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Four Dimensions of Integrating Chinese Culture Into College English Teaching From the Perspective of Tyler’s Basic Principles
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作者 CHEN Lijuan 《Sino-US English Teaching》 2024年第5期232-237,共6页
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
关键词 Tyler’s basic principles Chinese culture college English
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From Black Holes to Information Erasure: Uniting Bekenstein’s Bound and Landauer’s Principle
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作者 Boris Menin 《Journal of Applied Mathematics and Physics》 2023年第8期2185-2194,共10页
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
关键词 Astrophysics and Astronomy Bekenstein Bound Black Hole Thermodynamics Information and Energy Limits Information Theory and Quantum Mechanics Landauer’s principle
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Predicting H2S Oxidative Dehydrogenation over Graphene Oxides from First Principles
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作者 黄斌 陈碧波 陈荣 《Chinese Journal of Chemical Physics》 SCIE CAS CSCD 2015年第2期143-149,I0001,共8页
Spin-polarized periodic density functional theory was performed to characterize H2S adsorp- tion and dissociation on graphene oxides (GO) surface. The comprehensive reaction network of H2S oxidation with epoxy and h... Spin-polarized periodic density functional theory was performed to characterize H2S adsorp- tion and dissociation on graphene oxides (GO) surface. The comprehensive reaction network of H2S oxidation with epoxy and hydroxyl groups of GO was discussed. It is shown that the reduction reaction is mainly governed by epoxide ring opening and hydroxyl hydrogenation which is initiated by H transfer from H2S or its derivatives, hlrthermore, the presence of another OH group at the opposite side relative to the adsorbed H2S activates the oxygen group to facilitate epoxide ring opening and hydroxyl hydrogenation. For H2S interaction with -O and -OH groups adsorption on each side of graphene, the pathway is a favorable reaction path by the introduction of intermediate states, the predicted energy barriers are 3.2 and 10.4 kcal/mol, respectively, the second H transfer is tile rate-determining step in the whole reaction process. In addition, our calculations suggest that both epoxy and hydroxyl groups can enhance tile binding of S to the C-C bonds and the effect of hydroxyl group is more local than that of the epoxy. 展开更多
关键词 First principles H2s ADsORPTION DIssOCIATION
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S-T-S混合式循环互助教学模式用于少学时“化工原理”课程
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作者 吕玲 《教育教学论坛》 2024年第31期157-160,共4页
“化工原理”课程是化工及相关专业的专业基础课程,相关专业的学时少,课程难,需重点解决的问题是“三多”“三不愿”“三不明”。针对痛点问题,提出了线上线下混合式循环互助的创新设计思路,包括:教师帮助学生自制课前、课中、课后习题... “化工原理”课程是化工及相关专业的专业基础课程,相关专业的学时少,课程难,需重点解决的问题是“三多”“三不愿”“三不明”。针对痛点问题,提出了线上线下混合式循环互助的创新设计思路,包括:教师帮助学生自制课前、课中、课后习题,学生帮助教师反馈真实学习情况,学生帮助学生组团互助学习。问卷调查和评教结果显示,在一定程度上解决了“三多”“三不愿”的问题;通过建立“助教团队”反馈不同层次学生的学习情况,较好地解决了“三不明”的问题。学生的成绩与教改前相比有明显提高。 展开更多
关键词 线上线下 s-T-s教学模式 化工原理 痛点问题
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VECTORIAL EKELAND'S VARIATIONAL PRINCIPLE WITH A W-DISTANCE AND ITS EQUIVALENT THEOREMS 被引量:8
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作者 丘京辉 李博 贺飞 《Acta Mathematica Scientia》 SCIE CSCD 2012年第6期2221-2236,共16页
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
关键词 Takahashi's minimization theorem Ekeland's variational principle Caristi'sfixed point theorem Gerstewitz's function w-distance
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High-Order Hamilton's Principle and the Hamilton's Principle of High-Order Lagrangian Function 被引量:2
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作者 ZHAO Hong-Xia MA Shan-Jun 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第2期297-302,共6页
In this paper, based on the theorem of the high-order velocity energy, integration and variation principle, the high-order Hamilton's principle of general holonomic systems is given. Then, three-order Lagrangian equa... In this paper, based on the theorem of the high-order velocity energy, integration and variation principle, the high-order Hamilton's principle of general holonomic systems is given. Then, three-order Lagrangian equations and four-order Lagrangian equations are obtained from the high-order Hamilton's principle. Finally, the Hamilton's principle of high-order Lagrangian function is given. 展开更多
关键词 Hamilton's principle high-order velocity energy integration and variation principle Lagrangian function
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Recent Advances on Herglotz’s Generalized Variational Principle of Nonconservative Dynamics 被引量:3
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作者 ZHANG Yi 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2020年第1期13-26,共14页
This paper summarized the recent development on Herglotz’s generalized variational principle and its symmetries and conserved quantities for nonconservative dynamical systems.Taking Lagrangian mechanics,Hamiltonian m... This paper summarized the recent development on Herglotz’s generalized variational principle and its symmetries and conserved quantities for nonconservative dynamical systems.Taking Lagrangian mechanics,Hamiltonian mechanics and Birkhoffian mechanics as three research frames,we introduce Herglotz’s generalized variational principle,dynamical equations of Herglotz type,Noether symmetry and conserved quantities,and their generalization to time-delay dynamics,fractional dynamics and time-scale dynamics,and put forward some problems as suggestions for future research. 展开更多
关键词 nonconservative dynamics Herglotz’s generalized variational principle Lagrangian mechanics Hamil-tonian mechanics Birkhoffian mechanics
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Fractional Pfaff-Birkhoff Principle and Birkhoff′s Equations in Terms of Riesz Fractional Derivatives 被引量:3
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作者 周燕 张毅 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2014年第1期63-69,共7页
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
关键词 fractional derivative fractional Pfaff-Birkhoff principle fractional Birkhoff′s equation transversality condition
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EKELAND'S PRINCIPLE FOR SET-VALUED VECTOR EQUILIBRIUM PROBLEMS 被引量:2
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作者 龚循华 《Acta Mathematica Scientia》 SCIE CSCD 2014年第4期1179-1192,共14页
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
关键词 Ekeland's principle set-valued vector equilibrium problems weakly efficient solution c-approximate solution EXIsTENCE
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Classical Electromagnetic Fields of Moving Charges as a Vehicle to Probe the Connection between the Elementary Charge and Heisenberg’s Uncertainty Principle 被引量:2
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作者 Vernon Cooray Gerald Cooray 《Natural Science》 2017年第7期219-230,共12页
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
关键词 Transition Radiation Heisenberg’s Uncertainty principle Electronic CHARGE ELEMENTARY CHARGE size of the UNIVERsE
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New Reflection Principles for Maxwell's Equations and Their Applications 被引量:1
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作者 Hongyu Liu Masahiro Yamamoto Jun Zou 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2009年第1期1-17,共17页
Some new reflection principles for Maxwell's equations are first established, which are then applied to derive two novel identifiability results in inverse electromagnetic obstacle scattering problems with polyhed... Some new reflection principles for Maxwell's equations are first established, which are then applied to derive two novel identifiability results in inverse electromagnetic obstacle scattering problems with polyhedral scatterers. 展开更多
关键词 Maxwell's equations reflection principles inverse electromagnetic scattering identiflability and uniqueness.
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The Basic Principles of Kin Sociality and Eusociality: Human Evolution 被引量:7
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作者 Ding-Yu Chung 《Natural Science》 2016年第1期8-19,共12页
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
关键词 Kin sociality EUsOCIALITY Evolution Kin selection Group selection The Handicap-Care principle Human Evolution sUPERNATURAL Hamilton’s Rule DOMEsTICATION shrinking Brain Upper Paleolithic Revolution
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H_(2)S在Cr(111)面上吸附与解离的第一性原理研究
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作者 江佐禹 黄本生 +1 位作者 何子涛 罗霞 《原子与分子物理学报》 CAS 北大核心 2024年第2期9-14,共6页
采用了第一性原理研究了H_(2)S在Cr(111)面的吸附解离过程,利用吸附能、吸附构型和偏态密度图(PDOS)研究了H_(2)S及其解离产物在Cr(111)面上的吸附情况,都偏向倾斜吸附在Cr(111)面.同时研究了HS/H和S/H共吸附情况,得到共吸附物质在Cr(1... 采用了第一性原理研究了H_(2)S在Cr(111)面的吸附解离过程,利用吸附能、吸附构型和偏态密度图(PDOS)研究了H_(2)S及其解离产物在Cr(111)面上的吸附情况,都偏向倾斜吸附在Cr(111)面.同时研究了HS/H和S/H共吸附情况,得到共吸附物质在Cr(111)面上有明显的相互作用.最后使用线性同步和二次同步变换方法确定了解离反应的过渡态,了解到第一、二步解离的活化能分别为1.65 eV、0.82 eV,H_(2)S分子在Cr(111)面上的解离过程是放热反应,反应能为-2.90 eV. 展开更多
关键词 H_(2)s Cr(111) 吸附 解离 第一性原理
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Consistency and Validity of the Mathematical Models and the Solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and Non-Homogeneous Non-Isotropic Solid Continua 被引量:1
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作者 Karan S. Surana Emilio N. Alverio 《Applied Mathematics》 2020年第7期546-578,共33页
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
关键词 Energy Methods principle of Virtual Work Calculus of Variations Euler’s Equation Mathematical Model Classical and Non-Classical Continuum Mechanics
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Real-Time Co-optimization of Gear Shifting and Engine Torque for Predictive Cruise Control of Heavy-Duty Trucks
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作者 Hongqing Chu Xiaoxiang Na +4 位作者 Huan Liu Yuhai Wang Zhuo Yang Lin Zhang Hong Chen 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2024年第2期294-317,共24页
Fuel consumption is one of the main concerns for heavy-duty trucks.Predictive cruise control(PCC)provides an intriguing opportunity to reduce fuel consumption by using the upcoming road information.In this study,a rea... Fuel consumption is one of the main concerns for heavy-duty trucks.Predictive cruise control(PCC)provides an intriguing opportunity to reduce fuel consumption by using the upcoming road information.In this study,a real-time implementable PCC,which simultaneously optimizes engine torque and gear shifting,is proposed for heavy-duty trucks.To minimize fuel consumption,the problem of the PCC is formulated as a nonlinear model predictive control(MPC),in which the upcoming road elevation information is used.Finding the solution of the nonlinear MPC is time consuming;thus,a real-time implementable solver is developed based on Pontryagin’s maximum principle and indirect shooting method.Dynamic programming(DP)algorithm,as a global optimization algorithm,is used as a performance benchmark for the proposed solver.Simulation,hardware-in-the-loop and real-truck experiments are conducted to verify the performance of the proposed controller.The results demonstrate that the MPC-based solution performs nearly as well as the DP-based solution,with less than 1%deviation for testing roads.Moreover,the proposed co-optimization controller is implementable in a real-truck,and the proposed MPC-based PCC algorithm achieves a fuel-saving rate of 7.9%without compromising the truck’s travel time. 展开更多
关键词 Heavy-duty truck Predictive cruise control Model predictive control Pontryagin’s maximum principle Real-truck implementation
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A Good Example of Hemingway's Iceberg Principle:The Killers
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作者 庄新月 《海外英语》 2013年第4X期200-202,共3页
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
关键词 Hemingway’s ICEBERG principle The Killers the CHAR
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硅和镁质量分数对Al-Si-Mg合金机械力学性能参数影响的计算分析
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作者 郭柔 刘文豪 +2 位作者 薛预超 马瑞杰 胡心平 《齐鲁工业大学学报》 CAS 2024年第4期30-35,共6页
基于第一性原理,利用CASTEP模块,通过虚拟晶体近似的方法建模,采用GGA+PBE泛函关联函数,研究了Al-Si7-Mg X(X=0.1~0.5)、Al-Si X-Mg0.3(X=6~9)合金中的Si、Mg质量分数的变化对机械力学性能参数的影响。研究表明,随着研究组元质量分数的... 基于第一性原理,利用CASTEP模块,通过虚拟晶体近似的方法建模,采用GGA+PBE泛函关联函数,研究了Al-Si7-Mg X(X=0.1~0.5)、Al-Si X-Mg0.3(X=6~9)合金中的Si、Mg质量分数的变化对机械力学性能参数的影响。研究表明,随着研究组元质量分数的增加,晶格常数有所减小,最大值与最小值相差约0.265%;弹性常数C_(11)、C_(12)、C_(44)满足结构稳定性条件;体积模量B、剪切模量G、杨氏模量E、泊松比u随着A356中Si、Mg质量分数变化而变化;Mg质量分数的变化对剪切模量G、杨氏模量E的影响比Si质量分数的变化更敏感。计算结果与现有实验数据对比表明,计算结果接近实验数据,第一性原理计算Al-Si-Mg合金材料参数可行。 展开更多
关键词 第一性原理 Al-si-Mg 晶格常数 弹性模量 泊松比
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Kolmogorov’s Probability Spaces for “Entangled” Data-Subsets of EPRB Experiments: No Violation of Einstein’s Separation Principle 被引量:1
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作者 Karl Hess 《Journal of Modern Physics》 2020年第5期683-702,共20页
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
关键词 Bell’s Theorem Einstein’s separation principle EPRB Experiments
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SET-VALUED CARISTI’S FIXED POINT THEOREM AND EEELAND’S VARIATIONAL PRINCIPLE
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作者 张石生 罗群 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1989年第2期119-121,共3页
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
关键词 s FIXED POINT THEOREM AND EEELAND s VARIATIONAL principle sET-VALUED CARIsTI
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HEAT KERNELS AND HARDY'S UNCERTAINTY PRINCIPLE ON H-TYPE GROUPS
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作者 朱赋鎏 杨乔华 《Acta Mathematica Scientia》 SCIE CSCD 2008年第1期171-178,共8页
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.
关键词 H-type groups heat kernel Hardy's uncertainty principle
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