共查询到20条相似文献,搜索用时 31 毫秒
1.
Aequationes mathematicae - We study the functional equation for unknown functions $$f,g,h,k,\ell :S \rightarrow \mathbb {C}$$ , where S is a semigroup and $$m_1,m_2:S \rightarrow \mathbb {C}$$ are... 相似文献
2.
In this paper we prove that any residue class λ modulo a large prime number p can be represented in the form
for some positive integers m1, n1,... ,m5, n5 of the size O(p27/28). This improves one of the results from [6] on representability of λ modulo p in the form
with
. We also prove that any residue class modulo p can be represented in the form
with
. This improves the result of [7].
Received: 27 March 2006 相似文献
3.
In this paper, we obtain an asymptotic formula of the sum with \(\theta =\frac{1}{3}+\epsilon \). Moreover, if \(\theta =\frac{4}{5}+\epsilon \), we obtain a more refined asymptotic formula of this sum.
相似文献
$$\begin{aligned} \sum _{|m_i-x|\le x^{\theta }}d\big (m_1^2+m_2^2+m_3^2+m_4^2\big ) \quad (i=1,2,3,4) \end{aligned}$$
4.
Periodica Mathematica Hungarica - For the Fibonacci sequence the identity $$F_n^2+F_{n+1}^2 = F_{2n+1}$$ holds for all $$n \ge 0$$ . Let $${\mathcal {X}}:= (X_\ell )_{\ell \ge 1}$$ be the sequence... 相似文献
5.
Barry Simon 《Constructive Approximation》2006,23(2):229-240
For suitable classes of random Verblunsky coefficients, including
independent, identically distributed, rotationally invariant ones, we prove that if
$$
\bbE \biggl( \int\f{d\theta}{2\pi} \biggl|\biggl( \f{\calC + e^{i\theta}}{\calC-e^{i\theta}}
\biggr)_{k\ell}\biggr|^p \biggr) \leq C_1 e^{-\kappa_1 \abs{k-\ell}}
$$
for some $\kappa_1 < 0$ and $p < 1$, then for suitable $C_2$ and $\kappa_2 >0$,
$$
\bbE \Bigl( \sup_n \abs{(\calC^n)_{k\ell}}\Bigr) \leq C_2 e^{-\kappa_2 \abs{k-\ell}}.
$$
Here $\calC$ is the CMV matrix. 相似文献
6.
Designs, Codes and Cryptography - An $$(r,\ell )$$ -good polynomial is a polynomial of degree $$r+1$$ that is constant on $$\ell $$ subsets of $$\mathbb F_q$$ , each of size $$r+1$$ . For any... 相似文献
7.
Bin Heng SONG Huai Yu JIAN 《数学学报(英文版)》2005,21(5):1183-1190
We establish the existence of fundamental solutions for the anisotropic porous medium equation, ut = ∑n i=1(u^mi)xixi in R^n × (O,∞), where m1,m2,..., and mn, are positive constants satisfying min1≤i≤n{mi}≤ 1, ∑i^n=1 mi 〉 n - 2, and max1≤i≤n{mi} ≤1/n(2 + ∑i^n=1 mi). 相似文献
8.
We study the difference equation $$\sum\limits_{m_1 ,m_2 } {\Omega [\sigma m_1 ,m_2 (z)] = g(z), z \in D,}$$ where D is the unit square, g(z) ∈ A(D), σ m1, m2(z) = z + m 1 i + m 2, |m 1|+|m 2| = 2, and Ω(z)∈ A(cD) is an unknown function. 相似文献
9.
图的联结数与[a,b]-因子存在性 总被引:2,自引:0,他引:2
设G是一个n阶图,a,b,m1,m2是非负整数且满足1≤a<b和b≥m1.H1和H2是图G的两个边不交的子图且满足|E(H1)|=m1和|E(H2)|=m2.证明下列结论:若图G的联结数bind(G)>(a+b-1)(n-1)/bn-(a+b)-2(m1+m2)+2且n≥(b-1)(a+b-1)(a+b-2)+2b(m1+m2)/b(b-1),则图G有一个[a,b]-因子F满足E(H1)(∈)E(F)和E(H2)∩ E(F)=φ.进一步指出这个结果是最好的. 相似文献
10.
A. P. Oskolkov 《Journal of Mathematical Sciences》1985,28(5):751-758
One proves the global unique solvability in class \(W_\infty ^1 (0,T;C^{2,d} (\bar \Omega ) \cap H(\Omega ))\) of the initial-boundary-value problem for the quasilinear system $$\frac{{\partial \vec \upsilon }}{{\partial t}} + \upsilon _k \frac{{\partial \vec \upsilon }}{{\partial x_k }} - \mu _1 \frac{{\partial \Delta \vec \upsilon }}{{\partial t}} - \int\limits_0^t {K(t - \tau )\Delta \vec \upsilon (\tau )d\tau + grad p = \vec f,di\upsilon \bar \upsilon = 0,\upsilon , > 0.}$$ This system described the nonstationary flows of the elastic-viscous Kelvin-Voigt fluids with defining relation $$\left( {1 + \sum\limits_{\ell = 1}^L {\lambda _\ell } \frac{{\partial ^\ell }}{{\partial t^\ell }}} \right)\sigma = 2\left( {v + \sum\limits_{m = 1}^{L + 1} {\user2{\ae }_m } \frac{{\partial ^m }}{{\partial t^m }}} \right)D,L = 0,1,2,...;\lambda _L ,\user2{\ae }_{L + 1} > 0.$$ 相似文献
11.
In this paper, we prove that the maximal operatorsatisfiesis homogeneous of degree 0, has vanishing moment up to order M and satisfies Lq-Dini condition for some 相似文献
12.
Feng Juan Chen 《数学学报(英文版)》2010,26(6):1133-1138
Let m0,m1,m2,…be positive integers with mi〉 2 for all i. It is well known that each nonnegative integer n can be uniquely represented as n= a0 + a1m0+a2m0m1+…+atm0m1m2…mt-1,where 0≤ai≤mi-1 for all i and at≠0.let each fi be a function defined on {0,1,2…,mi-1} with fi(0)=0.write S(n)=i=0∑tfi(ai).In this paper, we give the asymptotic formula for x^-1∑n≤xS(n)^k,where k is a positive integer. 相似文献
13.
Endre Szemerédi 《Foundations of Computational Mathematics》2016,16(6):1737-1749
We discuss results obtained jointly with Van Vu on the length of arithmetic progressions in \(\ell \)-fold sumsets of the form and where \(\mathcal {A}\) is a set of integers. Applications are also discussed.
相似文献
$$\begin{aligned} \ell \mathcal {A}=\{a_1+\dots +a_\ell ~|~a_i\in \mathcal {A}\} \end{aligned}$$
$$\begin{aligned} \ell \mathcal {A}=\{a_1+\dots +a_\ell ~|~a_i\in \mathcal {A}\text { all distinct}\}, \end{aligned}$$
14.
In this paper, using the generalized Wronskian, we obtain a new sharp
bound for the generalized Masons theorem [1] for functions of several variables.
We also show that the Diophantine equation (The generalized Fermat-Catalan equation)
where
, such that k out of the
n-polynomials
are constant, and
under certain conditions for
has no non-constant solution.
Received: 20 March 2003 相似文献
15.
Iosif Pinelis 《Probability Theory and Related Fields》2007,139(3-4):605-635
Let be independent identically distributed random variables each having the standardized Bernoulli distribution with parameter
. Let if and . Let . Let f be such a function that f and f′′ are nondecreasing and convex. Then it is proved that for all nonnegative numbers one has the inequality where . The lower bound on m is exact for each . Moreover, is Schur-concave in .
A number of corollaries are obtained, including upper bounds on generalized moments and tail probabilities of (super)martingales
with differences of bounded asymmetry, and also upper bounds on the maximal function of such (super)martingales. Applications
to generalized self-normalized sums and t-statistics are given.
相似文献
16.
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
17.
M. V. Buslaeva 《Journal of Mathematical Sciences》1983,22(1):1032-1035
The asymptotic behavior asn, m → ∞ of the sum $$\sum\limits_{\kappa ,\ell = m}^{n - 1} {\exp \left[ {i\omega \sqrt n \left( {\sqrt \kappa + \sqrt \ell } \right)} \right]} \Phi \left( {1 - \frac{{\left| {\sqrt \kappa - \sqrt \ell } \right|}}{\Delta }} \right)$$ is studied where π(t)=0 for t?0 and φ(t)=t for t > 0. 相似文献
18.
Chen Yonggao 《数学学报(英文版)》1994,10(2):158-167
LetC be ann-dimensional sphere with diameter 1 and center at the origin inE
n
. The view-obstruction problem forn-dimensional spheres is to determine a constant ν(n) to be the lower bound of those α for which any half-lineL, given byx
i
=a
i
t (i=1,2,...,n) where parametert≥0 anda
i
(i=1,2,...,n) are positive real numbers, intersects
相似文献
20.
Mirko Lepović 《Journal of Applied Mathematics and Computing》2004,14(1-2):39-49
LetG be a simple graph and let $\bar G$ denotes its complement. We say thatG is integral if its spectrum consists entirely of integers. If $\overline {\alpha K_a \cup \beta K_b } $ is integral we show that it belongs to the class of integral graphs $$\overline {[\frac{{kt}}{\tau }x_o + \frac{{mt}}{\tau }z]K(t + \ell n)k + \ell m \cup [\frac{{kt}}{\tau }y_o + \frac{{(t + \ell n)k + \ell m}}{\tau }z]nK\ell m,} $$ where (i) t, k, l, m, n ∈ ? such that (m, n) =1, (n, t) =1 and (l, t)=1; (ii) τ=((t+ln)k+lm, mt) such that τ| kt; (iii) (x0, y0) is aparticular solution of the linear Diophantine equation ((t+ln)k+lm)x-(mt)y=τ and (iv) z≥z0 where z0 is the least integer such that $(\frac{{kt}}{\tau }x_0 + \frac{{mt}}{\tau }z_0 ) \geqslant 1$ and $(\frac{{kt}}{\tau }y_0 + \frac{{(t + \ell n)k + \ell m}}{\tau }z_0 ) \geqslant 1$ . 相似文献
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