Abstract. In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the LaplaceBeltrami operator on the unit sphere. The sufficient conditions for summability is obtained. The more general properties and representation by the eigenfunctions of the Laplace-Beltrami operator of the Liouville space L 1 is used. For the orders of Riesz means...

The ability to recognize patterns of operator behavior that could lead to poor outcomes is critical to monitoring the overall performance of the human-unmanned system team. We propose a method that relies on Bayesian machine learning in order to automatically derive a set of states that describe the behavior of an operator. More specifically, we use the Hidden Markov Model (HMM) formalism to in...

To find the Hermitian phase operator of a single-mode electromagnetic field in quantum mechanics, the Schrödinger representation is extended to a larger Hilbert space augmented by states with infinite excitation by nonstandard analysis. The Hermitian phase operator is shown to exist on the extended Hilbert space. This operator is naturally considered as the controversial limit of the approximat...

In order to make the operator freely walk in virtual environment (VE), a new prototype of VE system for assembly is presented in this paper. In this system, a special machine is designed and it enables the operator to walk inside the VE in any directions over a long distance without actually leaving the physical device. Images produced by the computer are projected upon the surface of a large s...

The purpose of this paper is to discuss the addition of a new operator, called an ACO operator, to a genetic algorithm. The operator is based on an analogy with Ant Colony Optimization. We use the ACO operator in an application of genetic algorithms to engineering design of conduit systems. The conduit optimization problem involves optimizing both the location of components of conduit systems a...

A novel edge operator is introduced based on steerable asymmetric linear filters consisting of radial wedge segments. An intensity profile is computed by averaging intensity values along a radial wedge segment as it "sweeps" about a small circular neighborhood. The "steerability" of the filters allows for interpolation of a continuous profile function for n discretely sampled postions of the ra...

In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and gen...

We study the construction of extrapolation spaces operator-valued multiplication operators on Bochner Lp-spaces by means Lp-fiber spaces.

In this work we established asymptotical behavior for Riesz means of the spectral function of the Laplace operator on unit sphere.