For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-al...For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-almost automorphic functions, we give sufficient conditions of the existence and uniqueness of almost automorphic solutions of a differential equation with a piecewise constant argument of generalized type. This is done using the Banach fixed point theorem.展开更多
In this work, we consider the flow through composite porous layers of variable permeability, with the middle layer representing a porous core bounded by two Darcy layers. Brinkman’s equation is valid in the middle la...In this work, we consider the flow through composite porous layers of variable permeability, with the middle layer representing a porous core bounded by two Darcy layers. Brinkman’s equation is valid in the middle layer and has been reduced to an Airy’s inhomogeneous differential equation. Solution is obtained in terms of Airy’s functions and the Nield-Kuznetsov function.展开更多
Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single...Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Green’s function for the T-stress is obtained in a straightforward manner. Furthermore, Green’s functions are derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimposing method. Then, Green’s function is used to predict the domain-switch-induced T-stress in a ferroelectric double cantilever beam （DCB） test. The T-stress induced by the electromechanical loading is used to judge the stable and unstable crack growth behaviors observed in the test. The prediction results generally agree with the experimental data.展开更多
By the generalized Borsuk theorem in coincidence degree theory, a p-Laplacian neutral functional differential equation is studied. A new result on the existence of periodic solution is obtained. The interest is that s...By the generalized Borsuk theorem in coincidence degree theory, a p-Laplacian neutral functional differential equation is studied. A new result on the existence of periodic solution is obtained. The interest is that some coeffcient in it is not a constant function and its sign can be changeable, which is different from that in the known literatures.展开更多
Respiratory variables, including tidal volume and respiratory rate, display significant variability. The probability density function (PDF) of respiratory variables has been shown to contain clinical information and c...Respiratory variables, including tidal volume and respiratory rate, display significant variability. The probability density function (PDF) of respiratory variables has been shown to contain clinical information and can predict the risk for exacerbation in asthma. However, it is uncertain why this PDF plays a major role in predicting the dynamic conditions of the respiratory system. This paper introduces a stochastic optimal control model for noisy spontaneous breathing, and obtains a Shrödinger’s wave equation as the motion equation that can produce a PDF as a solution. Based on the lobules-bronchial tree model of the lung system, the tidal volume variable was expressed by a polar coordinate, by use of which the Shrödinger’s wave equation of inter-breath intervals (IBIs) was obtained. Through the wave equation of IBIs, the respiratory rhythm generator was characterized by the potential function including the PDF and the parameter concerning the topographical distribution of regional pulmonary ventilations. The stochastic model in this study was assumed to have a common variance parameter in the state variables, which would originate from the variability in metabolic energy at the cell level. As a conclusion, the PDF of IBIs would become a marker of neuroplasticity in the respiratory rhythm generator through Shr?dinger’s wave equation for IBIs.展开更多
This paper presents the latest status of the open source advanced TCAD simulator called Nano-Electronic Simulation Software(NESS)which is currently under development at the Device Modeling Group of the University of G...This paper presents the latest status of the open source advanced TCAD simulator called Nano-Electronic Simulation Software(NESS)which is currently under development at the Device Modeling Group of the University of Glasgow.NESS is designed with the main aim to provide an open,flexible,and easy to use simulation environment where users are able not only to perform numerical simulations but also to develop and implement new simulation methods and models.Currently,NESS is organized into two main components:the structure generator and a collection of different numerical solvers;which are linked to supporting components such as an effective mass extractor and materials database.This paper gives a brief overview of each of the components by describing their main capabilities,structure,and theory behind each one of them.Moreover,to illustrate the capabilities of each component,here we have given examples considering various device structures,architectures,materials,etc.at multiple simulation conditions.We expect that NESS will prove to be a great tool for both conventional as well as exploratory device research programs and projects.展开更多
The description of the microscopic world in quantum mechanics is very different from that in classical physics, and there are some points of view that are contrary to intuition and logic. The first is the problem of r...The description of the microscopic world in quantum mechanics is very different from that in classical physics, and there are some points of view that are contrary to intuition and logic. The first is the problem of reality;quantum mechanics believes the behavior of micro particles is random and jumping. The second is the loss of certainty;the conjugate physical variables of a system cannot be determined synchronously, they satisfy the Heisenberg uncertainty principle. The third is the non-local correlation. The measurement of one particle in the quantum entanglement pair will influence the state of the other entangled particle simultaneously. In this paper, some concepts related to quantum entanglement, such as EPR correlation, quantum entanglement correlation function, Bell’s inequality and so on, are analyzed in detail. Analysis shows that the mystery and confusion in quantum theory may be caused by the logical problems in its basic framework. Bell’s inequality is only a mathematical theorem, but its physical meaning is actually unclear. The Bell state of quantum entangled pair may not satisfy the dynamic equation of quantum theory, so it cannot describe the true state of microscopic particles. In this paper, the correct correlation functions of spin entanglement pair and photonic entanglement pair are strictly derived according to normal logic. Quantum theory is a more fundamental theory than classical mechanics, and they are not equal relation in logic. However, there are still some unreasonable contents in the framework of quantum theory, which need to be improved. In order to disclose the real relationship between quantum theory and classical mechanics, we propose some experiments which provide intuitionistic teaching materials for the new interpretation of quantum theory.展开更多
文摘For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-almost automorphic functions, we give sufficient conditions of the existence and uniqueness of almost automorphic solutions of a differential equation with a piecewise constant argument of generalized type. This is done using the Banach fixed point theorem.
文摘In this work, we consider the flow through composite porous layers of variable permeability, with the middle layer representing a porous core bounded by two Darcy layers. Brinkman’s equation is valid in the middle layer and has been reduced to an Airy’s inhomogeneous differential equation. Solution is obtained in terms of Airy’s functions and the Nield-Kuznetsov function.
基金Project supported by the National Natural Science Foundation of China(Nos.10702071 and 11090334)the China Postdoctoral Science Foundation(No.201003281)+2 种基金the Shanghai Postdoctoral Scientific Program(No.10R21415800)the Shanghai Leading Academic Discipline Project(No.B302)sponsored by the"Sino-German Center for Research Promotion"under a project of"Crack Growth in Ferroelectrics Driven by Cyclic Electric Loading"
文摘Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Green’s function for the T-stress is obtained in a straightforward manner. Furthermore, Green’s functions are derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimposing method. Then, Green’s function is used to predict the domain-switch-induced T-stress in a ferroelectric double cantilever beam （DCB） test. The T-stress induced by the electromechanical loading is used to judge the stable and unstable crack growth behaviors observed in the test. The prediction results generally agree with the experimental data.
基金supported by Natural Science Foundation of Education Department of Anhui Province (No.KJ2010B353)Young Teacher’s Foundation of Anhui Normal University (No.2008xqn46)
文摘By the generalized Borsuk theorem in coincidence degree theory, a p-Laplacian neutral functional differential equation is studied. A new result on the existence of periodic solution is obtained. The interest is that some coeffcient in it is not a constant function and its sign can be changeable, which is different from that in the known literatures.
文摘Respiratory variables, including tidal volume and respiratory rate, display significant variability. The probability density function (PDF) of respiratory variables has been shown to contain clinical information and can predict the risk for exacerbation in asthma. However, it is uncertain why this PDF plays a major role in predicting the dynamic conditions of the respiratory system. This paper introduces a stochastic optimal control model for noisy spontaneous breathing, and obtains a Shrödinger’s wave equation as the motion equation that can produce a PDF as a solution. Based on the lobules-bronchial tree model of the lung system, the tidal volume variable was expressed by a polar coordinate, by use of which the Shrödinger’s wave equation of inter-breath intervals (IBIs) was obtained. Through the wave equation of IBIs, the respiratory rhythm generator was characterized by the potential function including the PDF and the parameter concerning the topographical distribution of regional pulmonary ventilations. The stochastic model in this study was assumed to have a common variance parameter in the state variables, which would originate from the variability in metabolic energy at the cell level. As a conclusion, the PDF of IBIs would become a marker of neuroplasticity in the respiratory rhythm generator through Shr?dinger’s wave equation for IBIs.
基金the European Union Horizon 2020 research and innovation programme under grant agreement No.688101 SUPERAID7 and has received further funding from EPSRC UKRI Innovation Fellowship scheme under grant agreement No.EP/S001131/1(QSEE),No.EP/P009972/1(QUANTDEVMOD)and No.EP/S000259/1(Variability PDK for design based research on FPGA/neuro computing)and from H2020-FETOPEN-2019 scheme under grant agreement No.862539-Electromed-FET OPEN.
文摘This paper presents the latest status of the open source advanced TCAD simulator called Nano-Electronic Simulation Software(NESS)which is currently under development at the Device Modeling Group of the University of Glasgow.NESS is designed with the main aim to provide an open,flexible,and easy to use simulation environment where users are able not only to perform numerical simulations but also to develop and implement new simulation methods and models.Currently,NESS is organized into two main components:the structure generator and a collection of different numerical solvers;which are linked to supporting components such as an effective mass extractor and materials database.This paper gives a brief overview of each of the components by describing their main capabilities,structure,and theory behind each one of them.Moreover,to illustrate the capabilities of each component,here we have given examples considering various device structures,architectures,materials,etc.at multiple simulation conditions.We expect that NESS will prove to be a great tool for both conventional as well as exploratory device research programs and projects.
文摘The description of the microscopic world in quantum mechanics is very different from that in classical physics, and there are some points of view that are contrary to intuition and logic. The first is the problem of reality;quantum mechanics believes the behavior of micro particles is random and jumping. The second is the loss of certainty;the conjugate physical variables of a system cannot be determined synchronously, they satisfy the Heisenberg uncertainty principle. The third is the non-local correlation. The measurement of one particle in the quantum entanglement pair will influence the state of the other entangled particle simultaneously. In this paper, some concepts related to quantum entanglement, such as EPR correlation, quantum entanglement correlation function, Bell’s inequality and so on, are analyzed in detail. Analysis shows that the mystery and confusion in quantum theory may be caused by the logical problems in its basic framework. Bell’s inequality is only a mathematical theorem, but its physical meaning is actually unclear. The Bell state of quantum entangled pair may not satisfy the dynamic equation of quantum theory, so it cannot describe the true state of microscopic particles. In this paper, the correct correlation functions of spin entanglement pair and photonic entanglement pair are strictly derived according to normal logic. Quantum theory is a more fundamental theory than classical mechanics, and they are not equal relation in logic. However, there are still some unreasonable contents in the framework of quantum theory, which need to be improved. In order to disclose the real relationship between quantum theory and classical mechanics, we propose some experiments which provide intuitionistic teaching materials for the new interpretation of quantum theory.
