Colength,multiplicity, and ideal closure operations

Abstract

In a formally unmixed Noetherian local ring, if the colength and multiplicity of an integrally closed ideal agree, then R is regular. We deduce this using the relationship between multiplicity and various ideal closure operations.     

Determination of the body force of a two-dimensional isotropic elastic body

Let Ω$\Omega$ represent a two-dimensional isotropic elastic body. We consider the problem of determining the body force F$F$ whose form φ(t)(_f1(x),_f2(x))$\phi \left(t\right)(f_1\left(x\right),f_2\left(x\right))$ with φ$\phi$ be given inexactly. The problem is nonlinear and ill-posed. Using the Fourier transform, the methods of Tikhonov’s regularization and truncated integration, we construct a regularized solution from the data given inexactly and explicitly derive the error estimate.     

Generalizations of vector quasivariational inclusion problems with set-valued maps

Existence theorems are given for the problem of finding a point (z ₀,x ₀) of a set E × K such that and, for all where α is a relation on 2 ^Y (i.e., a subset of 2 ^Y  × 2 ^Y ), and are some set-valued maps, and Y is a topological vector space. Detailed discussions are devoted to special cases of α and C which correspond to several generalized vector quasi-equilibrium problems with set-valued maps. In such special cases, existence theorems are obtained with or without pseudomonotonicity assumptions.     

A primal-dual active-set algorithm for bilaterally constrained total variation deblurring and piecewise constant Mumford-Shah segmentation problems

In this paper, we propose a fast primal-dual algorithm for solving bilaterally constrained total variation minimization problems which subsume the bilaterally constrained total variation image deblurring model and the two-phase piecewise constant Mumford-Shah image segmentation model. The presence of the bilateral constraints makes the optimality conditions of the primal-dual problem semi-smooth which can be solved by a semi-smooth Newton’s method superlinearly. But the linear system to solve at each iteration is very large and difficult to precondition. Using a primal-dual active-set strategy, we reduce the linear system to a much smaller and better structured one so that it can be solved efficiently by conjugate gradient with an approximate inverse preconditioner. Locally superlinear convergence results are derived for the proposed algorithm. Numerical experiments are also provided for both deblurring and segmentation problems. In particular, for the deblurring problem, we show that the addition of the bilateral constraints to the total variation model improves the quality of the solutions.     

Robust multicategory support vector machines using difference convex algorithm

The support vector machine (SVM) is one of the most popular classification methods in the machine learning literature. Binary SVM methods have been extensively studied, and have achieved many successes in various disciplines. However, generalization to multicategory SVM (MSVM) methods can be very challenging. Many existing methods estimate k functions for k classes with an explicit sum-to-zero constraint. It was shown recently that such a formulation can be suboptimal. Moreover, many existing MSVMs are not Fisher consistent, or do not take into account the effect of outliers. In this paper, we focus on classification in the angle-based framework, which is free of the explicit sum-to-zero constraint, hence more efficient, and propose two robust MSVM methods using truncated hinge loss functions. We show that our new classifiers can enjoy Fisher consistency, and simultaneously alleviate the impact of outliers to achieve more stable classification performance. To implement our proposed classifiers, we employ the difference convex algorithm for efficient computation. Theoretical and numerical results obtained indicate that for problems with potential outliers, our robust angle-based MSVMs can be very competitive among existing methods.     

Convergence of a hybrid viscosity approximation method for finding zeros of m-accretive operators

Numerical Algorithms - For finding a zero of an m-accretive operator in a real Banach space, we consider an implicit hybrid viscosity approximation method and show that its explicit variant...     

Full Stability of General Parametric Variational Systems

The paper introduces and studies the notions of Lipschitzian and Hölderian full stability of solutions to three-parametric variational systems described in the generalized equation formalism involving nonsmooth base mappings and partial subgradients of prox-regular functions acting in Hilbert spaces. Employing advanced tools and techniques of second-order variational analysis allows us to establish complete characterizations of, as well as directly verifiable sufficient conditions for, such full stability properties under mild assumptions. Furthermore, we derive exact formulas and effective quantitative estimates for the corresponding moduli. The obtained results are specified for important classes of variational inequalities and variational conditions in both finite and infinite dimensions.     

Isomeric ratios in photonuclear reactions of molybdenum isotopes induced by bremsstrahlung in the giant dipole resonance region

We have determined the isomeric ratios of isomeric pairs ^97m,gNb, ^95m,gNb and ^91m,gMo produced in ⁹⁸Mo(γ, p)^97m,gNb, ⁹⁶Mo(γ, p)^95m,gNb and ⁹²Mo(γ, n)^91m,gMo photonuclear reactions in the giant dipole resonance (GDR) region by the activation method. The results were analyzed, discussed and compared with the similar data from literature to examine the role of excitation energy, neutron configuration, channel effect and direct and pre-equilibrium processes in (γ, p) photonuclear reactions. In this work the isomeric ratios for ^97m,gNb from 14 to 19 MeV, for ^195m,gNb from14 to 24 MeV except 20 and 23.5 MeV and for ^91m,gMo at 14 and 15 MeV are the first time measurements.     

Explanation for Malischewsky's approximate expression for the Rayleigh wave velocity

An approach for obtaining approximations of the Rayleigh wave velocity created by the principle of least squares is introduced. In view of this approach, Malischewsky's approximation of the Rayleigh wave velocity for Poisson ratios v in the set of [-1, 0.5] proposed quite recently is explained. It is shown that Malischewsky's approximation obtained by trial and error is (almost) identical with the one established by this approach.