共查询到20条相似文献,搜索用时 15 毫秒
1.
Mindaugas Bloznelis 《Discrete Mathematics》2010,310(19):2560-2566
Let S(1),…,S(n),T(1),…,T(n) be random subsets of the set [m]={1,…,m}. We consider the random digraph D on the vertex set [n] defined as follows: the arc i→j is present in D whenever S(i)∩T(j)≠0?. Assuming that the pairs of sets (S(i),T(i)), 1≤i≤n, are independent and identically distributed, we study the in- and outdegree distributions of a typical vertex of D as n,m→∞. 相似文献
2.
Yuhong Liu 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(10):3376-3381
Given a continuous function f:Sm+n−2→Rm, and n points u1,u2,…,un∈Sm+n−2; does there exist a rotation r∈SO(m+n−1) such that f(ru1)=f(ru2)=?=f(run)? In this paper, we study the property of a continuous map from a sphere to a Euclidean space by using the theory of Smith periodic transformation and Brouwer degree of map theorem. The conjecture is proved under the case of n=2 and m being even. Furthermore, this conjecture is proved for the case when uj⋅uj+1=λ and the dimension of the sphere is not less than m+n−2. This paper generalizes the Borsuk-Ulam theorem and then presents its application. 相似文献
3.
Serguei V. Astashkin 《Journal of Functional Analysis》2009,256(12):4071-4094
Let X be a rearrangement invariant function space on [0,1]. We consider the Rademacher multiplicator space Λ(R,X) of all measurable functions x such that x⋅h∈X for every a.e. converging series h=∑anrn∈X, where (rn) are the Rademacher functions. We study the situation when Λ(R,X) is a rearrangement invariant space different from L∞. Particular attention is given to the case when X is an interpolation space between the Lorentz space Λ(φ) and the Marcinkiewicz space M(φ). Consequences are derived regarding the behaviour of partial sums and tails of Rademacher series in function spaces. 相似文献
4.
Judith Q. Longyear 《Discrete Mathematics》1973,4(4):379-382
It is shown that if r = 2, then for all m, n, h ≥ 3 and all “large enough” R, W such that mR = nW, there is a tactical configuration of rank 2 girth g = 2h, and degrees m and n on sets of cardinalities R and W. We also show that if r ≥ 3 then for all h and all compatible degree sets N = {n(i, j)≥3} and all large enough numbers R(1), R(2),…, R(r) satisfying R(i)n(i, j) = R(j)n(j, i) there is a tactical configuration of rank r, girth h, and degrees N on set with cardinalities R(1), R(2),…, R(r). 相似文献
5.
Shaofang Hong 《Journal of Number Theory》2005,113(1):1-9
Let n be a positive integer. Let S={x1,…,xn} be a set of n distinct positive integers. The least common multiple (LCM) matrix on S, denoted by [S], is defined to be the n×n matrix whose (i,j)-entry is the least common multiple [xi,xj] of xi and xj. The set S is said to be gcd-closed if for any xi,xj∈S,(xi,xj)∈S. For an integer m>1, let ω(m) denote the number of distinct prime factors of m. Define ω(1)=0. In 1997, Qi Sun conjectured that if S is a gcd-closed set satisfying maxx∈S{ω(x)}?2, then the LCM matrix [S] is nonsingular. In this paper, we settle completely Sun's conjecture. We show the following result: (i). If S is a gcd-closed set satisfying maxx∈S{ω(x)}?2, then the LCM matrix [S] is nonsingular. Namely, Sun's conjecture is true; (ii). For each integer r?3, there exists a gcd-closed set S satisfying maxx∈S{ω(x)}=r, such that the LCM matrix [S] is singular. 相似文献
6.
Huy Vui Hà 《Journal of Pure and Applied Algebra》2009,213(11):2167-2176
Let f,gi,i=1,…,l,hj,j=1,…,m, be polynomials on Rn and S?{x∈Rn∣gi(x)=0,i=1,…,l,hj(x)≥0,j=1,…,m}. This paper proposes a method for finding the global infimum of the polynomial f on the semialgebraic set S via sum of squares relaxation over its truncated tangency variety, even in the case where the polynomial f does not attain its infimum on S. Under a constraint qualification condition, it is demonstrated that: (i) The infimum of f on S and on its truncated tangency variety coincide; and (ii) A sums of squares certificate for nonnegativity of f on its truncated tangency variety. These facts imply that we can find a natural sequence of semidefinite programs whose optimal values converge, monotonically increasing to the infimum of f on S. 相似文献
7.
Jer-Shyong Lin 《Linear algebra and its applications》2010,432(1):14-23
Let A be a prime ring of characteristic not 2, with center Z(A) and with involution *. Let S be the set of symmetric elements of A. Suppose that f:S→A is an additive map such that [f(x),f(y)]=[x,y] for all x,y∈S. Then unless A is an order in a 4-dimensional central simple algebra, there exists an additive map μ:S→Z(A) such that f(x)=x+μ(x) for all x∈S or f(x)=-x+μ(x) for all x∈S. 相似文献
8.
Mohammad Reza Pournaki Seyed Amin Seyed Fakhari Siamak Yassemi 《Arkiv f?r Matematik》2013,51(1):185-196
Recently, Haghighi, Terai, Yassemi, and Zaare-Nahandi introduced the notion of a sequentially (S r ) simplicial complex. This notion gives a generalization of two properties for simplicial complexes: being sequentially Cohen–Macaulay and satisfying Serre’s condition (S r ). Let Δ be a (d?1)-dimensional simplicial complex with Γ(Δ) as its algebraic shifting. Also let (h i,j (Δ))0≤j≤i≤d be the h-triangle of Δ and (h i,j (Γ(Δ)))0≤j≤i≤d be the h-triangle of Γ(Δ). In this paper, it is shown that for a Δ being sequentially (S r ) and for every i and j with 0≤j≤i≤r?1, the equality h i,j (Δ)=h i,j (Γ(Δ)) holds true. 相似文献
9.
We prove Sobolev-type p(⋅)→q(⋅)-theorems for the Riesz potential operator Iα in the weighted Lebesgue generalized spaces Lp(⋅)(Rn,ρ) with the variable exponent p(x) and a two-parametrical power weight fixed to an arbitrary finite point and to infinity, as well as similar theorems for a spherical analogue of the Riesz potential operator in the corresponding weighted spaces Lp(⋅)(Sn,ρ) on the unit sphere Sn in Rn+1. 相似文献
10.
Strong commutativity preserving maps on Lie ideals 总被引:2,自引:0,他引:2
Jer-Shyong Lin 《Linear algebra and its applications》2008,428(7):1601-1609
Let A be a prime ring and let R be a noncentral Lie ideal of A. An additive map f:R→A is called strong commutativity preserving (SCP) on R if [f(x),f(y)]=[x,y] for all x,y∈R. In this paper we show that if f is SCP on R, then there exist λ∈C, λ2=1 and an additive map μ:R→Z(A) such that f(x)=λx+μ(x) for all x∈R where C is the extended centroid of A, unless charA=2 and A satisfies the standard identity of degree 4. 相似文献
11.
Caishi Wang 《Journal of Mathematical Analysis and Applications》2007,329(2):913-921
Let δa be the Dirac delta function at a∈R and (E)⊂(L2)⊂∗(E) the canonical framework of white noise analysis over white noise space (E∗,μ), where E∗=S∗(R). For h∈H=L2(R) with h≠0, denote by Mh the operator of multiplication by Wh=〈⋅,h〉 in (L2). In this paper, we first show that Mh is δa-composable. Thus the delta function δa(Mh) makes sense as a generalized operator, i.e. a continuous linear operator from (E) to ∗(E). We then establish a formula showing an intimate connection between δa(Mh) as a generalized operator and δa(Wh) as a generalized functional. We also obtain the representation of δa(Mh) as a series of integral kernel operators. Finally we prove that δa(Mh) depends continuously on a∈R. 相似文献
12.
Avner Friedman 《Journal of Mathematical Analysis and Applications》2007,327(1):643-664
We consider a free boundary problem modeling tumor growth in fluid-like tissue. The model equations include a diffusion equation for the nutrient concentration, and the Stokes equation with a source which represents the proliferation of tumor cells. The proliferation rate μ and the cell-to-cell adhesiveness γ which keeps the tumor intact are two parameters which characterize the “aggressiveness” of the tumor. For any positive radius R there exists a unique radially symmetric stationary solution with radius r=R. For a sequence μ/γ=Mn(R) there exist symmetry-breaking bifurcation branches of solutions with free boundary r=R+εYn,0(θ)+O(ε2) (n even ?2) for small |ε|, where Yn,0 is the spherical harmonic of mode (n,0). Furthermore, the smallest Mn(R), say Mn∗(R), is such that n∗=n∗(R)→∞ as R→∞. In this paper we prove that the radially symmetric stationary solution with R=RS is linearly stable if μ/γ<N∗(RS,γ) and linearly unstable if μ/γ>N∗(RS,γ), where N∗(RS,γ)?Mn∗(RS), and we prove that strict inequality holds if γ is small or if γ is large. The biological implications of these results are discussed at the end of the paper. 相似文献
13.
Kazushi Yoshitomi 《Indagationes Mathematicae》2005,16(2):289-299
Let q ∈ {2, 3} and let 0 = s0 < s1 < … < sq = T be integers. For m, n ∈ Z, we put ¯m,n = {j ∈ Z| m? j ? n}. We set lj = sj − sj−1 for j ∈ 1, q. Given (p1,, pq) ∈ Rq, let b: Z → R be a periodic function of period T such that b(·) = pj on sj−1 + 1, sj for each j ∈ 1, q. We study the spectral gaps of the Jacobi operator (Ju)(n) = u(n + 1) + u(n − 1) + b(n)u(n) acting on l2(Z). By [λ2j , λ2j−1] we denote the jth band of the spectrum of J counted from above for j ∈ 1, T. Suppose that pm ≠ pn for m ≠ n. We prove that the statements (i) and (ii) below are equivalent for λ ∈ R and i ∈ 1, T − 1. 相似文献
14.
Let R = (r1,…, rm) and S = (s1,…, sn) be nonnegative integral vectors, and let (R, S) denote the class of all m × n matrices of 0's and 1's having row sum vector R and column sum vector S. An invariant position of (R, S) is a position whose entry is the same for all matrices in (R, S). The interchange graph G(R, S) is the graph where the vertices are the matrices in (R, S) and where two matrices are joined by an edge provided they differ by an interchange. We prove that when 1 ≤ ri ≤ n ? 1 (i = 1,…, m) and 1 ≤ sj ≤ m ? 1 (j = 1,…, n), G(R, S) is prime if and only if (R, S) has no invariant positions. 相似文献
15.
Let Mn(F) denote the algebra of n×n matrices over the field F of complex, or real, numbers. Given a self-adjoint involution J∈Mn(C), that is, J=J*,J2=I, let us consider Cn endowed with the indefinite inner product [,] induced by J and defined by [x,y]?〈Jx,y〉,x,y∈Cn. Assuming that (r,n-r), 0?r?n, is the inertia of J, without loss of generality we may assume J=diag(j1,?,jn)=Ir⊕-In-r. For T=(|tik|2)∈Mn(R), the matrices of the form T=(|tik|2jijk), with all line sums equal to 1, are called J-doubly stochastic matrices. In the particular case r∈{0,n}, these matrices reduce to doubly stochastic matrices, that is, non-negative real matrices with all line sums equal to 1. A generalization of Birkhoff’s theorem on doubly stochastic matrices is obtained for J-doubly stochastic matrices and an application to determinants is presented. 相似文献
16.
Regina C. Elandt-Johnson 《Journal of multivariate analysis》1978,8(2):244-254
We call a set of univariate distributions with the same mathematical form but different parameter values a family . Consider a bivariate Gumbel Type A survival distribution, S12(x1, x2), defined in (2.1), for which both marginal distributions, S1(x1), S2(x2), belong to the same family, of distributions. It is proved in this paper that subject to weak conditions, the crude hazard rates, h1(t) and h2(t), are proportional if and only if the marginal hazard rates, λ1(t) and λ2(t), are proportional (Theorem 1). It is also shown that the survival functions of W = min(X1, X2), and of the identified minimum, Wi = Xi, for Xi < Xj, j ≠ i, belong to the same family as do S1(x1), S2(x2) (Corollary 1). Counter-examples of distributions other than Gumbel Type A, for which these properties do not hold, are given. Some applications to the analysis of competing risks, using a family of Gompertz distributions, are discussed. 相似文献
17.
R.C Riddell 《Journal of Functional Analysis》1975,18(3):213-270
Eigenvalue problems of the form g′(v) = λh′(v) are considered, with the normalizations g(v) = r or h(v) = r, where g and h are real-valued C1 functions on a real Banach space which are invariant under a periodic linear isometry. Theorems are proved on the existence of solutions λ(r), v(r), and on their dependence upon the normalization constant r > 0. In particular, the relation, as r → 0, of λ(r), v(r) to solutions of the linearized problem g″(0)v = λh″(0)v is discussed. The theorems are applied to elliptic problems for Euler-Lagrange operators corresponding to multiple integral functionals on closed subspaces of Sobolev spaces. 相似文献
18.
Ruyun Ma Chenghua Gao Xiaoling Han 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):6965-6969
We determine the principal eigenvalues of the linear indefinite weight problem Moreover, we investigate the existence of positive solutions for the corresponding nonlinear indefinite weight problem, where g:[0,1]→R is a continuous function which attains both positive and negative values, f∈C(R,R), and r is a parameter. 相似文献
19.
Let D be a region, {rn}n∈N a sequence of rational functions of degree at most n and let each rn have at most m poles in D, for m∈N fixed. We prove that if {rn}n∈N converges geometrically to a function f on some continuum S⊂D and if the number of zeros of rn in any compact subset of D is of growth o(n) as n→∞, then the sequence {rn}n∈N converges m1-almost uniformly to a meromorphic function in D. This result about meromorphic continuation is used to obtain Picard-type theorems for the value distribution of m1-maximally convergent rational functions, especially in Padé approximation and Chebyshev rational approximation. 相似文献
20.
Janusz Brzd?k 《Journal of Mathematical Analysis and Applications》2011,381(1):299-307
Let C be a convex symmetric subset of a real Banach space F and K be a subgroup of the group (F,+). Let E be a real linear space, h:E→F, and h(x+y)−h(x)−h(y)∈K+C for x,y∈E. We prove that under some additional assumptions h can be represented in the form: h=A+γ+κ with an additive (or linear) A:E→F and some γ:E→C, κ:E→K. 相似文献