a novel and eective method based on haar wavelets and block pulse functions(bpfs) is proposed to solve nonlinear fredholm integro-dierential equations of fractional order.the operational matrix of haar wavelets via bpfs is derived and together with haar waveletoperational matrix of fractional integration are used to transform the mentioned equation to asystem of algebraic equations. our new m...

In this research work, time-delay adaptive synchronization and anti-synchronization of chaotic fractional order systems are analyzed via the Caputo derivative, prob-lem variable is solved by using PID control law, laws variable-order frac-tional calculus, a law deduced from Lyapunov’s theory extended to calculus. two important problems in area: The first problem described which deals with syn-c...

In this paper we introduce and investigate a logic for the schema calculus of Z. The schema calculus is arguably the reason for Z 's popularity but so far no true calculus (a sound system of rules for reasoning about schema expressions) has been given. Presentations thus far have either failed to provide a calculus (e.g. the draft standard 3]) or have fallen back on informal descriptions at a s...

This paper presents a pre xed tableaux calculus for Proposi tional Dynamic Logic with Converse based on a combination of di erent techniques such as pre xed tableaux for modal logics and model checkers for mu calculus We prove the correctness and completeness of the calcu lus and illustrate its features We also discuss the transformation of the tableaux method naively NEXPTIME into an EXPTIME a...

The use of lambda calculus in richer settings, possibly involving parallelism, is examined in terms of its eeect on the equivalence between lambda terms. We concentrate here on Abramsky's lazy lambda calculus and we follow two directions. First, the lambda calculus is studied within a process calculus by examining the equivalence $ induced by Milner's encoding into the-calculus. We give exact o...

Some temporal query languages work directly on a timestamp representation of the temporal database, while others provide a more implicit access to the ow of time by means of temporal connectives. We study the diierences in expressive power between these two approaches. We rst consider rst-order logic (i.e., the relational calculus). We show that rst-order future temporal logic is strictly less ...

Some temporal query languages work directly on a timestamp repre sentation of the temporal database while others provide a more implicit access to the ow of time by means of temporal connectives We study the di erences in expressive power between these two approaches We rst consider rst order logic i e the relational calculus We show that rst order future temporal logic is strictly less powerfu...

We present the Isabelle/HOL formalisation of some key equa-tional properties of the untyped λ-calculus with one-sorted variable names. Existing machine formalisations of λ-calculus proofs typically rely on alternative representations and/or proof principles to facilitate mechanization and we briefly account for these works. Our own development remains faithful to the standard textbook presentat...

Gamification and game-based learning (GBL) has been widely implemented in educational processes, mainly elementary education; it applied less frequently university education. The objective was to test the effect of game-mediated teaching strategies on mathematics first-year engineering students. A quantitative study done within framework a design-based research. Eighty-one (81) students partici...

A language for programming-in-the-large should support architectural descriptions of an entire product line. The evaluation of programs-in-the-large should generate the architecture of individual products and should link implementations-in-the-small to form an executable product. The Standard ML (SML) module language 20] could serve this task, but it is not referentially transparent. Furthermor...