In the present paper, we study the initial inverse problem (backward problem) for a two-dimensional fractional differential equation with Riemann-Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well-posed in the sense of Hadamard. A truncated method is used to construct an approximate function for the solution (called the regularized solution). Furthermore, the error estimate of the regularized solution in L2 and Hτ norms is considered and illustrated by numerical example. 相似文献
Let the mod 2 Steenrod algebra, , and the general linear group, , act on with in the usual manner. We prove the conjecture of the first-named author in Spherical classes and the algebraic transfer, (Trans. Amer. Math Soc. 349 (1997), 3893-3910) stating that every element of positive degree in the Dickson algebra is -decomposable in for arbitrary 2$">. This conjecture was shown to be equivalent to a weak algebraic version of the classical conjecture on spherical classes, which states that the only spherical classes in are the elements of Hopf invariant one and those of Kervaire invariant one.
In this paper, we give an affirmative answer to the problem posed by S. Lin (2002, 2007) in [7] and [8], and give another answer to the question posed by Y. Ikeda, C. Liu and Y. Tanaka (2002) in [5]. 相似文献
Motivated by the idea of imposing paralleling computing on solving stochastic differential equations (SDEs), we introduce a new domain decomposition scheme to solve forward–backward stochastic differential equations (FBSDEs) parallel. We reconstruct the four step scheme in Ma et al. (1994) [1] and then associate it with the idea of domain decomposition methods. We also introduce a new technique to prove the convergence of domain decomposition methods for systems of quasilinear parabolic equations and use it to prove the convergence of our scheme for the FBSDEs. 相似文献
We consider the exterior Neumann problem of the Laplacian with boundary condition on a prolate spheroid. We propose to use spherical radial basis functions in the solution of the boundary integral equation arising from the Dirichlet–to–Neumann map. Our approach is particularly suitable for handling of scattered data, e.g. satellite data. We also propose a preconditioning technique based on domain decomposition method to deal with ill-conditioned matrices arising from the approximation problem. 相似文献
Journal of Optimization Theory and Applications - In the previous paper Bello-Cruz et al. (J Optim Theory Appl 188:378–401, 2021), we showed that the quadratic growth condition plays a key... 相似文献
In this paper, we establish some quotient calculus rules in terms of contingent derivatives for the two extended-real-valued functions defined on a Banach space and study a nonsmooth multiobjective fractional programming problem with set, generalized inequality and equality constraints. We define a new parametric problem associated with these problem and introduce some concepts for the (local) weak minimizers to such problems. Some primal and dual necessary optimality conditions in terms of contingent derivatives for the local weak minimizers are provided. Under suitable assumptions, sufficient optimality conditions for the local weak minimizers which are very close to necessary optimality conditions are obtained. An application of the result for establishing three parametric, Mond–Weir and Wolfe dual problems and several various duality theorems for the same is presented. Some examples are also given for our findings.
This paper concerns methods by which a trusted authority can distribute keys and/or broadcast a message over a network, so that each member of a privileged subset of users can compute a specified key or decrypt the broadcast message. Moreover, this is done in such a way that no coalition is able to recover any information on a key or broadcast message they are not supposed to know. The problems are studied using the tools of information theory, so the security provided is unconditional (i.e., not based on any computational assumption).In a recent paper st95a, Stinson described a method of constructing key predistribution schemes by combining Mitchell-Piper key distribution patterns with resilient functions; and also presented a construction method for broadcast encryption schemes that combines Fiat-Naor key predistribution schemes with ideal secret sharing schemes. In this paper, we further pursue these two themes, providing several nice applications of these techniques by using combinatorial structures such as orthogonal arrays, perpendicular arrays, Steiner systems and universal hash families. 相似文献
Two methods of fluid–structure coupling for turbomachinery are presented, the first one in the frequency domain and the second in both frequency and time domains. In both methods, the structure and the fluid are assumed to have circumferential cyclic symmetric properties and the unsteady aerodynamic forces are assumed to be linear in terms of the structural displacements. The motion equation of the reference sector in the travelling wave coordinates is projected on the complex eigenmodes for each phase number. The generalized unsteady aerodynamic forces are computed by solving the Euler equations and by assuming the structural motion to be harmonic with a constant phase angle between two adjacent sectors. In the frequency domain, the complex, nonlinear eigenvalue problem for the aeroelastic stability analysis is solved iteratively either by the double scanning method or by using Karpel's minimum state smoothing of the aerodynamic coefficient matrix. In the time domain, Karpel's smoothing method is used to obtain an approximation of the generalized unsteady aerodynamic forces by means of auxiliary state variables. These coupling methods are tested on a compressor blade row and the good agreement obtained between their results and those of the direct coupling method shows that the proposed numerical methods, already used in aircraft applications, are adapted to turbomachinery. 相似文献