In this paper, the generalized Taylor’s expansion is presented for fuzzy-valued functions. To achieve this aim, fuzzyfractional mean value theorem for integral, and some properties of Caputo generalized Hukuhara derivative are necessarythat we prove them in details. In application, the fractional Euler’s method is derived for solving fuzzy fractionaldifferential equations in the sense of Caputo...

We reduce Hochster's Canonical Element Conjecture (theorem since 2016) to a localization problem in characteristic free way. prove the validity of new variant Theorem (CET) and explain how deduction from original CET would provide us with proof CET. also show that Balanced Big Cohen-Macaulay Module can be settled by if big Cohen-Macaulayness modification module deduced existence maximal complex

in this paper, using the tools involving measures of noncompactness and darbo fixed point theorem forcondensing operator, we study the existence of solutions for a large class of generalized nonlinear quadraticfunctional integral equations. also, we show that solutions of these integral equations are locally attractive.furthermore, we present an example to show the efficiency and usefulness of ...

This note describes several methods of finding proofs used in APRVR, an agenda-based, natural-deduction theorem prover. APRSR retains a complete tree of all pending or completed goals and is able to choose the next goal to be processed from an agenda of pending goals. Through this mechanism some proof methods can be utilized that had been unavailable to an earlier prover that was not agenda-bas...

On a traditional view, the primary role of a mathematical proof is to warrant the truth of the resulting theorem. This view fails to explain why it is very often the case that a new proof of a theorem is deemed important. Three case studies from elementary arithmetic show, informally, that there are many criteria by which ordinary proofs are valued. I argue that at least some of these criteria ...

of the Dissertation Decision Procedures in Automated Deduction