共查询到20条相似文献,搜索用时 46 毫秒
1.
The base graph of a simple matroid M = ( E , ? ) is the graph G such that V ( G ) = ? and E ( G ) = { B B ′ : B , B ′ ∈ ? , | B \ B ′ | = 1 } , where the same notation is used for the vertices of G and the bases of M . It is proved that the base graph G of connected simple matroid M is Z 3-connected if |V (G )|≥5. We also proved that if M is not a connected simple matroid, then the base graph G of M does not admit a nowhere-zero 3-flow if and only if |V (G )| = 4. Furthermore, if for every connected component E i (i ≥2) of M , the matroid ase graph G i of M i = M |E i has |V (G i )|≥5, then G is Z 3-connected which also implies that G admits nowhere-zero 3-flow immediately. 相似文献
2.
Jiawang NIE 《Frontiers of Mathematics in China》2012,7(2):321-346
This paper studies the problem of minimizing a homogeneous polynomial (form) f (x ) over the unit sphere S n - 1 = { x ∈ ? n : ‖ x ‖ 2 = | 1 } . The problem is NP-hard when f (x ) has degree 3 or higher. Denote by f min (resp. f max) the minimum (resp. maximum) value of f (x ) on S n - 1 . First, when f (x ) is an even form of degree 2d , we study the standard sum of squares (SOS) relaxation for finding a lower bound of the minimum f min:max ? γ s . t . f ( x ) - γ · ‖ x ‖ 2 2 d ? i s S O S . Let f sos be the above optimal value. Then we show that for all n ≥2d ,1 ≤ f max ? - f s o s f max ? - f min ? ≤ C ( d ) ( n 2 d ) . Here, the constant C (d ) is independent of n . Second, when f (x ) is a multi-form and S n - 1 becomes a multi-unit sphere, we generalize the above SOS relaxation and prove a similar bound. Third, when f (x ) is sparse, we prove an improved bound depending on its sparsity pattern; when f (x ) is odd, we formulate the problem equivalently as minimizing a certain even form, and prove a similar bound. Last, for minimizing f (x ) over a hypersurface H ( g ) = { x ∈ ? n : g ( x ) = 1 } defined by a positive definite form g (x ), we generalize the above SOS relaxation and prove a similar bound. 相似文献
3.
We study the representations of the restricted two-parameter quantum groups of types B and G . For these restricted two-parameter quantum groups, we give some explicit conditions which guarantee that a simple module can be factored as the tensor product of a one-dimensional module with a module that is naturally a module for the quotient by central group-like elements. That is, given θ a primitive l th root of unity, the factorization of simple ? θ y , θ z , ( ) - modules is possible, if and only if (2(y - z ), l ) = 1 for = ? ? 2 n + 1 ; (3(y - z ), l ) = 1 for g= G 2. 相似文献
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5.
Let X^ε be a small perturbation Wishart process with values in the set of positive definite matrices of size m, i.e., the process X^ε is the solution of stochastic differential equation with non-Lipschitz diffusion coefficient: dXt^ε = √εXt^εtdBt' + dBt'√εXt^ε + ρImdt, X0 = x, where B is an rn x m matrix valued Brownian motion and B' denotes the transpose of the matrix B. In this paper, we prove that { (Xt^ε-Xt^0)/√εh^2(ε),ε 〉 0} satisfies a large deviation principle, and (Xt^ε - Xt^0)/√ε converges to a Gaussian process, where h(ε) → +∞ and √ε h(ε) →0 as ε →0. A moderate deviation principle and a functional central limit theorem for the eigenvalue process of X^ε are also obtained by the delta method. 相似文献
6.
At each time be a random sequence of non-negative numbers that are ultimately zero in a random environment . The existence and uniqueness of the nonnegative fixed points of the associated smoothing transformation in random environment are considered. These fixed points are solutions to the distributional equation for ,where are random variables in random environment which satisfy that for any environment ; under ; are independent of each other and , and have the same conditional distribution where T is the shift operator. This extends the classical results of J. D. Biggins [J. Appl. Probab., 1977, 14: 25-37] to the random environment case. As an application, the martingale convergence of the branching random walk in random environment is given as well. 相似文献
7.
Existence and multiplicity results for nonlinear Schrödinger-Poisson equation with general potential
Yuan SHAN 《Frontiers of Mathematics in China》2020,15(6):1189
This paper is concerned with the Schrödinger-Poisson equation Under certain hypotheses on V and a general spectral assumption, the existence and multiplicity of solutions are obtained via variational methods. 相似文献
8.
Consider a supercritical superprocess X = {Xt, t≥0} on a locally compact separable metric space (E,m). Suppose that the spatial motion of X is a Hunt process satisfying certain conditions and that the branching mechanism is of the form ψ ( x , λ ) = - a ( x ) λ + b ( x ) λ 2 + ∫ ( 0 , + ∞ ) ( e - λ y - 1 + λ y ) n ( x , d y ) , ? x ∈ E , λ > 0 , where a ∈ B b ( E ) , b ∈ B b + ( E ) , and n is a kernel from E to (0,+∞) satisfying sup ? x ∈ E ∫ 0 + ∞ y 2 n ( x , d y ) < + ∞ . Put T t f ( x ) = P δ x ? f , X t ? . Suppose that the semigroup {Tt; t≥0}is compact. Let λ0 be the eigenvalue of the (possibly non-symmetric) generator L of {Tt}that has the largest real part among all the eigenvalues of L, which is known to be real-valued. Let ? 0 and ? ^ 0 be the eigenfunctions of L and L ^ (the dual of L) associated with λ0, respectively. Assume λ0>0. Under some conditions on the spatial motion and the ? 0 -transform of the semigroup {Tt}, we prove that for a large class of suitable functions f, lim ? t → + ∞ e - λ 0 t ? f , X t ? = W ∞ ∫ E ? ^ 0 ( y ) f ( y ) m ( d y ) , ? P μ - a . s . , for any finite initial measure μ on E with compact support, where W∞ is the martingale limit defined by W ∞ : = lim ? t → + ∞ e - λ 0 t ? ? 0 , X t ? . Moreover, the exceptional set in the above limit does not depend on the initial measure μ and the function f. 相似文献
9.
We use the concept of the inside-(a, η, h) domain to construct a subsolution to the Dirichlet problem for minimal graphs over convex domains in hyperbolic space. As an application, we prove that the Hölder exponent for the problem is optimal for any . 相似文献
10.
We prove some transcendence results for the sums of some multivariate serms of the form ∑j1,j2,...,jm=0 ^∞Cj1j2...jm(r1^j1r2^j2...rm^jm) for n = 1, 2, where Cj1j2...jm are some rational functions of j1 + j2 + ... + jm. 相似文献
11.
Let be the solution to a linear stochastic heat equation driven by a Gaussian noise, which is a Brownian motion in time and a fractional Brownian motion in space with Hurst parameter : For any given , we show a decomposition of the stochastic process as the sum of a fractional Brownian motion with Hurst parameter H/2 (resp., H) and a stochastic process with C∞-continuous trajectories. Some applications of those decompositions are discussed. 相似文献
12.
This paper deals with anisotropic solutions u ∈ W 1 , ( p i ) ( Ω , ? N ) to the nonlinear elliptic system − Σ i = 1 n D i ( a i α ( χ , D u ( χ ) ) ) = − Σ i = 1 n D i F i α ( χ ) , α = 1 , 2 , ... , N , We present a monotonicity inequality for the matrix a = ( a i α ) ∈ ? N × n , whichguarantees global pointwise bounds for anisotropic solutionsu . 相似文献
13.
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
14.
Xiaoguang HE 《Frontiers of Mathematics in China》2018,13(6):1355-1368
Let f be a Hecke-Maass cusp form for SL(3; ) with Fourier coefficients Af(m; n); and let (x) be a -function supported on [1; 2] with derivatives bounded by 1. We prove an asymptotic formula for the nonlinear exponential sum , where and 相似文献
15.
Let (X, d, μ) be a metric measure space with non-negative Ricci curvature. This paper is concerned with the boundary behavior of harmonic function on the (open) upper half-space . We derive that a function f of bounded mean oscillation (BMO) is the trace of harmonic function on , whenever u satisfies the following Carleson measure condition where denotes the total gradient and denotes the (open) ball centered at with radius . Conversely, the above condition characterizes all the harmonic functions whose traces are in BMO space. 相似文献
16.
Liqun HU 《Frontiers of Mathematics in China》2015,10(5):1101
For the normalized Fourier coefficients of Maass cusp forms λ(n) and the normalized Fourier coefficients of holomorphic cusp forms a(n), we give the bound of ∑ m 1 2 + m 2 2 + m 3 2 ≤ x λ ( m 1 2 + m 2 2 + m 3 2 ) Λ ( m 1 2 + m 2 2 + m 3 2 ) and ∑ m 1 2 + m 2 2 + m 3 2 ≤ x a ( m 1 2 + m 2 2 + m 3 2 ) Λ ( m 1 2 + m 2 2 + m 3 2 ) . 相似文献
17.
We prove that if u is a weak solution of the d dimensional fractional Navier-Stokes equations for some initial data u0and if u belongs to path space p = L q ( 0 , T ; B p , ∞ r ) o r p = L 1 ( 0 , T ; B ∞ , ∞ r ) , then u is unique in the class of weak solutions when α>1. The main tools are Bony decomposition and Fourier localization technique. The results generalize and improve many recent known results. 相似文献
18.
Consider the generalized dispersive equation defined by{iδtu+Ф(√-△)u=0,(x,t)∈R^n×R,u(x,0)=f(x),F∈F(R^n),(*)whereФ(√-△)is a pseudo-differential operator with symbolФ(|ζ|).In the present paper,assuming thatФsatisfies suitable growth conditions and the initial data in H^s(R^n),we bound the Hausdorff dimension of the sets on which the pointwise convergence of solutions to the dispersive equations(*)fails.These upper bounds of Hausdorff dimension shall be obtained via the Kolmogorov-Seliverstov-Plessner method. 相似文献
19.
The main purpose of this paper is to consider the initial-boundary value problem for the 1D mixed nonlinear Schrödinger equation on the half-line with inhomogeneous boundary condition. We combine Laplace transform method with restricted norm method to prove the local well-posedness and continuous dependence on initial and boundary data in low regularity Sobolev spaces. Moreover, we show that the nonlinear part of the solution on the half-line is smoother than the initial data. 相似文献
20.
Let φ be a growth function, and let A : = - ( ? - i a ) ? ( ? - i a ) + V be a magnetic Schr?dinger operator on L 2 ( ? n ) , n ≥ 2 , where α : = ( α 1 , α 2 , ? , α n ) ∈ L l o c 2 ( ? n , ? n ) and 0 ≤ V ∈ L l o c 1 ( ? n ) . We establish the equivalent characterizations of the Musielak-Orlicz-Hardy space H A , φ ( ? n ) , defined by the Lusin area function associated with { e - t 2 A } t > 0 , in terms of the Lusin area function associated with { e - t A } t > 0 , the radial maximal functions and the nontangential maximal functions associated with { e - t 2 A } t > 0 and { e - t A } t > 0 , respectively. The boundedness of the Riesz transforms L k A - 1 / 2 , k ∈ { 1 , 2 , ? , n } , from H A , φ ( ? n ) to L φ ( ? n ) is also presented, where Lk is the closure of ? ? x k - i α k in L 2 ( ? n ) . These results are new even when φ ( x , t ) : = ω ( x ) t p for all x ∈ ? n and t ∈(0,+∞) with p ∈(0, 1] and ω ∈ A ∞ ( ? n ) (the class of Muckenhoupt weights on ? n ). 相似文献