A group G is said to be(l,m,n)-generated if it is a quotient of the triangle groupT(l,m,n)=(x,y,z|x^(l)=y^(m)=z^(n)=xyz=1).Moori posed in 1993 the question of finding all the triples(l,m,n)such that non-abelian finite...A group G is said to be(l,m,n)-generated if it is a quotient of the triangle groupT(l,m,n)=(x,y,z|x^(l)=y^(m)=z^(n)=xyz=1).Moori posed in 1993 the question of finding all the triples(l,m,n)such that non-abelian finite simple groups are(l,m,n)-generated.We partially answer this question for the Fischer sporadic simple group Fi23.In particular,we investigate all(2,q,r)-generations for the Fischer sporadic simple group Fi23,where q and r are distinct prime divisors of|Fi_(23)|.展开更多
Based on μ-, T- and H-dependent pairing and number equations and the premise that μ(T) is predominantly the cause of the variation of the upper critical field H<sub>c</sub><sub>2</sub>(T), wh...Based on μ-, T- and H-dependent pairing and number equations and the premise that μ(T) is predominantly the cause of the variation of the upper critical field H<sub>c</sub><sub>2</sub>(T), where μ, T and H denote the chemical potential, temperature and the applied field, respectively, we provide in this paper fits to the empirical H<sub>c</sub><sub>2</sub>(T) data of H<sub>3</sub>S reported by Mozaffari, et al. (2019) and deal with the issue of whether or not H<sub>3</sub>S exhibits the Meissner effect. Employing a variant of the template given by Dogan and Cohen (2021), we examine in detail the results of Hirsch and Marsiglio (2022) who have claimed that H<sub>3</sub>S does not exhibit the Meissner effect and Minkov, et al. (2023) who have claimed that it does. We are thus led to suggest that monitoring the chemical potential (equivalently, the number density of Cooper pairs N<sub>s</sub> at T = T<sub>c</sub>) should shed new light on the issue being addressed.展开更多
A new (2+1)-dimensional KdV equation is constructed by using Lax pair generating technique. Exact solutions of the new equation are studied by means of the singular manifold method. Bgcklund transformation in terms...A new (2+1)-dimensional KdV equation is constructed by using Lax pair generating technique. Exact solutions of the new equation are studied by means of the singular manifold method. Bgcklund transformation in terms of the singular manifold is obtained. And localized structures are also investigated.展开更多
In this paper, we discuss the pairing problem of generators in four affine Lie algebra. That is, for any given imaginary root vector x∈g(A) , there exists y such that x and y generate a subalgebra cont...In this paper, we discuss the pairing problem of generators in four affine Lie algebra. That is, for any given imaginary root vector x∈g(A) , there exists y such that x and y generate a subalgebra containing g′(A).展开更多
This paper introduces the generalized excited pair coherent state (GEPCS). Using the entangled state 〈η〉 representation of Wigner operator, it obtains the Wigner function for the GEPCS. In the ρ-γ phase space, ...This paper introduces the generalized excited pair coherent state (GEPCS). Using the entangled state 〈η〉 representation of Wigner operator, it obtains the Wigner function for the GEPCS. In the ρ-γ phase space, the variations of the Wigner function distributions with the parameters q, α, k and l are discussed. The tomogram of the GEPCS is calculated with the help of the Radon transform between the Wigner operator and the projection operator of the entangled state |η1, η2, τ1, τ2|. The entangled states |η〉 and |η1, η2, τ1, τ2〉 provide two good representative space for studying the Wigner functions and tomograms of various two-mode correlated quantum states.展开更多
In this paper, we introduce the concepts of additive generators and additive generator pair of <em>n</em>-dimensional overlap functions, in order to extend the dimensionality of overlap functions from 2 to...In this paper, we introduce the concepts of additive generators and additive generator pair of <em>n</em>-dimensional overlap functions, in order to extend the dimensionality of overlap functions from 2 to <em>n</em>. We mainly discuss the conditions under which an <em>n</em>-dimensional overlap function can be expressed in terms of its generator pair.展开更多
We prove the termination of flips for pseudo-effective NQC log canonical generalized pairs of dimension 4.As main ingredients,we verify the termination of flips for 3-dimensional NQC log canonical generalized pairs,an...We prove the termination of flips for pseudo-effective NQC log canonical generalized pairs of dimension 4.As main ingredients,we verify the termination of flips for 3-dimensional NQC log canonical generalized pairs,and show that the termination of flips for pseudo-effective NQC log canonical generalized pairs which admit NQC weak Zariski decompositions follows from the termination of flips in lower dimensions.展开更多
The typeⅡ codes have been studied widely in applications since their appearance. With analysis of the algebraic structure of finite field of order 4 (i.e., GF(4)), some necessary and sufficient conditions that a ...The typeⅡ codes have been studied widely in applications since their appearance. With analysis of the algebraic structure of finite field of order 4 (i.e., GF(4)), some necessary and sufficient conditions that a generalized H-code (i.e., GH-code) is a type Ⅱ code over GF(4) are given in this article, and an efficient and simple method to generate type Ⅱ codes from GH-codes over GF(4) is shown. The conclusions further extend the coding theory of type Ⅱ.展开更多
In this paper,we consider the first order Hardy inequalities using simple equalities.This basic setting not only permits to derive quickly many well-known Hardy inequalities with optimal constants,but also supplies im...In this paper,we consider the first order Hardy inequalities using simple equalities.This basic setting not only permits to derive quickly many well-known Hardy inequalities with optimal constants,but also supplies improved or new estimates in miscellaneous situations,such as multipolar potential,the exponential weight,hyperbolic space,Heisenberg group,the edge Laplacian,or the Grushin type operator.展开更多
基金The authors thank the Deanship of Scientific Research(DSR)at Al Imam Mohammad Ibn Saud Islamic University(IMSIU),Saudi Arabia,for supporting this research under Project No.361201.
文摘A group G is said to be(l,m,n)-generated if it is a quotient of the triangle groupT(l,m,n)=(x,y,z|x^(l)=y^(m)=z^(n)=xyz=1).Moori posed in 1993 the question of finding all the triples(l,m,n)such that non-abelian finite simple groups are(l,m,n)-generated.We partially answer this question for the Fischer sporadic simple group Fi23.In particular,we investigate all(2,q,r)-generations for the Fischer sporadic simple group Fi23,where q and r are distinct prime divisors of|Fi_(23)|.
文摘Based on μ-, T- and H-dependent pairing and number equations and the premise that μ(T) is predominantly the cause of the variation of the upper critical field H<sub>c</sub><sub>2</sub>(T), where μ, T and H denote the chemical potential, temperature and the applied field, respectively, we provide in this paper fits to the empirical H<sub>c</sub><sub>2</sub>(T) data of H<sub>3</sub>S reported by Mozaffari, et al. (2019) and deal with the issue of whether or not H<sub>3</sub>S exhibits the Meissner effect. Employing a variant of the template given by Dogan and Cohen (2021), we examine in detail the results of Hirsch and Marsiglio (2022) who have claimed that H<sub>3</sub>S does not exhibit the Meissner effect and Minkov, et al. (2023) who have claimed that it does. We are thus led to suggest that monitoring the chemical potential (equivalently, the number density of Cooper pairs N<sub>s</sub> at T = T<sub>c</sub>) should shed new light on the issue being addressed.
基金Supported by Research Fund for the Doctoral Program of Higher Education of China under Grant No.20070486094
文摘A new (2+1)-dimensional KdV equation is constructed by using Lax pair generating technique. Exact solutions of the new equation are studied by means of the singular manifold method. Bgcklund transformation in terms of the singular manifold is obtained. And localized structures are also investigated.
文摘In this paper, we discuss the pairing problem of generators in four affine Lie algebra. That is, for any given imaginary root vector x∈g(A) , there exists y such that x and y generate a subalgebra containing g′(A).
基金supported by the National Natural Science Foundation of China (Grant No 10574060)the Natural Science Foundation of Shandong Province of China (Grant No Y2004A09)
文摘This paper introduces the generalized excited pair coherent state (GEPCS). Using the entangled state 〈η〉 representation of Wigner operator, it obtains the Wigner function for the GEPCS. In the ρ-γ phase space, the variations of the Wigner function distributions with the parameters q, α, k and l are discussed. The tomogram of the GEPCS is calculated with the help of the Radon transform between the Wigner operator and the projection operator of the entangled state |η1, η2, τ1, τ2|. The entangled states |η〉 and |η1, η2, τ1, τ2〉 provide two good representative space for studying the Wigner functions and tomograms of various two-mode correlated quantum states.
文摘In this paper, we introduce the concepts of additive generators and additive generator pair of <em>n</em>-dimensional overlap functions, in order to extend the dimensionality of overlap functions from 2 to <em>n</em>. We mainly discuss the conditions under which an <em>n</em>-dimensional overlap function can be expressed in terms of its generator pair.
基金supported by the China National Postdoctoral Program for Innovative Talents(Grant No.BX2021269)by the China Postdoctoral Science Foundation(Grant No.2021M702925)。
文摘We prove the termination of flips for pseudo-effective NQC log canonical generalized pairs of dimension 4.As main ingredients,we verify the termination of flips for 3-dimensional NQC log canonical generalized pairs,and show that the termination of flips for pseudo-effective NQC log canonical generalized pairs which admit NQC weak Zariski decompositions follows from the termination of flips in lower dimensions.
基金the National Natural Science Foundation of China (60743007)Fujian Province Young Talent Program (2006F3044)+2 种基金Province Natural Science Foundation of Fujian (JA04169)Province Education Department Foundation of Fujian (JB05331)Beijing Municipal Commission of Education Disciplines and Graduate Education Projects (XK100130648)
文摘The typeⅡ codes have been studied widely in applications since their appearance. With analysis of the algebraic structure of finite field of order 4 (i.e., GF(4)), some necessary and sufficient conditions that a generalized H-code (i.e., GH-code) is a type Ⅱ code over GF(4) are given in this article, and an efficient and simple method to generate type Ⅱ codes from GH-codes over GF(4) is shown. The conclusions further extend the coding theory of type Ⅱ.
基金supported by the Science and Technology Commission of Shanghai Municipality(STCSM)(Grant No.18dz2271000)X.Huang is partially supported by the NSFC(Grant No.11971169).
文摘In this paper,we consider the first order Hardy inequalities using simple equalities.This basic setting not only permits to derive quickly many well-known Hardy inequalities with optimal constants,but also supplies improved or new estimates in miscellaneous situations,such as multipolar potential,the exponential weight,hyperbolic space,Heisenberg group,the edge Laplacian,or the Grushin type operator.