This paper researches the accuracy of the Differential Transformation Method (DTM) for solving the Holling Tanner models which are described as two-dimensional system of ODES with quadratic and rational nonlinearities. Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. The direct symboli...

We present a mathematical theory of the two-dimensional offset curves from the viewpoint of medial axis transform. We explore the local geometry of the offset curve in relation with the medial axis transform, culminating in the classification of points on the offset curve. We then study the domain decomposition from the viewpoint of offsets, and in particular introduce the concept of monotonic ...

This paper discusses a technique how to integrate formal description techniques (FDTs) with specification & design methods such as OMT so that we can have new methods to support writing formal specifications. The integration mechanism is based on transformation rules of specification documents produced following methods into the descriptions written in FDTs. The transformation rules specify the...

The advent of Bitcoin paved the way for a plethora of blockchain systems supporting diverse applications beyond cryptocurrencies. Although in-depth studies of the protocols, security, and privacy of blockchains are available, there is no formal model of the transaction semantics that a blockchain is supposed to guarantee. In this work, we fill this gap, motivated by the observation that the sem...

Recognition of mathematical notation involves two main components: symbol recognition and symbol-arrangement analysis. Symbol-arrangement analysis is particularly difficult for mathematics, due to the subtle use of space in this notation. We begin with a general discussion of the mathematics-recognition problem. This is followed by a review of existing approaches to mathematics recognition, inc...

The speciication and derivation of substitution for the de Bruijn representation of-terms is used to illustrate programming with a function-sequence monad. The resulting program is improved by interactive program transformation methods into an eecient implementation that uses primitive machine arithmetic. These transformations illustrate new techniques that assist the discovery of the arithmeti...

protein structural flexibility is important for catalysis, binding, protein design, and allostery. some simple methods have recently been introduced to compute protein flexibility directly from the protein structure without any mechanical models. for example the atomic mean square displacement (or b-factor) is related to the number of neighboring atoms. the protein structure can be modeled as a...

Graph transformation systems have been introduced for the formal specification of software systems. States are thereby modeled as graphs, and computations as graph derivations according to the rules of the specification. Operations on graph derivations provide means to reason about the distribution and composition of computations. In this paper we discuss the development of an algebra of graph ...

S. Bailey, P. Antilogus, R. Pain, R. Pereira, P. Ripoche, and C. Wu LPNHE, Paris, France G. Aldering, C. Aragon, S. Bongard, M. Childress, S. Loken, P. Nugent, S. Perlmutter, K. Runge, and R. C. Thomas LBL, Berkeley, CA C. Baltay, D. Rabinowitz, and R. Scalzo Yale University, New Haven, CT C. Buton, Y. Copin, E. Gangler, G. Smadja, and C. Tao IPNL, Lyon, France E. Pecontal and G. Rigaudier CRAL...

We present an algorithm for eecient parallelization of particle methods when the domain is the surface of a sphere. Such applications typically arise when dealing with directional data. We propose a domain decomposition scheme based on geometric partitioning that provides domains suitable for practical implementation. This algorithm has the advantage of being fast enough to be applied dynamical...