In this paper we characterize completely the existence of a C0-semigroup in L 1 (I) (I real interval) generated by a second-order diierential operator when suitable boundary conditions at the endpoints are imposed. In spaces of continuous functions similar characterizations have been obtained by Timmermans 6] on the maximal domain, by Cl ement and Timmermans 2] in the case of Ventcel's boundary...

A Banach space X has the complete continuity property (CCP) if each bounded linear operator from L1 into X is completely continuous (i.e., maps weakly convergent sequences to norm convergent sequences). The main theorem shows that a Banach space failing the CCP has a subspace with a nite dimensional decomposition which fails the CCP. If furthermore the space has some nice local structure (such ...

In this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. A numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. Truncation errors are derived for both continuous and discontinuous problems. Parameter uni...

We prove that if X and Y are operator spaces such that every completely bounded operator from X into Y is completely compact and Z is a completely complemented subspace of X ⊕ Y , then there exists a completely bounded automorphism τ : X ⊕ Y → X ⊕ Y with completely bounded inverse such that τZ = X0 ⊕ Y0, where X0 and Y0 are completely complemented subspaces of X and Y , respectively. If X and Y...

In this note‎, ‎we aim to show that several known generalizations of frames are equivalent to the continuous frame‎ ‎defined by Ali et al‎. ‎in 1993‎. ‎Indeed‎, ‎it is shown that these generalizations can be considered as an operator between two Hilbert spaces‎.

A characterisation of the quantum stochastic bounded generators of irreversible quantum state evolutions is given. This suggests the general form of quantum stochastic evolution equation with respect to the Poisson (jumps), Wiener (diffusion) or general Quantum Noise. The corresponding irreversible Heisenberg evolution in terms of stochastic completely positive (CP) cocycles is also characteriz...

The eigenfunctions and eigenvalues of the Laplace-Beltrami operator have proven to be a powerful tool for digital geometry processing, providing a description of geometry that is essentially independent of coordinates or the choice of discretization. However, since Laplace-Beltrami is purely intrinsic it struggles to capture important phenomena such as extrinsic bending, sharp edges, and fine s...

In this paper, we propose a novel nature-inspired meta-heuristic algorithm for continuous global optimization, named the phase transition-based optimization algorithm (PTBO). It mimics three completely different kinds of motion characteristics of elements in three different phases, which are the unstable phase, the meta-stable phase, and the stable phase. Three corresponding operators, which ar...

The weak value of an observable is experimentally accessible by weak measurements as theoretically analyzed by Aharonov et al. and recently experimentally demonstrated. We introduce a weak operator associated with the weak values and give a general framework of quantum operations to the weak operator in parallel with the Kraus representation of the completely positive map for the density operat...

The perturbation semigroup was first defined in the case of $*$-algebras by Chamseddine, Connes and van Suijlekom. In this paper, we take $\mathcal{E}$ as a concrete operator system with unit. We give definition gauge group $\mathcal{G}(\mathcal{E})$ $\mathcal{E}$, after that closed respect to Haagerup tensor norm. also show there is continuous homomorphism from collection unital completely bou...