Analysis of Extended Fisher-Kolmogorov Equation in 2D Utilizing the Generalized Finite Difference Method with Supplementary Nodes

In this study,we propose an efficient numerical framework to attain the solution of the extended Fisher-Kolmogorov(EFK)problem.The temporal derivative in the EFK equation is approximated by utilizing the Crank-Nicolson scheme.Following temporal discretization,the generalized finite difference method(GFDM)with supplementary nodes is utilized to address the nonlinear boundary value problems at each time node.These supplementary nodes are distributed along the boundary to match the number of boundary nodes.By incorporating supplementary nodes,the resulting nonlinear algebraic equations can effectively satisfy the governing equation and boundary conditions of the EFK equation.To demonstrate the efficacy of our approach,we present three numerical examples showcasing its performance in solving this nonlinear problem.

An Effective Meshless Approach for Inverse Cauchy Problems in 2D and 3D Electroelastic Piezoelectric Structures

In the past decade,notable progress has been achieved in the development of the generalized finite difference method(GFDM).The underlying principle of GFDM involves dividing the domain into multiple sub-domains.Within each sub-domain,explicit formulas for the necessary partial derivatives of the partial differential equations(PDEs)can be obtained through the application of Taylor series expansion and moving-least square approximation methods.Consequently,the method generates a sparse coefficient matrix,exhibiting a banded structure,making it highly advantageous for large-scale engineering computations.In this study,we present the application of the GFDM to numerically solve inverse Cauchy problems in two-and three-dimensional piezoelectric structures.Through our preliminary numerical experiments,we demonstrate that the proposed GFDMapproach shows great promise for accurately simulating coupled electroelastic equations in inverse problems,even with 3%errors added to the input data.

Free vibration and buckling analysis of polymeric composite beams reinforced by functionally graded bamboo fbers

Natural fibers have been extensively researched as reinforcement materials in polymers on account of their environmental and economic advantages in comparison with synthetic fibers in the recent years.Bamboo fibers are renowned for their good mechanical properties,abundance,and short cycle growth.As beams are one of the fundamental structural components and are susceptible to mechanical loads in engineering applications,this paper performs a study on the free vibration and buckling responses of bamboo fiber reinforced composite(BFRC)beams on the elastic foundation.Three different functionally graded(FG)layouts and a uniform one are the considered distributions for unidirectional long bamboo fibers across the thickness.The elastic properties of the composite are determined with the law of mixture.Employing Hamilton’s principle,the governing equations of motion are obtained.The generalized differential quadrature method(GDQM)is then applied to the equations to obtain the results.The achieved outcomes exhibit that the natural frequency and buckling load values vary as the fiber volume fractions and distributions,elastic foundation stiffness values,and boundary conditions(BCs)and slenderness ratio of the beam change.Furthermore,a comparative study is conducted between the derived analysis outcomes for BFRC and homogenous polymer beams to examine the effectiveness of bamboo fibers as reinforcement materials,demonstrating the significant enhancements in both vibration and buckling responses,with the exception of natural frequencies for cantilever beams on the Pasternak foundation with the FG-◇fiber distribution.Eventually,the obtained analysis results of BFRC beams are also compared with those for carbon nanotube reinforced composite(CNTRC)beams found in the literature,indicating that the buckling loads and natural frequencies of BFRC beams are lower than those of CNTRC beams.

Numerical Treatments for Crossover Cancer Model of Hybrid Variable-Order Fractional Derivatives

In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.

Preconditioned iterative methods for solving weighted linear least squares problems

A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation （GAOR） methods, is proposed to solve linear systems based on a class of weighted linear least squares problems. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods. Furthermore, the effectiveness of the proposed methods is shown in the numerical experiment.

A New Generating Method and Its Application

In this paper, a new generating method-opposite-direction accumulated generating operation is presented. The effectiveness of the method for different original sequences to choose different generating operation is discussed and the optimal parameters ɑ and b of grey model by a new structure of background and initial value are obtained. Some properties of a grey model are studied. The calculating precision of the example shows that the method is very effective.

Propagation of traveling wave solutions to the Vakhnenko-Parkes dynamical equation via modified mathematical methods

In this paper, we investigate some new traveling wave solutions to Vakhnenko-Parkes equation via three modified mathematical methods. The derived solutions have been obtained including periodic and solitons solutions in the form of trigonometric, hyperbolic, and rational function solutions. The graphical representations of some solutions by assigning particular values to the parameters under prescribed conditions in each solutions and comparing of solutions with those gained by other authors indicate that these employed techniques are more effective, efficient and applicable mathematical tools for solving nonlinear problems in applied science.

GENERALIZED INVERSE RATIONAL EXTRAPOLATION METHODS FOR MATRIX SEQUENCES

Assume that a convergent matrix sequence{An}:An→A（n→∞）, An,A∈C3×3.We want to form a new matrix sequence {Hn}, derived from {An}, which has also A aslimit and whose convergence is faster than the of {An}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {An} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is

Generalized Maximum Fuzzy Entropy Methods with Applications on Wind Speed Data

This study is connected with new Generalized Maximum Fuzzy Entropy Methods （GMax（F）EntM） in the form of MinMax（F）EntM and MaxMax（F）EntM belonging to us. These methods are based on primary maximizing Max（F）Ent measure for fixed moment vector function in order to obtain the special functional with maximum values of Max（F）Ent measure and secondary optimization of mentioned functional with respect to moment vector functions. Distributions, in other words sets of successive values of estimated membership function closest to （furthest from） the given membership function in the sense of Max（F）Ent measure, obtained by mentioned methods are defined as （MinMax（F）Ent）m which is closest to a given membership function and （MaxMax（F）Ent）m which is furthest from a given membership function. The aim of this study consists of applying MinMax（F）EntM and MaxMax（F）EntM on given wind speed data. Obtained results are realized by using MATLAB programme. The performances of distributions （MinMax（F）En0m and （MaxMax（F）Ent）m generated by using Generalized Maximum Fuzzy Entropy Methods are established by Chi-Square, Root Mean Square Error criterias and Max（F）Ent measure.

Research on Design Method of Non-Circular Gear Pair with Double Generating Angles

In order to enhance the bearing capacity of non-circular gear pair, the non-circular gear pair with double generating angles is proposed based on the design idea of unsymmetrical gear with double pressure angles. The tooth profile is designed by generating cutting theory, the pure rolling mathematic model that the center line of unsymmetrical rack roll along non-circular pitch curve is built, the digital model of non-circular gear with double generating angles is created through the second development method of CAD software, and then the drive characteristic and tooth strength are analyzed. The results show that the design method for double generating angles non-circular gear proposed in this paper is feasible, which is significant to improve the bearing capacity of non-circular gear pair.

Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.

Examination of the poverty-environmental degradation nexus in Sub-Saharan Africa

The relationship between environmental degradation and poverty has increasingly become the focus of national strategic decision-making in recent years.However,despite several theoretical explorations on the nexus,a dearth of empirical literature on the poverty-environmental degradation nexus,specifically on Sub-Saharan Africa(SSA),still exists.In this study,we investigated the poverty-environmental degradation nexus in SSA.We hypothesized that poverty is both a cause and effect of environmental degradation,and this relationship is explained as a vicious cycle.Unlike previous studies,we employed several alternative indicators of environmental degradation to examine the poverty-environmental degradation nexus in this study.We used data from 41 countries of SSA between 1996 and 2019 and employed the generalized method of moments(GMM)approach.The findings suggest a cyclical relationship between poverty and environmental degradation in SSA,which confirms that an increase in poverty leads to an increase in environmental degradation,especially in deforestation and PM2.5 emissions.Similarly,the increase in environmental degradation positively affects poverty in SSA.We also confirmed that exogenous conditioning factors such as population growth rate,education,industrialization,and income inequality,institutional quality indicators such as governance effectiveness,control of corruption,freedom ad civil liberty,and democracy,and endogenous factors including fossil fuel energy use,fuelwood energy use,household health expenditure,infant mortality rate,and agriculture productivity influence the nexus between poverty and environmental degradation.The findings on the relationship between poverty and environmental degradation in SSA are a testimonial evidence that both poverty and environmental degradation are significant issues in SSA.Hence,poverty alleviation policies in SSA should not lead to PM2.5 emissions and deforestation,which may as well force people into a poverty-environmental degradation trap.Instead,poverty reduction policies should simultaneously achieve environmental conservation.

Unified two-phase nonlocal formulation for vibration of functionally graded beams resting on nonlocal viscoelastic Winkler-Pasternak foundation

A nonlocal study of the vibration responses of functionally graded(FG)beams supported by a viscoelastic Winkler-Pasternak foundation is presented.The damping responses of both the Winkler and Pasternak layers of the foundation are considered in the formulation,which were not considered in most literature on this subject,and the bending deformation of the beams and the elastic and damping responses of the foundation as nonlocal by uniting the equivalently differential formulation of well-posed strain-driven(ε-D)and stress-driven(σ-D)two-phase local/nonlocal integral models with constitutive constraints are comprehensively considered,which can address both the stiffness softening and toughing effects due to scale reduction.The generalized differential quadrature method(GDQM)is used to solve the complex eigenvalue problem.After verifying the solution procedure,a series of benchmark results for the vibration frequency of different bounded FG beams supported by the foundation are obtained.Subsequently,the effects of the nonlocality of the foundation on the undamped/damping vibration frequency of the beams are examined.

Integration of GIS with the Generalized Reciprocal Method(GRM)for Determining Foundation Bearing Capacity:A Case Study in Opolo,Yenagoa Bayelsa State,Nigeria

This study addresses the pressing need to assess foundation bearing capacity in Opolo,Yenagoa,Bayelsa State,Nigeria.The significance lies in the dearth of comprehensive geotechnical data for construction planning in the region.Past research is limited and this study contributes valuable insights by integrating Geographic Information System(GIS)with the Generalized Reciprocal Method(GRM).To collect data,near-surface seismic refraction surveys were conducted along three designated lines,utilizing ABEM Terraloc Mark 6 equipment,Easy Refract,and ArcGIS 10.4.1 software.This methodology allowed for the determination of key geotechnical parameters essential for soil characterization at potential foundation sites.The results revealed three distinct geoseismic layers.The uppermost layer,within a depth of 0.89 to 1.50 meters,exhibited inadequate compressional and shear wave velocities and low values for oedometric modulus,shear modulus,N-value,ultimate bearing capacity,and allowable bearing capacity.This indicates the presence of unsuitable,soft,and weak alluvial deposits for substantial structural loads.In contrast,the second layer(1.52 to 3.84 m depth)displayed favorable geotechnical parameters,making it suitable for various construction loads.The third layer(15.00 to 26.05 m depth)exhibited varying characteristics.The GIS analysis highlighted the unsuitability of the uppermost layer for construction,while the second and third layers were found to be fairly competent and suitable for shallow footing and foundation design.In summary,this study highlights the importance of geotechnical surveys in Opolo’s construction planning.It offers vital information for informed choices,addresses issues in the initial layer,and suggests secure,sustainable construction options.

Exploring unbinding mechanism of drugs from SERT via molecular dynamics simulation and its implication in antidepressants

The human serotonin transporter(SERT)terminates neurotransmission by removing serotonin from the synaptic cleft,which is an essential process that plays an important role in depression.In addition to natural substrate serotonin,SERT is also the target of the abused drug cocaine and,clinically used antidepressants,escitalopram,and paroxetine.To date,few studies have attempted to investigate the unbinding mechanism underlying the orthosteric and allosteric modulation of SERT.In this article,the conserved property of the orthosteric and allosteric sites(S1 and S2)of SERT was revealed by combining the high resolutions of x-ray crystal structures and molecular dynamics(MD)simulations.The residues Tyr95 and Ser438 located within the S1 site,and Arg104 located within the S2 site in SERT illustrate conserved interactions(hydrogen bonds and hydrophobic interactions),as responses to selective serotonin reuptake inhibitors.Van der Waals interactions were keys to designing effective drugs inhibiting SERT and further,electrostatic interactions highlighted escitalopram as a potent antidepressant.We found that cocaine,escitalopram,and paroxetine,whether the S1 site or the S2 site,were more competitive.According to this potential of mean force(PMF)simulations,the new insights reveal the principles of competitive inhibitors that lengths of trails from central SERT to an opening were~18A for serotonin and~22 A for the above-mentioned three drugs.Furthermore,the distance between the natural substrate serotonin and cocaine(or escitalopram)at the allosteric site was~3A.Thus,it can be inferred that the potent antidepressants tended to bind at deeper positions of the S1 or the S2 site of SERT in comparison to the substrate.Continuing exploring the processes of unbinding four ligands against the two target pockets of SERT,this study observed a broad pathway in which serotonin,cocaine,escitalopram(at the S1 site),and paroxetine all were pulled out to an opening between MT1b and MT6a,which may be helpful to understand the dissociation mechanism of antidepressants.

Application of stiffness matrix of a beam element considering section distortion effect

According to the stationary principle of potential energy and the generalized coordinate method, a stiffness matrix of a beam element considering distortion effects is derived. Using the stiffness matrix of the beam element, a finite element program for computing thin-walled box steel beams is developed. And the program can take the section distortion and warping effects into account. The influences of diaphragm spacing on the mechanical behavior of thin-walled box beams are analyzed by the program. The numerical analysis shows that setting diaphragms have the greatest influence on the distortion normal stress, while there is very little influence on the bending normal stress. Only when the distance of adjacent diaphragms decreases to a certain value, will the distortion normal stress in the thin-walled box beam obviously reduce under the distortion load. Finally, a distortion-warping coefficient γ is introduced for simplifying the calculation of the longitudinal normal stress of thin-walled box beams. When the ratio of diaphragms adjacent space L to the maximum section dimension H is less than 2, the distortion-warping coefficient γ tends to one, which means that the distortion normal stress of the thin-walled box beam tends to zero, and the effect of the section distortion can be ignored.

Frequency domain identification of non-integer order dynamical systems

Two new methods, the generalized Levy method and the weighted iteration method, are presented for identification of non-integer order systems. The first method generalizes the Levy identification method from the integer order systems to the non-integer order systems. Then, the weighted iteration method is presented to overcome the shortcomings of the first method. Results show that the proposed methods have better performance compared with the integer order identification method. For the non-integer order systems, the proposed methods have the better fitting for the system frequency response. For the integer order system, if commensurate order scanning is applied, the proposed methods can also achieve the best integer order model which fits the system frequency response. At the same time, the proposed algorithms are more stable.

Environmental Regulation,Pollution Treatment Productivity,and Industrial Environmental TFP in China

Amidst growing environmental protection intensity by the Chinese government, this paper investigates the effects of environmental regulation on China＇s industrial pollution treatment productivity and environmental TFP. By estimating China＇s pollution treatment productivity between 2001 and 2008 and analyzing environmental regulation intensity and the effects of the relevant factors and pollution treatment productivity using panel data, this paper discovers that （1） pollution treatment productivity contributed a significant share of about 40% to industrial environmental TFP during the investigation period; （2） environmental regulation may not necessarily cause adverse impacts on pollution treatment efficiency and productivity but demonstrates a U-shaped relationship： when the share of pollution treatment cost in industrial value-added is above the range of 3.8%-5.1%, environmental regulation is likely to promote pollution treatment productivity and thus environmental TFP Judging by the estimation result, enhancing environmental protection and expediting the development of ecological civilization are conducive to China ＂s economic transition towards an intensive, efficient, circular, and sustainable development pattern. China＇s current industrial development has the capacity to tolerate a rather demanding level of pollution treatment and management and China needs to further rely on energy conservation and the environmental production industries to promote the progress of pollution treatment technologies.

A RECURSIVE GENERATIVE APPROACH IN OPTICAL PRISM CAPP

In this paper, the generative approach utilizes recursion to generate process sequence for a part, and then match detail procedure design and select process equipment. A set of recursive formulas are found. Finally a complete process program is produced. The method is simple than that of the knowledge system, the artificial neural networks and variant approach computer aided process planning(VACAPP).

A UNIFIED ENERGY APPROACH TO A CLASS OF MICROMECHANICS MODELS FOR COMPOSITE MATERIALS

Several micromechanics models for the determination of composite moduli are investigated in this paper,including the dilute solution,self-consistent method,generalized self-consistent method,and Mori-Tanaka's method.These mi- cromechanical models have been developed by following quite different approaches and physical interpretations.It is shown that all the micromechanics models share a common ground,the generalized Budiansky's energy-equivalence framework.The dif- ference among the various models is shown to be the way in which the average strain of the inclusion phase is evaluated.As a bonus of this theoretical development,the asymmetry suffered in Mori-Tanaka's method can be circumvented and the applica- bility of the generalized self-consistent method can be extended to materials contain- ing microcracks,multiphase inclusions,non-spherical inclusions,or non-cylindrical inclusions.The relevance to the differential method,double-inclusion model,and Hashin-Shtrikman bounds is also discussed.The application of these micromechanics models to particulate-reinforced composites and microcracked solids is reviewed and some new results are presented.