共查询到20条相似文献,搜索用时 859 毫秒
1.
Armen Edigarian 《Archiv der Mathematik》2013,101(4):373-379
For a quasi-balanced domain, we study holomorphic mappings ${F : D \times D \to D}$ such that F(z, z) = z and F(z, w) = F(w, z) for any ${z, w \in D}$ . We show that in many cases the existence of such a function is equivalent to the convexity of the domain D. 相似文献
2.
3.
Let D be an open disk of radius ≤1 in $\mathbb{C}$ , and let (? n ) be a sequence of ±1. We prove that for every analytic function $f: D \to \mathbb{C}$ without zeros in D, there exists a unique sequence (α n ) of complex numbers such that $f(z) = f(0)\prod_{n=1}^{\infty} (1+\epsilon_{n}z^{n})^{\alpha_{n}}$ for every z∈D. From this representation we obtain a numerical method for calculating products of the form ∏ p prime f(1/p) provided f(0)=1 and f′(0)=0; our method generalizes a well-known method of Pieter Moree. We illustrate this method on a constant of Ramanujan $\pi^{-1/2}\prod _{p~\text{prime}} \sqrt{p^{2}-p}\ln(p/(p-1))$ . From the properties of the exponents α n , we obtain a proof of the following congruences, which have been the subject of several recent publications motivated by some questions of Arnold: for every n×n integral matrix A, every prime number p, and every positive integer k we have $\operatorname{tr} A^{p^{k}} \equiv\operatorname{tr} A^{p^{k-1}} { \hbox {\rm { (mod\ $p^{k}$) }}}$ . 相似文献
4.
А. X. гЕРМАН 《Analysis Mathematica》1980,6(2):121-135
LetD be a simply connected domain, the boundary of which is a closed Jordan curveγ; \(\mathfrak{M} = \left\{ {z_{k, n} } \right\}\) , 0≦k≦n; n=1, 2, 3, ..., a matrix of interpolation knots, \(\mathfrak{M} \subset \Gamma ; A_c \left( {\bar D} \right)\) the space of the functions that are analytic inD and continuous on \(\bar D; \left\{ {L_n \left( {\mathfrak{M}; f, z} \right)} \right\}\) the sequence of the Lagrange interpolation polynomials. We say that a matrix \(\mathfrak{M}\) satisfies condition (B m ), \(\mathfrak{M}\) ∈(B m ), if for some positive integerm there exist a setB m containingm points and a sequencen p p=1 ∞ of integers such that the series \(\mathop \Sigma \limits_{p = 1}^\infty \frac{1}{{n_p }}\) diverges and for all pairsn i ,n j ∈{n p } p=1 ∞ the set \(\left( {\bigcap\limits_{k = 0}^{n_i } {z_{k, n_i } } } \right)\bigcap {\left( {\bigcup\limits_{k = 0}^{n_j } {z_{k, n_j } } } \right)} \) is contained inB m . The main result reads as follows. {Let D=z: ¦z¦ \(\Gamma = \partial \bar D\) and let the matrix \(\mathfrak{M} \subset \Gamma \) satisfy condition (Bm). Then there exists a function \(f \in A_c \left( {\bar D} \right)\) such that the relation $$\mathop {\lim \sup }\limits_{n \to \infty } \left| {L_n \left( {\mathfrak{M}, f, z} \right)} \right| = \infty $$ holds almost everywhere on γ. 相似文献
5.
Wang Xiaoying 《Periodica Mathematica Hungarica》2013,66(2):193-200
For any fixed positive integer D which is not a square, let (u, υ) = (u 1, υ 1) be the fundamental solution of the Pell equation u 2 ? Dυ 2 = 1. Further let $\mathbb{D}$ be the set of all positive integers D such that D is odd, D is not a square and gcd(D, υ 1) > max(1, √D/8). In this paper we prove that if (x, y, z) is a positive integer solution of the equation x y + y x = z 2 satisfying gcd(x, y) = 1 and xy is odd, then either $x \in \mathbb{D}$ or $y \in \mathbb{D}$ . 相似文献
6.
Let D be a finite and simple digraph with vertex set V(D), and let f: V(D) → {?1, 1} be a two-valued function. If k ≥?1 is an integer and ${\sum_{x \in N^-(v)}f(x) \ge k}$ for each ${v \in V(G)}$ , where N ?(v) consists of all vertices of D from which arcs go into v, then f is a signed total k-dominating function on D. A set {f 1, f 2, . . . , f d } of signed total k-dominating functions on D with the property that ${\sum_{i=1}^df_i(x)\le k}$ for each ${x \in V(D)}$ , is called a signed total (k, k)-dominating family (of functions) on D. The maximum number of functions in a signed total (k, k)-dominating family on D is the signed total (k, k)-domatic number on D, denoted by ${d_{st}^{k}(D)}$ . In this paper we initiate the study of the signed total (k, k)-domatic number of digraphs, and we present different bounds on ${d_{st}^{k}(D)}$ . Some of our results are extensions of known properties of the signed total domatic number ${d_{st}(D)=d_{st}^{1}(D)}$ of digraphs D as well as the signed total domatic number d st (G) of graphs G, given by Henning (Ars Combin. 79:277–288, 2006). 相似文献
7.
?tefko Miklavi? 《Graphs and Combinatorics》2013,29(1):121-130
Let q denote an integer at least two. Let ?? denote a bipartite distance-regular graph with diameter D ?? 3 and intersection numbers c i = (q i ? 1)/(q ? 1), 1 ?? i ?? D. Let X denote the vertex set of ?? and let ${V = \mathbb{C}^X}$ denote the vector space over ${\mathbb{C}}$ consisting of column vectors whose coordinates are indexed by X and whose entries are in ${\mathbb{C}}$ . For ${z \in X}$ , let ${{\hat z}}$ denote the vector in V with a 1 in the z-coordinate and 0 in all other coordinates. Fix ${x, y \in X}$ such that ?(x, y) = 2, where ? denotes the path-length distance function. For 0 ?? i, j ?? D define ${w_{ij} = \sum {\hat z}}$ , where the sum is over all ${z \in X}$ such that ?(x, z) = i and ?(y, z) = j. We define W?=?span{w ij | 0 ?? i, j ?? D}. In this paper we consider the space ${MW={\rm span} \{mw \mid m \in M, w \in W\}}$ , where M is the Bose?CMesner algebra of ??. We observe that MW is the minimal A-invariant subspace of V which contains W, where A is the adjacency matrix of ??. We give a basis for MW that is orthogonal with respect to the Hermitean dot product. We compute the square-norm of each basis vector. We compute the action of A on the basis. For the case in which ?? is the dual polar graph D D (q) we show that the basis consists of the characteristic vectors of the orbits of the stabilizer of x and y in the automorphism group of ??. 相似文献
8.
Bruno De Maria Antonia Passarelli di Napoli 《Calculus of Variations and Partial Differential Equations》2010,38(3-4):417-439
We prove a C 1,μ partial regularity result for minimizers of a non autonomous integral funcitional of the form $$\mathcal{F}(u; \Omega):=\int_{\Omega}f(x, Du)\ dx$$ under the so-called non standard growth conditions. More precisely we assume that $$c |z|^{p}\leq f(x ,z) \leq L (1+|z|^{q}),$$ for 2 ≤ p < q and that D z f(x, z) is α-Hölder continuous with respect to the x-variable. The regularity is obtained imposing that ${\frac{p}{q} < \frac{n+\alpha}{n}}$ but without any assumption on the growth of ${D^{2}_{z}f}$ . 相似文献
9.
A. R. Wadsworth 《manuscripta mathematica》2012,139(3-4):343-389
We prove formulas for SK1(E, τ), which is the unitary SK1 for a graded division algebra E finite-dimensional and semiramified over its center T with respect to a unitary involution τ on E. Every such formula yields a corresponding formula for SK1(D, ρ) where D is a division algebra tame and semiramified over a Henselian valued field and ρ is a unitary involution on D. For example, it is shown that if ${\sf{E} \sim \sf{I}_0 \otimes_{\sf{T}_0}\sf{N}}$ where I 0 is a central simple T 0-algebra split by N 0 and N is decomposably semiramified with ${\sf{N}_0 \cong L_1\otimes_{\sf{T}_0} L_2}$ with L 1, L 2 fields each cyclic Galois over T 0, then $${\rm SK}_1(\sf{E}, \tau) \,\cong\ {\rm Br}(({L_1}\otimes_{\sf{T}_0} {L_2})/\sf{T}_0;\sf{T}_0^\tau)\big/ \left[{\rm Br}({L_1}/\sf{T}_0;\sf{T}_0^\tau)\cdot {\rm Br}({L_2}/\sf{T}_0;\sf{T}_0^\tau) \cdot \langle[\sf{I}_0]\rangle\right].$$ 相似文献
10.
Let R be a semiprime ring with a derivation D. The focus is on the two identities with Engel condition on ${D: [x^m, D(x^{n_1}),\ldots,D(x^{n_s})]_s=0}$ for all ${x\in R}$ and ${[x^m, D(x)^{n_1},\ldots,D(x)^{n_s}]_s=0}$ for all ${x\in R}$ , where s, m, n 1, . . . , n s are fixed positive integers. Our results are natural generalizations of Posner’s theorem on centralizing derivations, Herstein’s theorem on derivations with power-central values and a recent result by A. Fo?ner, M. Fo?ner and Vukman. 相似文献
11.
Gabor Toth 《Journal of Geometry》2013,104(3):585-598
In 2009 Schneider obtained stability estimates in terms of the Banach–Mazur distance for several geometric inequalities for convex bodies in an n-dimensional normed space ${\mathbb{E}^n}$ . A unique feature of his approach is to express fundamental geometric quantities in terms of a single function ${\rho:\mathfrak{B} \times \mathfrak{B} \to \mathbb{R}}$ defined on the family of all convex bodies ${\mathfrak{B}}$ in ${\mathbb{E}^n}$ . In this paper we show that (the logarithm of) the symmetrized ρ gives rise to a pseudo-metric d D on ${\mathfrak{B}}$ inducing, from our point of view, a finer topology than Banach–Mazur’s d BM . Further, d D induces a metric on the quotient ${\mathfrak{B}/{\rm Dil}^+}$ of ${\mathfrak{B}}$ by the relation of positive dilatation (homothety). Unlike its compact Banach–Mazur counterpart, d D is only “boundedly compact,” in particular, complete and locally compact. The general linear group ${{\rm GL}(\mathbb{E}^n)}$ acts on ${\mathfrak{B}/{\rm Dil}^+}$ by isometries with respect to d D , and the orbit space is naturally identified with the Banach–Mazur compactum ${\mathfrak{B}/{\rm Aff}}$ via the natural projection ${\pi:\mathfrak{B}/{\rm Dil}^+\to\mathfrak{B}/{\rm Aff}}$ , where Aff is the affine group of ${\mathbb{E}^n}$ . The metric d D has the advantage that many geometric quantities are explicitly computable. We show that d D provides a simpler and more fitting environment for the study of stability; in particular, all the estimates of Schneider turn out to be valid with d BM replaced by d D . 相似文献
12.
We define local Hardy spaces of differential forms $h^{p}_{\mathcal{D}}(\wedge T^{*}M)$ for all p∈[1,∞] that are adapted to a class of first-order differential operators $\mathcal{D}$ on a complete Riemannian manifold M with at most exponential volume growth. In particular, if D is the Hodge–Dirac operator on M and Δ=D 2 is the Hodge–Laplacian, then the local geometric Riesz transform D(Δ+aI)?1/2 has a bounded extension to $h^{p}_{D}$ for all p∈[1,∞], provided that a>0 is large enough compared to the exponential growth of M. A characterization of $h^{1}_{\mathcal{D}}$ in terms of local molecules is also obtained. These results can be viewed as the localization of those for the Hardy spaces of differential forms $H^{p}_{D}(\wedge T^{*}M)$ introduced by Auscher, McIntosh, and Russ. 相似文献
13.
Liyuan Chen 《分析论及其应用》1994,10(4):56-71
In this paper,for the plane curve T=.we define an analytic family of maximal functions asso-ciated to T asM_2f(λ)=sup_n>oh~-1∫_R相似文献
14.
We define generalized (preference) domains \(\mathcal{D}\) as subsets of the hypercube {?1,1} D , where each of the D coordinates relates to a yes-no issue. Given a finite set of n individuals, a profile assigns each individual to an element of \(\mathcal{D}\) . We prove that, for any domain \(\mathcal{D}\) , the outcome of issue-wise majority voting φ m belongs to \(\mathcal{D}\) at any profile where φ m is well-defined if and only if this is true when φ m is applied to any profile involving only 3 elements of \(\mathcal{D}\) . We call this property triple-consistency. We characterize the class of anonymous issue-wise voting rules that are triple-consistent, and give several interpretations of the result, each being related to a specific collective choice problem. 相似文献
15.
L. G. Rybnikov 《Functional Analysis and Its Applications》2006,40(3):188-199
We construct a family of maximal commutative subalgebras in the tensor product of n copies of the universal enveloping algebra U (
) of a semisimple Lie algebra
. This family is parameterized by finite sequences μ, z
1, ..., z
n
, where μ ∈
* and z
i
∈ ℂ. The construction presented here generalizes the famous construction of the higher Gaudin Hamiltonians due to Feigin,
Frenkel, and Reshetikhin. For n = 1, the corresponding commutative subalgebras in the Poisson algebra S(
) were obtained by Mishchenko and Fomenko with the help of the argument shift method. For commutative algebras of our family,
we establish a connection between their representations in the tensor products of finite-dimensional
-modules and the Gaudin model.
__________
Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 40, No. 3, pp. 30–43, 2006
Original Russian Text Copyright ? by L. G. Rybnikov 相似文献
16.
Toshiyuki Kobayashi 《Transformation Groups》2012,17(2):523-546
We initiate a new line of investigation on branching problems for generalized Verma modules with respect to reductive symmetric pairs $ \left( {\mathfrak{g},\mathfrak{g}'} \right) $ . In general, Verma modules may not contain any simple module when restricted to a reductive subalgebra. In this article we give a necessary and sufficient condition on the triple $ \left( {\mathfrak{g},\mathfrak{g}',\mathfrak{p}} \right) $ such that the restriction $ {\left. X \right|_{\mathfrak{g}'}} $ always contains simple $ \mathfrak{g}' $ -modules for any $ \mathfrak{g} $ -module X lying in the parabolic BGG category $ {\mathcal{O}^\mathfrak{p}} $ attached to a parabolic subalgebra $ \mathfrak{p} $ of $ \mathfrak{g} $ . Formulas are derived for the Gelfand?CKirillov dimension of any simple module occurring in a simple generalized Verma module. We then prove that the restriction $ {\left. X \right|_{\mathfrak{g}'}} $ is generically multiplicity-free for any $ \mathfrak{p} $ and any $ X \in {\mathcal{O}^\mathfrak{p}} $ if and only if $ \left( {\mathfrak{g},\mathfrak{g}'} \right) $ is isomorphic to (A n , A n-1), (B n , D n ), or (D n+1, B n ). Explicit branching laws are also presented. 相似文献
17.
We present a reflexive Banach space \(\mathfrak{X}_{usm}\) which is Hereditarily Indecomposable and satisfies the following properties. In every subspace Y of \(\mathfrak{X}_{usm}\) there exists a weakly null normalized sequence {y n } n , such that every subsymmetric sequence {z n } n is isomorphically generated as a spreading model of a subsequence of {y n } n . Also, in every block subspace Y of \(\mathfrak{X}_{usm}\) there exists a seminormalized block sequence {z n } and \(T:\mathfrak{X}_{usm} \to \mathfrak{X}_{usm}\) an isomorphism such that for every n ∈ ?, T(z 2n?1) = z 2n . Thus the space is an example of an HI space which is not tight by range in a strong sense. 相似文献
18.
We consider a class of Kolmogorov equation $$Lu={\sum^{p_0}_{i,j=1}{\partial_{x_i}}(a_{ij}(z){\partial_{x_j}}u)}+{\sum^{N}_{i,j=1}b_{ij}x_{i}{\partial_{x_j}}u-{\partial_t}u}={\sum^{p_0}_{j=1}{\partial_{x_j}}F_{j}(z)}$$ in a bounded open domain ${\Omega \subset \mathbb{R}^{N+1}}$ , where the coefficients matrix (a ij (z)) is symmetric uniformly positive definite on ${\mathbb{R}^{p_0} (1 \leq p_0 < N)}$ . We obtain interior W 1,p (1 < p < ∞) regularity and Hölder continuity of weak solutions to the equation under the assumption that coefficients a ij (z) belong to the ${VMO_L\cap L^\infty}$ and ${({b_{ij}})_{N \times N}}$ is a constant matrix such that the frozen operator ${L_{z_0}}$ is hypoelliptic. 相似文献
19.
Rolf Källström 《Arkiv f?r Matematik》2014,52(2):291-299
Let \((R, \frak{m}, k_{R})\) be a regular local k-algebra satisfying the weak Jacobian criterion, and such that k R /k is an algebraic field extension. Let \(\mathcal{D}_{R}\) be the ring of k-linear differential operators of R. We give an explicit decomposition of the \(\mathcal{D}_{R}\) -module \(\mathcal{D}_{R}/\mathcal{D}_{R} \frak{m}_{R}^{n+1}\) as a direct sum of simple modules, all isomorphic to \(\mathcal{D}_{R}/\mathcal{D}_{R} \frak{m}\) , where certain “Pochhammer” differential operators are used to describe generators of the simple components. 相似文献
20.
Gelu Popescu 《Integral Equations and Operator Theory》2013,75(1):87-133
In this paper, we study noncommutative domains ${\mathbb{D}_f^\varphi(\mathcal{H}) \subset B(\mathcal{H})^n}$ generated by positive regular free holomorphic functions f and certain classes of n-tuples ${\varphi = (\varphi_1, \ldots, \varphi_n)}$ of formal power series in noncommutative indeterminates Z 1, . . . , Z n . Noncommutative Poisson transforms are employed to show that each abstract domain ${\mathbb{D}_f^\varphi}$ has a universal model consisting of multiplication operators (M Z1, . . . , M Z n ) acting on a Hilbert space of formal power series. We provide a Beurling type characterization of all joint invariant subspaces under M Z1, . . . , M Z n and show that all pure n-tuples of operators in ${\mathbb{D}_f^\varphi(\mathcal{H})}$ are compressions of ${M_{Z_1} \otimes I, \ldots, M_{Z_n} \otimes I}$ to their coinvariant subspaces. We show that the eigenvectors of ${M_{Z_1}^*, \ldots, M_{Z_n}^*}$ are precisely the noncommutative Poisson kernels ${\Gamma_\lambda}$ associated with the elements ${\lambda}$ of the scalar domain ${\mathbb{D}_{f,<}^\varphi(\mathbb{C}) \subset \mathbb{C}^n}$ . These are used to solve the Nevanlinna-Pick interpolation problem for the noncommutative Hardy algebra ${H^\infty(\mathbb{D}_f^\varphi)}$ . We introduce the characteristic function of an n-tuple ${T=(T_1, \ldots , T_n) \in \mathbb{D}_f^\varphi(\mathcal{H})}$ , present a model for pure n-tuples of operators in the noncommutative domain ${\mathbb{D}_f^\varphi(\mathcal{H})}$ in terms of characteristic functions, and show that the characteristic function is a complete unitary invariant for pure n-tuples of operators in ${\mathbb{D}_f^\varphi(\mathcal{H})}$ . 相似文献