In this paper we introduce a new concept namely, generalized Voronoi partition and use it to formulate two heterogeneous multi-agent search strategies. The core idea is optimal deployment of agents having sensors with heterogeneous capabilities, in a search space so as to maximize search effectiveness. We address a few theoretical issues such as optimality of deployment, convergence and spatial...

This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of functions in an extended multifunction space (Sengupta and Ray, 2000), and the topological theory of convergence. Order, chaos, and complexity are described as dis...

The standard error bounds for interpolation by kernels or radial basis functions are generalized to symmetric PDE collocation problems. This involves generalized Power Functions, and these can be explicitly calculated. Final error bounds then are a product of Power Function values and the norm of the solution in the native space of the kernel. Since the latter can also be estimated well, the wh...

using a bessel generalized translation, we obtain an analog of titchmarsh's theorem for the bessel transform for functions satisfying the lipschitz condition in the space $mathrm{l}_{p,alpha}(mathbb{r}_{+})$, where $alpha>-frac{1}{2}$ and $1

In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular tosome degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.

In this paper, we propose the mathematical and finite element analysis of a second order Partial Differential Equation endowed with a generalized Robin boundary condition which involves the Laplace–Beltrami operator, by introducing a function space H1(Ω; Γ) of H1(Ω)-functions with H1(Γ)-traces, where Γ ⊆ ∂Ω. Based on a variational method, we prove that the solution of the generalized Robin boun...

In this paper, we propose the mathematical and finite element analysis of a second order Partial Differential Equation endowed with a generalized Robin boundary condition which involves the Laplace–Beltrami operator, by introducing a function space H1(Ω; Γ) of H1(Ω)-functions with H1(Γ)-traces, where Γ ⊆ ∂Ω. Based on a variational method, we prove that the solution of the generalized Robin boun...

in this paper‎, ‎using a generalized dunkl translation operator‎, ‎we obtain a generalization of titchmarsh's theorem for the dunkl transform for functions satisfying the$(psi,p)$-lipschitz dunkl condition in the space $mathrm{l}_{p,alpha}=mathrm{l}^{p}(mathbb{r},|x|^{2alpha+1}dx)$‎, ‎where $alpha>-frac{1}{2}$.

We study the orthogonal polynomial expansion on sparse grids for a function of d variables in a weighted L space. A fast algorithm is developed to compute the orthogonal polynomial expansion by combining the fast cosine transform, a fast transform from the Chebyshev orthogonal polynomial basis to the orthogonal polynomial basis for the weighted L space, and a fast algorithm of computing hierarc...