共查询到20条相似文献,搜索用时 31 毫秒
1.
Austin J. Lemoine 《Stochastic Processes and their Applications》1973,1(3):251-268
A delayed random walk is defined here as a partial sum process of independent random variables in which the first N summands (N optional) are distributed F1,…,FN, respectively, while all remaining summands are distributed F0, where {Fk, k ≥ 0} is a sequence of proper distribution functions on the real line. Delayed random walks arise naturally in the study of certain generalized single server queues. This paper examines optional times of the process such as . Conditions insuring the finiteness of E {π} and E {π2} are obtained, generating functions calculated, and illustrative examples given. The bivariate functions and are studied for the case where N ≡ 1. 相似文献
2.
William O Ray 《Journal of Mathematical Analysis and Applications》1984,103(1):162-171
Let {Fr}0?r?p be a family of Banach spaces satisfying, if 0?r1?r2?p, (i)Fr1 ? Fr2; (ii); and (iii) is a convex function. Let G0 be a Banach space and. be a Gâteaux differentiate mapping, and suppose that ′(x)(Fp) is dense in G0. Under appropriate assumptions, the equation (x)=0 has a solution in Fr for 0?r?p. The results extend the Inverse Function Theorem of J. Moser to the class of Gâteaux differentiable operators. 相似文献
3.
Patrick J Browne 《Journal of Differential Equations》1977,23(2):285-292
In this paper we study the linked nonlinear multiparameter system , where xr? [ar, br], yr is subject to Sturm-Liouville boundary conditions, and the continuous functions ars satisfy ¦ . Conditions on the polynomial operators Mr, Prs are produced which guarantee a sequence of eigenfunctions for this problem yn(x) = Πr=1kyrn(xr), n ? 1, which form a basis in . Here [a, b] = [a1, b1 × … × [ak, bk]. 相似文献
4.
D Zwick 《Journal of Mathematical Analysis and Applications》1984,104(2):435-436
For a(1) ? a(2) ? ··· ? a(n) ? 0, b(1) ? b(2) ? ··· ? b(n) ? 0, the ordered values of ai, bi, i = 1, 2,…, n, m fixed, m ? n, and p ? 1 it is shown that where is the integer such that and . The inequality is shown to be sharp. When p < 1 and a(i)'s are in increasing order then the inequality is reversed. 相似文献
5.
Eng-Bin Lim 《Journal of Differential Equations》1978,30(1):49-53
The author discusses the best approximate solution of the functional differential equation x′(t) = F(t, x(t), x(h(t))), 0 < t < l satisfying the initial condition x(0) = x0, where x(t) is an n-dimensional real vector. He shows that, under certain conditions, the above initial value problem has a unique solution y(t) and a unique best approximate solution of degree k (cf. [1]) for a given positive integer k. Furthermore, , where ¦ · ¦ is any norm in Rn. 相似文献
6.
7.
Results on partition of energy and on energy decay are derived for solutions of the Cauchy problem . Here the Aj's are constant, k × k Hermitian matrices, x = (x1,…, xn), t represents time, and u = u(t, x) is a k-vector. It is shown that the energy of Mu approaches a limit , where M is an arbitrary matrix; that there exists a sufficiently large subspace of data ?, which is invariant under the solution group U0(t) and such that depending on ? and that the local energy of nonstatic solutions decays as . More refined results on energy decay are also given and the existence of wave operators is established, considering a perturbed equation at infinity. 相似文献
8.
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
9.
Elliptic boundary value problems for systems of nonlinear partial differential equations of the form , i = 1(1)N, j, k = 1(1)n, pi ? 0, ? being a small parameter, with Dirichlet boundary conditions are considered. It is supposed that a formal approximation Z is given which satisfies the boundary conditions and the differential equations upto the order χ(?) = o(1) in some norm. Then, using the theory of differential inequalities, it is shown that under certain conditions the difference between the exact solution u of the boundary value problem and the formal approximation Z, taken in the sense of a suitable norm, can be made small. 相似文献
10.
We consider the multiparameter eigenvalue problem (Tr + ∑s = 1kλsVrs) xr = 0, xr ≠ 0, 1 ? r ? k, where Tr and Vrs are self-adjoint linear operators on Hilbert spaces Hr, the Vrs being bounded. The problem may be posed in either ⊕r = 1kHr or ⊕r = 1kHr and we develop variational approaches for both settings. We explore the rôles played in both settings by for some nonozero and related cones in k. We also compare certain geometrical conditions on C with analytical definiteness conditions already in the literature. 相似文献
11.
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
12.
Rym Worms 《Comptes Rendus Mathematique》2002,334(8):709-712
We compare assumptions used in [4] in order to study the rate of convergence to 0, as u→s+(F), of , where is the survival function of the excesses over u, s+(F)=sup{x,F(x)<1} is the upper end point of the distribution function (d.f.) F and is the survival function of the Generalized Pareto Distribution, with assumptions used in [2] in order to study the rate of convergence to 0, as n→+∞, of , where Hγ is the d.f. of an extreme value distribution. In each case, an indicator linked to regular variation assumptions had been introduced. We characterize situations where these two indicators coincide, and others where they are different. To cite this article: R. Worms, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 709–712. 相似文献
13.
Stanley J Benkoski 《Journal of Number Theory》1976,8(2):218-223
If r, k are positive integers, then denotes the number of k-tuples of positive integers (x1, x2, …, xk) with 1 ≤ xi ≤ n and (x1, x2, …, xk)r = 1. An explicit formula for is derived and it is shown that .If S = {p1, p2, …, pa} is a finite set of primes, then 〈S〉 = {p1a1p2a2…psas; pi ∈ S and ai ≥ 0 for all i} and denotes the number of k-tuples (x1, x3, …, xk) with 1 ≤ xi ≤ n and (x1, x2, …, xk)r ∈ 〈S〉. Asymptotic formulas for are derived and it is shown that . 相似文献
14.
15.
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
16.
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
17.
A technique for the numerical approximation of matrix-valued Riemann product integrals is developed. For a ? x < y ? b, Im(x, y) denotes , and Am(x, y) denotes an approximation of Im(x, y) of the form , where ak and yik are fixed numbers for i = 1, 2,…, m and k = 1, 2,…, N and xik = x + (y ? x)yik. The following result is established. If p is a positive integer, F is a function from the real numbers to the set of w × w matrices with real elements and F(1) exists and is continuous on [a, b], then there exists a bounded interval function H such that, if n, r, and s are positive integers, , then Further, if F(j) exists and is continuous on [a, b] for j = 1, 2,…, p + 1 and A is exact for polynomials of degree less than p + 1 ? j for j = 1, 2,…, p, then the preceding result remains valid when Aj is substituted for Ij. 相似文献
18.
Karen A Ames 《Journal of Mathematical Analysis and Applications》1984,103(1):172-183
Solutions of Cauchy problems for the singular equations (in a Hilbert space setting) and , ω={(x1,…,xM)εm: 0 < xi < ci for each i=1,…,m} are shown to be unique and to depend Hölder continuously on the initial data in suitably chosen measures for 0?t < T < ∞. Logarithmic convexity arguments are used to derive the inequalities from which such results can be deduced. 相似文献
19.
J.E Nymann 《Journal of Number Theory》1975,7(4):406-412
Given a set S of positive integers let denote the number of k-tuples 〈m1, …, mk〉 for which and (m1, …, mk) = 1. Also let denote the probability that k integers, chosen at random from , are relatively prime. It is shown that if P = {p1, …, pr} is a finite set of primes and S = {m : (m, p1 … pr) = 1}, then if k ≥ 3 and where d(S) denotes the natural density of S. From this result it follows immediately that as n → ∞. This result generalizes an earlier result of the author's where and S is then the whole set of positive integers. It is also shown that if S = {p1x1 … prxr : xi = 0, 1, 2,…}, then as n → ∞. 相似文献
20.
For the Favard class Fr in the space C2π of continuous 2π-periodic functions we solve the following problem. Given x
and knots x0< x1 < ··· < xv−1., xu− 2π we determine weights xki(0 k · n, 0 j < r) such that is minimal. The optimal weights are unique (except for a trivial case) and we obtain them from a system of periodic polynomial splines ukj(0 k < n, 0 j< r): αkj = ukj(x). These splines induce an interpolation operator whose degree of approximation with respect to the class Fr is minimal if the knots are equidistant. Finally, we describe an efficient numerical procedure which shows how to compute the interpolation spline in the equidistant case. 相似文献