共查询到20条相似文献,搜索用时 546 毫秒
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Let K be a closed convex subset of a q-uniformly smooth separable Banach space, T:K→K a strictly pseudocontractive mapping, and f:K→K an L-Lispschitzian strongly pseudocontractive mapping. For any t∈(0,1), let xt be the unique fixed point of tf+(1-t)T. We prove that if T has a fixed point, then {xt} converges to a fixed point of T as t approaches to 0. 相似文献
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Let k be any field, G be a finite group acting on the rational function field k(xg:g∈G) by h⋅xg=xhg for any h,g∈G. Define k(G)=k(xg:g∈G)G. Noether’s problem asks whether k(G) is rational (= purely transcendental) over k. A weaker notion, retract rationality introduced by Saltman, is also very useful for the study of Noether’s problem. We prove that, if G is a Frobenius group with abelian Frobenius kernel, then k(G) is retract k-rational for any field k satisfying some mild conditions. As an application, we show that, for any algebraic number field k, for any Frobenius group G with Frobenius complement isomorphic to SL2(F5), there is a Galois extension field K over k whose Galois group is isomorphic to G, i.e. the inverse Galois problem is valid for the pair (G,k). The same result is true for any non-solvable Frobenius group if k(ζ8) is a cyclic extension of k. 相似文献
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In this paper, we study the regularity of generalized solutions u(x,t) for the n -dimensional quasi-linear parabolic diffraction problem. By using various estimates and Steklov average methods, we prove that (1): for almost all t the first derivatives ux(x,t) are Hölder continuous with respect to x up to the inner boundary, on which the coefficients of the equation are allowed to be discontinuous; and (2): the first derivative ut(x,t) is Hölder continuous with respect to (x,t) across the inner boundary. 相似文献
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For a linear equation x′=A(t)x, we show that the asymptotic behavior of its solutions is reproduced by the solutions of the nonlinear equation x′=A(t)x+f(t,x) for any sufficiently small perturbation f. More precisely, we show that if the Lyapunov exponents of the linear equation are limits, even for general exponential rates ecρ(t) for an arbitrary function ρ, then the same happens with the Lyapunov exponents of the solutions of the nonlinear equations, without introducing new values. Our approach is based on Lyapunov’s theory of regularity. 相似文献
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Let R be a commutative ring with identity. We will say that an R-module M satisfies the weak Nakayama property, if IM=M, where I is an ideal of R, implies that for any x∈M there exists a∈I such that (a−1)x=0. In this paper, we will study modules satisfying the weak Nakayama property. It is proved that if R is a local ring, then R is a Max ring if and only if J(R), the Jacobson radical of R, is T-nilpotent if and only if every R-module satisfies the weak Nakayama property. 相似文献
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A class of second-order abstract dissipative evolution differential operators D with 0∈kerD is shown for which the fact that a non-zero t?u(t) belongs to a cone and −Du to a dual cone may hold only on time intervals whose length is less than or equal to a defined number. Then oscillatory functions are dealt with in the framework of Banach spaces with a cone and conditions for the existence of a uniform oscillatory time for solutions of the equation Du=0 are given. 相似文献
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In this paper, we prove a comparison result between a solution u(x,t), x∈Ω⊂R2, t∈(0,T), of a time depending equation involving the Monge–Ampère operator in the plane and the solution of a conveniently symmetrized parabolic equation. To this aim, we prove a derivation formula for the integral of a smooth function g(x,t) over sublevel sets of u, {x∈Ω:u(x,t)<?}, ?∈R, having the same perimeter in R2. 相似文献
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This paper investigates the solvability of discrete Dirichlet boundary value problems by the lower and upper solution method. Here, the second-order difference equation with a nonlinear right hand side f is studied and f(t,u,v) can have a superlinear growth both in u and in v. Moreover, the growth conditions on f are one-sided. We compute a priori bounds on solutions to the discrete problem and then obtain the existence of at least one solution. It is shown that solutions of the discrete problem will converge to solutions of ordinary differential equations. 相似文献
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Michel Mandjes Petteri Mannersalo Ilkka Norros Miranda van Uitert 《Stochastic Processes and their Applications》2006
Consider events of the form {Zs≥ζ(s),s∈S}, where Z is a continuous Gaussian process with stationary increments, ζ is a function that belongs to the reproducing kernel Hilbert space R of process Z, and S⊂R is compact. The main problem considered in this paper is identifying the function β∗∈R satisfying β∗(s)≥ζ(s) on S and having minimal R-norm. The smoothness (mean square differentiability) of Z turns out to have a crucial impact on the structure of the solution. As examples, we obtain the explicit solutions when ζ(s)=s for s∈[0,1] and Z is either a fractional Brownian motion or an integrated Ornstein–Uhlenbeck process. 相似文献
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We study the nonlinear boundary value problem consisting of the equation −y″+q(t)y=w(t)f(y) on [a,b] and a general separated homogeneous linear boundary condition. By comparing this problem with a corresponding linear Sturm–Liouville problem we obtain conditions for the existence and nonexistence of solutions of this problem. More specifically, let λn,n=0,1,2,…, be the n-th eigenvalues of the corresponding linear Sturm–Liouville problem. Then under certain assumptions, the boundary value problem has a solution with exactly n zeros in (a,b) if λn is in the interior of the range of f(y)/y,y∈(0,∞); and does not have any solution with exactly n zeros in (a,b) if λn is outside of the range of f(y)/y,y∈(0,∞). These conditions become necessary and sufficient when f(y)/y is monotone. The existences of multiple and even an infinite number of solutions are derived as consequences. We also discuss the changes of the number and the types of nontrivial solutions as the interval [a,b] shrinks, as q increases in a given direction, and as the boundary condition changes. 相似文献
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Given a point A in the real Grassmannian, it is well-known that one can construct a soliton solution uA(x,y,t) to the KP equation. The contour plot of such a solution provides a tropical approximation to the solution when the variables x, y, and t are considered on a large scale and the time t is fixed. In this paper we use several decompositions of the Grassmannian in order to gain an understanding of the contour plots of the corresponding soliton solutions. First we use the positroid stratification of the real Grassmannian in order to characterize the unbounded line-solitons in the contour plots at y?0 and y?0. Next we use the Deodhar decomposition of the Grassmannian–a refinement of the positroid stratification–to study contour plots at t?0. More specifically, we index the components of the Deodhar decomposition of the Grassmannian by certain tableaux which we call Go-diagrams , and then use these Go-diagrams to characterize the contour plots of solitons solutions when t?0. Finally we use these results to show that a soliton solution uA(x,y,t) is regular for all times t if and only if A comes from the totally non-negative part of the Grassmannian. 相似文献
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For α∈R, let pR(t,x,x) denote the diagonal of the transition density of the α-Bessel process in (0,1], killed at 0 and reflected at 1. As a function of x, if either α≥3 or α=1, then for t>0, the diagonal is nondecreasing. This monotonicity property fails if 1≠α<3. 相似文献
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The function Q(x):=∑n≥1(1/n)sin(x/n) was introduced by Hardy and Littlewood (1936) [5] in their study of Lambert summability, and since then it has attracted attention of many researchers. In particular, this function has made a surprising appearance in the recent disproof by Alzer, Berg and Koumandos (2005) [3] of a conjecture by Clark and Ismail (2003) [14]. More precisely, Alzer et al. have shown that the Clark and Ismail conjecture is true if and only if Q(x)≥−π/2 for all x>0. It is known that Q(x) is unbounded in the domain x∈(0,∞) from above and below, which disproves the Clark and Ismail conjecture, and at the same time raises a natural question of whether we can exhibit at least one point x for which Q(x)<−π/2. This turns out to be a surprisingly hard problem, which leads to an interesting and non-trivial question of how to approximate Q(x) for very large values of x. In this paper we continue the work started by Gautschi (2005) in [4] and develop several approximations to Q(x) for large values of x. We use these approximations to find an explicit value of x for which Q(x)<−π/2. 相似文献
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In this paper we present an extension of the removal lemma to integer linear systems over abelian groups. We prove that, if the k-determinantal of an integer (k×m) matrix A is coprime with the order n of a group G and the number of solutions of the system Ax=b with x1∈X1,…,xm∈Xm is o(nm−k), then we can eliminate o(n) elements in each set to remove all these solutions. 相似文献
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We derive a Molchan–Golosov-type integral transform which changes fractional Brownian motion of arbitrary Hurst index K into fractional Brownian motion of index H. Integration is carried out over [0,t], t>0. The formula is derived in the time domain. Based on this transform, we construct a prelimit which converges in L2(P)-sense to an analogous, already known Mandelbrot–Van Ness-type integral transform, where integration is over (−∞,t], t>0. 相似文献
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Let x(s), s∈Rd be a Gaussian self-similar random process of index H. We consider the problem of log-asymptotics for the probability pT that x(s), x(0)=0 does not exceed a fixed level in a star-shaped expanding domain T⋅Δ as T→∞. We solve the problem of the existence of the limit, θ?lim(−logpT)/(logT)D, T→∞, for the fractional Brownian sheet x(s), s∈[0,T]2 when D=2, and we estimate θ for the integrated fractional Brownian motion when D=1. 相似文献