Firstly,some properties for(p,q)-monogenic functions withα-weight in Clifford analysis are given.Then,the Cauchy-Pompeiu formula is proved.Finally,the Cauchy integral formula and the Cauchy integral theorem for(p,q)-...Firstly,some properties for(p,q)-monogenic functions withα-weight in Clifford analysis are given.Then,the Cauchy-Pompeiu formula is proved.Finally,the Cauchy integral formula and the Cauchy integral theorem for(p,q)-monogenic functions withα-weight are given.展开更多
Abstact:Through P.Gulding Theorem,the author solves the computation of volume in random rotating body,offers its related formula,develops its given formula and simplifies its calculating approach.In this sense,the for...Abstact:Through P.Gulding Theorem,the author solves the computation of volume in random rotating body,offers its related formula,develops its given formula and simplifies its calculating approach.In this sense,the formula that has been got is complete.展开更多
In this note, we prove a concentration theorem of （R,p）-anders. As a simple corollary, one can prove that （X, p）-anders do not admit coarse embeddings into Hadamard manifolds with bounded sectional curvatures.
Let R=Z/PkZ be the ring of integers modulo pk where p is a prime and k>1.Denote by n(r,m×n)tile number of m by n matrices with real rank r over R.In tile present paper.we compute n(r.m×n) and the number o...Let R=Z/PkZ be the ring of integers modulo pk where p is a prime and k>1.Denote by n(r,m×n)tile number of m by n matrices with real rank r over R.In tile present paper.we compute n(r.m×n) and the number of the orbits of Mm,n.(R)under GLm.(R)×GLm(R).where Mm.n(R) is the set of all m by n matrices over R.展开更多
An operator T is said to be paranormal if ｜｜T^2 x ｜｜ 〉｜｜Tx｜｜^2 holds for every unit vector x. Several extensions of paranormal operators are considered until now, for example absolute-k-paranormal and p-paran...An operator T is said to be paranormal if ｜｜T^2 x ｜｜ 〉｜｜Tx｜｜^2 holds for every unit vector x. Several extensions of paranormal operators are considered until now, for example absolute-k-paranormal and p-paranormal introduced in [10], [14], respectively. Yamazaki and Yanagida [38] introduced the class of absolute-（p, r）-paranormal operators as a further generalization of the classes of both absolute-k-paranormal and p-paranormal operators. An operator T ∈ B（H） is called absolute-（p, r）-paranormal operator if ｜｜｜T｜p｜T^＊ ｜^rx｜｜^r 〉 ｜｜｜T^＊｜^rx｜｜p＋r for every unit vector x ∈ H and for positive real numbers p 〉 0 and r 〉 0. The famous result of Browder, that self adjoint operators satisfy Browder＇s theorem, is extended to several classes of operators. In this paper we show that for any absolute-（p, r）- paranormal operator T, T satisfies Browder＇s theorem and a-Browder＇s theorem. It is also shown that if E is the Riesz idempotent for a nonzero isolated point μ of the spectrum of a absolute-（p, r）-paranormal operator T, then E is self-adjoint if and only if the null space of T -μ, N（T - μ） N（T^＊ - ^μ）.展开更多
For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and th...For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and the open mapping and closed graph theorems for closed convex set-valued maps.展开更多
E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixe...E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.展开更多
Simple formulas for the number of different cyclic and dihedral necklaces containing nj beads of the j-th color, and , are derived, using the Pólya enumeration theorem.
基金Supported by Natural Science Foundation of Xinjiang Uygur Autonomous Region(2021D01B35)Natural Science Foundation of colleges and universities in Xinjiang Uygur Au-tonomous Region(XJEDU2021Y048)Doctoral Initiation Fund of Xinjiang Institute of Engineering(2020xgy012302).
基金Supported by the National Natural Science Foundation of China(11871191)the Science Foundation of Hebei Province(A2023205006,A2019106037)+2 种基金the Key Development Foundation of Hebei Normal University in2024(L2024ZD08)the Graduate Student Innovation Project Fund of Hebei Province(CXZZBS2022066)the Key Foundation of Hebei Normal University(L2018Z01)。
文摘Firstly,some properties for(p,q)-monogenic functions withα-weight in Clifford analysis are given.Then,the Cauchy-Pompeiu formula is proved.Finally,the Cauchy integral formula and the Cauchy integral theorem for(p,q)-monogenic functions withα-weight are given.
基金Supported by the National Key R and D Program of China(2020YFA0713100)the Natural Science Foundation of Jiangsu Province(BK20230900)National Natural Science Foundation of China(12141104)。
文摘Abstact:Through P.Gulding Theorem,the author solves the computation of volume in random rotating body,offers its related formula,develops its given formula and simplifies its calculating approach.In this sense,the formula that has been got is complete.
文摘In this note, we prove a concentration theorem of （R,p）-anders. As a simple corollary, one can prove that （X, p）-anders do not admit coarse embeddings into Hadamard manifolds with bounded sectional curvatures.
文摘Let R=Z/PkZ be the ring of integers modulo pk where p is a prime and k>1.Denote by n(r,m×n)tile number of m by n matrices with real rank r over R.In tile present paper.we compute n(r.m×n) and the number of the orbits of Mm,n.(R)under GLm.(R)×GLm(R).where Mm.n(R) is the set of all m by n matrices over R.
基金supported by Taibah University Research Center Project(1433/803)
文摘An operator T is said to be paranormal if ｜｜T^2 x ｜｜ 〉｜｜Tx｜｜^2 holds for every unit vector x. Several extensions of paranormal operators are considered until now, for example absolute-k-paranormal and p-paranormal introduced in [10], [14], respectively. Yamazaki and Yanagida [38] introduced the class of absolute-（p, r）-paranormal operators as a further generalization of the classes of both absolute-k-paranormal and p-paranormal operators. An operator T ∈ B（H） is called absolute-（p, r）-paranormal operator if ｜｜｜T｜p｜T^＊ ｜^rx｜｜^r 〉 ｜｜｜T^＊｜^rx｜｜p＋r for every unit vector x ∈ H and for positive real numbers p 〉 0 and r 〉 0. The famous result of Browder, that self adjoint operators satisfy Browder＇s theorem, is extended to several classes of operators. In this paper we show that for any absolute-（p, r）- paranormal operator T, T satisfies Browder＇s theorem and a-Browder＇s theorem. It is also shown that if E is the Riesz idempotent for a nonzero isolated point μ of the spectrum of a absolute-（p, r）-paranormal operator T, then E is self-adjoint if and only if the null space of T -μ, N（T - μ） N（T^＊ - ^μ）.
基金The NSF (Q1107107) of Jiangsu Educational Commission.
文摘For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and the open mapping and closed graph theorems for closed convex set-valued maps.
基金Supported in part by Education Ministry,Anhui Province,China(No:2003kj047zd)
文摘E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.
文摘Simple formulas for the number of different cyclic and dihedral necklaces containing nj beads of the j-th color, and , are derived, using the Pólya enumeration theorem.
