共查询到20条相似文献,搜索用时 15 毫秒
1.
Miao LOU 《Frontiers of Mathematics in China》2019,14(1):123-134
Let f be a full-level cusp form for GLm(Z) with Fourier coefficients Af(cm-2,…, c1, n): Let λ(n) be either the von Mangoldt function Λ(n) or the k-th divisor function τk(n): We consider averages of shifted convolution sums of the type Σ|h|≤H |ΣX相似文献
2.
Let and let the Bessel operator defined on . We show that the oscillation and -variation operators of the Riesz transform associated with are bounded on BMO , where and . Moreover, we construct a -atom as a counterexample to show that the oscillation and -variation operators of are not bounded from to . Finally, we prove that the oscillation and the -variation operators for the smooth truncations associated with Bessel operators are bounded from to . 相似文献
3.
Let be a complete Riemannian manifold with , and let be two complete totally geodesic submanifolds in M. We prove that if n1 + n2 = n − 2 and if the distance , then Mi is isometric to , or with the canonical metric when ni>0, and thus, M is isometric to , or except possibly when n = 3 and M1 (or M2) with or n = 4 and M1 (or M2) . 相似文献
4.
We extend Vandermonde matrices to generalized Vandermonde tensors. We call an mth order n-dimensional real tensor A = ( A i 1 i 2 ... i m ) a type-1 generalized Vandermonde (GV) tensor, or GV1 tensor, if there exists a vector v = ( v 1 , v 2 ... v n ) T such that A i 1 i 2 ... i m = v i 1 i 2 + i 3 + ... + i m - m + 1 , and call A a type-2 (mth order ndimensional) GV tensor, or GV2 tensor, if there exists an (m-1)th order tensor B = ( B i 1 i 2 ... i m - 1 ) such that A i 1 i 2 ... i m = B i 1 i 2 ... i m - 1 i m - 1 . In this paper, we mainly investigate the type-1 GV tensors including their products, their spectra, and their positivities. Applications of GV tensors are also introduced. 相似文献
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6.
We give a recursive algorithm to compute the multivariable Zassenhaus formula e^X1+X2+…+Xn=e^X1eX2…e^Xn∏∞k=2e^Wk and derive an effective recursion formula of Wk. 相似文献
7.
Let be a fractional Brownian motion with Hurst index . Inspired by pathwise integrals and Wick product, in this paper, we consider the forward and symmetric Wick-Itô integrals with respect to BH as follows: in probability, where ◊ denotes the Wick product. We show that the two integrals coincide with divergence-type integral of BH for all . 相似文献
8.
Let(Ai,φi,i+1) be a generalized indue Live system of a sequeiiee (Ai) of unital separable C^*-algebras,with A =limi→∞(Ai,φi,i+1). Set φj,i=φi-1,i^0…0φj+1,j+2^0 φj,j+1 for all i>j. We prove that if φj,i are order zero completely positive contractions for all j and i>j, And L:=inf{λ|λ∈σ(φj,i(1Aj)) for all j uud i>j}>0, where σ(φj,i(1Aj)) is the speetrum of φj,i(1Aj),than limi→∞(Cu(Ai),Cu((φi,i+1))=Cu(A), where Cu(A) is a stable version of the Cuntz semigroup of C^*-algebra A. Let (An,φm,n) be a generalized inductive syfitem of C^*-algahrafl, with the ipmkn order zero completely positive contractions. We also prove that if the decomposition rank (nuclear dimension) of ,4n is no more t han some integer k for each n, then the decompostition rank (nuclear dimension) of A is also no more than k. 相似文献
9.
We study a superminimal surface M immersed into a hyperquadric Q2 in several cases classified by two global defined functions and , which were introduced by X. X. Jiao and J. Wang to study a minimal immersion f : . In case both and are not identically zero, it is proved that f is superminimal if and only if f is totally real or is also minimal, where is the standard inclusion map. In the rest case that or , the minimal immersion f is automatically superminimal. As a consequence, all the superminimal two-spheres in Q2 are completely described. 相似文献
10.
Zhao XU 《Frontiers of Mathematics in China》2020,15(5):1070
For a fixed even SL( ) Hecke{Maass form f, we get an estimate for the second moment of at special points, where runs over an orthogonal basis of Hecke{Maass cusp forms for . 相似文献
11.
The concept of a perfect coloring, introduced by P. Delsarte, generalizes the concept of completely regular code. We study the perfect 3-colorings (also known as the equitable partitions into three parts) on 6-regular graphs of order 9. A perfect n-colorings of a graph is a partition of its vertex set. It splits vertices into n parts A1, A2,...,An such that for all i,j∈{1,2,...,n}, each vertex of Ai is adjacent to aij vertices of Aj. The matrix A =(aij)n×n is called quotient matrix or parameter matrix. In this article, we start by giving an algorithm to find all different types of 6-regular graphs of order 9. Then, we classify all the realizable parameter matrices of perfect 3-colorings on 6-regular graphs of order 9. 相似文献
12.
Weili YAO 《Frontiers of Mathematics in China》2020,15(1):205-213
Let f be a holomorphic Hecke cusp form with even integral weight k≥2 for the full modular group,and letχbe a primitive Dirichlet character modulo q.Let Lf(s,χ)be the automorphic L-function attached to f andχ-We study the mean-square estimate of Lf(s,χ)and establish an asymptotic formula. 相似文献
13.
Rui ZHANG 《Frontiers of Mathematics in China》2019,14(5):1017
We prove that, with at most exceptions, all even positive integers up to Nare expressible in the form ,where are prime numbers. This gives large improvement of a recent result due to M. Zhang and J. J. Li. 相似文献
14.
We study the derivative operator of the generalized spherical mean S^γt. By considering a more general multiplier m^Ωγ,b=Vn-2/2+γ(|ξ|)|ξ|^bΩ(ξ') and finding the smallest γ such that m^Ωγ,b is an Hp multiplier, we obtain the optimal range of exponents (γ,β,p)to ensure the H^p(R^n) boundedness of a^βS^γ1f(x). As an application, we obtain the derivative estimates for the solution for the Cauchy problem of the wave equation on H^p(R^n) spaces. 相似文献
15.
Fourier transform of anisotropic mixed-norm Hardy spaces 总被引:1,自引:0,他引:1
Let a:=(a1,…,an)∈[1,∞)n,p:=(p1,…,pn)∈(0,1]n,Hpa(Rn)be the anisotropic mixed-norm Hardy space associated with adefined via the radial maximal function,and let f belong to the Hardy space Hpa(Rn).In this article,we show that the Fourier transform fcoincides with a continuous function g on?n in the sense of tempered distributions and,moreover,this continuous function g,multiplied by a step function associated with a,can be pointwisely controlled by a constant multiple of the Hardy space norm of f.These proofs are achieved via the known atomic characterization of Hpa(Rn)and the establishment of two uniform estimates on anisotropic mixed-norm atoms.As applications,we also conclude a higher order convergence of the continuous function gat the origin.Finally,a variant of the Hardy-Littlewood inequality in the anisotropic mixed-norm Hardy space setting is also obtained.All these results are a natural generalization of the well-known corresponding conclusions of the classical Hardy spaces Hp(Rn)with p∈0,1],and are even new for isotropic mixed-norm Hardy spaces on∈n. 相似文献
16.
We study the Schrödinger-KdV system where , , and ,i= 1,2,a.e. .We obtain the existence of nontrivial ground state solutions for the above system by variational methods and the Nehari manifold. 相似文献
17.
For n = 2 or 3 and , we study the oscillatory hyper Hilbert transform along an appropriate variable curve in (namely, is a curve in for each fixed x), where . We obtain some boundedness theorems of , under some suitable conditions on and . These results are extensions of some earlier theorems. However, is not a convolution in general. Thus, we only can partially employ the Plancherel theorem, and we mainly use the orthogonality principle to prove our main theorems. 相似文献
18.
We consider a pendulum type equation with p-Laplacian , where and p(t) are 1-periodic about every variable. The solutions of this equation present two interesting behaviors. On the one hand, by applying Moser's twist theorem, we find infinitely many invariant tori whenever which yields the bounded-ness of all solutions and the existence of quasi-periodic solutions starting at t = 0 on the invariant tori. On the other hand, if p(t) = 0 and has some specific forms, we find a full symbolic dynamical system made by solutions which oscillate between any two different trivial solutions of the equation. Such chaotic solutions stay close to the trivial solutions in some fixed intervals, according to any prescribed coin-tossing sequence. 相似文献
19.
The regularity of random attractors is considered for the non-autonomous fractional stochastic FitzHugh-Nagumo system.We prove that the system has a pullback random attractor that is compact in Hs(Rn)×L2(Rn)and attracts all tempered random sets of L2(Rn)×L2(Rn)in the topology of Hs(Rn)×L2(Rn)with s∈(0,1).By the idea of positive and negative truncations,spectral decomposition in bounded domains,and tail estimates,we achieved the desired results. 相似文献
20.
Xie-Bin CHEN 《Frontiers of Mathematics in China》2019,14(6):1117
We consider the problem of existence of a Hamiltonian cycle containing a matching and avoiding some edges in an n-cube , and obtain the following results. Let , and with . If M is a matching and every vertex is incident with at least two edges in the graph , then all edges of M lie on a Hamiltonian cycle in . Moreover, if or , then the upper bound of number of faulty edges tolerated is sharp. Our results generalize the well-known result for . 相似文献