In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation...In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.展开更多
Third order nonlinear ordinary differential equation, subject to appropriate boundary conditions, arising in fluid mechanics is solved exactly using more suggestive schemes- Dirichlet series and method of stretching v...Third order nonlinear ordinary differential equation, subject to appropriate boundary conditions, arising in fluid mechanics is solved exactly using more suggestive schemes- Dirichlet series and method of stretching variables. These methods have advantages over pure numerical methods in obtaining derived quantities accurately for various values of the parameters involved at a stretch and are valid in a much larger domain compared with classical numerical schemes.展开更多
The commencement speech becomes pivotal because it inspires,educates,and enlightens the graduates.Therefore,it is of great value to make a study on the speeches.This article analyzes two commencement speeches between ...The commencement speech becomes pivotal because it inspires,educates,and enlightens the graduates.Therefore,it is of great value to make a study on the speeches.This article analyzes two commencement speeches between China and America from the perspective of rhetoric,namely Aristotle’s appeals as the well as deductive and inductive method of reasoning and finds out that the similarities and differences of those two speeches concerning Aristotle’s appeals as the well as deductive and inductive method of reasoning.展开更多
The Current Standard Model of the Universe asserts that the universe is generated from a single Big Bang event followed by inflation. There is no center to this universe, hence, no preferential reference frame to desc...The Current Standard Model of the Universe asserts that the universe is generated from a single Big Bang event followed by inflation. There is no center to this universe, hence, no preferential reference frame to describe the motions of celestial objects. We propose a new, Shell Model of the Universe, which contends that the universe is created from multiple, concentric big bangs. Accordingly, that origin presents itself as a unique, preferential reference frame, which furnishes the simplest description of the motions of galaxies in the cosmos. This is similar in manner to how planetary motion is more straightforwardly described via a sun-centered Solar System rather than an earth-centered one. The appeal of the Shell Model of the Universe lies in its simplistic ability to resolve the paradox of quasars, explain the variability in Hubble’s Constant, and solve the problematic accelerated expansion of the universe.展开更多
The present study deals with a spatially homogeneous and anisotropic Bianehi-I cosmological models representing massive strings with magnetic field and decaying vacuum energy density A. The energy-momentum tensor, as ...The present study deals with a spatially homogeneous and anisotropic Bianehi-I cosmological models representing massive strings with magnetic field and decaying vacuum energy density A. The energy-momentum tensor, as formulated by Letelier （1983）, has been used to construct massive string cosmological models for which we assume the expansion scalar in the models is proportional to one of the components of shear tensor. The Einstein＇s field equations have been solved by applying a variation law for generalized Hubble＇s parameter in Bianchi-I space-time. The variation law for Hubble＇s parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential form. Using these two forms, Einstein＇s field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. We have made a comparative study of accelerating and decelerating models in the presence of string scenario. The study reveals that massive strings dominate in the decelerating universe whereas strings dominate in the accelerating universe. The strings eventually disappear from the universe for sufficiently large times, which is in agreement with current astronomical observations. The cosmological constant A is found to be a positive decreasing function of time which is corroborated by results from recent supernovae Ia observations. The physical and geometric properties of the models have been also discussed in detail.展开更多
This paper provides an adaptive closed-loop strategy for suppressing the pathological oscillations of the basal ganglia based on a variable universe fuzzy algorithm.The pathological basal ganglia oscillations in the t...This paper provides an adaptive closed-loop strategy for suppressing the pathological oscillations of the basal ganglia based on a variable universe fuzzy algorithm.The pathological basal ganglia oscillations in the theta(4-9 Hz)and beta(12-35 Hz)frequency bands have been demonstrated to be associated with the tremor and rigidity/bradykinesia symptoms in Parkinson’s disease(PD).Although the clinical application of open-loop deep brain stimulation(DBS)is effective,the stimulation waveform with the fixed parameters cannot be self-adjusted as the disease progresses,and thus the stimulation effects go poor.To deal with this difficult problem,a variable universe fuzzy closed-loop strategy is proposed to modulate different PD states.We establish a cortico-basal ganglia-thalamocortical network model to simulate pathological oscillations and test the control effect.The results suggest that the proposed closed-loop control strategy can accommodate the variation of brain states and symptoms,which may become an alternative method to administrate the symptoms in PD.展开更多
This paper presents a closed form solution and numerical analysis for Es- helby＇s elliptic inclusion in an infinite plate. The complex variable method and the confor- real mapping technique are used. The continuity c...This paper presents a closed form solution and numerical analysis for Es- helby＇s elliptic inclusion in an infinite plate. The complex variable method and the confor- real mapping technique are used. The continuity conditions for the traction and displace- ment along the interface in the physical plane are reduced to the similar conditions along the unit circle of the mapping plane. The properties of the complex potentials defined in the finite elliptic region are analyzed. From the continuity conditions, one can separate and obtain the relevant complex potentials defined in the inclusion and the matrix. From the obtained complex potentials, the dependence of the real strains and stresses in the inclusion from the assumed eigenstrains is evaluated. In addition, the stress distribution on the interface along the matrix side is evaluated. The results are obtained in the paper for the first time.展开更多
This paper proposes a straightforward and concise approach to analyze the Saint-Venant’s torsion of a circular shaft containing multiple elliptical inclusions or cracks based on the complex variable method.The comple...This paper proposes a straightforward and concise approach to analyze the Saint-Venant’s torsion of a circular shaft containing multiple elliptical inclusions or cracks based on the complex variable method.The complex potentials are first derived for the shaft with N elliptical inclusions by introducing Faber series expansion,and then the shear stresses and torsional rigidity are calculated.When the inclusions degenerate into cracks,the solutions for the intensity factors of stress are obtained.Finally,several numerical examples are carried out to discuss the effects of geometry parameters,different shear modulus ratios and array-types of the elliptical inclusions/cracks on the fields of stresses.The obtained results show that the proposed approach has advantages such as high accuracy and good convergence.展开更多
In this research we are going to define two new concepts: a) “The Potential of Events” (EP) and b) “The Catholic Information” (CI). The term CI derives from the ancient Greek language and declares all the Catholic...In this research we are going to define two new concepts: a) “The Potential of Events” (EP) and b) “The Catholic Information” (CI). The term CI derives from the ancient Greek language and declares all the Catholic (general) Logical Propositions (<img src="Edit_5f13a4a5-abc6-4bc5-9e4c-4ff981627b2a.png" width="33" height="21" alt="" />) which will true for every element of a set A. We will study the Riemann Hypothesis in two stages: a) By using the EP we will prove that the distribution of events e (even) and o (odd) of Square Free Numbers (SFN) on the axis Ax(N) of naturals is Heads-Tails (H-T) type. b) By using the CI we will explain the way that the distribution of prime numbers can be correlated with the non-trivial zeros of the function <em>ζ</em>(<em>s</em>) of Riemann. The Introduction and the Chapter 2 are necessary for understanding the solution. In the Chapter 3 we will present a simple method of forecasting in many very useful applications (e.g. financial, technological, medical, social, etc) developing a generalization of this new, proven here, theory which we finally apply to the solution of RH. The following Introduction as well the Results with the Discussion at the end shed light about the possibility of the proof of all the above. The article consists of 9 chapters that are numbered by 1, 2, …, 9.展开更多
This article introduces the computational analytical approach to solve the m-dimensional space-time variable Caputo fractional order advection–dispersion equation with the Dirichlet boundary using the two-step Adomia...This article introduces the computational analytical approach to solve the m-dimensional space-time variable Caputo fractional order advection–dispersion equation with the Dirichlet boundary using the two-step Adomian decomposition method and obtain the exact solution in just one iteration.Moreover,with the help of fixed point theory,we study the existence and uniqueness conditions for the positive solution and prove some new results.Also,obtain the Ulam–Hyers stabilities for the proposed problem.Two gen-eralized examples are considered to show the method’s applicability and compared with other existing numerical methods.The present method performs exceptionally well in terms of efficiency and simplicity.Further,we solved both examples using the two most well-known numerical methods and compared them with the TSADM solution.展开更多
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant Nos. 2004zx16 and Q2005A01
文摘In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.
文摘Third order nonlinear ordinary differential equation, subject to appropriate boundary conditions, arising in fluid mechanics is solved exactly using more suggestive schemes- Dirichlet series and method of stretching variables. These methods have advantages over pure numerical methods in obtaining derived quantities accurately for various values of the parameters involved at a stretch and are valid in a much larger domain compared with classical numerical schemes.
文摘The commencement speech becomes pivotal because it inspires,educates,and enlightens the graduates.Therefore,it is of great value to make a study on the speeches.This article analyzes two commencement speeches between China and America from the perspective of rhetoric,namely Aristotle’s appeals as the well as deductive and inductive method of reasoning and finds out that the similarities and differences of those two speeches concerning Aristotle’s appeals as the well as deductive and inductive method of reasoning.
文摘The Current Standard Model of the Universe asserts that the universe is generated from a single Big Bang event followed by inflation. There is no center to this universe, hence, no preferential reference frame to describe the motions of celestial objects. We propose a new, Shell Model of the Universe, which contends that the universe is created from multiple, concentric big bangs. Accordingly, that origin presents itself as a unique, preferential reference frame, which furnishes the simplest description of the motions of galaxies in the cosmos. This is similar in manner to how planetary motion is more straightforwardly described via a sun-centered Solar System rather than an earth-centered one. The appeal of the Shell Model of the Universe lies in its simplistic ability to resolve the paradox of quasars, explain the variability in Hubble’s Constant, and solve the problematic accelerated expansion of the universe.
基金Supported in part by the Council of Science and Technology,Uttar Pradesh,India
文摘The present study deals with a spatially homogeneous and anisotropic Bianehi-I cosmological models representing massive strings with magnetic field and decaying vacuum energy density A. The energy-momentum tensor, as formulated by Letelier （1983）, has been used to construct massive string cosmological models for which we assume the expansion scalar in the models is proportional to one of the components of shear tensor. The Einstein＇s field equations have been solved by applying a variation law for generalized Hubble＇s parameter in Bianchi-I space-time. The variation law for Hubble＇s parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential form. Using these two forms, Einstein＇s field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. We have made a comparative study of accelerating and decelerating models in the presence of string scenario. The study reveals that massive strings dominate in the decelerating universe whereas strings dominate in the accelerating universe. The strings eventually disappear from the universe for sufficiently large times, which is in agreement with current astronomical observations. The cosmological constant A is found to be a positive decreasing function of time which is corroborated by results from recent supernovae Ia observations. The physical and geometric properties of the models have been also discussed in detail.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62173241 and 62171312)the Natural Science Foundation of Tianjin,China(Grant Nos.20JCQNJC01160 and 19JCZDJC36500)the financial support provided by Opening Foundation of Key Laboratory of Opto-technology and Intelligent Control(Lanzhou Jiaotong University),Ministry of Education,China(Grant No.KFKT2020-01)
文摘This paper provides an adaptive closed-loop strategy for suppressing the pathological oscillations of the basal ganglia based on a variable universe fuzzy algorithm.The pathological basal ganglia oscillations in the theta(4-9 Hz)and beta(12-35 Hz)frequency bands have been demonstrated to be associated with the tremor and rigidity/bradykinesia symptoms in Parkinson’s disease(PD).Although the clinical application of open-loop deep brain stimulation(DBS)is effective,the stimulation waveform with the fixed parameters cannot be self-adjusted as the disease progresses,and thus the stimulation effects go poor.To deal with this difficult problem,a variable universe fuzzy closed-loop strategy is proposed to modulate different PD states.We establish a cortico-basal ganglia-thalamocortical network model to simulate pathological oscillations and test the control effect.The results suggest that the proposed closed-loop control strategy can accommodate the variation of brain states and symptoms,which may become an alternative method to administrate the symptoms in PD.
文摘This paper presents a closed form solution and numerical analysis for Es- helby＇s elliptic inclusion in an infinite plate. The complex variable method and the confor- real mapping technique are used. The continuity conditions for the traction and displace- ment along the interface in the physical plane are reduced to the similar conditions along the unit circle of the mapping plane. The properties of the complex potentials defined in the finite elliptic region are analyzed. From the continuity conditions, one can separate and obtain the relevant complex potentials defined in the inclusion and the matrix. From the obtained complex potentials, the dependence of the real strains and stresses in the inclusion from the assumed eigenstrains is evaluated. In addition, the stress distribution on the interface along the matrix side is evaluated. The results are obtained in the paper for the first time.
基金supported by the National Natural Science Fund of China (No. 11802040)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(No.18KJB130001)
文摘This paper proposes a straightforward and concise approach to analyze the Saint-Venant’s torsion of a circular shaft containing multiple elliptical inclusions or cracks based on the complex variable method.The complex potentials are first derived for the shaft with N elliptical inclusions by introducing Faber series expansion,and then the shear stresses and torsional rigidity are calculated.When the inclusions degenerate into cracks,the solutions for the intensity factors of stress are obtained.Finally,several numerical examples are carried out to discuss the effects of geometry parameters,different shear modulus ratios and array-types of the elliptical inclusions/cracks on the fields of stresses.The obtained results show that the proposed approach has advantages such as high accuracy and good convergence.
文摘In this research we are going to define two new concepts: a) “The Potential of Events” (EP) and b) “The Catholic Information” (CI). The term CI derives from the ancient Greek language and declares all the Catholic (general) Logical Propositions (<img src="Edit_5f13a4a5-abc6-4bc5-9e4c-4ff981627b2a.png" width="33" height="21" alt="" />) which will true for every element of a set A. We will study the Riemann Hypothesis in two stages: a) By using the EP we will prove that the distribution of events e (even) and o (odd) of Square Free Numbers (SFN) on the axis Ax(N) of naturals is Heads-Tails (H-T) type. b) By using the CI we will explain the way that the distribution of prime numbers can be correlated with the non-trivial zeros of the function <em>ζ</em>(<em>s</em>) of Riemann. The Introduction and the Chapter 2 are necessary for understanding the solution. In the Chapter 3 we will present a simple method of forecasting in many very useful applications (e.g. financial, technological, medical, social, etc) developing a generalization of this new, proven here, theory which we finally apply to the solution of RH. The following Introduction as well the Results with the Discussion at the end shed light about the possibility of the proof of all the above. The article consists of 9 chapters that are numbered by 1, 2, …, 9.
文摘This article introduces the computational analytical approach to solve the m-dimensional space-time variable Caputo fractional order advection–dispersion equation with the Dirichlet boundary using the two-step Adomian decomposition method and obtain the exact solution in just one iteration.Moreover,with the help of fixed point theory,we study the existence and uniqueness conditions for the positive solution and prove some new results.Also,obtain the Ulam–Hyers stabilities for the proposed problem.Two gen-eralized examples are considered to show the method’s applicability and compared with other existing numerical methods.The present method performs exceptionally well in terms of efficiency and simplicity.Further,we solved both examples using the two most well-known numerical methods and compared them with the TSADM solution.
