共查询到20条相似文献,搜索用时 31 毫秒
1.
On the total multiplicity of zeros of generalized polynomials related to nonoscillating trajectories
For a continuous curve L = {x: x = Z(t), t ∈ [a, b]} in R n , we study the number of zeros of the function l h (t) = 〈h, Z(t)〉, where h ∈ R n . We introduce the notion of multiple zeros for such functions and study the possibility of estimating the total multiplicity of such zeros under the assumption that the system {z 1(t), z 2(t), …, z n (t)} of coordinates of the function Z(t) is a Chebyshev system on [a, b]. 相似文献
2.
We investigate the equiconvergence on TN = [?π, π)N of expansions in multiple trigonometric Fourier series and in the Fourier integrals of functions f ∈ Lp(TN) and g ∈ Lp(RN), p > 1, N ≥ 3, g(x) = f(x) on TN, in the case where the “partial sums” of these expansions, i.e., Sn(x; f) and Jα(x; g), respectively, have “numbers” n ∈ ZN and α ∈ RN (nj = [αj], j = 1,..., N, [t] is the integral part of t ∈ R1) containing N ? 1 components which are elements of “lacunary sequences.” 相似文献
3.
For drifted Brownian motion X(t) = x-µ t + B t (µ > 0) starting from x > 0, we study the joint distribution of the first-passage time below zero ,t(x), and the first-passage area ,A(x), swept out by X till the time t(x). In particular, we establish differential equations with boundary conditions for the joint moments E[t(x) m A(x) n ], and we present an algorithm to find recursively them, for any m and n. Finally, the expected value of the time average of X till the time t(x) is obtained. 相似文献
4.
In this paper we obtain some results on the global existence of solution to Itô stochastic impulsive differential equations in M([0,∞),? n ) which denotes the family of ? n -valued stochastic processes x satisfying supt∈[0,∞) \(\mathbb{E}\)|x(t)|2 < ∞ under non-Lipschitz coefficients. The Schaefer fixed point theorem is employed to achieve the desired result. An example is provided to illustrate the obtained results. 相似文献
5.
We prove the existence of a completely integrable Pfaffian system ?x/?t i = A i (t)x, x ∈ R n , t = (t 1, t 2, t 3) ∈ R + 3 , i = 1, 2, 3, with infinitely differentiable bounded coefficients and with lower characteristic set of positive three-dimensional Lebesgue measure. 相似文献
6.
We consider the quasilinear Schrödinger equations of the form ?ε2Δu + V(x)u ? ε2Δ(u2)u = g(u), x∈ RN, where ε > 0 is a small parameter, the nonlinearity g(u) ∈ C1(R) is an odd function with subcritical growth and V(x) is a positive Hölder continuous function which is bounded from below, away from zero, and infΛV(x) < inf?ΛV(x) for some open bounded subset Λ of RN. We prove that there is an ε0 > 0 such that for all ε ∈ (0, ε0], the above mentioned problem possesses a sign-changing solution uε which exhibits concentration profile around the local minimum point of V(x) as ε → 0+. 相似文献
7.
The system where v = C*x is an output, u = S*y is a control, A(·) ∈ R n × n , B(·) ∈ R n × (n–p), C ∈ R n × (n–p), and D ∈ R n × (n–p), is considered. The elements αij(·) and βij(·) of the matrices A(·) and B(·) are arbitrary functionals satisfying the conditions It is assumed that A(·) ∈ Z 1 ∪ Z 3 and A*(·) ∈ Z 1 ∪ Z 3, where Z 1 is the class of matrices in which the first p elements of the kth superdiagonal are sign-definite and the elements above them are sufficiently small. The class Z 3 differs from Z t1 in that the elements between this superdiagonal and the (k + 1)th row are sufficiently small. If k > p, then the elements of the p × p square in the upper left corner of the matrix are sufficiently small as well. By using special quadratic Lyapunov functions, a matrix D for which y(t)–x(t) → 0 exponentially as t → ∞ is first found, and then a matrix S for which the vectors x(t) and y(t) have the same property is constructed.
相似文献
$$\frac{{dx}}{{dt}} = A\left( \cdot \right)x + B\left( \cdot \right)u,{\kern 1pt} \frac{{dy}}{{dt}} = A\left( \cdot \right)y + B\left( \cdot \right)u + D\left( {C*y - v} \right)$$
$$\mathop {\sup }\limits_{\left( \cdot \right)} |{\alpha _{ij}}\left( \cdot \right)| < \infty \left( {i,j \in 1,n} \right),\mathop {\sup }\limits_{\left( \cdot \right)} |{\beta _{ij}}\left( \cdot \right)| < \infty \left( {i \in 1,n,j \in 1,n - p} \right).$$
8.
In this paper we prove the following result. Let m ≥ 1, n ≥ 1 be fixed integers and let R be a prime ring with m + n + 1 ≤ char(R) or char(R) = 0. Suppose there exists an additive nonzero mapping D : R → R satisfying the relation 2D(x n+m+1) = (m + n + 1)(x m D(x)x n + x n D(x)x m ) for all \({x\in R}\). In this case R is commutative and D is a derivation. 相似文献
9.
This paper is devoted to a study of L~q-tracing of the fractional temperature field u(t, x)—the weak solution of the fractional heat equation(?_t +(-?_x)~α)u(t, x) = g(t, x) in L~p(R_+~(1+n)) subject to the initial temperature u(0, x) = f(x) in L~p(R~n). 相似文献
10.
Let d ≥ 1 and Z be a subordinate Brownian motion on R~d with infinitesimal generator ? + ψ(?),where ψ is the Laplace exponent of a one-dimensional non-decreasing L′evy process(called subordinator). We establish the existence and uniqueness of fundamental solution(also called heat kernel) pb(t, x, y) for non-local operator L~b= ? + ψ(?) + b ?, where Rb is an Rd-valued function in Kato class K_(d,1). We show that p~b(t, x, y)is jointly continuous and derive its sharp two-sided estimates. The kernel pb(t, x, y) determines a conservative Feller process X. We further show that the law of X is the unique solution of the martingale problem for(L~b, C_c~∞(R~d)) and X is a weak solution of Xt = X0+ Zt + integral from n=0 to t(b(Xs)ds, t ≥ 0).Moreover, we prove that the above stochastic differential equation has a unique weak solution. 相似文献
11.
A. A. Mogul’skii 《Siberian Mathematical Journal》2008,49(4):669-683
We obtain an integro-local limit theorem for the sum S(n) = ξ(1)+?+ξ(n) of independent identically distributed random variables with distribution whose right tail varies regularly; i.e., it has the form P(ξ≥t) = t ?β L(t) with β > 2 and some slowly varying function L(t). The theorem describes the asymptotic behavior on the whole positive half-axis of the probabilities P(S(n) ∈ [x, x + Δ)) as x → ∞ for a fixed Δ > 0; i.e., in the domain where the normal approximation applies, in the domain where S(n) is approximated by the distribution of its maximum term, as well as at the “junction” of these two domains. 相似文献
12.
Let R be a prime ring of char R ≠ 2, let d be a nonzero derivation of R, and let ρ be a nonzero right ideal of R such that [[d(x)x n , d(y)] m , [y, x] s ] t = 0 for all x, y ? ρ, where n ≥ 1, m ≥ 0, s ≥ 0, and t ≥ 1 are fixed integers. If [ρ, ρ]ρ ≠ 0 then d(ρ)ρ = 0. 相似文献
13.
V. M. Badkov 《Proceedings of the Steklov Institute of Mathematics》2009,264(1):39-43
Let {p n (t)} n=0 t8 be a system of algebraic polynomials orthonormal on the segment [?1, 1] with a weight p(t); let {x n,ν (p) } ν=1 n be zeros of a polynomial p n (t) (x x,ν (p) = cosθ n,ν (p) ; 0 < θ n,1 (p) < θ n,2 (p) < ... < θ n,n (p) < π). It is known that, for a wide class of weights p(t) containing the Jacobi weight, the quantities θ n,1 (p) and 1 ? x n,1 (p) coincide in order with n ?1 and n ?2, respectively. In the present paper, we prove that, if the weight p(t) has the form p(t) = 4(1 ? t 2)?1{ln2[(1 + t)/(1 ? t)] + π 2}?1, then the following asymptotic formulas are valid as n → ∞:
相似文献
$$\theta _{n,1}^{(p)} = \frac{{\sqrt 2 }}{{n\sqrt {\ln (n + 1)} }}\left[ {1 + {\rm O}\left( {\frac{1}{{\ln (n + 1)}}} \right)} \right],x_{n,1}^{(p)} = 1 - \left( {\frac{1}{{n^2 \ln (n + 1)}}} \right) + O\left( {\frac{1}{{n^2 \ln ^2 (n + 1)}}} \right).$$
14.
We consider a self-adjoint matrix elliptic operator A ε, ε > 0, on L 2(R d ;C n ) given by the differential expression b(D)*g(x/ε)b(D). The matrix-valued function g(x) is bounded, positive definite, and periodic with respect to some lattice; b(D) is an (m × n)-matrix first order differential operator such that m ≥ n and the symbol b(ξ) has maximal rank. We study the operator cosine cos(τA ε 1/2 ), where τ ∈ R. It is shown that, as ε → 0, the operator cos(τA ε 1/2 ) converges to cos(τ(A 0)1/2) in the norm of operators acting from the Sobolev space H s (R d ;C n ) (with a suitable s) to L 2(R d ;C n ). Here A 0 is the effective operator with constant coefficients. Sharp-order error estimates are obtained. The question about the sharpness of the result with respect to the type of the operator norm is studied. Similar results are obtained for more general operators. The results are applied to study the behavior of the solution of the Cauchy problem for the hyperbolic equation ? τ 2 u ε (x, τ) = ?A ε u ε (x, τ). 相似文献
15.
A. B. Kostin 《Differential Equations》2016,52(2):220-239
We study the inverse problem of the reconstruction of the coefficient ?(x, t) = ?0(x, t) + r(x) multiplying ut in a nonstationary parabolic equation. Here ?0(x, t) ≥ ?0 > 0 is a given function, and r(x) ≥ 0 is an unknown function of the class L∞(Ω). In addition to the initial and boundary conditions (the data of the direct problem), we pose the problem of nonlocal observation in the form ∫0Tu(x, t) dμ(t) = χ(x) with a known measure dμ(t) and a function χ(x). We separately consider the case dμ(t) = ω(t)dt of integral observation with a smooth function ω(t). We obtain sufficient conditions for the existence and uniqueness of the solution of the inverse problem, which have the form of ready-to-verify inequalities. We suggest an iterative procedure for finding the solution and prove its convergence. Examples of particular inverse problems for which the assumptions of our theorems hold are presented. 相似文献
16.
This paper is concerned with the oscillatory behavior of the damped half-linear oscillator (a(t)?p(x′))′ + b(t)?p(x′) + c(t)?p(x) = 0, where ?p(x) = |x|p?1 sgn x for x ∈ ? and p > 1. A sufficient condition is established for oscillation of all nontrivial solutions of the damped half-linear oscillator under the integral averaging conditions. The main result can be given by using a generalized Young’s inequality and the Riccati type technique. Some examples are included to illustrate the result. Especially, an example which asserts that all nontrivial solutions are oscillatory if and only if p ≠ 2 is presented. 相似文献
17.
For a finite group G and nonnegative integer n ≥ 0, one may consider the associated tower \(G \wr S_{n} := S_{n} \ltimes G^{n}\) of wreath product groups. Zelevinsky associated to such a tower the structure of a positive self-adjoint Hopf algebra (PSH-algebra) R(G) on the direct sum over integers n ≥ 0 of the Grothendieck groups K 0(R e p?G?S n ). In this paper, we study the interaction via induction and restriction of the PSH-algebras R(G) and R(H) associated to finite groups H ? G. A class of Hopf modules over PSH-algebras with a compatibility between the comultiplication and multiplication involving the Hopf k t h -power map arise naturally and are studied independently. We also give an explicit formula for the natural PSH-algebra morphisms R(H) → R(G) and R(G) → R(H) arising from induction and restriction. In an appendix, we consider a family of subgroups of wreath product groups analogous to the subgroups G(m, p, n) of the wreath product cyclotomic complex reflection groups G(m, 1, n). 相似文献
18.
A. S. Pechentsov 《Differential Equations》2017,53(8):1029-1034
We consider the Sturm–Liouville operator generated in the space L 2[0,+∞) by the expression l a,b:= ?d 2/dx 2 +x+aδ(x?b) and the boundary condition y(0) = 0. We prove that the eigenvalues λ n of this operator satisfy the inequalities λ1 0 < λ1 < λ2 0 and λn 0 ≤ λn < λn+1 0, n = 2, 3,..., where {?λn 0} is the sequence of zeros of the Airy function Ai (λ). We find the asymptotics of λn as n → +∞ depending on the parameters a and b. 相似文献
19.
Vincenzo De Filippis 《Czechoslovak Mathematical Journal》2016,66(2):481-492
Let R be a prime ring of characteristic different from 2 and 3, Qr its right Martindale quotient ring, C its extended centroid, L a non-central Lie ideal of R and n ≥ 1 a fixed positive integer. Let α be an automorphism of the ring R. An additive map D: R → R is called an α-derivation (or a skew derivation) on R if D(xy) = D(x)y + α(x)D(y) for all x, y ∈ R. An additive mapping F: R → R is called a generalized α-derivation (or a generalized skew derivation) on R if there exists a skew derivation D on R such that F(xy) = F(x)y + α(x)D(y) for all x, y ∈ R. 相似文献
20.
A classical result of Herstein asserts that any Jordan derivation on a prime ring with char(R) ≠ 2 is a derivation. It is our aim in this paper to prove the following result, which is in the spirit of Herstein’s theorem. Let R be a prime ring with char(R) = 0 or char(R) > 4, and let D: R → R be an additive mapping satisfying the relation D(x4) = D(x)x3 + xD(x2)x + x3D(x) for all x ∈ R. In this case, D is a derivation. 相似文献