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.

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.

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.

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.

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 Method to Obtain Complex Transfer Functions of Four Order DC-DC Converters

Two TFs （transfer functions） are needed to analyze switching DC-DC converters in control-voltage mode： the duty-cycle to output-voltage （control to output） and the input-voltage to output-voltage （line to output）. To obtain these TFs a small-signal analysis is required. The CCM （continuous conduction mode） and the DCM （discontinuous conduction mode） analysis are different. When a circuit includes the loss resistances of the components, the number of parameters increases considerably, making manual nodal-loop circuit analysis techniques impractical to obtain the TFs. Moreover, these circuits are bilinear （non-linear） and it is necessary to linearize the equations at a DC operating-point （approximate linearization）. Vorp6rian describes a PWM （pulse-width-modulated） switch model that includes all non-linear parts of the DC-DC switching converters. This model can be linearized and replaced on the switching converter schematic leading to a linear circuit. At this point it is possible to use symbolic analysis programs to obtain these TFs or to simply apply numerical values for either the Bode diagrams or the calculation of poles and zeros. Here we describe an application of Ekrem Cangeici＇s method on X DC-DC converter to obtain control to output and line to output TFs in CCM and DCM including loss resistances. The method presented in this paper is optimized to use in the online publishing platform OctaveRS. Also the control to output TF for PCC （peak current controlled） in CCM is obtained.

The Internet accessible mathematical computation framework

The Internet Accessible Mathematical Computation (IAMC) framework aims to make it easy to supply mathematical computing powers over the Internet/Web. The protocol-based IAMC framework enables developers to create interoperable clients and servers easily and independently. Presented are conceptual and experimental work on the IAMC framework architecture and major components: the Mathematical Computation Protocol (MCP), a client prototype (Dragonfly), a server prototype (Starfish), a mathematical encoding converter (XMEC), and an open mathematical compute engine interface (OMEI).

A stability condition for turbulence model:From EMMS model to EMMS-based turbulence model

The closure problem of turbulence is still a challenging issue in turbulence modeling. In this work, a stability condition is used to close turbulence. Specifically, we regard single-phase flow as a mixture of turbulent and non-turbulent fluids, separating the structure of turbulence. Subsequently, according to the picture of the turbulent eddy cascade, the energy contained in turbulent flow is decomposed into different parts and then quantified. A turbulence stability condition, similar to the principle of the energy-minimization multi-scale （EMMS） model for gas-solid systems, is formulated to close the dynamic constraint equa- tions of turbulence, allowing the inhomogeneous structural parameters of turbulence to be optimized. We name this model as the ＂EMMS-based turbulence model＂, and use it to construct the corresponding turbulent viscosity coefficient. To validate the EMMS-based turbulence model, it is used to simulate two classical benchmark problems, lid-driven cavity flow and turbulent flow with forced convection in an empty room, The numerical results show that the EMMS-hased turbulence model improves the accuracy of turbulence modeling due to it considers the principle of compromise in competition between viscosity and inertia.

Clause-level Relationship-aware Math Word Problems Solver

Automatically solving math word problems,which involves comprehension,cognition,and reasoning,is a crucial issue in artificial intelligence research.Existing math word problem solvers mainly work on word-level relationship extraction and the generation of expression solutions while lacking consideration of the clause-level relationship.To this end,inspired by the theory of two levels of process in comprehension,we propose a novel clause-level relationship-aware math solver(CLRSolver)to mimic the process of human comprehension from lower level to higher level.Specifically,in the lower-level processes,we split problems into clauses according to their natural division and learn their semantics.In the higher-level processes,following human′s multi-view understanding of clause-level relationships,we first apply a CNN-based module to learn the dependency relationships between clauses from word relevance in a local view.Then,we propose two novel relationship-aware mechanisms to learn dependency relationships from the clause semantics in a global view.Next,we enhance the representation of clauses based on the learned clause-level dependency relationships.In expression generation,we develop a tree-based decoder to generate the mathematical expression.We conduct extensive experiments on two datasets,where the results demonstrate the superiority of our framework.

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-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-

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）.