Canonical differential calculi are defined for finitely generated Abelian groups with involutions existing consistently. Two such the canonical calculi are presented. Fermionic representations for canonical calculi ar...Canonical differential calculi are defined for finitely generated Abelian groups with involutions existing consistently. Two such the canonical calculi are presented. Fermionic representations for canonical calculi are defined based on quantized calculi. Fermionic representations for aforementioned two canonical calculi are searched out.展开更多
We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their...We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their solutions.As an application,we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions.The obtained results are new,and they extend and improve some existing ones.Finally,an example is presented to illustrate the validity of our theoretical results.展开更多
We discuss quantum fluctuation in excited states （named thermo number states） of mesoscopic LC circuits at a finite temperature. By introducing the coherent thermo state into the thermo field dynamics pioneered by U...We discuss quantum fluctuation in excited states （named thermo number states） of mesoscopic LC circuits at a finite temperature. By introducing the coherent thermo state into the thermo field dynamics pioneered by Umezawa and using the natural representation of thermo squeezing operator we can concisely derive the fluctuation. The result shows that the noise becomes larger when either temperature or the excitation number increases.展开更多
In this paper Dirce group is constructed on the basis of algebraic properties of α’s and β’s matrices in Dirac equation. It is then establisbed that the dimensions of the matrices must be four (i. e., 4 × 4 m...In this paper Dirce group is constructed on the basis of algebraic properties of α’s and β’s matrices in Dirac equation. It is then establisbed that the dimensions of the matrices must be four (i. e., 4 × 4 matrices), and the concrete formulations of them in Pauli-Dirac representation are derived.展开更多
The finite element method has been considered as one of the most significant engineering advances of the twentieth century. This computational methodology has made substantial impact on many fields in science and also...The finite element method has been considered as one of the most significant engineering advances of the twentieth century. This computational methodology has made substantial impact on many fields in science and also has profoundly changed engineering design procedures and practice. This paper, mainly froln a solid mechanics perspective, and the Swansea viewpoint in particular, describes very briefly the origin of the methodology, then summaries selected milestones of the technical developments that have taken place over the last fifty years and illustrates their application to some practical engineering problems.展开更多
In this paper,an improvement has been made to the approximation technique of a complex domain through the stair-step approach to have a considerable accuracy,minimize computational cost,and avoid the hardship of manua...In this paper,an improvement has been made to the approximation technique of a complex domain through the stair-step approach to have a considerable accuracy,minimize computational cost,and avoid the hardship of manual work.A novel stair-step representation algorithm is used in this regard,where the entire procedure is carried out through our developed MATLAB routine.Arakawa C-grid is used in our approximation with(1/120)°grid resolution.As a test case,the method is applied to approximate the domain covering the area between 15°-23°N latitudes and 85°-95°E longitudes in the Bay of Bengal.Along with the approximation of the land-sea interface,coastal stations are also identified.Approximated land-sea interfaces and coastal stations are found to be in good agreement with the actual ones based on the similarity index,overlap fraction,and extra fraction criteria.The method can be used for approximating an irregular geometric domain to employ the finite difference method in solving problems related to long waves.As a test case,shallow water equations in Cartesian coordinates are solved on the domain of interest for simulating water levels due to the nonlinear tide-surge interaction associated with the storms April 1991 and AILA,2009 along the coast of Bangladesh.The same input except for the discretized domain and bathymetry as that of Paul et al.(2016)is used in our simulation.The results are found to be in reasonable agreement with the observed data procured from Bangladesh Inland Water Transport Authority.展开更多
The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The finite element formulation is based on the total Lagrangian approach. An exact representatio...The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The finite element formulation is based on the total Lagrangian approach. An exact representation of finite rotation is introduced. The strain energy function accounting for the material symmetry is obtained by the tensor representation theory. To avoid shear locking, the assumed strain technique for transverse shear is adopted. The conjugate gradient method with a proposed line search algorithm is employed to minimize energy and reach the final shape of fabric. The draping behavior of a rectangular piece of fabric over a rectangular table is simulated. (Author abstract) 9 Refs.展开更多
This paper constructs a new type of finite-dimensional thermal coherent states （FDTCS）, which differs from the proceeding thermal coherent state in construction, as realisations of SU（2） Lie algebra. Using the tec...This paper constructs a new type of finite-dimensional thermal coherent states （FDTCS）, which differs from the proceeding thermal coherent state in construction, as realisations of SU（2） Lie algebra. Using the technique of integration within an ordered product of operator, it investigates the orthonormality and completeness relation of the FDTCS. Based on the thermal Wigner operator in the thermal entangled state representation, the Wigner function of the FDTCS is obtained. The nonclassical properties of the FDTCS are discussed in terms of the negativity of its Wigner function.展开更多
In this article, we will consider questions of G-equivalence of paths for the case when G was the group of the real representation of a symplectic transformation in an n-dimensional quaternion vector space. In determi...In this article, we will consider questions of G-equivalence of paths for the case when G was the group of the real representation of a symplectic transformation in an n-dimensional quaternion vector space. In determining the solution of this problem, we give an explicit description of differential generators of a differential field of differential rational functions that are invariant under the action of this group. Necessary and sufficient conditions for the G-equivalence of paths in a 4n-dimensional real space are obtained with the help of differential generators.展开更多
In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the sys...In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the system of completely 1-summing mapping spaces. First we obtain that if V has WEP, V is locally reflexive in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if it is locally reflexive in the system (Ⅰ(⋅,⋅), t(⋅)). Furthermore we prove that an operator space V ⊆ B(H) is exact in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)). At last, we show that an operator space V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V = C.展开更多
基金Climb-Up (Pan Deng) Project of Department of Science and Technology of China，国家自然科学基金，Doctoral Programme Foundation of Institution of Higher Education of China
文摘Canonical differential calculi are defined for finitely generated Abelian groups with involutions existing consistently. Two such the canonical calculi are presented. Fermionic representations for canonical calculi are defined based on quantized calculi. Fermionic representations for aforementioned two canonical calculi are searched out.
文摘We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their solutions.As an application,we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions.The obtained results are new,and they extend and improve some existing ones.Finally,an example is presented to illustrate the validity of our theoretical results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10574060 and 10775097)the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A23)the Shandong Province Higher Educational Science and Technology Program (Grant No. J09LA07)
文摘We discuss quantum fluctuation in excited states （named thermo number states） of mesoscopic LC circuits at a finite temperature. By introducing the coherent thermo state into the thermo field dynamics pioneered by Umezawa and using the natural representation of thermo squeezing operator we can concisely derive the fluctuation. The result shows that the noise becomes larger when either temperature or the excitation number increases.
文摘In this paper Dirce group is constructed on the basis of algebraic properties of α’s and β’s matrices in Dirac equation. It is then establisbed that the dimensions of the matrices must be four (i. e., 4 × 4 matrices), and the concrete formulations of them in Pauli-Dirac representation are derived.
文摘The finite element method has been considered as one of the most significant engineering advances of the twentieth century. This computational methodology has made substantial impact on many fields in science and also has profoundly changed engineering design procedures and practice. This paper, mainly froln a solid mechanics perspective, and the Swansea viewpoint in particular, describes very briefly the origin of the methodology, then summaries selected milestones of the technical developments that have taken place over the last fifty years and illustrates their application to some practical engineering problems.
文摘In this paper,an improvement has been made to the approximation technique of a complex domain through the stair-step approach to have a considerable accuracy,minimize computational cost,and avoid the hardship of manual work.A novel stair-step representation algorithm is used in this regard,where the entire procedure is carried out through our developed MATLAB routine.Arakawa C-grid is used in our approximation with(1/120)°grid resolution.As a test case,the method is applied to approximate the domain covering the area between 15°-23°N latitudes and 85°-95°E longitudes in the Bay of Bengal.Along with the approximation of the land-sea interface,coastal stations are also identified.Approximated land-sea interfaces and coastal stations are found to be in good agreement with the actual ones based on the similarity index,overlap fraction,and extra fraction criteria.The method can be used for approximating an irregular geometric domain to employ the finite difference method in solving problems related to long waves.As a test case,shallow water equations in Cartesian coordinates are solved on the domain of interest for simulating water levels due to the nonlinear tide-surge interaction associated with the storms April 1991 and AILA,2009 along the coast of Bangladesh.The same input except for the discretized domain and bathymetry as that of Paul et al.(2016)is used in our simulation.The results are found to be in reasonable agreement with the observed data procured from Bangladesh Inland Water Transport Authority.
文摘The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The finite element formulation is based on the total Lagrangian approach. An exact representation of finite rotation is introduced. The strain energy function accounting for the material symmetry is obtained by the tensor representation theory. To avoid shear locking, the assumed strain technique for transverse shear is adopted. The conjugate gradient method with a proposed line search algorithm is employed to minimize energy and reach the final shape of fabric. The draping behavior of a rectangular piece of fabric over a rectangular table is simulated. (Author abstract) 9 Refs.
基金Project supported by the National Natural Science Foundation of China(Grant No.10574060)the Natural Science Foundation of Shandong Province,China(Grant No.Y2008A23and ZR2010AQ027)the Shandong Province Higher Educational Science and Technology Program,China(Grant Nos.J09LA07and J10LA15).
文摘This paper constructs a new type of finite-dimensional thermal coherent states （FDTCS）, which differs from the proceeding thermal coherent state in construction, as realisations of SU（2） Lie algebra. Using the technique of integration within an ordered product of operator, it investigates the orthonormality and completeness relation of the FDTCS. Based on the thermal Wigner operator in the thermal entangled state representation, the Wigner function of the FDTCS is obtained. The nonclassical properties of the FDTCS are discussed in terms of the negativity of its Wigner function.
文摘In this article, we will consider questions of G-equivalence of paths for the case when G was the group of the real representation of a symplectic transformation in an n-dimensional quaternion vector space. In determining the solution of this problem, we give an explicit description of differential generators of a differential field of differential rational functions that are invariant under the action of this group. Necessary and sufficient conditions for the G-equivalence of paths in a 4n-dimensional real space are obtained with the help of differential generators.
文摘In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the system of completely 1-summing mapping spaces. First we obtain that if V has WEP, V is locally reflexive in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if it is locally reflexive in the system (Ⅰ(⋅,⋅), t(⋅)). Furthermore we prove that an operator space V ⊆ B(H) is exact in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)). At last, we show that an operator space V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V = C.
