Integrating Chinese culture into college English can not only enhance students’humanities literacy and cultivate their cultural confidence,but also facilitate the inheritance and international dissemination of Chines...Integrating Chinese culture into college English can not only enhance students’humanities literacy and cultivate their cultural confidence,but also facilitate the inheritance and international dissemination of Chinese culture.Taking Tyler’s curriculum framework as the starting point,this paper analyzes some factors that affect the integration of Chinese culture into the college English teaching and proposes some strategies for the integration of Chinese culture into college English teaching by innovating teaching objectives,enriching teaching contents,transforming modes of course delivery,and reconstructing the assessment system.展开更多
In daily communication between teachers and students,many Chinese teachers fail to use politeness principle tactfully or appropriately.This article analyzes some basic principles of politeness and their application in...In daily communication between teachers and students,many Chinese teachers fail to use politeness principle tactfully or appropriately.This article analyzes some basic principles of politeness and their application in teachers-students communication.展开更多
This research aims to integrate Bekenstein’s bound and Landauer’s principle, providing a unified framework to understand the limits of information and energy in physical systems. By combining these principles, we ex...This research aims to integrate Bekenstein’s bound and Landauer’s principle, providing a unified framework to understand the limits of information and energy in physical systems. By combining these principles, we explore the implications for black hole thermodynamics, astrophysics, astronomy, information theory, and the search for new laws of nature. The result includes an estimation of the number of bits stored in a black hole (less than 1.4 × 10<sup>30</sup> bits/m<sup>3</sup>), enhancing our understanding of information storage in extreme gravitational environments. This integration offers valuable insights into the fundamental nature of information and energy, impacting scientific advancements in multiple disciplines.展开更多
By using the properties of w-distances and Gerstewitz's functions, we first give a vectorial Takahashi's nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland's variatio...By using the properties of w-distances and Gerstewitz's functions, we first give a vectorial Takahashi's nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland's variational principle, where the objective function is from a complete metric space into a pre-ordered topological vector space and the perturbation contains a w-distance and a non-decreasing function of the objective function value. From the general vectorial variational principle, we deduce a vectorial Caristfs fixed point theorem with a w-distance. Finally we show that the above three theorems are equivalent to each other. The related known results are generalized and improved. In particular, some conditions in the theorems of [Y. Araya, Ekeland's variational principle and its equivalent theorems in vector optimization, J. Math. Anal. Appl. 346(2008), 9-16] are weakened or even completely relieved.展开更多
In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland's theorem related to set-valued vector equilibrium problems. As applications, we der...In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland's theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient solution for set-valued vector equilibrium problems without the assumption of convexity of the constraint set and the assumptions of convexity and monotonicity of the set-valued mapping. We also obtain an existence theorem of ε-approximate solution for set-valued vector equilibrium problems without the assumptions of compactness and convexity of the constraint set.展开更多
The dynamical and physical behavior of a complex system can be more accurately described by using the fractional model.With the successful use of fractional calculus in many areas of science and engineering,it is nece...The dynamical and physical behavior of a complex system can be more accurately described by using the fractional model.With the successful use of fractional calculus in many areas of science and engineering,it is necessary to extend the classical theories and methods of analytical mechanics to the fractional dynamic system.Birkhoffian mechanics is a natural generalization of Hamiltonian mechanics,and its core is the Pfaff-Birkhoff principle and Birkhoff′s equations.The study on the Birkhoffian mechanics is an important developmental direction of modern analytical mechanics.Here,the fractional Pfaff-Birkhoff variational problem is presented and studied.The definitions of fractional derivatives,the formulae for integration by parts and some other preliminaries are firstly given.Secondly,the fractional Pfaff-Birkhoff principle and the fractional Birkhoff′s equations in terms of RieszRiemann-Liouville fractional derivatives and Riesz-Caputo fractional derivatives are presented respectively.Finally,an example is given to illustrate the application of the results.展开更多
The radiation fields generated when a charged particle is incident on or moving away from a perfectly conducting plane are obtained. These fields are known in the literature as transition radiation. The field equation...The radiation fields generated when a charged particle is incident on or moving away from a perfectly conducting plane are obtained. These fields are known in the literature as transition radiation. The field equations derived thus are used to evaluate the energy, momentum and the action associated with the radiation. The results show that for a charged particle moving with speed ν, the longitudinal momentum associated with the transition radiation is approximately equal to ΔU/c for values of ?1- ν/c smaller than about 10-3 where ΔU is the total radiated energy dissipated during the interaction and cis the speed of light in free space. The action of the radiation, defined as the product of the total energy dissipated and the duration of the emission, increases as 1- ν/c decreases and, for an electron, it becomes equal to h/4π when ν = c - νm where νm is the speed pertinent to the lowest possible momentum associated with a particle confined inside the universe and?h is the Planck constant. Combining these results with Heisenberg’s uncertainty principle, an expression that predicts the value of the elementary charge is derived.展开更多
Business English reading teaching under the mode of“literature circles”focuses on cultivating students’autonomy in reading,group cooperation,and the exchange of ideas among group members.In this teaching mode,teach...Business English reading teaching under the mode of“literature circles”focuses on cultivating students’autonomy in reading,group cooperation,and the exchange of ideas among group members.In this teaching mode,teachers are no longer the masters of the reading classroom,but the helpers,participants,and researchers in the process of students’reading.The reconstruction of teachers’role can promote the benign development of relationship not only between teachers and students,but also between students and students,inject new impetus and vitality into the classroom,and improve students’reading literacy.展开更多
The paper posits that kin sociality and eusociality are derived from the handicap-care principles based on the need-based care to the handicappers from the caregivers for the self-interest of the caregivers. In this p...The paper posits that kin sociality and eusociality are derived from the handicap-care principles based on the need-based care to the handicappers from the caregivers for the self-interest of the caregivers. In this paper, handicap is defined as the difficulty to survive and reproduce independently. Kin sociality is derived from the childhood handicap-care principle where the children are the handicapped children who receive the care from the kin caregivers in the inclusive kin group to survive. The caregiver gives care for its self-interest to reproduce its gene. The individual’s gene of kin sociality contains the handicapped childhood and the caregiving adulthood. Eusociality is derived from the adulthood handicap-care principle where responsible adults are the handicapped adults who give care and receive care at the same time in the interdependent eusocial group to survive and reproduce its gene. Queen bees reproduce, but must receive care from worker bees that work but must rely on queen bees to reproduce. A caregiver gives care for its self-interest to survive and reproduce its gene. The individual’s gene of eusociality contains the handicapped childhood-adulthood and the caregiving adulthood. The chronological sequence of the sociality evolution is individual sociality without handicap, kin sociality with handicapped childhood, and eusociality with handicapped adulthood. Eusociality in humans is derived from bipedalism and the mixed habitat. The chronological sequence of the eusocial human evolution is 1) the eusocial early hominins with bipedalism and the mixed habitat, 2) the eusocial early Homo species with bipedalism, the larger brain, and the open habitat, 3) the eusocial late Homo species with bipedalism, the largest brain, and the unstable habitat, and 4) extended eusocial Homo sapiens with bipedalism, the shrinking brain, omnipresent imagination, and the harsh habitat. The omnipresence of imagination in human culture converts eusociality into extended eusociality with both perception and omnipresent imagination.展开更多
Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous...Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (<i>I</i>) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (<em>δI</em>) set to zero is a necessary condition for an extremum of <i>I</i>. In this approach one could use <i>δI</i> = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from <i>δI</i> = 0, which is also satisfied by a solution obtained from <i>δI</i> = 0. The Euler’s equations obtained from <i>δI</i> = 0 indeed are the mathematical model associated with the energy functional <i>I</i>. In case of BVPs we follow the same approach except in this case, the energy functional <i>I</i> consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles <i>i.e.</i> conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.展开更多
With the development of the times and the progress of the society,the ancient education mode can no longer meet the requirements of the times.The concept of educating people must keep pace with the times.The way teach...With the development of the times and the progress of the society,the ancient education mode can no longer meet the requirements of the times.The concept of educating people must keep pace with the times.The way teachers and students get along is no longer like in ancient times,where teachers teach students to listen.In the new era,it is necessary to build a new model of interaction between teachers and students.If educators pay attention and come to understand students’psychology,listen to students’aspirations,tend to students’emotions,grow in love for education,and treat students from their hearts,they would be able to win the favor of students.Paying attention to students’emotional value can promote emotional communication between teachers and students.It is possible to adapt to the requirements of the new era for the construction of morality and ethics among teachers by caring for students’emotional value.展开更多
Hemingway established a well-known literary theory - iceberg principle.He said he always attempted to create his literary works according to this principle.In his opinion,if a prose writer has a pretty clear idea of w...Hemingway established a well-known literary theory - iceberg principle.He said he always attempted to create his literary works according to this principle.In his opinion,if a prose writer has a pretty clear idea of what he writes about,then he can omit the things he knows,and the readers will strongly feel that what the writer has omitted seems to have been written as long as what he writes is authentic.Hemingway himself once said,"The dignity of movement of an iceberg is due to only one eighth of it being above water."Here,one eighth refers to the information given by the author,and the rest refers to the unwrit ten information that can be acquired in readers'imagination on the basis of the one eighth.The Killers is a good example of Hemingway's iceberg principle.This essay will analyse the characters in it to show how the principle was used in this short story.With no doubt the iceberg principle leaves a large space for the readers to imagine and better understand Hemingway's works.展开更多
It is demonstrated that the use of Kolmogorov’s probability theory to describe results of quantum probability for EPRB (Einstein-Podolsky-Rosen-Bohm) experiments requires extreme care when different subsets of measur...It is demonstrated that the use of Kolmogorov’s probability theory to describe results of quantum probability for EPRB (Einstein-Podolsky-Rosen-Bohm) experiments requires extreme care when different subsets of measurement outcomes are considered. J. S. Bell and his followers have committed critical inaccuracies related to spin-gauge and probability measures of such subsets, because they use exclusively a single probability space for all data sets and sub-sets of data. It is also shown that Bell and followers use far too stringent epistemological requirements for the consequences of space-like separation. Their requirements reach way beyond Einstein’s separation principle and cannot be met by the major existing physical theories including relativity and even classical mechanics. For example, the independent free will does not empower the experimenters to choose multiple independent spin-gauges in the two EPRB wings. It is demonstrated that the suggestion of instantaneous influences at a distance (supposedly “derived” from experiments with entangled quantum entities) is a consequence of said inaccuracies and takes back rank as soon as the Kolmogorov probability measures are related to a consistent global spin-gauge and permitted to be different for different data subsets: Using statistical interpretations and different probability spaces for certain subsets of outcomes instead of probability amplitudes related to single quantum entities, permits physical explanations without a violation of Einstein’s separation principle.展开更多
This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and this set-valued Ca...This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and this set-valued Caristi’s fixed point theorem.The results stated in this paper improve and strengthen the corresponding results in[4].展开更多
This article obtains an explicit expression of the heat kernels on H-type groups and then follow the estimate of heat kernels to deduce the Hardy's uncertainty principle on the nilpotent Lie groups.
Variational principles are constructed using the semi-inverse method for two kinds of extended Korteweg-de Vries (KdV) equations, which can be regarded as simple models of the nonlinear oceanic internal waves and at...Variational principles are constructed using the semi-inverse method for two kinds of extended Korteweg-de Vries (KdV) equations, which can be regarded as simple models of the nonlinear oceanic internal waves and atmospheric long waves, respectively. The obtained variational principles have also been proved to be correct.展开更多
基金supported by Program of curriculum ideological and political education teaching reform,Zhoukou Normal University-Research on the Path of Ideological and Political Construction of College English Course in local universities from the perspective of cultural confidence(Fund No.SZJG-2022004)Program of Educational Curriculum Reform Henan Province-The exploration of the cultivation of the mentors in normal universities under the background of teacher professional certification(Fund No.2022-JSJYZD-028)+1 种基金the research and practice program of teaching and learning in Zhoukou Normal University(Fund No.JF2021016)achievements of the training program for young and middle-aged key teachers at Zhoukou Normal University in 2021.
文摘Integrating Chinese culture into college English can not only enhance students’humanities literacy and cultivate their cultural confidence,but also facilitate the inheritance and international dissemination of Chinese culture.Taking Tyler’s curriculum framework as the starting point,this paper analyzes some factors that affect the integration of Chinese culture into the college English teaching and proposes some strategies for the integration of Chinese culture into college English teaching by innovating teaching objectives,enriching teaching contents,transforming modes of course delivery,and reconstructing the assessment system.
文摘In daily communication between teachers and students,many Chinese teachers fail to use politeness principle tactfully or appropriately.This article analyzes some basic principles of politeness and their application in teachers-students communication.
文摘This research aims to integrate Bekenstein’s bound and Landauer’s principle, providing a unified framework to understand the limits of information and energy in physical systems. By combining these principles, we explore the implications for black hole thermodynamics, astrophysics, astronomy, information theory, and the search for new laws of nature. The result includes an estimation of the number of bits stored in a black hole (less than 1.4 × 10<sup>30</sup> bits/m<sup>3</sup>), enhancing our understanding of information storage in extreme gravitational environments. This integration offers valuable insights into the fundamental nature of information and energy, impacting scientific advancements in multiple disciplines.
基金Supported by the National Natural Science Foundation of China(10871141)
文摘By using the properties of w-distances and Gerstewitz's functions, we first give a vectorial Takahashi's nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland's variational principle, where the objective function is from a complete metric space into a pre-ordered topological vector space and the perturbation contains a w-distance and a non-decreasing function of the objective function value. From the general vectorial variational principle, we deduce a vectorial Caristfs fixed point theorem with a w-distance. Finally we show that the above three theorems are equivalent to each other. The related known results are generalized and improved. In particular, some conditions in the theorems of [Y. Araya, Ekeland's variational principle and its equivalent theorems in vector optimization, J. Math. Anal. Appl. 346(2008), 9-16] are weakened or even completely relieved.
基金supported by the National Natural Science Foundation of China (11061023)
文摘In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland's theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient solution for set-valued vector equilibrium problems without the assumption of convexity of the constraint set and the assumptions of convexity and monotonicity of the set-valued mapping. We also obtain an existence theorem of ε-approximate solution for set-valued vector equilibrium problems without the assumptions of compactness and convexity of the constraint set.
基金Supported by the National Natural Science Foundation of China(10972151,11272227)the Innovation Program for Postgraduate in Higher Education Institutions of Jiangsu Province(CXZZ11_0949)the Innovation Program for Postgraduate of Suzhou University of Science and Technology(SKCX11S_050)
文摘The dynamical and physical behavior of a complex system can be more accurately described by using the fractional model.With the successful use of fractional calculus in many areas of science and engineering,it is necessary to extend the classical theories and methods of analytical mechanics to the fractional dynamic system.Birkhoffian mechanics is a natural generalization of Hamiltonian mechanics,and its core is the Pfaff-Birkhoff principle and Birkhoff′s equations.The study on the Birkhoffian mechanics is an important developmental direction of modern analytical mechanics.Here,the fractional Pfaff-Birkhoff variational problem is presented and studied.The definitions of fractional derivatives,the formulae for integration by parts and some other preliminaries are firstly given.Secondly,the fractional Pfaff-Birkhoff principle and the fractional Birkhoff′s equations in terms of RieszRiemann-Liouville fractional derivatives and Riesz-Caputo fractional derivatives are presented respectively.Finally,an example is given to illustrate the application of the results.
文摘The radiation fields generated when a charged particle is incident on or moving away from a perfectly conducting plane are obtained. These fields are known in the literature as transition radiation. The field equations derived thus are used to evaluate the energy, momentum and the action associated with the radiation. The results show that for a charged particle moving with speed ν, the longitudinal momentum associated with the transition radiation is approximately equal to ΔU/c for values of ?1- ν/c smaller than about 10-3 where ΔU is the total radiated energy dissipated during the interaction and cis the speed of light in free space. The action of the radiation, defined as the product of the total energy dissipated and the duration of the emission, increases as 1- ν/c decreases and, for an electron, it becomes equal to h/4π when ν = c - νm where νm is the speed pertinent to the lowest possible momentum associated with a particle confined inside the universe and?h is the Planck constant. Combining these results with Heisenberg’s uncertainty principle, an expression that predicts the value of the elementary charge is derived.
基金“Research on Reading Teaching Mode of Business English Majors From the Perspective of Literature Circles”(Project No.:2021SCG112)Laboratory Opening Project in Quzhou University(Project No.KFXM201808).
文摘Business English reading teaching under the mode of“literature circles”focuses on cultivating students’autonomy in reading,group cooperation,and the exchange of ideas among group members.In this teaching mode,teachers are no longer the masters of the reading classroom,but the helpers,participants,and researchers in the process of students’reading.The reconstruction of teachers’role can promote the benign development of relationship not only between teachers and students,but also between students and students,inject new impetus and vitality into the classroom,and improve students’reading literacy.
文摘The paper posits that kin sociality and eusociality are derived from the handicap-care principles based on the need-based care to the handicappers from the caregivers for the self-interest of the caregivers. In this paper, handicap is defined as the difficulty to survive and reproduce independently. Kin sociality is derived from the childhood handicap-care principle where the children are the handicapped children who receive the care from the kin caregivers in the inclusive kin group to survive. The caregiver gives care for its self-interest to reproduce its gene. The individual’s gene of kin sociality contains the handicapped childhood and the caregiving adulthood. Eusociality is derived from the adulthood handicap-care principle where responsible adults are the handicapped adults who give care and receive care at the same time in the interdependent eusocial group to survive and reproduce its gene. Queen bees reproduce, but must receive care from worker bees that work but must rely on queen bees to reproduce. A caregiver gives care for its self-interest to survive and reproduce its gene. The individual’s gene of eusociality contains the handicapped childhood-adulthood and the caregiving adulthood. The chronological sequence of the sociality evolution is individual sociality without handicap, kin sociality with handicapped childhood, and eusociality with handicapped adulthood. Eusociality in humans is derived from bipedalism and the mixed habitat. The chronological sequence of the eusocial human evolution is 1) the eusocial early hominins with bipedalism and the mixed habitat, 2) the eusocial early Homo species with bipedalism, the larger brain, and the open habitat, 3) the eusocial late Homo species with bipedalism, the largest brain, and the unstable habitat, and 4) extended eusocial Homo sapiens with bipedalism, the shrinking brain, omnipresent imagination, and the harsh habitat. The omnipresence of imagination in human culture converts eusociality into extended eusociality with both perception and omnipresent imagination.
文摘Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (<i>I</i>) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (<em>δI</em>) set to zero is a necessary condition for an extremum of <i>I</i>. In this approach one could use <i>δI</i> = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from <i>δI</i> = 0, which is also satisfied by a solution obtained from <i>δI</i> = 0. The Euler’s equations obtained from <i>δI</i> = 0 indeed are the mathematical model associated with the energy functional <i>I</i>. In case of BVPs we follow the same approach except in this case, the energy functional <i>I</i> consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles <i>i.e.</i> conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.
文摘With the development of the times and the progress of the society,the ancient education mode can no longer meet the requirements of the times.The concept of educating people must keep pace with the times.The way teachers and students get along is no longer like in ancient times,where teachers teach students to listen.In the new era,it is necessary to build a new model of interaction between teachers and students.If educators pay attention and come to understand students’psychology,listen to students’aspirations,tend to students’emotions,grow in love for education,and treat students from their hearts,they would be able to win the favor of students.Paying attention to students’emotional value can promote emotional communication between teachers and students.It is possible to adapt to the requirements of the new era for the construction of morality and ethics among teachers by caring for students’emotional value.
文摘Hemingway established a well-known literary theory - iceberg principle.He said he always attempted to create his literary works according to this principle.In his opinion,if a prose writer has a pretty clear idea of what he writes about,then he can omit the things he knows,and the readers will strongly feel that what the writer has omitted seems to have been written as long as what he writes is authentic.Hemingway himself once said,"The dignity of movement of an iceberg is due to only one eighth of it being above water."Here,one eighth refers to the information given by the author,and the rest refers to the unwrit ten information that can be acquired in readers'imagination on the basis of the one eighth.The Killers is a good example of Hemingway's iceberg principle.This essay will analyse the characters in it to show how the principle was used in this short story.With no doubt the iceberg principle leaves a large space for the readers to imagine and better understand Hemingway's works.
文摘It is demonstrated that the use of Kolmogorov’s probability theory to describe results of quantum probability for EPRB (Einstein-Podolsky-Rosen-Bohm) experiments requires extreme care when different subsets of measurement outcomes are considered. J. S. Bell and his followers have committed critical inaccuracies related to spin-gauge and probability measures of such subsets, because they use exclusively a single probability space for all data sets and sub-sets of data. It is also shown that Bell and followers use far too stringent epistemological requirements for the consequences of space-like separation. Their requirements reach way beyond Einstein’s separation principle and cannot be met by the major existing physical theories including relativity and even classical mechanics. For example, the independent free will does not empower the experimenters to choose multiple independent spin-gauges in the two EPRB wings. It is demonstrated that the suggestion of instantaneous influences at a distance (supposedly “derived” from experiments with entangled quantum entities) is a consequence of said inaccuracies and takes back rank as soon as the Kolmogorov probability measures are related to a consistent global spin-gauge and permitted to be different for different data subsets: Using statistical interpretations and different probability spaces for certain subsets of outcomes instead of probability amplitudes related to single quantum entities, permits physical explanations without a violation of Einstein’s separation principle.
文摘This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and this set-valued Caristi’s fixed point theorem.The results stated in this paper improve and strengthen the corresponding results in[4].
基金supported by National Science Foundation of China (10571044)
文摘This article obtains an explicit expression of the heat kernels on H-type groups and then follow the estimate of heat kernels to deduce the Hardy's uncertainty principle on the nilpotent Lie groups.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.61070041 and 40775064)
文摘Variational principles are constructed using the semi-inverse method for two kinds of extended Korteweg-de Vries (KdV) equations, which can be regarded as simple models of the nonlinear oceanic internal waves and atmospheric long waves, respectively. The obtained variational principles have also been proved to be correct.