cosine and wavelets. Also, we propose temporal domain algorithms such as block-matching algorithms, which focus your search on the maximum coincidence of the current image with the reference one. The algorithms used during the implementation of this research work were written with the mathematical programming language MATLAB. In addition, we review the basic concepts of image processing, video, compression algorithms and motion estimation frequently used. The evaluation of the algorithms was carried out with a set of images provided by a previous acquisition system. We show the improvement of visual quality, the amount of compressed or reconstructed information and the behavior of the methods in the search for similarities between pixels or images. Finally, we contribute to the dissemination of new lines of scientific research that lead to the expansion and improvement of the study, the generation of new knowledge, since it is a young area within the Education discipline of Nicaragua.

Fernando José Hernández Gómez

Heuristic Algorithms of Coincidence for the Estimation of Movements in Compression of Images

图像压缩中运动估计的匹配启发式算法

The notion of intersection body is introduced by Lutwak in 1988, it is one of important research contents and led to the studies of Busemann-Petty problem in the Brunn-Minkowski theory. Based on the properties of the intersection bodies, Schuster introduced the notion of radial Blaschke-Minkowski homomorphisms and proved a lot of related inequalities. In this paper, by applying the dual mixed volume theory and analytic inequalities, we first give a lower bound of the dual quermassintegrals for the mixed radial Blaschke-Minkowski homomorphisms. As its an application, we get a reverse form of the well-known Busemann intersection inequality. Further, a Brunn-Minkowski type inequality of the Lp radial Minkowski sum for the dual quermassintegrals of mixed radial Blaschke-Minkowski homomorphisms is established, and then the intersection body version of this Brunn-Minkowski type inequality is yielded. From this, we not only extend Schuster's related result but also obtain the Brunn-Minkowski type inequalities of Lp harmonic radial sum and Lp radial Blaschke sum, respectively.

Weidong Wang

Inequalities for the Mixed Radial Blaschke-Minkowski Homomorphisms and the Applications

混合径向Blaschke-Minkowski同态的不等式及其应用

Intuitionistic Fuzzy set (IFS) theory plays an important role in real life and engineering problems. There are many model involving fuzzy matrices to deal with different complicated aspects. Intuitionistic fuzzy set (IFS) is useful in providing a flexible model for developing the uncertainty and vagueness involved in making decisions where the theories of uncertainty are very useful to treat with mathematics that needs to address. In other words, the application of intuitionistic fuzzy sets instead of fuzzy sets means the introduction of another degree of freedom into a set description. Intuitionistic fuzzy set (IFS) called the generalization of fuzzy sets was proposed in K. T. Atanassov. So, we can use it in decision making. We examined the definition of IFS and puts new definitions of IFS (Intuitionistic fuzzy set) in this paper and suggested its implementation in the Corona Covid-19. For several similar real-life cases the suggested approach can be applied.

Abdelmonem Mohamed Kozae

Mohamed Shokry

Manar Omran

Intuitionistic Fuzzy Set and Its Application in Corona Covid-19

直觉模糊集及其在新冠疫情中的应用

The main objective of this paper is to solve numerically the differential equations of fractional order with homogeneous boundary conditions by the Galerkin weighted residual method. In this method, linear combinations of some types of functions are used to find the approximate solutions which must satisfy the homogeneous boundary conditions. Such type of functions should be differentiated and integrated easily, so the piecewise polynomials, namely, Bernstein, Bernoulli and Modified Legendre polynomials are used as basis functions in this paper. The fractional derivatives are used in the conjecture of Riemann-Liouville and Caputo sense. Thus, we develop the Galerkin weighted residual formulation, in matrix form, to the linear fractional order boundary value problems, in details, which is easy to understand. The accuracy and applicability of the present method are demonstrated through few numerical examples. We observe that the approximate results converge monotonically to the exact solutions. In addition, we compare the approximate results with the exact solutions, and also with the existing solutions which are available in the literature. The absolute errors are depicted in tabular form as well as graphical representations, a reliable accuracy is achieved. The proposed method may be applied to fractional order partial differential equations also.

Umme Ruman

Md. Shafiqul Islam

Numerical Solutions of Linear Fractional Order BVP by Galerkin Residual Method with Differentiable Polynomials

用可微多项式的Galerkin残差法求解线性分数阶BVP的数值解

In this paper we have proved the approximating solutions of the nonlinear first order abstract measure differential equation by using Dhage’s iteration method. The main result is based on the iteration method included in the hybrid fixed point theorem in a partially ordered normed linear space. Also we have solved an example for the applicability of given results in the paper. Sharma [2] initiated the study of nonlinear abstract differential equations and some basic results concerning the existence of solutions for such equations. Later, such equations were studied by various authors for different aspects of the solutions under continuous and discontinuous nonlinearities. The study of fixed point theorem for contraction mappings in partial ordered metric space is initiated by different authors. The study of hybrid fixed point theorem in partially ordered metric space is initiated by Dhage with applications to nonlinear differential and integral equations. The iteration method is also embodied in hybrid fixed point theorem in partially ordered spaces by Dhage [12]. The Dhage iteration method is a powerful tool for proving the existence and approximating results for nonlinear measure differential equations. The approximation of the solutions are obtained under weaker mixed partial continuity and partial Lipschitz conditions. In this paper we adopted this iteration method technique for abstract measure differential equations.

Dnyanoba Maroti Suryawanshi

Sidheshwar Sangram Bellale

Pratiksha Prakash Lenekar

Approximating Solutions of Non Linear First Order Abstract Measure Differential Equations by Using Dhage Iteration Method

使用Dhage迭代法近似求解非线性一阶抽象测度微分方程的解

To fully analyze, mine, and utilize the information and knowledge implied in problem resolving use cases, this paper proposed the autonomous learning method based on machine inducting, hypothesis formulating, and result verifying, which was similar to the biological process of cows ruminating, called rumination computing. Firstly, after inducting and summarizing over 1080 mathematic application problem, the system architecture and general algorithm for humanoid automatic resolving mathematic application problems were represented, which typically included functional modules such as commonsense knowledge base, domain knowledge base, and local knowledge base, preprocessing, word segmentation and part of speech tagging, semantic framework matching, global semantic analyzing, thinking mechanism implementing, etc. Secondly, after the use case solutions were approved, three typical rumination computing modes, including vocabulary sequence, semantic relationship, and computing action, were introduced based on the correct results, resolving steps, and basic rumination actions. The rumination computing step plan was formulated, new knowledge was obtained from the commonsense and results verification, so the continuous autonomous learning loop for machine thinking was formed. Detailed explanations were provided for the three core algorithms implemented (rumination framework algorithm, rumination semantic algorithm, rumination action algorithm). Then, by specific mathematic application problem humanoid resolving user cases, the above three types of rumination computing modes were illumined.

Ping Zhu

Pohua Lv

Weiming Zou

Xuetao Jiang

Jin Shi

Yang Zhang

Yirong Ma

Principle and Application for Rumination Computing Algorithms

反刍计算算法原理与应用

Atoms themselves have no thoughts and cannot be thinking. Why does the human body, which is composed of atoms, have consciousness? The widely used concepts of information and intelligence in today’s science, which are related to this, do not yet have appropriate general definitions. Answering these interesting questions is a crucial issue for technological development in the historical context of human society entering the era of intelligence. The key lies in how to fully utilize the existing fundamental theories subtly related to information science. Here we attempt to give the definition of general information and general intelligence from the perspective of generalized natural computing, based on the least action principle, Hamilton-Jacobi equation, dynamic programming, reinforcement learning, and point out the relationship between the two. The least action principle for describing conservative systems can be seen as an intelligent manifestation of natural matter, and its equivalent form, the Hamilton-Jacobi equation, can be extended to describe quantum phenomena and is a special case of continuous dynamic programming equations. Dynamic programming is an efficient optimization method under deterministic models, while reinforcement learning, as a manifestation of biological intelligence, is its model-free version. The statement that reinforcement learning is the most promising machine learning method has a profound physical foundation. General information is defined as the degree to which a certain environmental element determines the behavior of the subject. General intelligence is defined as the automatic optimization ability of the action or value function of a system with a certain degree of conservatism. Intelligence is a basic property of material systems, rather than an emergent property that only complex systems possess. Consciousness is an advanced intelligent phenomenon, a reconstruction of quasi conservative systems based on complex systems.

Linsen Zhang

General Definitions of Information, Intelligence, and Consciousness from the Perspective of Generalized Natural Computing

广义自然计算视角下的信息、智能与意识的一般定义

Digital signal processing (DSP) is a promising alternative to accomplish a wide variety of signal processing operations. Multiplications and divisions have been urgently proposed to perform different DSP operations in real-time applications. However, the design and implementation of multiplication and division calculations have some limitations such as strict timing, bounded power consumption, and higher accuracy. The exact execution of these complex operations consumes great hardware resources and power consumption. Approximate computation for the main and complex arithmetic functions is a demand solution to decrease power, area, and delay. In this paper, low-power and high-accuracy approximate multiplication and division processes have been implemented using a 90 nm CMOS process, 1.0 V supply voltage standard cell library. The approximate multiplication and division algorithm depends on enhanced logarithmic converters. The logarithm-based arithmetic exhibits a good performance with decreasing the used hardware resources and runs at a higher speed. The proposed scheme achieves less hardware with minimal power consumption. The proposed approximate structure demonstrates up to a 62% saving in power with a rise in the accuracy level as compared with the prior approximate works. At the same time, the proposed multiplier and divider can carry out the multiplication and division processes in 1.8 ns, respectively.

Dina Ellaithy

Approximate Multiplication and Division Calculation for DSP Applications

用于DSP应用的近似乘法和除法计算

Class imbalance in data poses challenges for classifier learning, drawing increased attention in data mining and machine learning. The occurrence of class overlap in real-world data exacerbates the learning difficulty. In this paper, a novel pseudo oversampling method (POM) is proposed to learn imbalanced and overlapping data. It is motivated by the point that overlapping samples from different classes share the same distribution space, and therefore information underlying in majority (negative) overlapping samples can be extracted and used to generate additional positive samples. A fuzzy logic-based membership function is defined to assess negative overlaps using both local and global information. Subsequently, the identified negative overlapping samples are shifted into the positive sample region by a transformation matrix, centered around the positive samples. POM outperforms 15 methods across 14 datasets, displaying superior performance in terms of metrics of &amp;lt;i&amp;gt;G&amp;lt;sub&amp;gt;m&amp;lt;/sub&amp;gt;&amp;lt;/i&amp;gt;, &amp;lt;I&amp;gt;F&amp;lt;/I&amp;gt;&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt; and &amp;lt;I&amp;gt;AUC&amp;lt;/I&amp;gt;.

Tingting Pan

Witold Pedrycz

Jie Yang

Dahai Zhang

Pseudo Oversampling Based on Feature Transformation and Fuzzy Membership Functions for Imbalanced and Overlapping Data

基于特征变换和模糊隶属函数的伪过采样方法用于不平衡且重叠数据

This research investigates the flow of a Powell-Eyring Nanofluid flowing over an exponentially stretching sheet. Thermal radiation, Soret, dissipation, and Dufour effects have been put into consideration. The obtained partial differential equations(PDE) have been transformed into ordinary differential equations (ODE) using similarity transformation. Numerical solutions are obtained in MATLAB using bvp4c frame work of fourth order accuracy integration scheme. It has been observed that the boundary layer for momentum increases with the velocity ratio while the boundary layers for thermal and concentration decrease. The velocity diminishes with increasing magnetic parameter while the temperature and concentration increased. The temperature increases with an increase in thermophoresis and Brownian motion. Increasing the fluid parameter resulted in decreased Nusselt number, skin friction, and Sherwood number. Increasing Powell-Eyring fluid parameter decreases the Nusselt number and Sherwood number but increases skin friction. This research may find use in the development of microelectronics, chemical processes, human targeted drug delivery, and heating and cooling system.

Abbreviation	ACM
Journal Impact	4.72
Quartiles(Global)	MATHEMATICS, APPLIED(Q1)

ISSN	1683-3511, 2328-5605, 2328-5613
h-index	26

Publication Information	Publisher: Institute of Applied Mathematics of Baku State University，Publishing cycle: Semiannual，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2008，Proportion of original research papers: 95.83%，Self Citation Rate:13.00%， Gold OA Rate: 0.00%
Average review cycle	网友分享经验：平均6月
Average recruitment ratio	网友分享经验：约50%

Applied and Computational Mathematics

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