Graphite is a universal host material for ion intercalation. Li+-graphite intercalation compounds (GICs) have been successfully utilized as the anode material in commercial lithium-ion batteries.Similarly, anion-graph...Graphite is a universal host material for ion intercalation. Li+-graphite intercalation compounds (GICs) have been successfully utilized as the anode material in commercial lithium-ion batteries.Similarly, anion-graphite intercalation compounds (AGICs) have been coming into their own in dual-ion batteries [1]. It is imperative to deepen an understanding of anion storage mechanisms in graphite electrode.展开更多
Memristors are now becoming a prominent candidate to serve as the building blocks of non-von Neumann inmemory computing architectures.By mapping analog numerical matrices into memristor crossbar arrays,efficient multi...Memristors are now becoming a prominent candidate to serve as the building blocks of non-von Neumann inmemory computing architectures.By mapping analog numerical matrices into memristor crossbar arrays,efficient multiply accumulate operations can be performed in a massively parallel fashion using the physics mechanisms of Ohm’s law and Kirchhoff’s law.In this brief review,we present the recent progress in two niche applications:neural network accelerators and numerical computing units,mainly focusing on the advances in hardware demonstrations.The former one is regarded as soft computing since it can tolerant some degree of the device and array imperfections.The acceleration of multiple layer perceptrons,convolutional neural networks,generative adversarial networks,and long short-term memory neural networks are described.The latter one is hard computing because the solving of numerical problems requires high-precision devices.Several breakthroughs in memristive equation solvers with improved computation accuracies are highlighted.Besides,other nonvolatile devices with the capability of analog computing are also briefly introduced.Finally,we conclude the review with discussions on the challenges and opportunities for future research toward realizing memristive analog computing machines.展开更多
The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite n...The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite number of elements. Without dividing the domain, as usual, into a bounded one and aim exterior one, he derives aim initial value problem of an ordinary differential equation for the combined stiffness matrix, then obtains the approximate solution with a small amount of computer work. Numerical examples are given.展开更多
Consciousness is controlled by activation of the ascending reticular activating system(ARAS).The ARAS consists mainly of the lower and upper parts between the thalamus and cerebral cortex(Edlow et al.,2012;Yeo et al.,...Consciousness is controlled by activation of the ascending reticular activating system(ARAS).The ARAS consists mainly of the lower and upper parts between the thalamus and cerebral cortex(Edlow et al.,2012;Yeo et al.,2013;Jang et al.,2014).Because the ARAS is composed of several neuronal circuits connecting the brainstem to the cortex.These neuronal connections begin from the reticular formation(RF)of the brainstem and the in-展开更多
Anovel beamforming algorithmnamed Delay Multiply and Sum(DMAS),which excels at enhancing the resolution and contrast of ultrasonic image,has recently been proposed.However,there are nested loops in this algorithm,so t...Anovel beamforming algorithmnamed Delay Multiply and Sum(DMAS),which excels at enhancing the resolution and contrast of ultrasonic image,has recently been proposed.However,there are nested loops in this algorithm,so the calculation complexity is higher compared to the Delay and Sum(DAS)beamformer which is widely used in industry.Thus,we proposed a simple vector-based method to lower its complexity.The key point is to transform the nested loops into several vector operations,which can be efficiently implemented on many parallel platforms,such as Graphics Processing Units(GPUs),and multi-core Central Processing Units(CPUs).Consequently,we considered to implement this algorithm on such a platform.In order to maximize the use of computing power,we use the GPUs andmulti-core CPUs inmixture.The platform used in our test is a low cost Personal Computer(PC),where a GPU and a multi-core CPU are installed.The results show that the hybrid use of a CPU and a GPU can get a significant performance improvement in comparison with using a GPU or using amulti-core CPU alone.The performance of the hybrid system is increased by about 47%–63%compared to a single GPU.When 32 elements are used in receiving,the fame rate basically can reach 30 fps.In the best case,the frame rate can be increased to 40 fps.展开更多
Typical Hall plates for practical magnetic field sensing purposes are plane, simply-connected regions with peripheral contacts. Their output voltage is the sum of even and odd functions of the applied magnetic field. ...Typical Hall plates for practical magnetic field sensing purposes are plane, simply-connected regions with peripheral contacts. Their output voltage is the sum of even and odd functions of the applied magnetic field. They are commonly called offset and Hall voltage. Contemporary smart Hall sensor circuits extract the Hall voltage via spinning current Hall probe schemes, thereby cancelling out the offset very efficiently. The magnetic field response of such Hall plates can be computed via the electric potential or via the stream function. Conversely, Hall plates with holes show new phenomena: 1) the stream function exists only for a limited class of multiply-connected domains, and 2) a sub-class of 1) behaves like a Hall/Anti-Hall bar configuration, i.e., no Hall voltage appears between any two points on the hole boundary if current contacts are on their outer boundary. The paper studies the requirements under which these effects occur. Canonical cases of simply and doubly connected domains are computed analytically. The focus is on 2D multiply-connected Hall plates where all boundaries are insulating and where all current contacts are point sized.展开更多
The addition of electrons to form gas-phase multiply charged anions(MCAs)normally requires sophisticated experiments or calculations.In this work,the factors stabilizing the MCAs,the maximum electron uptake of gas-pha...The addition of electrons to form gas-phase multiply charged anions(MCAs)normally requires sophisticated experiments or calculations.In this work,the factors stabilizing the MCAs,the maximum electron uptake of gas-phase molecules,X,and the electronic stability of MCAs X^(Q-),are discussed.The drawbacks encountered when applying computational and/or conceptual density functional theory(DFT)to MCAs are highlighted.We develop and test a different model based on the valence-state concept.As in DFT,the electronic energy,E(N,v_(ex)),is a continuous function of the average electron number,N,and the external potential,v_(ex),of the nuclei.The valence-state-parabola is a second-order polynomial that allows extending E(N,v_(ex))to dianions and higher MCAs.The model expresses the maximum electron acceptance,Q_(max),and the higher electron affinities,A_Q,as simple functions of the firstelectron affinity,A_1,and the ionization energy,I,of the"ancestor"system.Thus,the maximum electron acceptance is Q_(max,calc)=1+12A_1/7(I-A_1).The ground-state parabola model of the conceptual DFT yields approximately half of this value,and it is termed Q_(max,GS)=?+A_1/(I-A_1).A large variety of molecules are evaluated including fullerenes,metal clusters,super-pnictogens,super-halogens(OF_3),super-alkali species(OLi_3),and neutral or charged transition-metal complexes,AB_(m )L_n^(0/+/-).The calculated second electron affinity A_(2,calc)=A_1-(7/12)(I-A_1)is linearly correlated to the literature references A_(2,lit) with a correlation coefficient R=0.998.A_2 or A_3 values are predicted for further 24 species.The appearance sizes,n_(ap)^(3-),of triply charged anionic clusters and fullerenes are calculated in agreement with the literature.展开更多
In this paper, a finite element method is developed to numerically evaluate the shear coefficient of Timoshenko's beam with multiply conneeted cross section. With focus on analyzing shear stresses distributed at t...In this paper, a finite element method is developed to numerically evaluate the shear coefficient of Timoshenko's beam with multiply conneeted cross section. With focus on analyzing shear stresses distributed at the neutral axis of the beam, an improved definition of the shear coefficient is presented. Based on this definition, a Galerkin-type finite element formulation is proposed to analyze the shear stresses and shear deflections. Numerical solutions of the examples for some typical cross-sections are compared with the theoretical results. The shear coefficient of tower sections of the Tsing Ma Bridge is calculated by use of the proposed approach, so that the finite element modeling of the bridge can be developed with the accurate values of the sectional properties.展开更多
In engineering practice,analysis of interfacial thermal stresses in composites is a crucial task for assuring structural integrity when sever environmental temperature changes under operations.In this article,the dire...In engineering practice,analysis of interfacial thermal stresses in composites is a crucial task for assuring structural integrity when sever environmental temperature changes under operations.In this article,the directly transformed boundary integrals presented previously for treating generally anisotropic thermoelasticity in two-dimension are fully regularized by a semi-analytical approach for modeling thin multi-layers of anisotropic/isotropic composites,subjected to general thermal loads with boundary conditions prescribed.In this process,an additional difficulty,not reported in the literature,arises due to rapid fluctuation of an integrand in the directly transformed boundary integral equation.In conventional analysis,thin adhesives are usually neglected due to modeling difficulties.A major concern arises regarding the modeling error caused by such negligence of the thin adhesives.For investigating the effect of the thin adhesives considered,the regularized integral equation is applied for analyzing interfacial stresses in multiply bonded composites when thin adhesives are considered.Since all integrals are completely regularized,very accurate integration values can be still obtained no matter how the source point is close to the integration element.Comparisons are made for some examples when the thin adhesives are considered or neglected.Truly,this regularization task has laid sound fundamentals for the boundary element method to efficiently analyze the interfacial thermal stresses in 2D thin multiply bonded anisotropic composites.展开更多
In this article, we discuss the approximate method of solving the Riemann-Hilbert boundary value problem for nonlinear uniformly elliptic complex equation of first order (0.1) with the boundary conditions (0.2) in a m...In this article, we discuss the approximate method of solving the Riemann-Hilbert boundary value problem for nonlinear uniformly elliptic complex equation of first order (0.1) with the boundary conditions (0.2) in a multiply connected unbounded domain D, the above boundary value problem will be called Problem A. If the complex Equation (0.1) satisfies the conditions similar to Condition C of (1.1), and the boundary condition (0.2) satisfies the conditions similar to (1.5), then we can obtain approximate solutions of the boundary value problems (0.1) and (0.2). Moreover the error estimates of approximate solutions for the boundary value problem is also given. The boundary value problem possesses many applications in mechanics and physics etc., for instance from (5.114) and (5.115), Chapter VI, [1], we see that Problem A of (0.1) possesses the important application to the shell and elasticity.展开更多
Multiply-connected Hall plates show different phenomena than singly connected Hall plates. In part I (published in Journal of Applied Physics and Mathematics), we discussed topologies where a stream function can be de...Multiply-connected Hall plates show different phenomena than singly connected Hall plates. In part I (published in Journal of Applied Physics and Mathematics), we discussed topologies where a stream function can be defined, with special reference to Hall/Anti-Hall bar configurations. In part II, we focus on topologies where no conventional stream function can be defined, like Corbino disks. If current is injected and extracted at different boundaries of a multiply-connected conductive region, the current density shows spiral streamlines at strong magnetic field. Spiral streamlines also appear in simply-connected Hall plates when current contacts are located in their interior instead of their boundary, particularly if the contacts are very small. Spiral streamlines and circulating current are studied for two complementary planar device geometries: either all boundaries are conducting or all boundaries are insulating. The latter case means point current contacts and it can be treated similarly to singly connected Hall plates with peripheral contacts through the definition of a so-called loop stream function. This function also establishes a relation between Hall plates with complementary boundary conditions. The theory is explained by examples.展开更多
This article discusses the general boundary value problem for the nonlinear uniformly elliptic equation of second order in D (0.1) and the boundary condition,(0.2) in a multiply connected infinite domain D with the bo...This article discusses the general boundary value problem for the nonlinear uniformly elliptic equation of second order in D (0.1) and the boundary condition,(0.2) in a multiply connected infinite domain D with the boundary T. The above boundary value problem is called Problem G. Problem G extends the work [8] in which the equation (0.1) includes a nonlinear lower term and the boundary condition (0.2) is more general. If the complex equation (0.1) and the boundary condition (0.2) meet certain assumptions, some solvability results for Problem G can be obtained. By using reduction to absurdity, we first discuss a priori estimates of solutions and solvability for a modified problem. Then we present results on solvability of Problem G.展开更多
初学复变函数时,对确定某些初等函数的支点,往往感到困难,下面仅就自己的学习情况谈点体会。 第一、z=∞为f（z）=multiply from j=1 to K（z-z（j0））αi支点的充要条件是sum from j=1 to k αj≠N（整数） 证明:在z=∞的充分小邻域...初学复变函数时,对确定某些初等函数的支点,往往感到困难,下面仅就自己的学习情况谈点体会。 第一、z=∞为f（z）=multiply from j=1 to K（z-z（j0））αi支点的充要条件是sum from j=1 to k αj≠N（整数） 证明:在z=∞的充分小邻域内作一简单闭曲线C,使z10,z20……zK0落于C的内域内,在C上任取一点Z0。展开更多
Static phase offset (SPO) in conventional multiplying delay-locked loops (MDLLs) dramatically degrades the deterministic jitter performance. To overcome the issue, this paper presents a new SPO reduction technique for...Static phase offset (SPO) in conventional multiplying delay-locked loops (MDLLs) dramatically degrades the deterministic jitter performance. To overcome the issue, this paper presents a new SPO reduction technique for MDLLs. The technique is based on the observation that the SPO of MDLL is mainly caused by the non-idealities on charge pump (e.g. sink and source current mismatch), and control line (e.g. gate leakage of loop filter and voltage controlled delay line (VCDL) control circuit). With a high gain stage inserting between phase detector/phase frequency detector (PD/PFD) and charge pump, the equivalent SPO has been decreased by a factor equal to the gain of the gain stage. The effectiveness of the proposed technique is validated by a Simulink model of MDLL. The equivalent SPO is measured by the power level of reference spur.展开更多
关于不等式multiply from i=1 to n(x_i+(1/x_i))≥(n+(1/n))~n(x_i为正数,sum from i=1 to n x_i=1)的正确性,《数学通讯》已有多篇文章给出了证明,本文将这个不等式推广到较一般的情形。从sum from i=1 to n x_i的值上推广有: 定理1 ...关于不等式multiply from i=1 to n(x_i+(1/x_i))≥(n+(1/n))~n(x_i为正数,sum from i=1 to n x_i=1)的正确性,《数学通讯》已有多篇文章给出了证明,本文将这个不等式推广到较一般的情形。从sum from i=1 to n x_i的值上推广有: 定理1 (1)如果x_i∈R+(i=1,2,…,n),展开更多
如何计算sum from t=1 to n multiply from j=i to i+r-1 j（r∈N）的值（表达式）方法多种多样,但一般都比较繁琐。联想到高级中学《代数》第三册P82习题18<sub>（2）</sub>的组合数恒等式,可得: C<sub>r</sub>...如何计算sum from t=1 to n multiply from j=i to i+r-1 j（r∈N）的值（表达式）方法多种多样,但一般都比较繁琐。联想到高级中学《代数》第三册P82习题18<sub>（2）</sub>的组合数恒等式,可得: C<sub>r</sub><sup>r</sup>+C<sub>r+1</sub><sup>r</sup>+C<sub>r+2</sub><sup>r</sup>+…+C<sub>2+r-1</sub><sup>r</sup>=C<sub>2+r</sub><sup>r+1</sup> 将此式展开后两端乘以r<sub>1</sub>,即可得:展开更多
Two lithium-based ionic liquids(ILs,L-C3N3,and L-P3N3)were synthesized and evaluated as novel lubricant additives for multiply alkylated cyclopentanes(MACs).They were found to be approximately 1.0%soluble in MACs at r...Two lithium-based ionic liquids(ILs,L-C3N3,and L-P3N3)were synthesized and evaluated as novel lubricant additives for multiply alkylated cyclopentanes(MACs).They were found to be approximately 1.0%soluble in MACs at room temperature(RT),whereas traditional ILs,such as 1-ethyl-3-methylimidazolium tetrafluoroborate(L-B102),1-hexyl-3-methylimidazolium hexafluorophosphate(L-P106),and 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide(L-F102),could not be dissolved in this base oil.Friction tests indicated that these ILs exhibit excellent friction-reducing and anti-wear properties both at RT and at 100°C.They can improve the tribological properties of MACs at RT to a greater extent than the commonly used lubricant zinc dialkyldithiophosphate(T204),even at a concentration of 0.1%.The load ramp test showed that MACs with L-C3N3 and L-P3N3 also exhibit high load-carrying capabilities.Scanning electron microscope(SEM)and X-ray photoelectron spectrometer(XPS)results indicated that physical adsorption and complex tribochemical reactions occurred between the ILs and metal surfaces during the sliding process,thereby forming a surface protective film that significantly contributed to the excellent tribological properties of the new ILs.展开更多
For any multiply connected domain Ω in R2, let S be the boundary of the convex hull in H3 of R2\Ω which faces Ω. Suppose in addition that there exists a lower bound l > 0 of the hyperbolic lengths of closed geod...For any multiply connected domain Ω in R2, let S be the boundary of the convex hull in H3 of R2\Ω which faces Ω. Suppose in addition that there exists a lower bound l > 0 of the hyperbolic lengths of closed geodesics in Ω. Then there is always a K-quasiconformal mapping from S to Ω, which extends continuously to the identity on S = Ω, where K depends only on l. We also give a numerical estimate of K by using the parameter l.展开更多
基金financially supported by the National Natural Science Foundation of China(21975251)。
文摘Graphite is a universal host material for ion intercalation. Li+-graphite intercalation compounds (GICs) have been successfully utilized as the anode material in commercial lithium-ion batteries.Similarly, anion-graphite intercalation compounds (AGICs) have been coming into their own in dual-ion batteries [1]. It is imperative to deepen an understanding of anion storage mechanisms in graphite electrode.
基金the National Key Research and Development Plan of MOST of China(2019YFB2205100,2016YFA0203800)the National Natural Science Foundation of China(No.61874164,61841404,51732003,61674061)Hubei Engineering Research Center on Microelectronics.
文摘Memristors are now becoming a prominent candidate to serve as the building blocks of non-von Neumann inmemory computing architectures.By mapping analog numerical matrices into memristor crossbar arrays,efficient multiply accumulate operations can be performed in a massively parallel fashion using the physics mechanisms of Ohm’s law and Kirchhoff’s law.In this brief review,we present the recent progress in two niche applications:neural network accelerators and numerical computing units,mainly focusing on the advances in hardware demonstrations.The former one is regarded as soft computing since it can tolerant some degree of the device and array imperfections.The acceleration of multiple layer perceptrons,convolutional neural networks,generative adversarial networks,and long short-term memory neural networks are described.The latter one is hard computing because the solving of numerical problems requires high-precision devices.Several breakthroughs in memristive equation solvers with improved computation accuracies are highlighted.Besides,other nonvolatile devices with the capability of analog computing are also briefly introduced.Finally,we conclude the review with discussions on the challenges and opportunities for future research toward realizing memristive analog computing machines.
基金This work was supported by the China State Major Key Project for Basic Researches Science Fund of the Ministry of Education
文摘The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite number of elements. Without dividing the domain, as usual, into a bounded one and aim exterior one, he derives aim initial value problem of an ordinary differential equation for the combined stiffness matrix, then obtains the approximate solution with a small amount of computer work. Numerical examples are given.
基金supported by the National Research Foundation (NRF) of Korea Grant funded by the Korean Government (MSIP) No. 2015R1A2A2A01004073
文摘Consciousness is controlled by activation of the ascending reticular activating system(ARAS).The ARAS consists mainly of the lower and upper parts between the thalamus and cerebral cortex(Edlow et al.,2012;Yeo et al.,2013;Jang et al.,2014).Because the ARAS is composed of several neuronal circuits connecting the brainstem to the cortex.These neuronal connections begin from the reticular formation(RF)of the brainstem and the in-
基金This work was supported by the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN201801606)the Natural Sci-ence Foundation Project of CQ CSTC(cstc2017jcyjAX0092)+3 种基金the Scientific Research Program of Chongqing University of Education(Grant Nos.KY201924C,2017XJZDWT02)the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJ1601410)the Project‘Future School(Infant Education)’of National Center For Schooling Development Programme of China(Grant No.CSDP18FC2202)the Chongqing Electronics Engineering Technology Research Center for Interactive Learning,and the Chongqing Big Data Engineering Laboratory for Children.
文摘Anovel beamforming algorithmnamed Delay Multiply and Sum(DMAS),which excels at enhancing the resolution and contrast of ultrasonic image,has recently been proposed.However,there are nested loops in this algorithm,so the calculation complexity is higher compared to the Delay and Sum(DAS)beamformer which is widely used in industry.Thus,we proposed a simple vector-based method to lower its complexity.The key point is to transform the nested loops into several vector operations,which can be efficiently implemented on many parallel platforms,such as Graphics Processing Units(GPUs),and multi-core Central Processing Units(CPUs).Consequently,we considered to implement this algorithm on such a platform.In order to maximize the use of computing power,we use the GPUs andmulti-core CPUs inmixture.The platform used in our test is a low cost Personal Computer(PC),where a GPU and a multi-core CPU are installed.The results show that the hybrid use of a CPU and a GPU can get a significant performance improvement in comparison with using a GPU or using amulti-core CPU alone.The performance of the hybrid system is increased by about 47%–63%compared to a single GPU.When 32 elements are used in receiving,the fame rate basically can reach 30 fps.In the best case,the frame rate can be increased to 40 fps.
文摘Typical Hall plates for practical magnetic field sensing purposes are plane, simply-connected regions with peripheral contacts. Their output voltage is the sum of even and odd functions of the applied magnetic field. They are commonly called offset and Hall voltage. Contemporary smart Hall sensor circuits extract the Hall voltage via spinning current Hall probe schemes, thereby cancelling out the offset very efficiently. The magnetic field response of such Hall plates can be computed via the electric potential or via the stream function. Conversely, Hall plates with holes show new phenomena: 1) the stream function exists only for a limited class of multiply-connected domains, and 2) a sub-class of 1) behaves like a Hall/Anti-Hall bar configuration, i.e., no Hall voltage appears between any two points on the hole boundary if current contacts are on their outer boundary. The paper studies the requirements under which these effects occur. Canonical cases of simply and doubly connected domains are computed analytically. The focus is on 2D multiply-connected Hall plates where all boundaries are insulating and where all current contacts are point sized.
文摘The addition of electrons to form gas-phase multiply charged anions(MCAs)normally requires sophisticated experiments or calculations.In this work,the factors stabilizing the MCAs,the maximum electron uptake of gas-phase molecules,X,and the electronic stability of MCAs X^(Q-),are discussed.The drawbacks encountered when applying computational and/or conceptual density functional theory(DFT)to MCAs are highlighted.We develop and test a different model based on the valence-state concept.As in DFT,the electronic energy,E(N,v_(ex)),is a continuous function of the average electron number,N,and the external potential,v_(ex),of the nuclei.The valence-state-parabola is a second-order polynomial that allows extending E(N,v_(ex))to dianions and higher MCAs.The model expresses the maximum electron acceptance,Q_(max),and the higher electron affinities,A_Q,as simple functions of the firstelectron affinity,A_1,and the ionization energy,I,of the"ancestor"system.Thus,the maximum electron acceptance is Q_(max,calc)=1+12A_1/7(I-A_1).The ground-state parabola model of the conceptual DFT yields approximately half of this value,and it is termed Q_(max,GS)=?+A_1/(I-A_1).A large variety of molecules are evaluated including fullerenes,metal clusters,super-pnictogens,super-halogens(OF_3),super-alkali species(OLi_3),and neutral or charged transition-metal complexes,AB_(m )L_n^(0/+/-).The calculated second electron affinity A_(2,calc)=A_1-(7/12)(I-A_1)is linearly correlated to the literature references A_(2,lit) with a correlation coefficient R=0.998.A_2 or A_3 values are predicted for further 24 species.The appearance sizes,n_(ap)^(3-),of triply charged anionic clusters and fullerenes are calculated in agreement with the literature.
文摘In this paper, a finite element method is developed to numerically evaluate the shear coefficient of Timoshenko's beam with multiply conneeted cross section. With focus on analyzing shear stresses distributed at the neutral axis of the beam, an improved definition of the shear coefficient is presented. Based on this definition, a Galerkin-type finite element formulation is proposed to analyze the shear stresses and shear deflections. Numerical solutions of the examples for some typical cross-sections are compared with the theoretical results. The shear coefficient of tower sections of the Tsing Ma Bridge is calculated by use of the proposed approach, so that the finite element modeling of the bridge can be developed with the accurate values of the sectional properties.
基金The financial support provided from the Ministry of Science and Technology of Taiwan is greatly appreciated by the authors(MOST 108-2221-E-006-186).
文摘In engineering practice,analysis of interfacial thermal stresses in composites is a crucial task for assuring structural integrity when sever environmental temperature changes under operations.In this article,the directly transformed boundary integrals presented previously for treating generally anisotropic thermoelasticity in two-dimension are fully regularized by a semi-analytical approach for modeling thin multi-layers of anisotropic/isotropic composites,subjected to general thermal loads with boundary conditions prescribed.In this process,an additional difficulty,not reported in the literature,arises due to rapid fluctuation of an integrand in the directly transformed boundary integral equation.In conventional analysis,thin adhesives are usually neglected due to modeling difficulties.A major concern arises regarding the modeling error caused by such negligence of the thin adhesives.For investigating the effect of the thin adhesives considered,the regularized integral equation is applied for analyzing interfacial stresses in multiply bonded composites when thin adhesives are considered.Since all integrals are completely regularized,very accurate integration values can be still obtained no matter how the source point is close to the integration element.Comparisons are made for some examples when the thin adhesives are considered or neglected.Truly,this regularization task has laid sound fundamentals for the boundary element method to efficiently analyze the interfacial thermal stresses in 2D thin multiply bonded anisotropic composites.
文摘In this article, we discuss the approximate method of solving the Riemann-Hilbert boundary value problem for nonlinear uniformly elliptic complex equation of first order (0.1) with the boundary conditions (0.2) in a multiply connected unbounded domain D, the above boundary value problem will be called Problem A. If the complex Equation (0.1) satisfies the conditions similar to Condition C of (1.1), and the boundary condition (0.2) satisfies the conditions similar to (1.5), then we can obtain approximate solutions of the boundary value problems (0.1) and (0.2). Moreover the error estimates of approximate solutions for the boundary value problem is also given. The boundary value problem possesses many applications in mechanics and physics etc., for instance from (5.114) and (5.115), Chapter VI, [1], we see that Problem A of (0.1) possesses the important application to the shell and elasticity.
文摘Multiply-connected Hall plates show different phenomena than singly connected Hall plates. In part I (published in Journal of Applied Physics and Mathematics), we discussed topologies where a stream function can be defined, with special reference to Hall/Anti-Hall bar configurations. In part II, we focus on topologies where no conventional stream function can be defined, like Corbino disks. If current is injected and extracted at different boundaries of a multiply-connected conductive region, the current density shows spiral streamlines at strong magnetic field. Spiral streamlines also appear in simply-connected Hall plates when current contacts are located in their interior instead of their boundary, particularly if the contacts are very small. Spiral streamlines and circulating current are studied for two complementary planar device geometries: either all boundaries are conducting or all boundaries are insulating. The latter case means point current contacts and it can be treated similarly to singly connected Hall plates with peripheral contacts through the definition of a so-called loop stream function. This function also establishes a relation between Hall plates with complementary boundary conditions. The theory is explained by examples.
文摘This article discusses the general boundary value problem for the nonlinear uniformly elliptic equation of second order in D (0.1) and the boundary condition,(0.2) in a multiply connected infinite domain D with the boundary T. The above boundary value problem is called Problem G. Problem G extends the work [8] in which the equation (0.1) includes a nonlinear lower term and the boundary condition (0.2) is more general. If the complex equation (0.1) and the boundary condition (0.2) meet certain assumptions, some solvability results for Problem G can be obtained. By using reduction to absurdity, we first discuss a priori estimates of solutions and solvability for a modified problem. Then we present results on solvability of Problem G.
文摘初学复变函数时,对确定某些初等函数的支点,往往感到困难,下面仅就自己的学习情况谈点体会。 第一、z=∞为f（z）=multiply from j=1 to K（z-z（j0））αi支点的充要条件是sum from j=1 to k αj≠N（整数） 证明:在z=∞的充分小邻域内作一简单闭曲线C,使z10,z20……zK0落于C的内域内,在C上任取一点Z0。
文摘Static phase offset (SPO) in conventional multiplying delay-locked loops (MDLLs) dramatically degrades the deterministic jitter performance. To overcome the issue, this paper presents a new SPO reduction technique for MDLLs. The technique is based on the observation that the SPO of MDLL is mainly caused by the non-idealities on charge pump (e.g. sink and source current mismatch), and control line (e.g. gate leakage of loop filter and voltage controlled delay line (VCDL) control circuit). With a high gain stage inserting between phase detector/phase frequency detector (PD/PFD) and charge pump, the equivalent SPO has been decreased by a factor equal to the gain of the gain stage. The effectiveness of the proposed technique is validated by a Simulink model of MDLL. The equivalent SPO is measured by the power level of reference spur.
文摘关于不等式multiply from i=1 to n(x_i+(1/x_i))≥(n+(1/n))~n(x_i为正数,sum from i=1 to n x_i=1)的正确性,《数学通讯》已有多篇文章给出了证明,本文将这个不等式推广到较一般的情形。从sum from i=1 to n x_i的值上推广有: 定理1 (1)如果x_i∈R+(i=1,2,…,n),
文摘如何计算sum from t=1 to n multiply from j=i to i+r-1 j（r∈N）的值（表达式）方法多种多样,但一般都比较繁琐。联想到高级中学《代数》第三册P82习题18<sub>（2）</sub>的组合数恒等式,可得: C<sub>r</sub><sup>r</sup>+C<sub>r+1</sub><sup>r</sup>+C<sub>r+2</sub><sup>r</sup>+…+C<sub>2+r-1</sub><sup>r</sup>=C<sub>2+r</sub><sup>r+1</sup> 将此式展开后两端乘以r<sub>1</sub>,即可得:
基金The National Natural Science Foundation of China(NSFC)(Nos.51105353,51175492,and 21173243)The National Key Basic Research and Development(973)Program of China project(2013CB632300).
文摘Two lithium-based ionic liquids(ILs,L-C3N3,and L-P3N3)were synthesized and evaluated as novel lubricant additives for multiply alkylated cyclopentanes(MACs).They were found to be approximately 1.0%soluble in MACs at room temperature(RT),whereas traditional ILs,such as 1-ethyl-3-methylimidazolium tetrafluoroborate(L-B102),1-hexyl-3-methylimidazolium hexafluorophosphate(L-P106),and 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide(L-F102),could not be dissolved in this base oil.Friction tests indicated that these ILs exhibit excellent friction-reducing and anti-wear properties both at RT and at 100°C.They can improve the tribological properties of MACs at RT to a greater extent than the commonly used lubricant zinc dialkyldithiophosphate(T204),even at a concentration of 0.1%.The load ramp test showed that MACs with L-C3N3 and L-P3N3 also exhibit high load-carrying capabilities.Scanning electron microscope(SEM)and X-ray photoelectron spectrometer(XPS)results indicated that physical adsorption and complex tribochemical reactions occurred between the ILs and metal surfaces during the sliding process,thereby forming a surface protective film that significantly contributed to the excellent tribological properties of the new ILs.
基金supported by National Natural Science Foundation of China (Grant Nos. 10671004, 10831004)the Doctoral Education Program Foundation of China (Grant No. 20060001003)
文摘For any multiply connected domain Ω in R2, let S be the boundary of the convex hull in H3 of R2\Ω which faces Ω. Suppose in addition that there exists a lower bound l > 0 of the hyperbolic lengths of closed geodesics in Ω. Then there is always a K-quasiconformal mapping from S to Ω, which extends continuously to the identity on S = Ω, where K depends only on l. We also give a numerical estimate of K by using the parameter l.
