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1.
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
2.
We investigate k-uniform loose paths. We show that the largest Heigenvalues of their adjacency tensors, Laplacian tensors, and signless Laplacian tensors are computable. For a k-uniform loose path with length l ≥ 3 , we show that the largest H-eigenvalue of its adjacency tensor is ( ( 1 + 5 ) / 2 ) 2 / k when l = 3 and λ ( A ) = 3 1 / k when l = 4 , respectively. For the case of l ≥ 5 , we tighten the existing upper bound 2. We also show that the largest H-eigenvalue of its signless Laplacian tensor lies in the interval (2, 3) when l ≥ 5 . Finally, we investigate the largest H-eigenvalue of its Laplacian tensor when k is even and we tighten the upper bound 4. 相似文献
3.
Yuchao WANG 《Frontiers of Mathematics in China》2015,10(6):1449
value of a given binary linear form at prime arguments. Let λ1 and λ2 be positive real numbers such that λ1/λ2 is irrational and algebraic. For any (C, c) well-spaced sequence V and δ>0, let E(V , X, δ) denote the number of υ∈V with υ≤X for which the inequality | λ 1 p 1 + λ 2 ρ 2 − υ | < υ − δ has no solution in primes p1, p2. It is shown that for any ε>0,we have E(V , X, δ) «max(X 3 5 + 2 δ + ε , X 2 3 + 4 3 δ + ε ). 相似文献
4.
Submanifolds in space forms satisfy the well-known DDVV inequality. A submanifold attaining equality in this inequality pointwise is called a Wintgen ideal submanifold. As conformal invariant objects, Wintgen ideal submanifolds are investigated in this paper using the framework of M?bius geometry. We classify Wintgen ideal submanfiolds of dimension m ≥ 3 and arbitrary codimension when a canonically defined 2-dimensional distribution ? 2 is integrable. Such examples come from cones, cylinders, or rotational submanifolds over super-minimal surfaces in spheres, Euclidean spaces, or hyperbolic spaces, respectively. We conjecture that if ? 2 generates a k-dimensional integrable distribution ? k and k<m, then similar reduction theorem holds true. This generalization when k = 3 has been proved in this paper. 相似文献
5.
We study the exponential sums involving l:burmr coeffcients ot Maass forms and exponential functions of the form e(anZ), where 0 ≠ α∈R and 0 〈 β 〈 1. An asymptotic formula is proved for the nonlinear exponential sum ∑x〈n≤2x λg(n)e(αnβ), when β = 1/2 and |α| is close to 2√ q C Z+, where Ag(n) is the normalized n-th Fourier coefficient of a Maass cusp form for SL2 (Z). The similar natures of the divisor function 7(n) and the representation function r(n) in the circle problem in nonlinear exponential sums of the above type are also studied. 相似文献
6.
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
7.
We consider a branching random walk on N with a random environment in time (denoted by ξ). Let Zn be the counting measure of particles of generation n, and let Zn(t) be its Laplace transform. We show the convergence of the free energy n-llog Zn(t), large deviation principles, and central limit theorems for the sequence of measures {Zn}, and a necessary and sufficient condition for the existence of moments of the limit of the martingale Zn(t)/E[Zn(t)ξ]. 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.
For a square-free integer d other than 0 and 1, let K = ? ( d ) , where ? is the set of rational numbers. Then K is called a quadratic field and it has degree 2 over ? . For several quadratic fields K = ? ( d ) , the ring Rdof integers of K is not a unique-factorization domain. For d<0, there exist only a finite number of complex quadratic fields, whose ring Rd of integers, called complex quadratic ring, is a unique-factorization domain, i.e., d = −1,−2,−3,−7,−11,−19,−43,−67,−163. Let ϑ denote a prime element of Rd, and let n be an arbitrary positive integer. The unit groups of R d / 〈 v n 〉 was determined by Cross in 1983 for the case d = −1. This paper completely determined the unit groups of R d / 〈 v n 〉 for the cases d = −2,−3. 相似文献
10.
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
11.
Let G be a simple connected graph, and let d i be the degree of its i-th vertex. The sum-connectivity index of the graph G is defined as χ ( G ) = Σ v i v j ∈ E ( G ) ? ( d i + d j ) − 1 / 2 . We discuss the effect on χ(G) of inserting an edge into a graph. Moreover, we obtain the relations between sum-connectivity index and Randić index. 相似文献
12.
Let be a Morita ring, where the bimodule homomorphisms and are zero. We study the finite presentedness, locally coherence, pure projectivity, pure injectivity, and FP-injectivity of modules over . Some applications are then given. 相似文献
13.
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
14.
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
15.
Let (Xt)t≥0 be a symmetric strong Markov process generated by non-local regular Dirichlet form (D, D (D)) as follows: D ( f , g ) = ∫ ? d ∫ ? d ( f ( x ) - f ( y ) ) ( g ( x ) - g ( y ) ) J ( x , y ) d x d y , ? f , g ∈ D ( D ) , where J(x, y) is a strictly positive and symmetric measurable function on ? d × ? d . We study the intrinsic hypercontractivity, intrinsic supercontractivity, and intrinsic ultracontractivity for the Feynman-Kac semigroup T t V ( f ) ( x ) = E x ( exp ? ( - ∫ 0 t V ( X s ) d s ) f ( X t ) ) , ? x ∈ ? d , f ∈ L 2 ( ? d ; d x ) . In particular, we prove that for J ( x , y ) ≈ | x - y | - d - a l { | x - y | ≤ 1 } + e - | x - y | l { | x - y | > 1 } with α ∈(0, 2) and V ( x ) = | x | λ with λ>0, ( T t V ) t ≥ 0 is intrinsically ultracontractive if and only if λ>1; and that for symmetric α-stable process (Xt)t≥0 with α ∈(0, 2) and V ( x ) = log ? λ ( 1 + | x | ) with some λ>0, ( T t V ) t ≥ 0 is intrinsically ultracontractive (or intrinsically supercontractive) if and only if λ>1, and ( T t V ) t ≥ 0 is intrinsically hypercontractive if and only if λ ≥ 1 . Besides, we also investigate intrinsic contractivity properties of ( T t V ) t ≥ 0 for the case that lim inf ? | x | → + ∞ V ( x ) < + ∞ 相似文献
16.
Let K be the familiar class of normalized convex functions in the unit disk. Keogh and Merkes proved the well-known result that max ? f ∈ K | a 3 − λ a 2 2 | ≤ max ? { 1 / 3 , | λ − 1 | } , λ ∈ ? , and the estimate is sharp for each λ. We investigate the corresponding problem for a subclass of quasi-convex mappings of type B defined on the unit ball in a complex Banach space or on the unit polydisk in ? n . The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied. 相似文献
17.
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
18.
19.
Shangquan BU 《Frontiers of Mathematics in China》2015,10(2):239
Using known operator-valued Fourier multiplier results on vectorvalued H?lder continuous function spaces, we completely characterize the wellposedness of the degenerate differential equations ( M u ) ' ( t ) = A u ( t ) + f ( t ) for t ∈ R in H?lder continuous function spaces C a ( R ; X ) by the boundedness of the M-resolvent of A, where A and M are closed operators on a Banach space X satisfying D ( A ) ? D ( M ) . 相似文献
20.
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