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1.
傅里叶变换与小波分析   总被引:1,自引:0,他引:1  
正1小波分析的发展历史1807年,法国的热学工程师J.B.J.Fourier提出任一函数都能展开成三角函数的无穷级数,从而开启了主要研究函数的傅里叶变换及其性质的傅里叶分析理论。1909年,Haar提出了第一个最简单的小波(Haar小波)。在1974年,法国从事石油信号处理的工程师J.Morlet首先提出小波变换的概念,且根据物理和信号处理的实际经验的需要建立了反演公式,但当时这一公式未能得到数学家的认可。直到1986年,著名数学家Y.Meyer偶然构造出一个真正的小波基,并与S.Mallat合作建立了构造小  相似文献
2.
This paper is concerned in the option pricing in a discrete time incomplete market. We emphasize the interplay between option pricing and residual risk as well as imperfect hedging. It has been shown that the value of a European option satisfies a hyperbolic, rather than parabolic, partial differential equation. The closed-form solution for this hyperbolic equation has been obtained, which will collapse to the Black–Scholes formula as the time scaling converges to zero.  相似文献
3.
We introduce the notions of a band category and of a weakly orthodox category over a band. Our focus is to describe a class of weakly $B$ -orthodox semigroups, where $B$ denotes a band of idempotents. In particular, we investigate orthodox semigroups, by using orthodox groupoids. Weakly $B$ -orthodox semigroups are analogues of orthodox semigroups, where the relations $\widetilde{\mathcal {R}}_B$ and $\widetilde{\mathcal {L}}_B$ play the role that ${\mathcal {R}}$ and $\mathcal {L}$ take in the regular case. We show that the category of weakly $B$ -orthodox semigroups and admissible morphisms is equivalent to the category of weakly orthodox categories over bands and orthodox functors. The same class of weakly $B$ -orthodox semigroups was studied in an earlier article by Gould and the author using generalised categories. Our approach here is more akin to that of Nambooripad. The significant difference in strategy is that it is more convenient to consider categories equipped with pre-orders, rather than with partial orders.  相似文献
4.
An orthogroup is a completely regular orthodox semigroup. The main purpose of this paper is to find a representation of a (generalised) orthogroup with band of idempotents B in terms of a fundamental (generalised) orthogroup. The latter is a subsemigroup of the Hall semigroup W B (or of its generalisations V B ,U B and S B ). We proceed in the regular case by constructing a fundamental completely regular subsemigroup \(\overline{W_{B}}\) of W B , using two different methods. Our subsemigroup plays the role for orthogroups that W B plays for orthodox semigroups, in that it contains a representation of every orthogroup with band of idempotents B, with kernel of the representation being μ, the greatest congruence contained in \(\mathcal{H}\) . To develop an analogous theory for classes of generalised orthogroups, that is, to extend beyond the regular case, we replace \(\mathcal{H}\) by \(\widetilde{\mathcal{H}}_{B}\) . Generalised orthogroups are then classes of weakly B-superabundant semigroups with (C). We first consider those satisfying an idempotent connected condition (IC) or (WIC). We construct fundamental weakly B-superabundant subsemigroups \(\overline{V_{B}}\) (respectively, \(\overline{U_{B}}\) ) of V B (respectively, U B ) with (C) and (IC) (respectively, with (C) and (WIC)) such that any weakly B-superabundant semigroup with (C) and (IC) (respectively, with (C) and (WIC)) admits a representation to \(\overline{V_{B}}\) (respectively, \(\overline{U_{B}}\) ), with kernel of the respresentation being μ B , the greatest congruence contained in \(\widetilde{\mathcal{H}}_{B}\) . Finally, we remove the idempotent connected condition and find a representation for an arbitrary weakly B-superabundant semigroup with (C), making use of fresh technology, constructing a fundamental weakly B-superabundant subsemigroup \(\overline{S_{B}}\) of S B , with the appropriate universal properties. We note that our results are needed in a parallel paper to complete the representation of arbitrary weakly B-superabundant semigroups with (C) as spined products of superabundant Ehresmann semigroups and subsemigroups of S B .  相似文献
5.
This paper is concerned with solutions to the so-called coupled Sylvester-transpose matrix equations, which include the generalized Sylvester matrix equation and Lyapunov matrix equation as special cases. By extending the idea of conjugate gradient method, an iterative algorithm is constructed to solve this kind of coupled matrix equations. When the considered matrix equations are consistent, for any initial matrix group, a solution group can be obtained within finite iteration steps in the absence of roundoff errors. The least Frobenius norm solution group of the coupled Sylvester-transpose matrix equations can be derived when a suitable initial matrix group is chosen. By applying the proposed algorithm, the optimal approximation solution group to a given matrix group can be obtained by finding the least Frobenius norm solution group of new general coupled matrix equations. Finally, a numerical example is given to illustrate that the algorithm is effective.  相似文献
6.
Using the cone theory and the lattice structure, we establish some methods of computation of the topological degree for the nonlinear operators which are not assumed to be cone mappings. As applications, existence results of nontrivial solutions for singular Sturm-Liouville problems are given. The nonlinearity in the equations can take negative values and may be unbounded from below.  相似文献
7.
In this paper, an infinite horizon $H_2/H_\infty $ control problem is addressed for a broad class of discrete-time Markov jump systems with ( $x,u,v$ )-dependent noises. First of all, under the condition of exact detectability, the stochastic Popov–Belevich–Hautus (PBH) criterion is utilized to establish an extended Lyapunov theorem for a generalized Lyapunov equation. Further, a necessary and sufficient condition is presented for the existence of state-feedback $H_2/H_\infty $ optimal controller on the basis of two coupled matrix Riccati equations, which may be solved by a backward iterative algorithm. A numerical example with simulations is supplied to illustrate the proposed theoretical results.  相似文献
8.
In this paper, some solution expressions to the quaternion matrix equation X?AXF=BY are obtained. They are the further conclusions of the paper (Song et al. in Int. J. Comput. Math. 89:890–900, 2012). By applying of Kronecker map and complex representation of a quaternion matrix, the sufficient conditions for finding the solution have been established. At the end of the article, numerical examples show the applications of the proposed explicit solution.  相似文献
9.
In this paper, we introduce a new class of smoothing functions, which include some popular smoothing complementarity functions. We show that the new smoothing functions possess a system of favorite properties. The existence and continuity of a smooth path for solving the nonlinear complementarity problem (NCP) with a P 0 function are discussed. The Jacobian consistency of this class of smoothing functions is analyzed. Based on the new smoothing functions, we investigate a smoothing Newton algorithm for the NCP and discuss its global and local superlinear convergence. Some preliminary numerical results are reported.  相似文献
10.
In this paper a log-exponential smoothing method for mathematical programs with complementarity constraints (MPCC) is analyzed, with some new interesting properties and convergence results provided. It is shown that the stationary points of the resulting smoothed problem converge to the strongly stationary point of MPCC, under the linear independence constraint qualification (LICQ), the weak second-order necessary condition (WSONC), and some reasonable assumption. Moreover, the limit point satisfies the weak second-order necessary condition for MPCC. A notable fact is that the proposed convergence results do not restrict the complementarity constraint functions approach to zero at the same order of magnitude.  相似文献
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