Search results for " Operator"

Some results about operators in nested Hilbert spaces

2005

With the use of interpolation methods we obtain some results about the domain of an operator acting on the nested Hilbert space {ℋf}f∈∑ generated by a self-adjoint operatorA and some estimates of the norms of its representatives. Some consequences in the particular case of the scale of Hilbert spaces are discussed.

Crowded comparison operators for constraints handling in NSGA-II for optimal design of the compensation system in electrical distribution networks

2006

This paper proposes an improvement of an efficient multiobjective optimization algorithm, Non-dominated Sorting Genetic Algorithm II, NSGA-II, that has been here applied to solve the problem of optimal capacitors placement in distribution systems. The studied improvement involves the Crowded Comparison Operator and modifies it in order to handle several constraints. The problem of optimal location and sizing of capacitor banks for losses reduction and voltage profile flattening in medium voltage (MV) automated distribution systems is a difficult combinatorial constrained optimization problem which is deeply studied in literature. In this paper, the efficiency of the proposed Crowded Compari…

A combinatorial algorithm for the optimization of refraction seismics data inversion

1993

Abstract The problem of data inversion in refraction seismics can be split in two parts: data first must be preprocessed in order to determine the travel-time curve; this essentially is a geometrical problem, complicated, however, by its pattern recognition aspects. Once the geometrical problem is solved, the second part, the inversion proper, is straightforward, as the soil layering model can be calculated according to well-known algorithms. The more difficult part of the problem is the former, which implies a type of pattern recognition; because of this type of difficulty, the geometrical part of the problem usually is committed to the skill of a human operator. This paper describes an al…

Spectral properties of random non-self-adjoint operators

2015

In this thesis we are interested in the spectral properties of random non-self-adjoint operators. Weare going to consider primarily the case of small random perturbations of the following two types of operators: 1. a class of non-self-adjoint h-differential operators Ph, introduced by M. Hager [32], in the semiclassical limit (h→0); 2. large Jordan block matrices as the dimension of the matrix gets large (N→∞). In case 1 we are going to consider the operator Ph subject to small Gaussian random perturbations. We let the perturbation coupling constant δ be e (-1/Ch) ≤ δ ⩽ h(k), for constants C, k > 0 suitably large. Let ∑ be the closure of the range of the principal symbol. Previous results o…

Efficacia ed efficienza dei protocolli di pulizia e disinfezione in sale operatorie

2006

On One Identification Problem in Linear Elasticity

1990

In practice we meet problems, when having the solution of partial differential equation, we want to discover parts in the domain of its definition where the solution has some specific properties. In [1] and [2] the problem of identification of a curve φ, lying inside of Ω such that the flux \(\int{_{\varphi }}\frac{\partial u}{\partial n}ds\) is maximal has been studied, where u is the solution of mixed—boundary value problem for Laplacian operator.

A New Hybrid Mutation Operator for Multiobjective Optimization with Differential Evolution

2011

Differential evolution has become one of the most widely used evolution- ary algorithms in multiobjective optimization. Its linear mutation operator is a sim- ple and powerful mechanism to generate trial vectors. However, the performance of the mutation operator can be improved by including a nonlinear part. In this pa- per, we propose a new hybrid mutation operator consisting of a polynomial based operator with nonlinear curve tracking capabilities and the differential evolution’s original mutation operator, to be efficiently able to handle various interdependencies between decision variables. The resulting hybrid operator is straightforward to implement and can be used within most evoluti…

Milton’s conjecture on the regularity of solutions to isotropic equations

2003

Abstract We present examples showing that the threshold for the integrability of the gradient of solutions to isotropic equations is 2K/(K−1). The main tools are p-laminates and Beltrami Operators.

Operators on Partial Inner Product Spaces: Towards a Spectral Analysis

2014

Given a LHS (Lattice of Hilbert spaces) $V_J$ and a symmetric operator $A$ in $V_J$, in the sense of partial inner product spaces, we define a generalized resolvent for $A$ and study the corresponding spectral properties. In particular, we examine, with help of the KLMN theorem, the question of generalized eigenvalues associated to points of the continuous (Hilbertian) spectrum. We give some examples, including so-called frame multipliers.

The Partial Inner Product Space Method: A Quick Overview

2010

Many families of function spaces play a central role in analysis, in particular, in signal processing (e.g., wavelet or Gabor analysis). Typical are spaces, Besov spaces, amalgam spaces, or modulation spaces. In all these cases, the parameter indexing the family measures the behavior (regularity, decay properties) of particular functions or operators. It turns out that all these space families are, or contain, scales or lattices of Banach spaces, which are special cases ofpartial inner product spaces(PIP-spaces). In this context, it is often said that such families should be taken as a whole and operators, bases, and frames on them should be defined globally, for the whole family, instead o…