共查询到20条相似文献,搜索用时 31 毫秒
1.
C?t?lin Ciuperc? 《Journal of Pure and Applied Algebra》2003,178(1):25-48
Let A be a local ring with maximal ideal . For an arbitrary ideal I of A, we define the generalized Hilbert coefficients . When the ideal I is -primary, jk(I)=(0,…,0,(−1)kek(I)), where ek(I) is the classical kth Hilbert coefficient of I. Using these coefficients we give a numerical characterization of the homogeneous components of the S2-ification of S=A[It,t−1], extending previous results obtained by the author to not necessarily -primary ideals. 相似文献
2.
Gerard J. Chang Jer-Jeong Chen David Kuo Sheng-Chyang Liaw 《Discrete Applied Mathematics》2007,155(8):1007-1013
For positive integers j?k, an L(j,k)-labeling of a digraph D is a function f from V(D) into the set of nonnegative integers such that |f(x)-f(y)|?j if x is adjacent to y in D and |f(x)-f(y)|?k if x is of distance two to y in D. Elements of the image of f are called labels. The L(j,k)-labeling problem is to determine the -number of a digraph D, which is the minimum of the maximum label used in an L(j,k)-labeling of D. This paper studies -numbers of digraphs. In particular, we determine -numbers of digraphs whose longest dipath is of length at most 2, and -numbers of ditrees having dipaths of length 4. We also give bounds for -numbers of bipartite digraphs whose longest dipath is of length 3. Finally, we present a linear-time algorithm for determining -numbers of ditrees whose longest dipath is of length 3. 相似文献
3.
Jorge Buescu 《Journal of Mathematical Analysis and Applications》2004,296(1):244-255
We study positive integral operators in with continuous kernel k(x,y). We show that if the operator is compact and Hilbert-Schmidt. If in addition k(x,x)→0 as |x|→∞, k is represented by an absolutely and uniformly convergent bilinear series of uniformly continuous eigenfunctions and is trace class. Replacing the first assumption by the stronger then and the bilinear series converges also in L1. Sharp norm bounds are obtained and Mercer's theorem is derived as a special case. 相似文献
4.
J.R. Cannon 《Journal of Mathematical Analysis and Applications》2005,311(1):147-161
The authors study the problem , and u(0,t)=u(1,t)=ψ(t), where ψ(t)=u0 for t2k<t<t2k+1 and ψ(t)=0 for , with t0=0 and the sequence tk is determined by the equations , for , and , for k=2,4,6,… and where 0<m<M. Note that the switching points , are unknown. Existence and uniqueness are demonstrated. Theoretical estimates of the tk and tk+1−tk are obtained and numerical verifications of the estimates are presented. The case of ux(0,t)=ux(1,t)=ψ(t) is also considered and analyzed. 相似文献
5.
Yohei Tachiya 《Journal of Number Theory》2007,125(1):182-200
We prove the transcendence results for the infinite product , where Ek(x), Fk(x) are polynomials, α is an algebraic number, and r?2 is an integer. As applications, we give necessary and sufficient conditions for transcendence of and , where Fn and Ln are Fibonacci numbers and Lucas numbers respectively, and {ak}k?0 is a sequence of algebraic numbers with log‖ak‖=o(rk). 相似文献
6.
Oleksiy A. Ignatyev 《Applied mathematics and computation》2010,216(2):388-394
The linear autonomous system of difference equations x(n+1)=Ax(n) is considered, where is a real nonsingular k×k matrix. In this paper it has been proved that if W(x) is any homogeneous polynomial of m-th degree in x, then there exists a unique homogeneous polynomial V(x) of m-th degree such that ΔV=V(Ax)-V(x)=W(x) if and only if where are the eigenvalues of the matrix A. The theorem on the instability has also been proved. 相似文献
7.
Man Kam Kwong 《Journal of Differential Equations》2008,245(8):2333-2351
We study the linear differential equation , on I=(0,1), where the coefficient f(x) is strictly positive and continuous on I, and satisfies the Hartman-Wintner condition at x=0. The four main results of the paper are: (i) a criterion for rectifiable oscillations of (P), characterized by the integrability of on I; (ii) a stability result for rectifiable and unrectifiable oscillations of (P), in terms of a perturbation on f(x); (iii) the s-dimensional fractal oscillations (for which we assume also f(x)∼cx−α when x→0, α>2, and s=max{1,3/2−2/α}); and (iv) the co-existence of rectifiable and unrectifiable oscillations in the absence of the Hartman-Wintner condition on f(x). Explicit examples related to the above results are given. 相似文献
8.
A triangle {a(n,k)}0?k?n of nonnegative numbers is LC-positive if for each r, the sequence of polynomials is q-log-concave. It is double LC-positive if both triangles {a(n,k)} and {a(n,n−k)} are LC-positive. We show that if {a(n,k)} is LC-positive then the log-concavity of the sequence {xk} implies that of the sequence {zn} defined by , and if {a(n,k)} is double LC-positive then the log-concavity of sequences {xk} and {yk} implies that of the sequence {zn} defined by . Examples of double LC-positive triangles include the constant triangle and the Pascal triangle. We also give a generalization of a result of Liggett that is used to prove a conjecture of Pemantle on characteristics of negative dependence. 相似文献
9.
Pedro Ortega Salvador Consuelo Ramírez Torreblanca 《Journal of Mathematical Analysis and Applications》2006,322(2):803-814
We characterize weighted modular inequalities of weak and strong type for the Hardy-Steklov operators T defined by , where g is a positive function and s, h are increasing and continuous functions such that s(x)?h(x) for all x. 相似文献
10.
Szymon W?sowicz 《Journal of Mathematical Analysis and Applications》2007,332(2):1229-1241
It is well known that every convex function (where I⊂R is an interval) admits an affine support at every interior point of I (i.e. for any x0∈IntI there exists an affine function such that a(x0)=f(x0) and a?f on I). Convex functions of higher order (precisely of an odd order) have a similar property: they are supported by the polynomials of degree no greater than the order of convexity. In this paper the attaching method is developed. It is applied to obtain the general result—Theorem 2, from which the mentioned above support theorem and some related properties of convex functions of higher (both odd and even) order are derived. They are applied to obtain some known and new Hadamard-type inequalities between the quadrature operators and the integral approximated by them. It is also shown that the error bounds of quadrature rules follow by inequalities of this kind. 相似文献
11.
12.
Let k be a positive integer with k?2 and let be a family of functions meromorphic on a domain D in , all of whose poles have multiplicity at least 3, and of whose zeros all have multiplicity at least k+1. Let a(z) be a function holomorphic on D, a(z)?0. Suppose that for each , f(k)(z)≠a(z) for z∈D. Then is a normal family on D. 相似文献
13.
P. Ille 《Discrete Mathematics》2009,309(11):3518-3522
In 1960, Sabidussi conjectured that if a graph G is isomorphic to the lexicographic product G[G], then the wreath product of by itself is a proper subgroup of . A positive answer is provided by constructing an automorphism Ψ of G[G] which satisfies: for every vertex x of G, there is an infinite subset I(x) of V(G) such that Ψ({x}×V(G))=I(x)×V(G). 相似文献
14.
For positive integers n>k, let be the polynomial obtained by truncating the binomial expansion of n(1+x) at the kth stage. These polynomials arose in the investigation of Schubert calculus in Grassmannians. In this paper, the authors prove the irreducibility of Pn,k(x) over the field of rational numbers when 2≤2k≤n<3(k+1). 相似文献
15.
Titus W. Hilberdink 《Journal of Number Theory》2010,130(3):707-715
In this paper we study generalised prime systems for which the integer counting function NP(x) is asymptotically well behaved, in the sense that NP(x)=ρx+O(xβ), where ρ is a positive constant and . For such systems, the associated zeta function ζP(s) is holomorphic for . We prove that for , for any ε>0, and also for ε=0 for all such σ except possibly one value. The Dirichlet divisor problem for generalised integers concerns the size of the error term in NkP(x)−Ress=1(ζPk(s)xs/s), which is O(xθ) for some θ<1. Letting αk denote the infimum of such θ, we show that . 相似文献
16.
17.
Biagio Ricceri 《Topology and its Applications》2006,153(17):3308-3312
In this paper, we establish some minimax theorems, of purely topological nature, that, through the variational methods, can be usefully applied to nonlinear differential equations. Here is a (simplified) sample: Let X be a Hausdorff topological space, I⊆R an interval and . Assume that the function Ψ(x,⋅) is lower semicontinuous and quasi-concave in I for all x∈X, while the function Ψ(⋅,q) has compact sublevel sets and one local minimum at most for each q in a dense subset of I. Then, one has
18.
The numerical range W(A) of a bounded linear operator A on a Hilbert space is the collection of complex numbers of the form (Av,v) with v ranging over the unit vectors in the Hilbert space. In terms of the location of W(A), inclusion regions are obtained for W(Ak) for positive integers k, and also for negative integers k if A−1 exists. Related inequalities on the numerical radius and the Crawford number are deduced. 相似文献
19.
Dimitar K. Dimitrov Fernando R. Rafaeli 《Journal of Computational and Applied Mathematics》2009,233(3):699-702
Denote by xnk(α), k=1,…,n, the zeros of the Laguerre polynomial . We establish monotonicity with respect to the parameter α of certain functions involving xnk(α). As a consequence we obtain sharp upper bounds for the largest zero of . 相似文献
20.
Sebastián Lorca 《Journal of Mathematical Analysis and Applications》2004,295(1):276-286
We study the existence of positive solutions to the elliptic equation ε2Δu(x,y)−V(y)u(x,y)+f(u(x,y))=0 for (x,y) in an unbounded domain subject to the boundary condition u=0 whenever is nonempty. Our potential V depends only on the y variable and is a bounded or unbounded domain which may coincide with . The positive parameter ε is tending to zero and our solutions uε concentrate along minimum points of the unbounded manifold of critical points of V. 相似文献