Let G be a discrete group with a weight w on it. For p>1, we define a class of generalized Figà-Talamanca-Herz algebras Ap(G, w,α,θ) and obtain their (w,α,θ)-Dual spaces. Moreover, we show that the general...Let G be a discrete group with a weight w on it. For p>1, we define a class of generalized Figà-Talamanca-Herz algebras Ap(G, w,α,θ) and obtain their (w,α,θ)-Dual spaces. Moreover, we show that the generalized Figà-Talamanca-Herz algebras have an approximation property when G is a proper discrete group and satisfies the p-RD property.展开更多
Thermodynamic properties of the mixed spin-1 and spin-1/2 Ising-Heisenberg model are studied on a honeycomb lattice using a new approach in the mean-field approximation to analyze the effects of longitudinal Dz and tr...Thermodynamic properties of the mixed spin-1 and spin-1/2 Ising-Heisenberg model are studied on a honeycomb lattice using a new approach in the mean-field approximation to analyze the effects of longitudinal Dz and transverse Dx crystal fields. The phase diagrams are calculated in detail by studying the thermal variations of the order parameters, i.e., magnetizations and quadrupole moments, and compared with the literature to assess the reliability of the new approach. It is found that the model yields both second- and first-order phase transitions, and tricritical points. The compensation behavior of the model is also investigated for the sublattice magnetizations, and longitudinal and transverse quadrupolar moments. The latter type of compensation is observed in the literature but its possible importance is overlooked.展开更多
In this article, the approximate amenability of semigroup algebra e1(S) is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup...In this article, the approximate amenability of semigroup algebra e1(S) is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup S, the notions of amenability, approximate amenability and bounded approximate amenability of e1(S) are equivalent. We use this to give a direct proof of the approximate amenability of e1 (S) for a Brandt semigroup S. Moreover, we characterize the approximate amenability of e1(S), where S is a uniformly locally finite band semigroup.展开更多
By the use of approximation method a general criterion of algebraic independence of complex numbers is established. As its application the algebraic independence of values of certain gap series at algebraic and transc...By the use of approximation method a general criterion of algebraic independence of complex numbers is established. As its application the algebraic independence of values of certain gap series at algebraic and transcendental points is given.展开更多
We use a combination of both algebraic and numerical techniques to construct a C-1-continuous, piecewise (m, n) rational epsilon-approximation of a real algebraic plane curve of degree d. At singular points we use the...We use a combination of both algebraic and numerical techniques to construct a C-1-continuous, piecewise (m, n) rational epsilon-approximation of a real algebraic plane curve of degree d. At singular points we use the classical Weierstrass Preparation Theorem and Newton power series factorizations, based on the technique of Hensel lifting. These, together with modified rational Pade approximations, are used to efficiently construct locally approximate, rational parametric representations for all real branches of an algebraic plane curve. Besides singular points we obtain an adaptive selection of simple points about which the curve approximations yield a small number of pieces yet achieve C-1 continuity between pieces. The simpler cases of C-1 and C-0 continuity are also handled in a similar manner. The computation of singularity, the approximation error bounds and details of the implementation of these algorithms are also provided.展开更多
Let f(x)be a continued fraction with elements a<sub>n</sub>x,where coefficients a<sub>n</sub> are positive alge- braic numbers.Using the criterion of[1]for any nonzero real algebraic numbers ...Let f(x)be a continued fraction with elements a<sub>n</sub>x,where coefficients a<sub>n</sub> are positive alge- braic numbers.Using the criterion of[1]for any nonzero real algebraic numbers α<sub>1</sub>,...,α<sub>s</sub> with distinct absolute values the algebraic independence of the values f(α<sub>1</sub>),...,f(α<sub>s</sub>)is proved under certain as- sumption concerning only with a<sub>n</sub>.For some transcendental numbers ζ the algebraic independence of values f(ζ<sup>j</sup>)(j∈Z)is also established.展开更多
In this work, the magnetic properties of Ising and XY antiferromagnetic thin-films are investigated each as a function of Neel temperature and thickness for layers (n = 2, 3, 4, 5, 6, and bulk (∞) by means of a me...In this work, the magnetic properties of Ising and XY antiferromagnetic thin-films are investigated each as a function of Neel temperature and thickness for layers (n = 2, 3, 4, 5, 6, and bulk (∞) by means of a mean-field and high temperature series expansion (HTSE) combined with Pade approximant calculations. The scaling law of magnetic susceptibility and magnetization is used to determine the critical exponent γ, veff (mean), ratio of the critical exponents γ/v, and magnetic properties of Ising and XY antiferromagnetic thin-films for different thickness layers n = 2, 3, 4, 5, 6, and bulk (∞).展开更多
Quantum dynamics and statistics of an atom laser with nonlinear binary interactions are investigated inthe framework of mean-field approximation. The linearized effective Hamiltonian of the system is accurately solvab...Quantum dynamics and statistics of an atom laser with nonlinear binary interactions are investigated inthe framework of mean-field approximation. The linearized effective Hamiltonian of the system is accurately solvable.It is shown that, although the input radio frequency field is in an ordinary Glauber coherent state, the output matterwave will periodically exhibit quadrature squeezing effects purely originated from the nonlinear atom-atom collisions.展开更多
Starting with the many-body SchrSdinger Hamiltonian in R2, we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise attractive interaction approaches to the minimum of the Gros...Starting with the many-body SchrSdinger Hamiltonian in R2, we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise attractive interaction approaches to the minimum of the Gross-Pitaevskii energy functional in the mean- field regime, as the particle number N → ∞ and however the scattering length → 0. By fixing N|k|, this leads to the mean-field approximation of Bose-Einstein condensates with attractive interactions in R^2.展开更多
We show that a QWEP von Neumann algebra has the weak* positive approximation property if and only if it is seemingly injective in the following sense: there is a factorization of the identity of Id_(M)= vu : M→uB(H)...We show that a QWEP von Neumann algebra has the weak* positive approximation property if and only if it is seemingly injective in the following sense: there is a factorization of the identity of Id_(M)= vu : M→uB(H)→vM with u normal, unital, positive and v completely contractive. As a corollary, if M has a separable predual, M is isomorphic(as a Banach space) to B(l2). For instance this applies(rather surprisingly) to the von Neumann algebra of any free group. Nevertheless, since B(H) fails the approximation property(due to Szankowski) there are M ’s(namely B(H)^(**) and certain finite examples defined using ultraproducts) that are not seemingly injective.Moreover, for M to be seemingly injective it suffices to have the above factorization of I dM through B(H) with u, v positive(and u still normal).展开更多
By using the characteristic properties of the anti-Hermitian generalized anti-Hamiltonian matrices, we prove some necessary and sufficient conditions of the solvability for algebra inverse eigenvalue problem of anti-H...By using the characteristic properties of the anti-Hermitian generalized anti-Hamiltonian matrices, we prove some necessary and sufficient conditions of the solvability for algebra inverse eigenvalue problem of anti-Hermitian generalized anti-Hamiltonian matrices, and obtain a general expression of the solution to this problem. By using the properties of the orthogonal projection matrix, we also obtain the expression of the solution to optimal approximate problem of an n× n complex matrix under spectral restriction.展开更多
The collection of all the rough sets of an approximation space has been given several algebraic interpretations, including Stone algebras, regular double Stone algebras, semi-simple Nelson algebras, pre-rough algebras...The collection of all the rough sets of an approximation space has been given several algebraic interpretations, including Stone algebras, regular double Stone algebras, semi-simple Nelson algebras, pre-rough algebras and 3-valued Lukasiewicz algebras. A 3-valued Lukasiewicz algebra is a Stone algebra, a regular double Stone algebra, a semi-simple Nelson algebra, a pre-rough algebra. Thus, we call the algebra constructed by the collection of rough sets of an approximation space a rough 3-valued Lukasiewicz algebra.In this paper,the rough 3-valued Lukasiewicz algebras, which are a special kind of 3-valued Lukasiewicz algebras, are studied. Whether the rough 3-valued Lukasiewicz algebra is a axled 3-valued Lukasiewicz algebra is examined.展开更多
In this paper, first, we consider closed convex and bounded subsets of infinite-dimensional unital Banach algebras and show with regard to the general conditions that these sets are not quasi-Chebyshev and pseudo-Cheb...In this paper, first, we consider closed convex and bounded subsets of infinite-dimensional unital Banach algebras and show with regard to the general conditions that these sets are not quasi-Chebyshev and pseudo-Chebyshev. Examples of those algebras are given including the algebras of continuous functions on compact sets. We also see some results in C*-algebras and Hilbert C*-modules. Next, by considering some conditions, we study Chebyshev of subalgebras in C*-algebras.展开更多
The notions of quasi k-Gorenstein algebras and W^t-approximation representations are introduced. The existence and uniqueness (up to projective equivalences) of W^t-approximation representations over quasi k-Gorenstei...The notions of quasi k-Gorenstein algebras and W^t-approximation representations are introduced. The existence and uniqueness (up to projective equivalences) of W^t-approximation representations over quasi k-Gorenstein algebras are established. Some applications of W^t-approximation representations to homologically finite subcategories are given.展开更多
Persistence approximation property was introduced by Hervé Oyono-Oyono and Guoliang Yu. This property provides a geometric obstruction to Baum-Connes conjecture. In this paper, the authors mainly discuss the pers...Persistence approximation property was introduced by Hervé Oyono-Oyono and Guoliang Yu. This property provides a geometric obstruction to Baum-Connes conjecture. In this paper, the authors mainly discuss the persistence approximation property for maximal Roe algebras. They show that persistence approximation property of maximal Roe algebras follows from maximal coarse Baum-Connes conjecture. In particular, let X be a discrete metric space with bounded geometry, assume that X admits a fibred coarse embedding into Hilbert space and X is coarsely uniformly contractible, then Cmax*(X) has persistence approximation property. The authors also give an application of the quantitative K-theory to the maximal coarse Baum-Connes conjecture.展开更多
文摘Let G be a discrete group with a weight w on it. For p>1, we define a class of generalized Figà-Talamanca-Herz algebras Ap(G, w,α,θ) and obtain their (w,α,θ)-Dual spaces. Moreover, we show that the generalized Figà-Talamanca-Herz algebras have an approximation property when G is a proper discrete group and satisfies the p-RD property.
文摘Thermodynamic properties of the mixed spin-1 and spin-1/2 Ising-Heisenberg model are studied on a honeycomb lattice using a new approach in the mean-field approximation to analyze the effects of longitudinal Dz and transverse Dx crystal fields. The phase diagrams are calculated in detail by studying the thermal variations of the order parameters, i.e., magnetizations and quadrupole moments, and compared with the literature to assess the reliability of the new approach. It is found that the model yields both second- and first-order phase transitions, and tricritical points. The compensation behavior of the model is also investigated for the sublattice magnetizations, and longitudinal and transverse quadrupolar moments. The latter type of compensation is observed in the literature but its possible importance is overlooked.
文摘In this article, the approximate amenability of semigroup algebra e1(S) is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup S, the notions of amenability, approximate amenability and bounded approximate amenability of e1(S) are equivalent. We use this to give a direct proof of the approximate amenability of e1 (S) for a Brandt semigroup S. Moreover, we characterize the approximate amenability of e1(S), where S is a uniformly locally finite band semigroup.
基金Subject supported by the National Natural Science Foundation of China
文摘By the use of approximation method a general criterion of algebraic independence of complex numbers is established. As its application the algebraic independence of values of certain gap series at algebraic and transcendental points is given.
文摘We use a combination of both algebraic and numerical techniques to construct a C-1-continuous, piecewise (m, n) rational epsilon-approximation of a real algebraic plane curve of degree d. At singular points we use the classical Weierstrass Preparation Theorem and Newton power series factorizations, based on the technique of Hensel lifting. These, together with modified rational Pade approximations, are used to efficiently construct locally approximate, rational parametric representations for all real branches of an algebraic plane curve. Besides singular points we obtain an adaptive selection of simple points about which the curve approximations yield a small number of pieces yet achieve C-1 continuity between pieces. The simpler cases of C-1 and C-0 continuity are also handled in a similar manner. The computation of singularity, the approximation error bounds and details of the implementation of these algorithms are also provided.
基金Supported by the National Natural Science Foundation of China
文摘Let f(x)be a continued fraction with elements a<sub>n</sub>x,where coefficients a<sub>n</sub> are positive alge- braic numbers.Using the criterion of[1]for any nonzero real algebraic numbers α<sub>1</sub>,...,α<sub>s</sub> with distinct absolute values the algebraic independence of the values f(α<sub>1</sub>),...,f(α<sub>s</sub>)is proved under certain as- sumption concerning only with a<sub>n</sub>.For some transcendental numbers ζ the algebraic independence of values f(ζ<sup>j</sup>)(j∈Z)is also established.
文摘In this work, the magnetic properties of Ising and XY antiferromagnetic thin-films are investigated each as a function of Neel temperature and thickness for layers (n = 2, 3, 4, 5, 6, and bulk (∞) by means of a mean-field and high temperature series expansion (HTSE) combined with Pade approximant calculations. The scaling law of magnetic susceptibility and magnetization is used to determine the critical exponent γ, veff (mean), ratio of the critical exponents γ/v, and magnetic properties of Ising and XY antiferromagnetic thin-films for different thickness layers n = 2, 3, 4, 5, 6, and bulk (∞).
文摘Quantum dynamics and statistics of an atom laser with nonlinear binary interactions are investigated inthe framework of mean-field approximation. The linearized effective Hamiltonian of the system is accurately solvable.It is shown that, although the input radio frequency field is in an ordinary Glauber coherent state, the output matterwave will periodically exhibit quadrature squeezing effects purely originated from the nonlinear atom-atom collisions.
基金supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry of China,National Center for Mathematics and Interdisciplinary Sciences in China
文摘Starting with the many-body SchrSdinger Hamiltonian in R2, we prove that the ground state energy of a two-dimensional interacting Bose gas with the pairwise attractive interaction approaches to the minimum of the Gross-Pitaevskii energy functional in the mean- field regime, as the particle number N → ∞ and however the scattering length → 0. By fixing N|k|, this leads to the mean-field approximation of Bose-Einstein condensates with attractive interactions in R^2.
文摘We show that a QWEP von Neumann algebra has the weak* positive approximation property if and only if it is seemingly injective in the following sense: there is a factorization of the identity of Id_(M)= vu : M→uB(H)→vM with u normal, unital, positive and v completely contractive. As a corollary, if M has a separable predual, M is isomorphic(as a Banach space) to B(l2). For instance this applies(rather surprisingly) to the von Neumann algebra of any free group. Nevertheless, since B(H) fails the approximation property(due to Szankowski) there are M ’s(namely B(H)^(**) and certain finite examples defined using ultraproducts) that are not seemingly injective.Moreover, for M to be seemingly injective it suffices to have the above factorization of I dM through B(H) with u, v positive(and u still normal).
基金Project(10171031) supported by the National Natural Science Foundation of China
文摘By using the characteristic properties of the anti-Hermitian generalized anti-Hamiltonian matrices, we prove some necessary and sufficient conditions of the solvability for algebra inverse eigenvalue problem of anti-Hermitian generalized anti-Hamiltonian matrices, and obtain a general expression of the solution to this problem. By using the properties of the orthogonal projection matrix, we also obtain the expression of the solution to optimal approximate problem of an n× n complex matrix under spectral restriction.
基金The 973 NationalKey BasicResearchand Development Program of China (No .2002CB312106 ) theChinaPostdoctoralScience Foundation (N o.2004035715)+1 种基金 the Science & Technology Program of Zhejiang Province in C hina(N o.2004C31098 )thePostdoctoraSlcienceFoundationofZhejiangProvinceinChina (No .2004-bsh-023).
文摘The collection of all the rough sets of an approximation space has been given several algebraic interpretations, including Stone algebras, regular double Stone algebras, semi-simple Nelson algebras, pre-rough algebras and 3-valued Lukasiewicz algebras. A 3-valued Lukasiewicz algebra is a Stone algebra, a regular double Stone algebra, a semi-simple Nelson algebra, a pre-rough algebra. Thus, we call the algebra constructed by the collection of rough sets of an approximation space a rough 3-valued Lukasiewicz algebra.In this paper,the rough 3-valued Lukasiewicz algebras, which are a special kind of 3-valued Lukasiewicz algebras, are studied. Whether the rough 3-valued Lukasiewicz algebra is a axled 3-valued Lukasiewicz algebra is examined.
文摘In this paper, first, we consider closed convex and bounded subsets of infinite-dimensional unital Banach algebras and show with regard to the general conditions that these sets are not quasi-Chebyshev and pseudo-Chebyshev. Examples of those algebras are given including the algebras of continuous functions on compact sets. We also see some results in C*-algebras and Hilbert C*-modules. Next, by considering some conditions, we study Chebyshev of subalgebras in C*-algebras.
文摘The notions of quasi k-Gorenstein algebras and W^t-approximation representations are introduced. The existence and uniqueness (up to projective equivalences) of W^t-approximation representations over quasi k-Gorenstein algebras are established. Some applications of W^t-approximation representations to homologically finite subcategories are given.
基金supported by the National Natural Science Foundation of China(Nos.11771143,11831006,11420101001).
文摘Persistence approximation property was introduced by Hervé Oyono-Oyono and Guoliang Yu. This property provides a geometric obstruction to Baum-Connes conjecture. In this paper, the authors mainly discuss the persistence approximation property for maximal Roe algebras. They show that persistence approximation property of maximal Roe algebras follows from maximal coarse Baum-Connes conjecture. In particular, let X be a discrete metric space with bounded geometry, assume that X admits a fibred coarse embedding into Hilbert space and X is coarsely uniformly contractible, then Cmax*(X) has persistence approximation property. The authors also give an application of the quantitative K-theory to the maximal coarse Baum-Connes conjecture.