An abstract form of the nonlinear Cauchy-Kowalewski theorem

An Elementary Proof of the Strong Form of the Cauchy Theorem

A difficult step in the derivation of the strong forms of the Cauchy theorem, Green's lemma, and related theorems from the corresponding weak forms is the construction, for a given rectifiable Jordan curve J, of a sequence of Jordan polygons lying interior to / , converging to J", and having uniformly bounded lengths. This note presents what the author believes to be a simpler elementary constr...

Inhomogeneous Two-Parameter Abstract Cauchy Problem

An abstract standardisation theorem

The standardisation theorem is a key theorem in the-calculus. It implies that any normal form can be reached by the normal order (leftmost outermost) strategy. The theorem states that any reduction may be rearranged in a top-down and left-to-right order. This also holds in orthogonal term rewriting systems (TRS), although the left-to-right order is more subtle. We give a new presentation of the...

the impact of using inspirational quotes on abstract vocabulary recall

the present study is an attempt to investigate the potential impact of inspirational quotes on improving english abstract vocabulary recall. to achieve this goal, a multiple choice language proficiency test of 60 items including vocabulary and grammar component was administered to a sample of 63 second-semester male and female students whose age ranged between 17 to 22 and they were studying en...

On the Solvability of an Inverse Fractional Abstract Cauchy Problem

This note is devoted to study an inverse Cauchy problem in a Hilbert space H for fractional abstract differential equations of the form; ), ( ) ( ) ( = ) ( t g t f t u A dt t u d    with the initial condition H u u = (0) 0 and the overdetermination condition: ), ( = ) ), ( ( t w v t u where (.,.) is the inner product in H , f is a real unknown function w is a given real function, 0 u , v ar...