共查询到20条相似文献,搜索用时 31 毫秒
1.
In this Note we consider nonnegative solutions for the nonlinear equation in , where is the so called Pucci operator and the ei are the eigenvalues of M et Λ?λ>0. We prove that if u satisfies the decreasing estimate for some β satisfying (β?1)(p?1)>2+α then u is radial. In a second time we prove that if and u is a nonnegative radial solution of (1), u(x)=g(r), such that g″ changes sign at most once, then u is zero. To cite this article: I. Birindelli, F. Demengel, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
2.
J Bustoz 《Journal of Mathematical Analysis and Applications》1981,79(1):71-79
It is known that the classical orthogonal polynomials satisfy inequalities of the form Un2(x) ? Un + 1(x) Un ? 1(x) > 0 when x lies in the spectral interval. These are called Turan inequalities. In this paper we will prove a generalized Turan inequality for ultraspherical and Laguerre polynomials. Specifically if Pnλ(x) and Lnα(x) are the ultraspherical and Laguerre polynomials and . We also prove the inequality is a positive constant depending on α and β. 相似文献
3.
Ludwig Arnold 《Linear algebra and its applications》1976,13(3):185-199
It is proved that Wigner's semicircle law for the distribution of eigenvalues of random matrices, which is important in the statistical theory of energy levels of heavy nuclei, possesses the following completely deterministic version. Let An=(aij), 1?i, ?n, be the nth section of an infinite Hermitian matrix, {λ(n)}1?k?n its eigenvalues, and {uk(n)}1?k?n the corresponding (orthonormalized column) eigenvectors. Let , put (bookeeping function for the length of the projections of the new row v1n of An onto the eigenvectors of the preceding matrix An?1), and let finally (empirical distribution function of the eigenvalues of . Suppose (i) , (ii) limnXn(t)=Ct(0<C<∞,0?t?1). Then ,where W is absolutely continuous with (semicircle) density 相似文献
4.
Let and be polynomials with real zeros satisfying An?1 = Bn?1 = 0, and let Using the recently proved validity of the van der Waerden conjecture on permanents, some results on the real zeros of H(x) are obtained. These results are related to classical results on composite polynomials. 相似文献
5.
A.M Fink 《Journal of Mathematical Analysis and Applications》1982,90(1):251-258
Presented in this report are two further applications of very elementary formulae of approximate differentiation. The first is a new derivation in a somewhat sharper form of the following theorem of V. M. Olovyani?nikov: LetNn (n ? 2) be the class of functionsg(x) such thatg(x), g′(x),…, g(n)(x) are ? 0, bounded, and nondecreasing on the half-line ?∞ < x ? 0. A special element ofNnis. Ifg(x) ∈ Nnis such that, thenfor
1
. Moreover, if we have equality in (1) for some value of v, then we have there equality for all v, and this happens only if in (?∞, 0].The second application gives sufficient conditions for the differentiability of asymptotic expansions (Theorem 4). 相似文献
6.
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
7.
Teruo Ikebe 《Journal of Functional Analysis》1975,20(2):158-177
A spectral representation for the self-adjoint Schrödinger operator H = ?Δ + V(x), x? R3, is obtained, where V(x) is a long-range potential: , grad , being the Laplace-Beltrami operator on the unit sphere Ω. Namely, we shall construct a unitary operator from PL2(R3) onto being the orthogonal projection onto the absolutely continuous subspace for H, such that for any Borel function α(λ), . 相似文献
8.
R.C. Griffiths 《Journal of multivariate analysis》1975,5(2):271-277
Orthogonal polynomials on the multivariate negative binomial distribution, where α > 0, Θ1 > 0, x = ΣΘi, x0, x1, …, xp = 0,1, … are constructed and their properties studied. 相似文献
9.
Let X = {x1, x2,…} be a finite set and associate to every xi a real number αi. Let f(n) [g (n)] be the least value such that given any family of subsets of X having maximum degree n [cardinality n], one can find integers αi, i=1,2,… so that αi ? αi|<1 and for all . We prove . 相似文献
10.
Let (m?n) denote the linear space of all m × n complex or real matrices according as = or . Let c=(c1,…,cm)≠0 be such that c1???cm?0. The c-spectral norm of a matrix A?m×n is the quantity . where σ1(A)???σm(A) are the singular values of A. Let d=(d1,…,dm)≠0, where d1???dm?0. We consider the linear isometries between the normed spaces and , and prove that they are dual transformations of the linear operators which map (d) onto (c), where . 相似文献
11.
Real constant coefficient nth order elliptic operators, Q, which generate strongly continuous semigroups on L2(k) are analyzed in terms of the elementary generator, , for n even. Integral operators are defined using the fundamental solutions pn(x, t) to ut = Au and using real polynomials ql,…, qk on m by the formula, for q = (ql,…, qk), m. It is determined when, strongly on L2(k), . If n = 2 or k = 1, this can always be done. Otherwise the symbol of Q must have a special form. 相似文献
12.
Let Ms, be the number of solutions of the equation in the finite field GF(p). For a prime p ≡ 1(mod 3), , , and . Here d is uniquely determined by . 相似文献
13.
This paper considers canonical forms for the similarity action of Gl(n) on : , Those canonical forms are obtained as an application of a more general method to select canonical elements Mc in the orbits of a matrix group G acting on a set of matrices . We define a total order (?) on , different from the lexicographic order l? [0l?x ? x <0, but and consider normalized -elements with a minimal number of parameters: It is shown that the row and column echelon forms, the Jordan canonical form, and “nice” control canonical forms for reachable (A,B)-pairs have a homogeneous interpretation as such (?)-minimal orbit elements. Moreover new canonical forms for the general action (?) are determined via this method. 相似文献
14.
Scott B. Guthery 《Journal of Number Theory》1974,6(3):201-210
If f is a monotone function subject to certain restrictions, then one can associate with any real number x between zero and one a sequence {an(x)} of integers such that . In this paper properties of the function F defined by , where g is any function satisfying the same restrictions as f, are discussed. Principally, F is found to be useful in finding stationary measures on the sequences {an(x)}. 相似文献
15.
Let , 0<aT?T<∞, and {W(t);0?t<∞} be a standard Wiener process. This exposition studies the almost sure behaviour of , under varying conditions on aT and T/aT. The following analogue of Lévy's modulus of continuity of a Wiener Process is also given: and this may be viewed as the exact “modulus of non-differentiability” of a Wiener Process. 相似文献
16.
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
17.
R.J Cook 《Journal of Number Theory》1983,17(1):80-92
Let k be an odd positive integer. Davenport and Lewis have shown that the equations with integer coefficients, have a nontrivial solution in integers x1,…, xN provided that Here it is shown that for any ? > 0 and k > k0(?) the equations have a nontrivial solution provided that 相似文献
18.
An n-tournament is a complete labelled digraph on n vertices without loops or multiple arcs. A tournament's score sequence is the sequence of the out-degrees of its vertices arranged in nondecreasing order. The number Sn of distinct score sequences arising from all possible n-tournaments, as well as certain generalizations are investigated. A lower bound of the form (C1 a constant) and an upper bound of the form are proved. A q-extension of the Catalan numbers is defined. It is conjectured that all coefficients in the polynomial Cn(q) are at most . It is shown that if this conjecture is true, then 相似文献
19.
Bernard Harris 《Journal of Combinatorial Theory, Series A》1973,15(1):66-74
P. Erdös and P. Turán [8] (Acta Math. Acad. Sci. Hungar., 18 (1967), 309–320) have shown that, if K(n, x) is the number of elements P in Sn, the symmetric group on n letters, whose order O(P) satisfies then In this paper the analogous result for the symmetric semigroup is obtained. Let α?Tn, the symmetric semigroup on n letters (the set of all mappings of {1, 2,…, n} into {1, 2,…, n}) and let O(α) be the order of α. If L(n, x) is the number of α?Tn with then 相似文献
20.
Thomas G. Kurtz 《Stochastic Processes and their Applications》1978,6(3):223-240
A variety of continuous parameter Markov chains arising in applied probability (e.g. epidemic and chemical reaction models) can be obtained as solutions of equations of the form where , the Y1 are independent Poisson processes, and N is a parameter with a natural interpretation (e.g. total population size or volume of a reacting solution).The corresponding deterministic model, satisfies Under very general conditions limN→∞XN(t)=X(t) a.s. The process XN(t) is compared to the diffusion processes given by and Under conditions satisfied by most of the applied probability models, it is shown that XN,ZN and V can be constructed on the same sample space in such a way that and 相似文献