共查询到20条相似文献,搜索用时 62 毫秒
1.
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
2.
И. И. Баврин 《Analysis Mathematica》1979,5(4):257-267
LetD denote a bounded complete bicircular domain (centered at (0, 0)) in the space C of two complex variablesz 1 andz 1. Extremal problems are treated in the classP D which is a generalization, to the two complex variables case, of the class of close-to-starlike functions regular in a disc. Our considerations include estimates of the basic functionals, in particular, those specific for the functions of several complex variables; exactness of estimates is considered, as well. For example, we obtain estimates of the functionals $$A_k (D) = \mathop {\sup }\limits_{(z_1 ,z_2 ) \in D} \mathop \sum \limits_{l = 0}^k |a_{k - l,l} |^2 |z_1 |^{2(k - l)} |z_2 |^{2l} ,B_k (D) = \mathop {\sup }\limits_{(z_1 ,z_2 ) \in D} \left| {\mathop \sum \limits_{l = 0}^k a_{k - l,l} z_1^{k - l} z_2^l } \right|,k = 1,2 \ldots .$$ It is also proved that the Carathéodory class is a subclass of the classP D. 相似文献
3.
Shi Jihuai 《中国科学A辑(英文版)》1998,41(1):22-32
A necessary and sufficient condition for the boundedness of the operator: $(T_{s,u,u} f)(\xi ) = h^{u + \tfrac{v}{a}} (\xi )\smallint _{\Omega _a } h^s (\xi ')K_{s,u,v} (\xi ,\xi ')f(\xi ')dv(\xi ') on L^p (\Omega _a ,dv_\lambda ),1< p< \infty $ , is obtained, where $\Omega _a = \left\{ {\xi = (z,w) \in \mathbb{C}^{n + m} :z \in \mathbb{C}^n ,w \in \mathbb{C}^m ,|z|^2 + |w|^{2/a}< 1} \right\},h(\xi ) = (1 - |z|^2 )^a - |w|^2 $ andK x,u,v (ξ,ξ′).This generalizes the works in literature from the unit ball or unit disc to the weakly pseudoconvex domain ω a . As an appli cation, it is proved thatf?L H p (ω a ,dv λ) implies $h\tfrac{{|a|}}{a} + |\beta |(\xi )D_2^a D_z^\beta f \in L^p (\Omega _a ,dv_\lambda ),1 \leqslant p< \infty $ , for any multi-indexa=(α1,?,α n and ß = (ß1, —ß). An interesting question is whether the converse holds. 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.
For symmetric operators B i (B i = d ?B i ) and positive operators $A_{i}\succeq\tilde{A}_{i}$ , we compare moments of $\|B_{1}A_{1}^{p}+\cdots+B_{n}A_{n}^{p}\|$ and $\|B_{1}\tilde{A}_{1}^{p}+\cdots +B_{n}\tilde{A}_{n}^{p}\|$ . 相似文献
6.
Gerard Brunick 《Probability Theory and Related Fields》2013,155(1-2):265-302
We study the martingale problem associated with the operator $$ Lu(s, x) = \partial_su(s, x) + \frac{1}{2} \sum_{i,j=1}^{d_0} a^{ij}(s, x) \partial_{ij}u(s, x) + \sum_{i,j=1}^d B^{ij} x^j \partial_iu(s, x), $$ where d 0 ≤ d. We show that the martingale problem is well-posed when the function a is continuous and strictly positive definite on ${\mathbb{R}^{d_0}}$ and the matrix B takes a particular lower-diagonal, block form. We then localize this result to show that the martingale problem remains well-posed when B is replaced by a sufficiently smooth vector field whose Jacobian matrix satisfies a nondegeneracy condition. 相似文献
7.
Yohei Tachiya 《Results in Mathematics》2005,48(3-4):344-370
The aim of this paper is to prove the transcendence of certain infinite products. As applications, we get necessary and sufficient conditions for transcendence of the value of $\Pi_{k=0}^{\infty}(1+a_{k}^{(1)}{z_{1}r^{k}}+\cdot\cdot\cdot+a_{k}^{(m)}{z_{m}r^{k}})$ at appropriate algebraic points, where r ≥ 2 is an integer and {an (i)}n≥ 0 (1 ≤ i ≤ m) are suitable sequences of algebraic numbers. 相似文献
8.
Bernd Greuel 《Results in Mathematics》1997,32(1-2):80-86
Generalizing two results of Rieger [8] and Selberg [10] we give asymptotic formulas for sums of type $${\matrix {\sum \limits_{n\leq x}\cr n\equiv l({\rm mod}k)\cr f_{\kappa}(n)\equiv s_{\kappa}({\rm mod}p_{\kappa})\cr (\kappa=1,\dots,r)\cr}}\qquad \chi(n)\qquad {\rm and} {\matrix {\sum \limits_{n\leq x}\cr n\equiv l({\rm mod}k)\cr f_{\kappa}(n)\equiv s_{\kappa}({\rm mod}p_{\kappa})\cr (\kappa=1,\dots,r)\cr}}\qquad \chi(n),$$ where χ is a suitable multiplicative function, f1,…, f r are “small” additive, prime-independent arithmetical functions and k, l are coprime. The proofs are based on an analytic method which consists of considering the Dirichlet series generated by $ \chi(n)z_{1}^{f_{1}(n)}\cdot... \cdot z_{r}^{f_{r}(n)},z_{1}\dots z_{r} $ complex. 相似文献
9.
A. A. Ryabinin 《Journal of Mathematical Sciences》1994,68(4):577-584
For series of random variables $\sum\limits_{k = 1}^\infty {a_k x_k }$ ,a K ∈R 1, {X K } K=1 ∞ being an Ising system, i.e., for each n ≥ 2 the joint distribution of {X K } K=1 n has the form $$P_n (t_1 ,...,t_n ) = ch^{ - (n - 1)} J \cdot exp(J\sum\limits_{k - 1}^{n - 1} {t_k t_{k + 1} )\prod\limits_{k = 1}^n {\frac{1}{2}\delta (t_{k^{ - 1} }^2 ),J > 0} }$$ one obtains a criterion for almost everywhere convergence: $\sum\limits_{k = 1}^\infty {a_k^2< \infty }$ . The relation between the asymptotic behavior of large deviations of the sum and the rate of decrease of the sequence {ak} of the coefficients is investigated. 相似文献
10.
Analogs of the arcsine distribution for sequences linearly generated by independent random variables
Yu. A. Davydov 《Journal of Mathematical Sciences》1983,23(3):2266-2275
Let {ξk}, kz ...?1,0,1, ..., be a sequence of independent identically distributed random variables with . Let {Ck} be a numerical sequence such that \(\Sigma _{ - \infty }^\infty c_k^2< \infty \) Let $$X_n = \sum\limits_{ - \infty }^\infty {c_{k - n} \xi _k } , S_n = \sum\limits_1^n {X_k } $$ . This article investigates the limit behavior of the distributions of functionals of the following type: $$\mathcal{V}_n = \tfrac{1}{n}\sum\limits_1^n {h\left( {S_k } \right)} $$ , where h is a bounded function on R1. 相似文献
11.
B. V. Dekster 《Israel Journal of Mathematics》1985,50(3):169-180
Theorem. Let a set X?Rn have unit circumradius and let B be the unit ball containing X. Put C =conv \(\bar X\) D =diam C (=diam X), k =dim C,d i = √(2i + 2)/i. Then: (i) D∈[dn, 2]; (ii) k≧m where m∈{2,3,...,n} satisfies D∈[dm, dm?1) (di decreases by i); (iii) In case k=m (by (ii), this is always the case when m=n), C contains a k-simplex Δ such that: (α) its vertices are on δB; (β) the centre of B belongs toint Δ; (γ) the inequalitiesλ k (D) ≦l ≦D with $$\lambda _k (D) = D\sqrt {\frac{{4k - 2D^2 (k - 1)}}{{2 - (k - 2)(D^2 - 2)}}, D \in (d_k ,d_{k - 1} )} $$ are unimprovable estimates for length l of any edge of Δ. 相似文献
12.
The Maximal Variation of Martingales of Probabilities and Repeated Games with Incomplete Information
Abraham Neyman 《Journal of Theoretical Probability》2013,26(2):557-567
The variation of a martingale $p_{0}^{k}=p_{0},\ldots,p_{k}$ of probabilities on a finite (or countable) set X is denoted $V(p_{0}^{k})$ and defined by $$ V\bigl(p_0^k\bigr)=E\Biggl(\sum_{t=1}^k\|p_t-p_{t-1}\|_1\Biggr). $$ It is shown that $V(p_{0}^{k})\leq\sqrt{2kH(p_{0})}$ , where H(p) is the entropy function H(p)=?∑ x p(x)logp(x), and log stands for the natural logarithm. Therefore, if d is the number of elements of X, then $V(p_{0}^{k})\leq\sqrt{2k\log d}$ . It is shown that the order of magnitude of the bound $\sqrt{2k\log d}$ is tight for d≤2 k : there is C>0 such that for all k and d≤2 k , there is a martingale $p_{0}^{k}=p_{0},\ldots,p_{k}$ of probabilities on a set X with d elements, and with variation $V(p_{0}^{k})\geq C\sqrt{2k\log d}$ . An application of the first result to game theory is that the difference between v k and lim j v j , where v k is the value of the k-stage repeated game with incomplete information on one side with d states, is bounded by $\|G\|\sqrt{2k^{-1}\log d}$ (where ∥G∥ is the maximal absolute value of a stage payoff). Furthermore, it is shown that the order of magnitude of this game theory bound is tight. 相似文献
13.
F. Móricz 《Analysis Mathematica》1983,9(1):57-67
Основной целью работ ы является обобщение одного результата Кратца и Т раутнера [4], известного для одном ерных функциональны х рядов, на кратные ряды. Этот рез ультат касается суммируемо сти функционального ряда почти всюду при слабых пред положениях. В частности, он примен им к суммируемости по Чезаро и по Риссу. Мы рассматриваемd-кр атный ряд $$\mathop \sum \limits_{k_1 = 0}^\infty \cdots \mathop \sum \limits_{k_d = 0}^\infty c_{k_1 ,...,k_d } f_{k_1 ,...,k_d } (x), \mathop \sum \limits_{k_1 = 0}^\infty \cdots \mathop \sum \limits_{k_d = 0}^\infty c_{k_1 ,...,k_d }^2< \infty $$ и предполагается, что функции \(f_{k_1 ,...,k_d } (x)\) интегрируе мы по пространству с полож ительной мерой и имеют почти вс юду ограниченные фун кции Лебега для метода суммирова ния Т. Метод Т определяетсяd-мерной матрицей \(T = \{ a_{m_1 ,...,m_d ;k_1 ,...,k_d } \} \) сл едующим образом: $$t_{m_1 ,...,m_d } (x) = \mathop \sum \limits_{k_1 = 0}^\infty \cdots \mathop \sum \limits_{k_d = 0}^\infty a_{m_1 ,...,m_d ;k_1 ,...,k_d } c_{k_1 ,...,k_d } f_{k_1 ,...,k_d } (x).$$ Эти средние существу ют, поскольку мы предп олагаем, что \(a_{m_1 ,...,m_d ;k_1 ,...,k_d } = 0\) ,если max(k 1,...,k d) достаточно вели к (в зависимости, конеч но, отm 1,...,m d). При некоторых дополнительных усло виях на матрицуТ (см. (7)– (9) в разделе 3) устанавлива ется почти всюду регулярная схо димость средних \(t_{m_1 ,...,m_d } (x) \user2{} \user2{(}m_1 \user2{,}...\user2{,}m_d \user2{)} \to \infty \) . Как вспомогательный результат, в работе об общается теорема Алексича [1] о сх одимости почти всюду некоторы х подпоследовательн остей частных сумм функцио нального ряда. 相似文献
14.
We consider tuples {N jk }, j = 1, 2, ..., k = 1, ..., q j , of nonnegative integers such that $$ \sum\limits_{j = 1}^\infty {\sum\limits_{k = 1}^{q_j } {jN_{jk} } } \leqslant M. $$ Assuming that q j ~ j d?1, 1 < d < 2, we study how the probabilities of deviations of the sums $ \sum\nolimits_{j = j_1 }^{j_2 } {\sum\nolimits_{k = 1}^{q_j } {N_{jk} } } $ N jk from the corresponding integrals of the Bose-Einstein distribution depend on the choice of the interval [j 1,j 2]. 相似文献
15.
Let Zj be the Euclidean space of vectors \((z_{j,1,...,} z_{j_{j \cdot n_j + 1} } ), Z = \mathop \oplus \limits_{j = 1}^P Z_j\) . The function u: Z → ?+, u ?0, is said to be logarithmically p-subharmonic if log u(z) is upper semicontinuous with respect to the totality of the variables and subharmonic or identically equal to ?∞ with respect to each zj when the remaining ones are fixed. For such functions, with the growth estimate $$log u(z) \leqslant \delta \mathop \Pi \limits_{j = 1}^P (1 + |z_{j,n_j + 1} |) + N(\mathop {\sum\limits_{\mathop {1 \leqslant j \leqslant p}\limits_{} } {z_{j,k}^2 } }\limits_{1 \leqslant k \leqslant n_j } )^{1/2} + C; \delta ,N \geqslant 0, C \in \mathbb{R}$$ one proves theorems on equivalence of∞) (Lq)-norms of their restrictions to \(X = \mathop \oplus \limits_{j = 1}^P (Z_{j,1} ,...,z_{j,n_j } )\) and to a relatively dense subset of it, generalizing the known Cartwright and Plancherel-Pólya results. 相似文献
16.
Jacques Wolfmann 《Designs, Codes and Cryptography》2000,20(1):73-88
Let R=GR(4,m) be the Galois ring of cardinality 4m and let T be the Teichmüller system of R. For every map λ of T into { -1,+1} and for every permutation Π of T, we define a map φ λ Π of Rinto { -1,+1} as follows: if x∈R and if x=a+2b is the 2-adic representation of x with x∈T and b∈T, then φ λ Π (x)=λ(a)+2Tr(Π(a)b), where Tr is the trace function of R . For i=1 or i=-1, define D i as the set of x in R such thatφ λ Π =i. We prove the following results: 1) D i is a Hadamard difference set of (R,+). 2) If φ is the Gray map of R into ${\mathbb{F}}_2^{2m}$ , then (D i) is a difference set of ${\mathbb{F}}_2^{2m}$ . 3) The set of D i and the set of φ(D i) obtained for all maps λ and Π, both are one-to-one image of the set of binary Maiorana-McFarland difference sets in a simple way. We also prove that special multiplicative subgroups of R are difference sets of kind D i in the additive group of R. Examples are given by means of morphisms and norm in R. 相似文献
17.
Fausto Acanfora 《Ricerche di matematica》2012,61(2):299-306
In this paper we study the stability of the solutions of some nonlinear Neumann problems, under perturbations of the domains in the Hausdorff complementary topology. We consider the problem $${{\left\{\begin{array}{c}-\text{ div}\;\left(a\left( x,\nabla u_{\Omega}\right)\right)=0 \;\text{in}\; \Omega \\ {a\left( x, \nabla u_{\Omega}\right) \cdot \nu=0\; \text{on}\; \partial\Omega}\end{array}\right.}}$$ where ${{\mathbf{R}^n \times \mathbf{R}^n \rightarrow \mathbf{R}^n}}$ is a Caratheodory function satisfying the standard monotonicity and growth conditions of order p, 1?<?p?<???. If ?? h is a uniformly bounded sequence of connected open sets in R n , n ??? 2, we prove that if ${{\Omega_{h}^{c} \rightarrow \Omega^{c}}}$ in the Hausdorff metric, ${|\Omega_{h}| \rightarrow |\Omega|}$ and the geodetic distances satisfy the inequality ${d_{\Omega}\left( x,y\right) \leq \liminf_{h} d_{\Omega_{h}} \left( x,y\right)}$ for every ${x, y \in \Omega,}$ then ${\nabla u_{\Omega_h} \rightarrow\nabla u_{\Omega}}$ strongly in L p , provided that W 1, ??(??) is dense in the space L 1, p (??) of all functions whose gradient belongs to L p (??, R n ). 相似文献
18.
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
19.
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
20.
Let p, n ∈ ? with 2p ≥ n + 2, and let I a be a polyharmonic spline of order p on the grid ? × a? n which satisfies the interpolating conditions $I_{a}\left( j,am\right) =d_{j}\left( am\right) $ for j ∈ ?, m ∈ ? n where the functions d j : ? n → ? and the parameter a > 0 are given. Let $B_{s}\left( \mathbb{R}^{n}\right) $ be the set of all integrable functions f : ? n → ? such that the integral $$ \left\| f\right\| _{s}:=\int_{\mathbb{R}^{n}}\left| \widehat{f}\left( \xi\right) \right| \left( 1+\left| \xi\right| ^{s}\right) d\xi $$ is finite. The main result states that for given $\mathbb{\sigma}\geq0$ there exists a constant c>0 such that whenever $d_{j}\in B_{2p}\left( \mathbb{R}^{n}\right) \cap C\left( \mathbb{R}^{n}\right) ,$ j ∈ ?, satisfy $\left\| d_{j}\right\| _{2p}\leq D\cdot\left( 1+\left| j\right| ^{\mathbb{\sigma}}\right) $ for all j ∈ ? there exists a polyspline S : ? n+1 → ? of order p on strips such that $$ \left| S\left( t,y\right) -I_{a}\left( t,y\right) \right| \leq a^{2p-1}c\cdot D\cdot\left( 1+\left| t\right| ^{\mathbb{\sigma}}\right) $$ for all y ∈ ? n , t ∈ ? and all 0 < a ≤ 1. 相似文献