As an extension of the fact that a sectorial operator can determine an analytic semigroup, we first show that a sectorial operator can determine a real analytic α-order fractional resolvent which is defined in terms of MittagLeffler function and the curve integral. Then we give some properties of real analytic α-order fractional resolvent. Finally, based on these properties, we discuss the regu...

We discuss the continuity of analytic resolvent in the uniform operator topology and then obtain the compactness of Cauchy operator by means of the analytic resolvent method. Based on this result, we derive the existence of mild solutions for nonlocal fractional differential equations when the nonlocal item is assumed to be Lipschitz continuous and neither Lipschitz nor compact, respectively. A...

In this paper, we consider the controllability problems for a class of impulsive fractional partial neutral quasilinear functional differential inclusions with infinite delay and (α, x)-resolvent family. In particular, a set of sufficient conditions are derived for the approximate controllability of nonlinear impulsive fractional dynamical systems by assuming the associated linear system is app...

In this paper we continue our program of extending the methods of geometric scattering theory to encompass the analysis of the Laplacian on symmetric spaces of rank greater than one and their geometric perturbations. In our previous work [9] we described the resolvent, and specifically the asymptotic behavior of the Green’s function, on SL(3)/ SO(3) using methods from three-particle scattering....

Taking advantages of popular Resolvent-based (Rslv) and Minimum conflict set (MCS) nogood learning, we propose two new techniques: Unique nogood First Resolvent-based (UFRslv) and Redundant conflict value assignment Free Resolvent-based (RFRslv) nogood learning. By removing conflict value assignments that are redundant, these two new nogood learning techniques can obtain shorter and more effici...

The existence of linear differential resolvents for z for any root z of an ordinary polynomial with coefficients in a given ordinary differential field has been established, where α is an indeterminate constant with respect to the derivation of the given field. In this paper we consider several alphas. We will call a finite sum of indeterminate powers of a variable v a pseudopolynomial in v . W...

We show a new remarkable connection between the symmetric form of a quantum stochastic differential equation (QSDE) and the strong resolvent limit of Schrödinger equations in Fock space: the strong resolvent limit is unitary equivalent to QSDE in the adapted (or Ito) form, and the weak limit is unitary equivalent to the symmetric (or Stratonovich) form of QSDE. We prove that QSDE is unitary equ...

For the Laplacian ∆ defined on a p.c.f. self-similar fractal, we give an explicit formula for the resolvent kernel of the Laplacian with Dirichlet boundary conditions, and also with Neumann boundary conditions. That is, we construct a symmetric function G(λ) which solves (λI − ∆)−1 f (x) = ∫ G(λ)(x, y) f (y) dμ(y). The method is similar to Kigami’s construction of the Green kernel in [Kig01, §3...

We present resolvent-based learning as a new nogood learning method for a distributed constraint satisfaction algorithm. This method is based on a look-back technique in constraint satisfaction algorithms and can efficiently make effective nogoods. We combine the method with the asynchronous weakcommitment search algorithm (AWC) and evaluate the performance of the resultant algorithm on distrib...

We prove in this paper resolvent estimates for the boundary values of resolvents of selfadjoint operators on a Krein space: if H is a selfadjoint operator on a Krein space H, equipped with the Krein scalar product 〈·|·〉, A is the generator of a C0−group on H and I ⊂ R is an interval such that: 1) H admits a Borel functional calculus on I, 2) the spectral projection 1lI (H) is positive in the Kr...