Journal of Computational Mathematics

Aims and ScopeThe Journal of Computational Mathematics is published bi-monthly.It is aninternational journal covering all branches of modern computational mathematicssuch as numerical linear algebra,numerical optimization,computational geometry,numerical PDEs and inverse problems. Papers containing new ideas, creative ap-proaches and/or innovative applications as well as invited reviews are expected toappear regularly in the journal.Instructions for AuthorsTo speed up the refereeing and publication processes, all transactions and com-munications between the journal and the authors will be done electronically.All manuscripts should be in the form PDF or postscript or MS Word files.

Journal of Computational Mathematics

Aims and ScopeThe Journal of Computational Mathematics is published bi-monthly.It is aninternational journal covering all branches of modern computational mathematicssuch as numerical linear algebra, numerical optimization,computational geometry,numerical PDEs and inverse problems.Papers containing new ideas,creative ap-proaches and/or innovative applications as well as invited reviews are expected toappear regularly in the journal.Instructions for AuthorsTo speed up the refereeing and publication processes,all transactions and com-munications between the journal and the authors will be done electronically.All manuscripts should be in the form PDF or postscript or MS Word files.

Journal of Computational Mathematics

Aims and ScopeThe Journal of Computational Mathematics is published bi-monthly.It is aninternational journal covering all branches of modern computational mathematicssuch as numerical linear algebra,numerical optimization,computational geometry,numerical PDEs and inverse problems.Papers containing new ideas,creative ap-

Journal of Computational Mathematics

Aims and ScopeThe Journal of Computational Mathematics is published bi-monthly.It is aninternational journal covering all branches of modern computational mathematicssuch as numerical linear algebra,numerical optimization,computational geometry,numerical PDEs and inverse problems.Papers containing new ideas,creative ap-

Journal of Computational Mathematics

Aims and ScopeThe Journal of Computational Mathematics is published bi-monthly.It is aninternational journal covering all branches of modern computational mathematicssuch as numerical linear algebra,numerical optimization,computational geometry,numerical PDEs and inverse problems.Papers containing new ideas,creative ap-

JOURNAL OF COMPUTATIONAL MATHEMATICSINFORMATION FOR AUTHORS

The Journal of Computational Mathematics is an international journal on numerical methods, analysis and applications. It publishs original research papers in English, French or German, but preferably in English. From 1998, it has appeared bimonthly (instead of quarterly).

JOURNAL OF COMPUTATIONAL MATHEMATICS INFORMATION FOR AUTHORS

The Journal of Computational Mathematics is an international journal on numerical methods, analysis and applications. It publishs original research papers in English, French or German, but preferably in English. From 1998, it has appeared bimonthly (instead of quarterly).

JOURNAL OF COMPUTATIONAL MATHEMATICS INFORMATION FOR AUTHORS

The Journal of Computational Mathematics is an international journal on numerical methods, analysis and applications. It publishs original research papers in English, French or German, but preferably in English. From 1998, it has appeared bimonthly (instead of quarterly).

Learning to represent 2D human face with mathematical model

How to represent a human face pattern?While it is presented in a continuous way in human visual system,computers often store and process it in a discrete manner with 2D arrays of pixels.The authors attempt to learn a continuous surface representation for face image with explicit function.First,an explicit model(EmFace)for human face representation is pro-posed in the form of a finite sum of mathematical terms,where each term is an analytic function element.Further,to estimate the unknown parameters of EmFace,a novel neural network,EmNet,is designed with an encoder-decoder structure and trained from massive face images,where the encoder is defined by a deep convolutional neural network and the decoder is an explicit mathematical expression of EmFace.The authors demonstrate that our EmFace represents face image more accurate than the comparison method,with an average mean square error of 0.000888,0.000936,0.000953 on LFW,IARPA Janus Benchmark-B,and IJB-C datasets.Visualisation results show that,EmFace has a higher representation performance on faces with various expressions,postures,and other factors.Furthermore,EmFace achieves reasonable performance on several face image processing tasks,including face image restoration,denoising,and transformation.

Algorithm for Visualization of Zero Divisor Graphs of the Ring ℤn Using MAPLE Coding

This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤn modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.

A Comparative Study of Adomian Decomposition Method with Variational Iteration Method for Solving Linear and Nonlinear Differential Equations

This study compares the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM) for solving nonlinear differential equations in engineering. Differential equations are essential for modeling dynamic systems in various disciplines, including biological processes, heat transfer, and control systems. This study addresses first, second, and third-order nonlinear differential equations using Mathematica for data generation and graphing. The ADM, developed by George Adomian, uses Adomian polynomials to handle nonlinear terms, which can be computationally intensive. In contrast, VIM, developed by He, directly iterates the correction functional, providing a more straightforward and efficient approach. This study highlights VIM’s rapid convergence and effectiveness of VIM, particularly for nonlinear problems, where it simplifies calculations and offers direct solutions without polynomial derivation. The results demonstrate VIM’s superior efficiency and rapid convergence of VIM compared with ADM. The VIM’s minimal computational requirements make it practical for real-time applications and complex system modeling. Our findings align with those of previous research, confirming VIM’s efficiency of VIM in various engineering applications. This study emphasizes the importance of selecting appropriate methods based on specific problem requirements. While ADM is valuable for certain nonlinearities, VIM’s approach is ideal for many engineering scenarios. Future research should explore broader applications and hybrid methods to enhance the solution’s accuracy and efficiency. This comprehensive comparison provides valuable guidance for selecting effective numerical methods for differential equations in engineering.

An activated variable parameter gradient‐based neural network for time‐variant constrained quadratic programming and its applications

This study proposes a novel gradient‐based neural network model with an activated variable parameter,named as the activated variable parameter gradient‐based neural network(AVPGNN)model,to solve time‐varying constrained quadratic programming(TVCQP)problems.Compared with the existing models,the AVPGNN model has the following advantages:(1)avoids the matrix inverse,which can significantly reduce the computing complexity;(2)introduces the time‐derivative of the time‐varying param-eters in the TVCQP problem by adding an activated variable parameter,enabling the AVPGNN model to achieve a predictive calculation that achieves zero residual error in theory;(3)adopts the activation function to accelerate the convergence rate.To solve the TVCQP problem with the AVPGNN model,the TVCQP problem is transformed into a non‐linear equation with a non‐linear compensation problem function based on the Karush Kuhn Tucker conditions.Then,a variable parameter with an activation function is employed to design the AVPGNN model.The accuracy and convergence rate of the AVPGNN model are rigorously analysed in theory.Furthermore,numerical experiments are also executed to demonstrate the effectiveness and superiority of the proposed model.Moreover,to explore the feasibility of the AVPGNN model,appli-cations to the motion planning of a robotic manipulator and the portfolio selection of marketed securities are illustrated.

Global Characteristics of the Envelope of Family of Trajectories in Resistive Media

In our recent article [1], we discussed the universal geometric characteristics of the envelope of family of trajectories of projectiles projected with the same speeds and different velocities in a vertical plane under the sole influence of gravity;our current investigation is its natural extension. As shown in [1] even for the simplest case where gravity is the only acting external agent literature overlooked reveling the characteristics of the envelope such as its arc-length, the surface area of the enclosed surface and etc. Calculation leading to these has carried out mostly longhand [1]. The current extended version embodies a realistic scenario where the projectiles in addition to gravity encounter linear velocity-dependent media resistance. In order to fulfil objectives similar to [1], we develop two distinct strategies obtaining the analytic equation for the envelope. On one hand, we solve the equations of motion applying traditional longhand approach. On the other hand, we adopt a Computer Algebra System (CAS), e.g. Mathematica [2] [3]. Having these outputs at hand, via mixed-mode calculation—some longhand and some via CAS—we explore its global geometric characteristics such as its arc-length, the surface area of the enclosure. Because of the calculation complexities we could not have achieved our set goals.

A Reynolds mass flux model for gas separation process simulation:Ⅰ. Modeling and validation

Separation process undertaken in packed columns often displays anisotropic turbulent mass diffusion. The anisotropic turbulent mass diffusion can be characterized rigorously by using the Reynolds mass flux(RMF) model.With the RMF model, the concentration and temperature as well as the velocity distributions can be simulated numerically. The modeled Reynolds mass flux equation is adopted to close the turbulent mass transfer equation,while the modeled Reynolds heat flux and Reynolds stress equations are used to close the turbulent heat and momentum transfer equations, so that the Boussinesq postulate and the isotropic assumption are abandoned. To validate the presented RMF model, simulation is carried out for CO2 absorption into aqueous Na OH solutions in a packed column(0.1 m id, packed with 12.7 mm Berl saddles up to a height of 6.55 m). The simulated results are compared with the experimental data and satisfactory agreement is found both in concentration and temperature distributions. The sequel Part II extends the model application to the simulation of an unsteady state adsorption process in a packed column.

Research on scheduling strategy for automated storage and retrieval system

With the continuous and rapid growth of transport demand,scheduling strategy of warehouse has become a key issue in the field of logistics transportation.The structural differences of the warehouse,the automated storage and retrieval system(AS/RS)model and the two-end dual stackers scheduling model(TDSM)are considered,and a new improved genetic algorithm(NIGA)is proposed.It can adjust the algorithm structure according to the density of population fitness value,and effectively optimize the stacker path.In the TDSM,an improved anti-collision principle is proposed to avoid collision of two stackers.Besides,combined with the optimal anti-collision boundary inspection mechanism,the best working area for the two stackers is allocated by using NIGA.Finally,the new improved GA is compared with GA and the adaptive GA on specific storage and retrieval tasks.The simulation results show that the proposed NIGA well outperforms other GAs in most instances,which indicates that it is an effective approach for the AS/RS and the TDSM scheduling optimization problem.

Preface Special Issue for“the 2nd Sino-German Workshop on Computational and Applied Mathematics”

The 2nd Sino-German Workshop on Computational and Applied Mathematics took place in Hangzhou, China, from October 9-13, 2007. The long list of senior Chinese numerical analysts who had spent a year or more somewhere in Germany as Humboldt fellows had led to the first Sino-German Workshop in Berlin held at the Humboldt-Universitat zu Berlin in 2005. The particular purpose of the second German-Chinese Workshop on Computational and Applied Mathematics was to attract more junior Chinese scientists to the actual research activities in Germany. A summer school in Beijing on adaptive finite element methods with Carsten Carstensen and Roll Rannacher piror to the Hangzhou workshop underlined this activity to foster the collaboration of the new generations in the fields of computational and applied mathematics. This special issue reflects the present topics therein in both countries and can be summarised under five headings （i）-（v）.

A New Scheme to Projective Synchronization of Fractional-Order Chaotic Systems

We demonstrate that the projective synchronization can be observed in coupled fractional-order chaotic systems. A new systematic and powerful coupling scheme is developed to investigate the projective synchronization via the open-plus-closed-loop control, which allows us to arbitrarily manipulate the scaling factor of projective synchronization. The proposed scheme is proved analytically on the basis of the stability theorem of the fractional differential equations. Numerical simulations on the fraction-order chaotic Chen system are presented to justify the theoretical analysis.