The paper introduces a smoothing method to the lower order penalty function for constrained optimization problems. It is shown that, under some mild conditions, an optimal solution of the smoothed penalty problem is an approximate optimal solution of the original problem. Based on the smoothed penalty function, an algorithm is presented and its convergence is proved under some mild assumptions....

The scalar and vector Laplacians are basic operators in physics and engineering. In applications, they frequently show up perturbed by lowerorder terms. The effect of such perturbations on mixed finite element methods in the scalar case is well understood, but that in the vector case is not. In this paper, we first show that, surprisingly, for certain elements there is degradation of the conver...

Let q ∈ (1, 2); it is known that each x ∈ [0, 1/(q− 1)] has an expansion of the form x = ∑ ∞ n=1 anq −n with an ∈ {0, 1}. It was shown in [3] that if q < ( √ 5 + 1)/2, then each x ∈ (0, 1/(q − 1)) has a continuum of such expansions; however, if q > ( √ 5 + 1)/2, then there exist infinitely many x having a unique expansion [4]. In the present paper we begin the study of parameters q for which th...

for each a" . Assume also that u"W 2p loc( ) satisfies j 4 uj 6 Ajuj+Bj 5 uj: (1.3) Then if u vanishes on an open set it vanishes identically. Here W 2p is the Sobolev space, i.e., functions whose second derivatives are in L. Our proof will show (see the remark at the end of Section 2) that p can be taken ? The first author is supported in part by NSF Grant #DMS93-15963. The second author is su...

Robust time delay estimation is necessary for many microphone array applications. Reverberant echoes and background noise can corrupt the estimates. Typically the signals and noise are modeled as Gaussian random processes and second moment information is used for time delay estimation. However, many signals are impulsive and should be modeledusing alpha-stable distributions. Because ofthis impu...

In this paper, we propose to use a class of filters based on fractional lower order statistics (FLOS) for still image restoration in the presence of α-stable noise. For this purpose, we present a family of 2-D finite-impulse response (FIR) adaptive filters optimized by the least mean lp-norm (LMP) algorithm. Experiments performed on natural images prove that the proposed algorithms provide supe...

Properties of convex and monotone capacities of infinite order in Polish spaces are studied and used to justify the representation of certain situations of imprecise risk (imprecisely known probabilities) by lower probabilities, which are monotone of infinite order. Decision making with imprecise risk is then modeled, and linear utility theory is shown to be generalizable to the case of impreci...

In this article, we derive an asymptotic formula for the second moment of S(t) which includes the lower order terms using a prediction from the ratios conjecture of Conrey, Farmer and Zirnbauer. The formula matches very well with actual values of the second moment.

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We prove that if a nite lattice L has order dimension at most d, then the homology of the order complex of its proper part L vanishes in dimensions d ? 1 and higher. In case L can be embedded as a join-sublattice in N d then L actually has the homotopy type of a simplicial complex with d vertices. 1. Introduction. The order dimension OrderDim(P) of a nite partially ordered set (poset for short)...