This article focuses on the relationship between mathematical morphology operations and rough sets,mainly based on the context of image retrieval and the basic image correspondence problem.Mathematical morphological p...This article focuses on the relationship between mathematical morphology operations and rough sets,mainly based on the context of image retrieval and the basic image correspondence problem.Mathematical morphological procedures and set approximations in rough set theory have some clear parallels.Numerous initiatives have been made to connect rough sets with mathematical morphology.Numerous significant publications have been written in this field.Others attempt to show a direct connection between mathematical morphology and rough sets through relations,a pair of dual operations,and neighborhood systems.Rough sets are used to suggest a strategy to approximatemathematicalmorphology within the general paradigm of soft computing.A single framework is defined using a different technique that incorporates the key ideas of both rough sets and mathematical morphology.This paper examines rough set theory from the viewpoint of mathematical morphology to derive rough forms of themorphological structures of dilation,erosion,opening,and closing.These newly defined structures are applied to develop algorithm for the differential analysis of chest X-ray images from a COVID-19 patient with acute pneumonia and a health subject.The algorithm and rough morphological operations show promise for the delineation of lung occlusion in COVID-19 patients from chest X-rays.The foundations of mathematical morphology are covered in this article.After that,rough set theory ideas are taken into account,and their connections are examined.Finally,a suggested image retrieval application of the concepts from these two fields is provided.展开更多
An information system is a type of knowledge representation,and attribute reduction is crucial in big data,machine learning,data mining,and intelligent systems.There are several ways for solving attribute reduction pr...An information system is a type of knowledge representation,and attribute reduction is crucial in big data,machine learning,data mining,and intelligent systems.There are several ways for solving attribute reduction problems,but they all require a common categorization.The selection of features in most scientific studies is a challenge for the researcher.When working with huge datasets,selecting all available attributes is not an option because it frequently complicates the study and decreases performance.On the other side,neglecting some attributes might jeopardize data accuracy.In this case,rough set theory provides a useful approach for identifying superfluous attributes that may be ignored without sacrificing any significant information;nonetheless,investigating all available combinations of attributes will result in some problems.Furthermore,because attribute reduction is primarily a mathematical issue,technical progress in reduction is dependent on the advancement of mathematical models.Because the focus of this study is on the mathematical side of attribute reduction,we propose some methods to make a reduction for information systems according to classical rough set theory,the strength of rules and similarity matrix,we applied our proposed methods to several examples and calculate the reduction for each case.These methods expand the options of attribute reductions for researchers.展开更多
In this article,the reduced differential transform method is introduced to solve the nonlinear fractional model of Tumor-Immune.The fractional derivatives are described in the Caputo sense.The solutions derived using ...In this article,the reduced differential transform method is introduced to solve the nonlinear fractional model of Tumor-Immune.The fractional derivatives are described in the Caputo sense.The solutions derived using this method are easy and very accurate.The model is given by its signal flow diagram.Moreover,a simulation of the system by the Simulink of MATLAB is given.The disease-free equilibrium and stability of the equilibrium point are calculated.Formulation of a fractional optimal control for the cancer model is calculated.In addition,to control the system,we propose a novel modification of its model.This modification is based on converting the model to a memristive one,which is a first time in the literature that such idea is used to control this type of diseases.Also,we study the system’s stability via the Lyapunov exponents and Poincare maps before and after control.Fractional order differential equations(FDEs)are commonly utilized to model systems that have memory,and exist in several physical phenomena,models in thermoelasticity field,and biological paradigms.FDEs have been utilized to model the realistic biphasic decline manner of elastic systems and infection of diseases with a slower rate of change.FDEs are more useful than integer-order in modeling sophisticated models that contain physical phenomena.展开更多
In this paper,we studied the vibration performance,energy transfer and stability of the offshore wind turbine tower system under mixed excitations.The method of multiple scales is utilized to calculate the approximate...In this paper,we studied the vibration performance,energy transfer and stability of the offshore wind turbine tower system under mixed excitations.The method of multiple scales is utilized to calculate the approximate solutions of wind turbine system.The proportional-derivative controller was applied for reducing the oscillations of the controlled system.Adding the controller to single degree of freedom system equation is responsible for energy transfers in offshore wind turbine tower system.The steady state solution of stability at worst resonance cases is studied and examined.The offshore wind turbine system behavior was studied numerically at its different parameters values.Furthermore,the response and numerical results were obtained and discussed.The stability is also analyzed using technique of phase plane and equations of frequency response.In addition,the numerical results and comparison between analytical and numerical solutions were obtained with MAPLE and MATLAB algorithms.展开更多
The effect of Zn2+ ions on the microstructure and electrical properties of Mn1-xZnxFe2O4 (0.0 ≤ x ≤ 0.5 in steps of 0.1) through a solid state reaction has been investigated. The structural properties have been inve...The effect of Zn2+ ions on the microstructure and electrical properties of Mn1-xZnxFe2O4 (0.0 ≤ x ≤ 0.5 in steps of 0.1) through a solid state reaction has been investigated. The structural properties have been investigated using X-ray diffraction (XRD) technique. The XRD analysis confirms that all samples are in a single-phase cubic spinel structure. The experimental lattice parameter (aexp) was decreased with increasing Zn2+ ions substitution due to the smaller ionic radius of zinc content. The crystallite size (t) of samples was estimated by Scherrer’s formula and found in the range (90 - 115 nm). Dc electrical resistivity and Seebeck voltage coefficients were measured as a function of temperature using the two probe methods. The temperature variation of resistivity exhibits two breaks, each break referring to a change in the activation energy. The Curie temperature estimated from dc resistivity measurement decreases with increasing Zn2+ ions. Seebeck voltage coefficient measurements reveal n-type conduction for all samples.展开更多
The detection of error and its correction is an important area of mathematics that is vastly constructed in all communication systems.Furthermore,combinatorial design theory has several applications like detecting or ...The detection of error and its correction is an important area of mathematics that is vastly constructed in all communication systems.Furthermore,combinatorial design theory has several applications like detecting or correcting errors in communication systems.Network(graph)designs(GDs)are introduced as a generalization of the symmetric balanced incomplete block designs(BIBDs)that are utilized directly in the above mentioned application.The networks(graphs)have been represented by vectors whose entries are the labels of the vertices related to the lengths of edges linked to it.Here,a general method is proposed and applied to construct new networks designs.This method of networks representation has simplified the method of constructing the network designs.In this paper,a novel representation of networks is introduced and used as a technique of constructing the group generated network designs of the complete bipartite networks and certain circulants.A technique of constructing the group generated network designs of the circulants is given with group generated graph designs(GDs)of certain circulants.In addition,the GDs are transformed into an incidence matrices,the rows and the columns of these matrices can be both viewed as a binary nonlinear code.A novel coding error detection and correction application is proposed and examined.展开更多
An orthogonal double cover (ODC) of a graph H is a collection of subgraphs (pages) of H, so that they cover every edge of H twice and the intersection of any two of them contains exactly one edge. An ODC G of H is cyc...An orthogonal double cover (ODC) of a graph H is a collection of subgraphs (pages) of H, so that they cover every edge of H twice and the intersection of any two of them contains exactly one edge. An ODC G of H is cyclic (CODC) if the cyclic group of order is a subgroup of the automorphism group of G. In this paper, we introduce a general orthogonal labelling for CODC of circulant graphs and construct CODC by certain classes of graphs such as complete bipartite graph, the union of the co-cycles graph with a star, the center vertex of which, belongs to the co-cycles graph and graphs that are connected by a one vertex.展开更多
This paper outlines the vibrational motion of a nonlinear system with a spring of linear stiffness. Homotopy perturbation technique (HPT) is used to obtain the asymptotic solution of the governing equation of motion. ...This paper outlines the vibrational motion of a nonlinear system with a spring of linear stiffness. Homotopy perturbation technique (HPT) is used to obtain the asymptotic solution of the governing equation of motion. The numerical solution of this equation is obtained using the fourth order Runge-Kutta method (RKM). The comparison between both solutions reveals high consistency between them which confirms that, the accuracy of the obtained solution using aforementioned perturbation technique. The time history of the attained solution is represented through some plots to reveal the good effect of the different parameters of the considered system on the motion at any instant. The conditions of the stability of the attained solution are presented and discussed.展开更多
The study deals with the multi-choice mathematical programming problem, where the right hand side of the constraints is multi-choice in nature. However, the problem of multi-choice linear programming cannot be solved ...The study deals with the multi-choice mathematical programming problem, where the right hand side of the constraints is multi-choice in nature. However, the problem of multi-choice linear programming cannot be solved directly by standard linear or nonlinear programming techniques. The aim of this paper is to transform such problems to a standard mathematical linear programming problem. For each constraint, exactly one parameter value is selected out of a multiple number of parameter values. This process of selection can be established in different ways. In this paper, we present a new simple technique enabling us to handle such problem as a mixed integer linear programming problem and consequently solve them by using standard linear programming software. Our main aim depends on inserting a specific number of binary variables and using them to construct a linear combination which gives just one parameter among the multiple choice values for each choice of the values of the binary variables. A numerical example is presented to illustrate our analysis.展开更多
The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The a...The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The adaptive harmonic balance(AHB)method is an improved HBM method.This paper presents a modified AHB method with the asymptotic harmonic selection(AHS)procedure.This new harmonic selection procedure selects harmonics from the frequency spectra of nonlinear terms instead of estimating the contribution of each harmonic to the whole nonlinear response,by which the additional calculation is avoided.A modified continuation method is proposed to deal with the variable size of nonlinear algebraic equations at different values of path parameters,and then all solution branches of the amplitude-frequency response are obtained.Numerical experiments are carried out to verify the performance of the AHB-AHS method.Five typical nonlinear dynamic equations with different types of nonlinearities and excitations are chosen as the illustrative examples.Compared with the classical HBM and Runge-Kutta methods,the proposed AHB-AHS method is of higher accuracy and better convergence.The AHB-AHS method proposed in this paper has the potential to investigate the nonlinear vibrations of complex high-dimensional nonlinear systems.展开更多
In this paper, we develop a new numerical method which is based on an exponential spline and Shishkin mesh discretization to solve singularly perturbed boundary value problems, which contain a small uncertain perturba...In this paper, we develop a new numerical method which is based on an exponential spline and Shishkin mesh discretization to solve singularly perturbed boundary value problems, which contain a small uncertain perturbation parameter. The proposed method uses interval analysis principle to deal with the uncertain parameter and the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Furthermore, sensitivity analysis has been conducted using different methods to assess how much the solution is sensitive to the changes of the perturbation parameter. Numerical results are provided to show the applicability and efficiency of the proposed method, which is ε-uniform convergence of almost second order.展开更多
A decomposition of a graph H is a partition of the edge set of H into edge-disjoint subgraphs . If for all , then G is a decomposition of H by G. Two decompositions and of the complete bipartite graph are orthogonal i...A decomposition of a graph H is a partition of the edge set of H into edge-disjoint subgraphs . If for all , then G is a decomposition of H by G. Two decompositions and of the complete bipartite graph are orthogonal if, for all . A set of decompositions of is a set of k mutually orthogonal graph squares (MOGS) if and are orthogonal for all and . For any bipartite graph G with n edges, denotes the maximum number k in a largest possible set of MOGS of by G. Our objective in this paper is to compute where is a path of length d with d + 1 vertices (i.e. Every edge of this path is one-to-one corresponding to an isomorphic to a certain graph F).展开更多
This paper concerns the homogenization problems for porous piezocomposites with infinitely thin metalized pore surfaces.To determine the effective properties,we used the effective moduli method and the finite element ...This paper concerns the homogenization problems for porous piezocomposites with infinitely thin metalized pore surfaces.To determine the effective properties,we used the effective moduli method and the finite element approaches,realized in the ANSYS package.As a simple model of the representative volume,we applied a unit cell of porous piezoceramic material in the form of a cube with one spherical pore.We modeled metallization by introducing an additional layer of material with very large permittivity coefficients along the pore boundary.Then we simulated the nonuniform polarization field around the pore.For taking this effect into account,we previously solved the electrostatic problem for a porous dielectric material with the same geometric structure.From this problem,we obtained the polarization field in the porous piezomaterial;after that,we modified the material properties of the finite elements from dielectric to piezoelectric with element coordinate systems whose corresponding axes rotated along the polarization vectors.As a result,we obtained the porous unit cell of an inhomogeneously polarized piezoceramic matrix.From the solutions of these homogenization problems,we observed that the examined porous piezoceramics composite with metalized pore boundaries has more extensive effective transverse and shear piezomoduli,and effective dielectric constants compared to the conventional porous piezoceramics.The analysis also showed that the effect of the polarization field inhomogeneity is insignificant on the ordinary porous piezoceramics;however,it is more significant on the porous piezoceramics with metalized pore surfaces.展开更多
This paper presents a numerical homogenization analysis of a porous piezoelectric composite with a partially metalized pore surface.The metal layers can be added to the pore surfaces to improve the mechanical and elec...This paper presents a numerical homogenization analysis of a porous piezoelectric composite with a partially metalized pore surface.The metal layers can be added to the pore surfaces to improve the mechanical and electromechanical properties of ordinary porous piezocomposites.Physically,constructing that composite with completely metalized pore surfaces is a challenging process,and imperfect metallization is more expected.Here,we investigate the effects of possible incomplete metallization of pore surfaces on the composite’s equivalent properties.We applied the effective moduli theory,which was developed for the piezoelectric medium based on the Hill-Mandel principle,and the finite element method to compute the effective moduli of the considered composites.Using specific algorithms and programs in the ANSYS APDL programming language,we constructed the representative unit cell element models and performed various computational experiments.Due to the presence of metal inclusion,we found that the dielectric and piezoelectric properties of the considered composites differ dramatically from the corresponding properties of the ordinary porous piezocomposites.The results of this work showed that piezocomposites with partially metallized pore surfaces can have a higher anisotropy,compared to the pure piezoceramic matrix,due to the defects in metal coatings.展开更多
In this paper,we discussed the enhanced Kudryashov’s and general projective Riccati equations tech-niques for obtaining exact solutions to the fifth-order nonlinear water wave(FONLWWE)equation.Using the enhanced Kudr...In this paper,we discussed the enhanced Kudryashov’s and general projective Riccati equations tech-niques for obtaining exact solutions to the fifth-order nonlinear water wave(FONLWWE)equation.Using the enhanced Kudryashov’s method,we were able to achieve solitary wave and singular soliton solutions.Solitary-shock hybrid wave,singular soliton,and periodic wave solutions were discovered when we em-ployed the general projective Riccati equations approach.We can say the given methods are effective and powerful for obtaining exact solutions.Our findings in this paper are critical for explaining a wide range of scientific and oceanographic applications involving ocean gravity waves and other related phenomena.展开更多
文摘This article focuses on the relationship between mathematical morphology operations and rough sets,mainly based on the context of image retrieval and the basic image correspondence problem.Mathematical morphological procedures and set approximations in rough set theory have some clear parallels.Numerous initiatives have been made to connect rough sets with mathematical morphology.Numerous significant publications have been written in this field.Others attempt to show a direct connection between mathematical morphology and rough sets through relations,a pair of dual operations,and neighborhood systems.Rough sets are used to suggest a strategy to approximatemathematicalmorphology within the general paradigm of soft computing.A single framework is defined using a different technique that incorporates the key ideas of both rough sets and mathematical morphology.This paper examines rough set theory from the viewpoint of mathematical morphology to derive rough forms of themorphological structures of dilation,erosion,opening,and closing.These newly defined structures are applied to develop algorithm for the differential analysis of chest X-ray images from a COVID-19 patient with acute pneumonia and a health subject.The algorithm and rough morphological operations show promise for the delineation of lung occlusion in COVID-19 patients from chest X-rays.The foundations of mathematical morphology are covered in this article.After that,rough set theory ideas are taken into account,and their connections are examined.Finally,a suggested image retrieval application of the concepts from these two fields is provided.
文摘An information system is a type of knowledge representation,and attribute reduction is crucial in big data,machine learning,data mining,and intelligent systems.There are several ways for solving attribute reduction problems,but they all require a common categorization.The selection of features in most scientific studies is a challenge for the researcher.When working with huge datasets,selecting all available attributes is not an option because it frequently complicates the study and decreases performance.On the other side,neglecting some attributes might jeopardize data accuracy.In this case,rough set theory provides a useful approach for identifying superfluous attributes that may be ignored without sacrificing any significant information;nonetheless,investigating all available combinations of attributes will result in some problems.Furthermore,because attribute reduction is primarily a mathematical issue,technical progress in reduction is dependent on the advancement of mathematical models.Because the focus of this study is on the mathematical side of attribute reduction,we propose some methods to make a reduction for information systems according to classical rough set theory,the strength of rules and similarity matrix,we applied our proposed methods to several examples and calculate the reduction for each case.These methods expand the options of attribute reductions for researchers.
基金funded by“Taif University Researchers Supporting Project number(TURSP-2020/160),Taif University,Taif,Saudi Arabia”.
文摘In this article,the reduced differential transform method is introduced to solve the nonlinear fractional model of Tumor-Immune.The fractional derivatives are described in the Caputo sense.The solutions derived using this method are easy and very accurate.The model is given by its signal flow diagram.Moreover,a simulation of the system by the Simulink of MATLAB is given.The disease-free equilibrium and stability of the equilibrium point are calculated.Formulation of a fractional optimal control for the cancer model is calculated.In addition,to control the system,we propose a novel modification of its model.This modification is based on converting the model to a memristive one,which is a first time in the literature that such idea is used to control this type of diseases.Also,we study the system’s stability via the Lyapunov exponents and Poincare maps before and after control.Fractional order differential equations(FDEs)are commonly utilized to model systems that have memory,and exist in several physical phenomena,models in thermoelasticity field,and biological paradigms.FDEs have been utilized to model the realistic biphasic decline manner of elastic systems and infection of diseases with a slower rate of change.FDEs are more useful than integer-order in modeling sophisticated models that contain physical phenomena.
基金This work was supported by Taif University under research grant 1-439-6067.The authors would like to acknowledge the scientific support provided by the university.
文摘In this paper,we studied the vibration performance,energy transfer and stability of the offshore wind turbine tower system under mixed excitations.The method of multiple scales is utilized to calculate the approximate solutions of wind turbine system.The proportional-derivative controller was applied for reducing the oscillations of the controlled system.Adding the controller to single degree of freedom system equation is responsible for energy transfers in offshore wind turbine tower system.The steady state solution of stability at worst resonance cases is studied and examined.The offshore wind turbine system behavior was studied numerically at its different parameters values.Furthermore,the response and numerical results were obtained and discussed.The stability is also analyzed using technique of phase plane and equations of frequency response.In addition,the numerical results and comparison between analytical and numerical solutions were obtained with MAPLE and MATLAB algorithms.
文摘The effect of Zn2+ ions on the microstructure and electrical properties of Mn1-xZnxFe2O4 (0.0 ≤ x ≤ 0.5 in steps of 0.1) through a solid state reaction has been investigated. The structural properties have been investigated using X-ray diffraction (XRD) technique. The XRD analysis confirms that all samples are in a single-phase cubic spinel structure. The experimental lattice parameter (aexp) was decreased with increasing Zn2+ ions substitution due to the smaller ionic radius of zinc content. The crystallite size (t) of samples was estimated by Scherrer’s formula and found in the range (90 - 115 nm). Dc electrical resistivity and Seebeck voltage coefficients were measured as a function of temperature using the two probe methods. The temperature variation of resistivity exhibits two breaks, each break referring to a change in the activation energy. The Curie temperature estimated from dc resistivity measurement decreases with increasing Zn2+ ions. Seebeck voltage coefficient measurements reveal n-type conduction for all samples.
基金support from Taif University Researchers Supporting Project Number(TURSP-2020/031),Taif University,Taif,Saudi Arabia.
文摘The detection of error and its correction is an important area of mathematics that is vastly constructed in all communication systems.Furthermore,combinatorial design theory has several applications like detecting or correcting errors in communication systems.Network(graph)designs(GDs)are introduced as a generalization of the symmetric balanced incomplete block designs(BIBDs)that are utilized directly in the above mentioned application.The networks(graphs)have been represented by vectors whose entries are the labels of the vertices related to the lengths of edges linked to it.Here,a general method is proposed and applied to construct new networks designs.This method of networks representation has simplified the method of constructing the network designs.In this paper,a novel representation of networks is introduced and used as a technique of constructing the group generated network designs of the complete bipartite networks and certain circulants.A technique of constructing the group generated network designs of the circulants is given with group generated graph designs(GDs)of certain circulants.In addition,the GDs are transformed into an incidence matrices,the rows and the columns of these matrices can be both viewed as a binary nonlinear code.A novel coding error detection and correction application is proposed and examined.
文摘An orthogonal double cover (ODC) of a graph H is a collection of subgraphs (pages) of H, so that they cover every edge of H twice and the intersection of any two of them contains exactly one edge. An ODC G of H is cyclic (CODC) if the cyclic group of order is a subgroup of the automorphism group of G. In this paper, we introduce a general orthogonal labelling for CODC of circulant graphs and construct CODC by certain classes of graphs such as complete bipartite graph, the union of the co-cycles graph with a star, the center vertex of which, belongs to the co-cycles graph and graphs that are connected by a one vertex.
文摘This paper outlines the vibrational motion of a nonlinear system with a spring of linear stiffness. Homotopy perturbation technique (HPT) is used to obtain the asymptotic solution of the governing equation of motion. The numerical solution of this equation is obtained using the fourth order Runge-Kutta method (RKM). The comparison between both solutions reveals high consistency between them which confirms that, the accuracy of the obtained solution using aforementioned perturbation technique. The time history of the attained solution is represented through some plots to reveal the good effect of the different parameters of the considered system on the motion at any instant. The conditions of the stability of the attained solution are presented and discussed.
文摘The study deals with the multi-choice mathematical programming problem, where the right hand side of the constraints is multi-choice in nature. However, the problem of multi-choice linear programming cannot be solved directly by standard linear or nonlinear programming techniques. The aim of this paper is to transform such problems to a standard mathematical linear programming problem. For each constraint, exactly one parameter value is selected out of a multiple number of parameter values. This process of selection can be established in different ways. In this paper, we present a new simple technique enabling us to handle such problem as a mixed integer linear programming problem and consequently solve them by using standard linear programming software. Our main aim depends on inserting a specific number of binary variables and using them to construct a linear combination which gives just one parameter among the multiple choice values for each choice of the values of the binary variables. A numerical example is presented to illustrate our analysis.
基金Project supported by the National Natural Science Foundation of China(Nos.11972129 and12372008)the National Major Science and Technology Projects of China(No.2017-IV-0008-0045)+3 种基金the Natural Science Foundation of Heilongjiang Province of China(No.YQ2022A008)the Fundamental Research Funds for the Central Universities of China(No.HIT.OCEF.2023006)the Polish National Science Centre of Poland under the OPUS 18 grant(No.2019/35/B/ST8/00980)the Tianjin University Independent Innovation Foundation of China(No.2023XJS-0038)。
文摘The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The adaptive harmonic balance(AHB)method is an improved HBM method.This paper presents a modified AHB method with the asymptotic harmonic selection(AHS)procedure.This new harmonic selection procedure selects harmonics from the frequency spectra of nonlinear terms instead of estimating the contribution of each harmonic to the whole nonlinear response,by which the additional calculation is avoided.A modified continuation method is proposed to deal with the variable size of nonlinear algebraic equations at different values of path parameters,and then all solution branches of the amplitude-frequency response are obtained.Numerical experiments are carried out to verify the performance of the AHB-AHS method.Five typical nonlinear dynamic equations with different types of nonlinearities and excitations are chosen as the illustrative examples.Compared with the classical HBM and Runge-Kutta methods,the proposed AHB-AHS method is of higher accuracy and better convergence.The AHB-AHS method proposed in this paper has the potential to investigate the nonlinear vibrations of complex high-dimensional nonlinear systems.
文摘In this paper, we develop a new numerical method which is based on an exponential spline and Shishkin mesh discretization to solve singularly perturbed boundary value problems, which contain a small uncertain perturbation parameter. The proposed method uses interval analysis principle to deal with the uncertain parameter and the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Furthermore, sensitivity analysis has been conducted using different methods to assess how much the solution is sensitive to the changes of the perturbation parameter. Numerical results are provided to show the applicability and efficiency of the proposed method, which is ε-uniform convergence of almost second order.
文摘A decomposition of a graph H is a partition of the edge set of H into edge-disjoint subgraphs . If for all , then G is a decomposition of H by G. Two decompositions and of the complete bipartite graph are orthogonal if, for all . A set of decompositions of is a set of k mutually orthogonal graph squares (MOGS) if and are orthogonal for all and . For any bipartite graph G with n edges, denotes the maximum number k in a largest possible set of MOGS of by G. Our objective in this paper is to compute where is a path of length d with d + 1 vertices (i.e. Every edge of this path is one-to-one corresponding to an isomorphic to a certain graph F).
基金the framework of the RFBR project 16-58-48009 IND omi and DST.
文摘This paper concerns the homogenization problems for porous piezocomposites with infinitely thin metalized pore surfaces.To determine the effective properties,we used the effective moduli method and the finite element approaches,realized in the ANSYS package.As a simple model of the representative volume,we applied a unit cell of porous piezoceramic material in the form of a cube with one spherical pore.We modeled metallization by introducing an additional layer of material with very large permittivity coefficients along the pore boundary.Then we simulated the nonuniform polarization field around the pore.For taking this effect into account,we previously solved the electrostatic problem for a porous dielectric material with the same geometric structure.From this problem,we obtained the polarization field in the porous piezomaterial;after that,we modified the material properties of the finite elements from dielectric to piezoelectric with element coordinate systems whose corresponding axes rotated along the polarization vectors.As a result,we obtained the porous unit cell of an inhomogeneously polarized piezoceramic matrix.From the solutions of these homogenization problems,we observed that the examined porous piezoceramics composite with metalized pore boundaries has more extensive effective transverse and shear piezomoduli,and effective dielectric constants compared to the conventional porous piezoceramics.The analysis also showed that the effect of the polarization field inhomogeneity is insignificant on the ordinary porous piezoceramics;however,it is more significant on the porous piezoceramics with metalized pore surfaces.
基金This research was done in the framework of the RFBR project 20-31-90102.
文摘This paper presents a numerical homogenization analysis of a porous piezoelectric composite with a partially metalized pore surface.The metal layers can be added to the pore surfaces to improve the mechanical and electromechanical properties of ordinary porous piezocomposites.Physically,constructing that composite with completely metalized pore surfaces is a challenging process,and imperfect metallization is more expected.Here,we investigate the effects of possible incomplete metallization of pore surfaces on the composite’s equivalent properties.We applied the effective moduli theory,which was developed for the piezoelectric medium based on the Hill-Mandel principle,and the finite element method to compute the effective moduli of the considered composites.Using specific algorithms and programs in the ANSYS APDL programming language,we constructed the representative unit cell element models and performed various computational experiments.Due to the presence of metal inclusion,we found that the dielectric and piezoelectric properties of the considered composites differ dramatically from the corresponding properties of the ordinary porous piezocomposites.The results of this work showed that piezocomposites with partially metallized pore surfaces can have a higher anisotropy,compared to the pure piezoceramic matrix,due to the defects in metal coatings.
文摘In this paper,we discussed the enhanced Kudryashov’s and general projective Riccati equations tech-niques for obtaining exact solutions to the fifth-order nonlinear water wave(FONLWWE)equation.Using the enhanced Kudryashov’s method,we were able to achieve solitary wave and singular soliton solutions.Solitary-shock hybrid wave,singular soliton,and periodic wave solutions were discovered when we em-ployed the general projective Riccati equations approach.We can say the given methods are effective and powerful for obtaining exact solutions.Our findings in this paper are critical for explaining a wide range of scientific and oceanographic applications involving ocean gravity waves and other related phenomena.
