共查询到20条相似文献,搜索用时 15 毫秒
1.
Paul Terwilliger 《Discrete Mathematics》1982,41(3):295-302
We find lower bounds on eigenvalue multiplicities for highly symmetric graphs. In particular we prove:Theorem 1. If Γ is distance-regular with valency k and girth g (g?4), and λ (λ≠±?k) is an eigenvalue of Γ, then the multiplicity of λ is at least if g≡0 or 1 (mod 4), if g≡2 or 3 (mod 4) where [ ] denotes integer part. Theorem 2. If the automorphism group of a regular graph Γ with girth g (g?4) and valency k acts transitively on s-arcs for some s, , then the multiplicity of any eigenvalue λ (λ≠±?k) is at least if s is even, if s is odd. 相似文献
2.
Jean-Louis Tassoul Gilles Aubin 《Journal of Mathematical Analysis and Applications》1974,45(1):116-126
This paper deals with finite-amplitude axisymmetric disturbances in a self-gravitating fluid column of finite radius R. It is shown that the cutoff wavelength λnl above which gravitational breakup occurs now depends on the relative amplitude of the initial perturbation. Actually, for small-but finite-amplitude disturbances, , where λl ( = 5.8898R) designates the cutoff wavelength predicted in the linear approximation. 相似文献
3.
David L Russell 《Journal of Mathematical Analysis and Applications》1982,87(2):528-550
We suppose that K is a countable index set and that is a sequence of distinct complex numbers such that forms a Riesz (strong) basis for L2[a, b], a < b. Let Σ = {σ1, σ2,…, σm} consist of m complex numbers not in Λ. Then, with p(λ) = Πk = 1m (λ ? σk), forms a Riesz (strong) bas Sobolev space Hm[a, b]. If we take σ1, σ2,…, σm to be complex numbers already in Λ, then, defining p(λ) as before, forms a Riesz (strong) basis for the space H?m[a, b]. We also discuss the extension of these results to “generalized exponentials” tneλkt. 相似文献
4.
Matania Ben-Artzi 《Journal of Differential Equations》1980,38(1):51-60
Let H = ?Δ + V, where the potential V is spherically symmetric and can be decomposed as a sum of a short-range and a long-range term, V(r) = VS(r) + VL. Let λ = lim supr→∞VL(r) < ∞ (we allow λ = ? ∞) and set λ+ = max(λ, 0). Assume that for some r0, VL(r) ?C2k(r0, ∞) and that there exists δ > 0 such that . Assume further that and that 2kδ > 1. It is shown that: (a) The restriction of H to C∞(Rn) is essentially self-adjoint, (b) The essential spectrum of H contains the closure of (λ, ∞). (c) The part of H over (λ, ∞) is absolutely continuous. 相似文献
5.
Consider the matrix problem in the case where A is known precisely, the problem is ill conditioned, and ε is a random noise vector. Compute regularized “ridge” estimates,,where 1 denotes matrix transpose. Of great concern is the determination of the value of λ for which x?λ “best” approximates . Let ,and define λ0 to be the value of λ for which Q is a minimum. We look for λ0 among solutions of dQ/dλ = 0. Though Q is not computable (since ε is unknown), we can use this approach to study the behavior of λ0 as a function of y and ε. Theorems involving “noise to signal ratios” determine when λ0 exists and define the cases λ0 > 0 and λ0 = ∞. Estimates for λ0 and the minimum square error Q0 = Q(λ0) are derived. 相似文献
6.
R.J. Cook 《Journal of Number Theory》1979,11(1):49-68
It is shown that if λ1, …, λ5 are non-zero real numbers, not all of the same sign, and at least one of the ratios (1 ≤ j ≤ 3) is irrational then the values taken by for integer values of x1, …, x5 are everywhere dense on the real line. Similar results are proved for the polynomials and . 相似文献
7.
Stephen Bancroft 《Journal of Mathematical Analysis and Applications》1975,50(2):384-414
In this paper we discuss the problem of determining a T-periodic solution of the differential equation x = A(t)x + f(t, x, λ) + b(t), where the perturbation parameter λ is a vector in a parameter-space Rk. The customary approach assumes that λ = λ(?), ??R. One then establishes the existence of an ?0 > 0 such that the differential equation has a T-periodic solution for all ? satisfying 0 < ? < ?0. More specifically it is usually assumed that λ(?) has the form λ(?) = ?λ0 where λ0 is a fixed vector in Rk. This means that attention is confined in the perturbation procedure to examining the dependence of on λ as λ varies along a line segment terminating at the origin in the parameter-space Rk. The results established here generalize this previous work by allowing one to study the dependence of on λ as λ varies through a “conical-horn” whose vertex rests at the origin in Rk. In the process an implicit-function formula is developed which is of some interest in its own right. 相似文献
8.
S.K. Bajpai Joseph Tanne Donald Whittier 《Journal of Mathematical Analysis and Applications》1974,48(3):736-742
Let f(z), an analytic function with radius of convergence R (0 < R < ∞) be represented by the gap series ∑k = 0∞ckzλk. Set and define the growth constants ?, λ, T, t by , and if 0 < ? < ∞, . Then, assuming 0 < t < T < ∞, we obtain a decomposition theorem for f(z). 相似文献
9.
P.J. Cook 《Journal of Number Theory》1977,9(1):142-152
It is shown that λ1, λ2,…, λ6, μ are not all of the same sign and at least one ratio is irrational then the values taken by for integer values of x1 ,…, x6, y are everywhere dense on the real line. A similar result holds for expressions of the form . 相似文献
10.
Stanisław Lewanowicz 《Journal of Computational and Applied Mathematics》1979,5(3):193-206
In this paper we are constructing a recurrence relation of the form for integrals (called modified moments) in which Ck(λ) is the k-th Gegenbauer polynomial of order , and f is a function satisfying the differential equation of order n, where p0, p1, …, pn ? 0 are polynomials, and mk〈λ〉[p] is known for every k. We give three methods of construction of such a recurrence relation. The first of them (called Method I) is optimum in a certain sense. 相似文献
11.
Tibor Krisztin 《Journal of Mathematical Analysis and Applications》1985,109(2):509-521
Let be the classes of univalent functions defined in , which are convex of order β, starlike of order β and close-to-convex of order β type λ. Let . We discuss the properties of the function f when this function F belongs to the class K(β, λ) and its various subclasses. 相似文献
12.
It is shown that if satisfies , where σk(A) denotes the sum of all kth order subpermanent of A, then Per[λJn+(1?λ)A] is strictly decreasing in the interval 0<λ<1. 相似文献
13.
Douglas N. Clark 《Journal of Functional Analysis》1973,14(3):269-280
The operator acting on H=∝02π⊕L2(vt), where m and vt, 0 ? t ? 2π are measures on [0, 2π] with m smooth and e(s, t) = exp[?∝ts∝Tdvλ(θ) dm(λ)], satisfies . It is, therefore, unitarily equivalent to a scalar Sz.-Nagy-Foia? canonical model. The purpose of this paper is to determine the model explicitly and to give a formula for the unitary equivalence. 相似文献
14.
Denote by λ2(T) the second largest eigenvalue of a tree T. An easy algorithm is given to decide whether λ2(T)?λ for a given number λ, and a structure theorem for trees withλ2(T)?λ is proved. Also, it is shown that a tree T with n vertices has ; this bound is best possible for odd n. 相似文献
15.
Lawrence Turyn 《Journal of Differential Equations》1980,38(2):239-259
We consider the regular linear Sturm-Liouville problem (second-order linear ordinary differential equation with boundary conditions at two points x = 0 and x = 1, those conditions being separated and homogeneous) with several real parameters λ1,…,λN. Solutions to this problem correspond to eigenvaluesλ = (λ1,…,λN) forming sets N determined by the number of zeroes in (0, 1) of solutions. We describe properties of these sets including: boundedness, and when unbounded, asymptotic directions. Using these properties some results are given for the system of N Sturm-Liouville problems which share only the parameters λ. Sharp results are given for the system of two problems sharing two parameters. The eigensurfaces for a single problem are closely related to the cone , particularly in questions of boundedness. The cone K and related objects are discussed, and a result is given which relates cones with two oscillation conditions known as “Right-Definiteness” and “Left-Definiteness.” 相似文献
16.
F.R.K. Chung 《Journal of Combinatorial Theory, Series A》1983,35(3):252-262
Suppose is a collection of 3-subsets of {1,2,…,n}. The problem of determining the least integer with the property that if then contains a k-star (i.e., k 3-sets such that the intersection of any pair of them consists of exactly the same element) is studied. It is proved that, for k odd, and, for k even, . 相似文献
17.
Arthur Lubin 《Journal of Functional Analysis》1974,17(4):388-394
Let m and vt, 0 ? t ? 2π be measures on T = [0, 2π] with m smooth. Consider the direct integral = ⊕L2(vt) dm(t) and the operator on , where e(s, t) = exp ∫st ∫Tdvλ(θ) dm(λ). Let μt be the measure defined by for all continuous ?, and let ?t(z) = exp[?∫ (eiθ + z)(eiθ ? z)?1dμt(gq)]. Call {vt} regular iff for all for 1 a.e. 相似文献
18.
In this Note we present some results on the existence of radially symmetric solutions for the nonlinear elliptic equation
(1)
Here N?3, p>1 and denotes the Pucci's extremal operators with parameters 0<λ?Λ. The goal is to describe the solution set as function of the parameter p. We find critical exponents , that satisfy: (i) If then there is no nontrivial solution of (). (ii) If then there is a unique fast decaying solution of (). (iii) If then there is a unique pseudo-slow decaying solution to (). (iv) If pp+<p then there is a unique slow decaying solution to (). Similar results are obtained for the operator . To cite this article: P.L. Felmer, A. Quaas, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 909–914. 相似文献
19.
Morris L Eaton 《Journal of multivariate analysis》1976,6(3):422-425
Let Σ be an n × n positive definite matrix with eigenvalues λ1 ≥ λ2 ≥ … ≥ λn > 0 and let M = {x, y | x?Rn, y?Rn, x ≠ 0, y ≠ 0, x′y = 0}. Then for x, y in M, we have that and the inequality is sharp. If is a partitioning of Σ, let θ1 be the largest canonical correlation coefficient. The above result yields . 相似文献
20.
Robert L McFarland 《Journal of Combinatorial Theory, Series A》1973,15(1):1-10
A construction is given for difference sets in certain non-cyclic groups with the parameters , , , n = q2s for every prime power q and every positive integer s. If qs is odd, the construction yields at least inequivalent difference sets in the same group. For q = 5, s = 2 a difference set is obtained with the parameters (v, k, λ, n) = (4000, 775, 150, 625), which has minus one as a multiplier. 相似文献