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1.
Existence of solutions for lower semicontinuous quasi-equilibrium problems   总被引:7,自引:0,他引:7  
In this paper, we deal with the following quasi-equilibrium problem: given a nonempty subset C of a topological vector space X, a nonempty set D, two functions T : CD, f : X × DR and a multifunction S : C → 2X, find such that , and for all . Such a problem, recently introduced in [1], extends and unifies several variational inequality problems, generalized complementarity problems and Nash equilibrium problems. We prove several existence results in which the upper semicontinuity of the multifunction S is not assumed.  相似文献   

2.
In finite element analysis, isoparametric mapping defined as [(ξ, η) → (x, y): X = Niξi] is widely used. It is a one-to-one mapping and its construction is especially elegant for elements of a variable number of nodes showing its versatile applicability to model curved boundaries. In certain analyses, such as remeshing in dynamic analyses or contouring and others, the inverse of this mapping is inevitably valuable, but its determination is not so straightforward. To avoid solving a system of nonlinear equations, generally an iterative technique of order N2 in a two-dimensional mesh is often resorted to. In the paper, this technique is improved by systematically bisecting along a predefined line that reduces the iterations to only order N. Its applications in remeshing and nodal quantity contouring are demonstrated and a possible extension for stress contouring is also discussed. The FORTRAN subroutines for the technique proposed are also given.  相似文献   

3.
A previous application of the Newton divided difference series of the displacement function Ez = (1 + Δ)z = e Dz, where the operators Δ and D are the variables, to purely exponential interpolation employing general-factorial differences and derivatives, {Pi;mi=0 (Δ - Si)}f(0) and {Pi;mi=0 (D - ti)}f(0), in which the si's and ti's are distinct[1], is here extended to mixed polynomial-exponential interpolation where the si's and ti's are no longer distinct.  相似文献   

4.
In this paper, we obtain some new sufficient conditions for the existence of nontrivial m-periodic solutions of the following nonlinear difference equation
by using the critical point method, where f: Z × R → R is continuous in the second variable, m ≥ 2 is a given positive integer, pn+m = pn for any n  Z and f(t + m, z) = f(t, z) for any (t, z)  Z × R, (−1)δ = −1 and δ > 0.  相似文献   

5.
The aim of this paper is double. First, we point out that the hypothesis D(t1)D(t2) = D(t2)D(t1) imposed in [1] can be removed. Second, a constructive method for obtaining analytic-numerical solutions with a prefixed accuracy in a bounded domain Ω(t0,t1) = [0,p] × [t0,t1], for mixed problems of the type ut(x,t) − D(t)uxx(x,t) = 0, 0 < x < p, t> 0, subject to u(0,t) = u(p,t) = 0 and u(x,0) = F(x) is proposed. Here, u(x,t) and F(x) are r-component vectors, D(t) is a Cr × r valued analytic function and there exists a positive number δ such that every eigenvalue z of (1/2) (D(t) + D(t)H) is bigger than δ. An illustrative example is included.  相似文献   

6.
Some results of fuzzy BCK-filters   总被引:6,自引:0,他引:6  
Let X be a bounded BCK-algebra and f a fuzzy set in X. If a fuzzy BCK-filter μ in X satisfies that (i) fμ, (ii) for any fuzzy BCK-filter ν in X, fν implies μν, then μ is said to be generated by f and denote μ by [f) for short. In the present paper, we give a procedure to construct the [f) by f. As applications of this result we prove that the set of all fuzzy BCK-filters in a bounded BCK-algebra forms a complete and infinitely distributive lattice.  相似文献   

7.
For arbitrary equally sized square complex matrices A and Q (Q Hermitian), the paper provides a complete algebraic test for verifying the existence of a Hermitian solution X of the nonstrict Lyapunov inequality A*X + XA + Q 0. If existing, we exhibit how to construct a solution. Our approach involves the validation problem for the linear matrix inequality Σj=1k (Aj*XjBj + Bj*Xj*Aj) + Q> 0 in Xj, for which we provide an algebraic solvability test and a construct solutions if the kernels of Aj or, dually, those of Bj form an isotonic sequence.  相似文献   

8.
This paper describes some new techniques for the rapid evaluation and fitting of radial basic functions. The techniques are based on the hierarchical and multipole expansions recently introduced by several authors for the calculation of many-body potentials. Consider in particular the N term thin-plate spline, s(x) = Σj=1N djφ(xxj), where φ(u) = |u|2log|u|, in 2-dimensions. The direct evaluation of s at a single extra point requires an extra O(N) operations. This paper shows that, with judicious use of series expansions, the incremental cost of evaluating s(x) to within precision ε, can be cut to O(1+|log ε|) operations. In particular, if A is the interpolation matrix, ai,j = φ(xixj, the technique allows computation of the matrix-vector product Ad in O(N), rather than the previously required O(N2) operations, and using only O(N) storage. Fast, storage-efficient, computation of this matrix-vector product makes pre-conditioned conjugate-gradient methods very attractive as solvers of the interpolation equations, Ad = y, when N is large.  相似文献   

9.
We formulate a class of difference schemes for stiff initial-value problems, with a small parameter ε multiplying the first derivative. We derive necessary conditions for uniform convergence with respect to the small parameter ε, that is the solution of the difference scheme uih satisfies |uihu(xi)| Ch, where C is independent of h and ε. We also derive sufficient conditions for uniform convergence and show that a subclass of schemes is also optimal in the sense that |uihu(xi)| C min (h, ε). Finally, we show that this class contains higher-order schemes.  相似文献   

10.
Let ( ,(+1)n) be the adic system associated to the substitution: 1 → 12,…,(n − 1) → 1n, n → 1. In Sirvent (1996) it was shown that there exist a subset Cn of and a map hn: CCn such that the dynamical system (C, hn) is semiconjugate to ( ). In this paper we compute the Hausdorff and Billingsley dimensions of the geometrical realizations of the set Cn on the (nl)-dimensional torus. We also show that the dynamical system (Cn,hn) cannot be realized on the (n − 1)-torus.  相似文献   

11.
Richard   《Neurocomputing》2008,71(7-9):1477-1499
Generalization, in its most basic form, is an artificial neural network's (ANN's) ability to automatically classify data that were not seen during training. This paper presents a framework in which generalization in ANNs is quantified and different types of generalization are viewed as orders. The ordering of generalization is a means of categorizing different behaviours. These orders enable generalization to be evaluated in a detailed and systematic way. The approach used is based on existing definitions which are augmented in this paper. The generalization framework is a hierarchy of categories which directly aligns an ANN's ability to perform table look-up, interpolation, extrapolation, and hyper-extrapolation tasks.

The framework is empirically validated. Validation is undertaken with three different types of regression task: (1) a one-to-one (o–o) task, f(x):xiyj; (2) the second, in its f(x):{xi,xi+1, …}→yj formulation, maps a many-to-one (m–o) task; and (3) the third f(x):xi→{yj,yj+1, …} a one-to-many (o–m) task. The first and second are assigned to feedforward nets, while the third, due to its complexity, is assigned to a recurrent neural net.

Throughout the empirical work, higher-order generalization is validated with reference to the ability of a net to perform symmetrically related or isomorphic functions generated using symmetric transformations (STs) of a net's weights. The transformed weights of a base net (BN) are inherited by a derived net (DN). The inheritance is viewed as the reuse of information. The overall framework is also considered in the light of alignment to neural models; for example, which order (or level) of generalization can be performed by which specific type of neuron model.

The complete framework may not be applicable to all neural models; in fact, some orders may be special cases which apply only to specific neuron models. This is, indeed, shown to be the case. Lower-order generalization is viewed as a general case and is applicable to all neuron models, whereas higher-order generalization is a particular or special case. This paper focuses on initial results; some of the aims have been demonstrated and amplified through the experimental work.  相似文献   


12.
Let X1,…, Xr+1 be independent random variables, XiGa (ai, θ, δi), i = 1,…, r + 1. Define and Vi = Xi/Xr+1, i = 1,…, r. Then, (U1,…, Ur) and (V1,…, Vr) follow noncentral Dirichlet Type 1 and Type 2 distributions, respectively. In this article several properties of these distributions and their connections with the uniform, the noncentral multivariate-F and the noncentral multivariate-t distributions are discussed.  相似文献   

13.
A subdivision scheme for constructing smooth surfaces interpolating scattered data in R3 is proposed. It is also possible to impose derivative constraints in these points. In the case of functional data, i.e., data are given in a properly triangulated set of points {(xi, yi)}i=1N from which none of the pairs (xi,yi) and (xj,yj) with ij coincide, it is proved that the resulting surface (function) is C1. The method is based on the construction of a sequence of continuous splines of degree 3. Another subdivision method, based on constructing a sequence of splines of degree 5 which are once differentiable, yields a function which is C2 if the data are not ‘too irregular’. Finally the approximation properties of the methods are investigated.  相似文献   

14.
We derive asymptotic approximations for the sequence f(n) defined recursively by f(n)=min1j<n {f(j)+f(nj)}+g(n), when the asymptotic behavior of g(n) is known. Our tools are general enough and applicable to another sequence F(n)=max1j<n {F(j)+F(nj)+min{g(j),g(nj)}}, also frequently encountered in divide-and-conquer problems. Applications of our results to algorithms, group testing, dichotomous search, etc. are discussed.  相似文献   

15.
We call a function f in n variables an order-configuration function if for any x1,…, xn such that xi1xin we have f(x1,…, xn) = xt, where t is determined by the n-tuple (i1,…, in) corresponding to that ordering. Equivalently, it is a function built as a minimum of maxima, or a maximum of minima. Well-known examples are the minimum, the maximum, the median, and more generally rank functions, or the composition of rank functions. Such types of functions are often used in nonlinear processing of digital signals or images (for example in the median or separable median filter, min-max filters, rank filters, etc.). In this paper we study the mathematical properties of order-configuration functions and of a wider class of functions that we call order-subconfiguration functions. We give several characterization theorems for them. We show through various examples how our concepts can be used in the design of digital signal filters or image transformations based on order-configuration functions.  相似文献   

16.
The evolution of the gingerbread man   总被引:3,自引:0,他引:3  
Two versions of the evolution of the Gingerbread Man for the iteration zzx + c are presented. A previously published version shows an asymmetric evolution as positive real x increases, while a new version shows a symmetric evolution, and several interesting features. Fractal “growth” is described that occurs along certain “shock” lines with this new evolution. A floating “object” appears while approaching certain positive even integer values of x. Finally, a few comments are made about images created from negative values of x.  相似文献   

17.
The iterative map xn+1 = rnxn (1 - xn) is investigated with rn changing periodically between two values A and B. Different periodicities are assumed, e.g., {rn} = {BABA …} or {rn} = {BBABA BBABA …}. The Lyapunov exponent (a measure of average stability) is displayed with high resolution on the A-B-plane. The resulting images have aesthetically appealing self-similar structures. Furthermore, these images allow with one glimpse the identification of a number of system properties: coexistence of attractors, superstable curves, order by alternation of chaotic processes, and chaos by periodic resetting from a stable into an unstable fixed point.  相似文献   

18.
It is pointed out in this brief paper that the l1 optimization problem minQ ε lqp1 | HU * Q * V |1, H ε lmn1, U ε lmq1, V ε lpn1 can be solved in one step rather than two. The solution of the dual problem is obviated by the direct solution of the primal problem via linear programming. The method here is applicable to finite-dimensional problems or approximating finite-dimensional problems, in the general case.  相似文献   

19.
The paper presents sufficient conditions for the existence of positive solutions of the equation x″(t) + q(t)f(t,x(t),x′(t)) = 0 with the Dirichlet conditions x(0) = 0, x(1) = 0 and of the equation (p(t)x′(t))′ + p(t)q(t)f(t,x(t),p(t)x′(t)) = 0 with the boundary conditions limto+ p(t)x′(t) = 0, x(1) = 0. Our nonlinearity f is allowed to change sign and f may be singular at x = 0. The proofs are based on a combination of the regularity and sequential techniques and the method of lower and upper functions.  相似文献   

20.
This paper presents a sum-of-product neural network (SOPNN) structure. The SOPNN can learn to implement static mapping that multilayer neural networks and radial basis function networks normally perform. The output of the neural network has the sum-of-product form ∑Npi=1Nvj=1 fij (xj), where xj's are inputs, Nv is the number of inputs, fij( ) is a function generated through network training, and Np is the number of product terms. The function fij(xj) can be expressed as ∑kwijkBjk(xj), where Bjk( ) is a single-variable basis function and Wijk's are weight values. Linear memory arrays can be used to store the weights. If Bjk( ) is a Gaussian function, the new neural network degenerates to a Gaussian function network. This paper focuses on the use of overlapped rectangular pulses as the basis functions. With such basis functions, WijkBjk(xj) will equal either zero or Wijk, and the computation of fij(xj) becomes a simple addition of some retrieved Wijk's. The structure can be viewed as a basis function network with a flexible form for the basis functions. Learning can start with a small set of submodules and have new submodules added when it becomes necessary. The new neural network structure demonstrates excellent learning convergence characteristics and requires small memory space. It has merits over multilayer neural networks, radial basis function networks and CMAC in function approximation and mapping in high-dimensional input space. The technique has been tested for function approximation, prediction of a time series, learning control, and classification.  相似文献   

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