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In this paper, we first prove that the local time associated with symmetric -stable processes is of bounded -variation for any partly based on Barlow’s estimation of the modulus of the local time of such processes. The fact that the local time is of bounded -variation for any enables us to define the integral of the local time as a Young integral for less smooth functions being of bounded -variation with . When , Young’s integration theory is no longer applicable. However, rough path theory is useful in this case. The main purpose of this paper is to establish a rough path theory for the integration with respect to the local times of symmetric -stable processes for . 相似文献
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Let denote the finite field of order q of characteristic p. We study the p-adic valuations for zeros of L-functions associated with exponential sums of the following family of Laurent polynomials where , . When , the estimate of the associated exponential sum appears in Iwaniecʼs work on small eigenvalues of the Laplace–Beltrami operator acting on automorphic functions with respect to the group , and Adolphson and Sperber gave complex absolute values for zeros of the corresponding L-function. Using the decomposition theory of Wan, we determine the generic Newton polygon (q-adic values of the reciprocal zeros) of the L-function. Working on the chain level version of Dworkʼs trace formula and using Wanʼs decomposition theory, we are able to give an explicit Hasse polynomial for the generic Newton polygon in low dimensions, i.e., . 相似文献
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Jae-Myoung KIM 《数学物理学报(B辑英文版)》2017,37(4):1033-1047
We present a regularity condition of a suitable weak solution to the MHD equations in three dimensional space with slip boundary conditions for a velocity and magnetic vector fields. More precisely, we prove a suitable weak solution are H¨older continuous near boundary provided that the scaled mixed L_(x,t)~(p,q) -norm of the velocity vector field with 3/p + 2/q ≤ 2,2 q ∞ is sufficiently small near the boundary. Also, we will investigate that for this solution u ∈ L_(x,t)~(p,q) with 1≤3/p+2/q≤3/2, 3 p ∞, the Hausdorff dimension of its singular set is no greater than max{p, q}(3/p+2/q-1). 相似文献
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Partitioning a set into similar, if not, identical, parts is a fundamental research topic in combinatorics. The question of partitioning the integers in various ways has been considered throughout history. Given a set of integers where , let the gap sequence of this set be the unordered multiset . This paper addresses the following question, which was explicitly asked by Nakamigawa: can the set of integers be partitioned into sets with the same gap sequence? The question is known to be true for any set where the gap sequence has length at most two. This paper provides evidence that the question is true when the gap sequence has length three. Namely, we prove that given positive integers and , there is a positive integer such that for all , the set of integers can be partitioned into 4-sets with gap sequence , . 相似文献
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Let be a finite field of odd order and , where are positive integers, are distinct odd primes and . In this paper, we study the irreducible factorization of over and all primitive idempotents in the ring .Moreover, we obtain the dimensions and the minimum Hamming distances of all irreducible cyclic codes of length over . 相似文献
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Let denote the chromatic polynomial of a graph on vertices. The ‘shameful conjecture’ due to Bartels and Welsh states that, Let denote the expected number of colors used in a uniformly random proper -coloring of . The above inequality can be interpreted as saying that , where is the empty graph on nodes. This conjecture was proved by F.M. Dong, who in fact showed that, for all . There are examples showing that this inequality is not true for all . In this paper, we show that the above inequality holds for all , where is the largest degree of . It is also shown that the above inequality holds true for all when is a claw-free graph. 相似文献
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Shuguan Ji 《Journal of Differential Equations》2018,264(9):5527-5540
This paper is concerned with the periodic solutions for the one dimensional nonlinear wave equation with either constant or variable coefficients. The constant coefficient model corresponds to the classical wave equation, while the variable coefficient model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. For finding the periodic solutions of variable coefficient wave equation, it is usually required that the coefficient satisfies with , which actually excludes the classical constant coefficient model. For the case , it is indicated to remain an open problem by Barbu and Pavel (1997) [6]. In this work, for the periods having the form ( are positive integers) and some types of boundary value conditions, we find some fundamental properties for the wave operator with either constant or variable coefficients. Based on these properties, we obtain the existence of periodic solutions when the nonlinearity is monotone and bounded. Such nonlinearity may cross multiple eigenvalues of the corresponding wave operator. In particular, we do not require the condition . 相似文献
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Suppose q is a prime power and is a univariate polynomial with exactly t monomial terms and degree . To establish a finite field analogue of Descartes' Rule, Bi, Cheng, and Rojas (2013) proved an upper bound of on the number of cosets in needed to cover the roots of f in . Here, we give explicit f with root structure approaching this bound: When q is a perfect -st power we give an explicit t-nomial vanishing on distinct cosets of . Over prime fields , computational data we provide suggests that it is harder to construct explicit sparse polynomials with many roots. Nevertheless, assuming the Generalized Riemann Hypothesis, we find explicit trinomials having distinct roots in . 相似文献
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A cycle of order is called a -cycle. A non-induced cycle is called a chorded cycle. Let be an integer with . Then a graph of order is chorded pancyclic if contains a chorded -cycle for every integer with . Cream, Gould and Hirohata (Australas. J. Combin. 67 (2017), 463–469) proved that a graph of order satisfying for every pair of nonadjacent vertices , in is chorded pancyclic unless is either or , the Cartesian product of and . They also conjectured that if is Hamiltonian, we can replace the degree sum condition with the weaker density condition
and still guarantee the same conclusion. In this paper, we prove this conjecture by showing that if a graph of order with contains a -cycle, then contains a chorded -cycle, unless and is either or , Then observing that and are exceptions only for , we further relax the density condition for sufficiently large . 相似文献
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