Kamal Abdali - Academia.edu (original) (raw)

Papers by Kamal Abdali

Lecture Notes in Control and Information Sciences, 1997

$Research paper thumbnail of Modular polynomial arithmetic in partial fraction decomposition$

Algorithms for general partial fraction decomposition are obtained by using modular polynomial ar... more Algorithms for general partial fraction decomposition are obtained by using modular polynomial arithmetic. An algorithm is presented to compute inverses modulo a power of a polynomial in terms of inverses modulo that polynomial. This algorithm is used to make an improvement in the Kung-Tong partial fraction decomposition algorithm.

Springer eBooks, Jan 25, 2006

Al-Ittihad, 1979

A month in the Islamic lunar calendar begins on the day following the first evening during which ... more A month in the Islamic lunar calendar begins on the day following the first evening during which the waxing crescent becomes visible. Thus, the central problem in the preparation of Islamic calendars in advance is to formulate the computational procedures for determining the youngest visible phase of the moon. In temperate latitudes, the crescent to start a new lunar month is sometimes visible during the evening of the

Lecture Notes in Computer Science, 1986

This paper presents a formulation for the standard semantics of block structure and ALGOL 60 styl... more This paper presents a formulation for the standard semantics of block structure and ALGOL 60 style call-by-name. The main features of this formulation are the use of continuations and streams. Continuations are used in such a way that the semantics can be defined without requiring the idea of an explicit store. Thus the concepts of address or L- and R-

Lecture Notes in Computer Science, 1989

The quadtrees matrix representation has been recently proposed as an alternative to the conventio... more The quadtrees matrix representation has been recently proposed as an alternative to the conventional linear storage of matrices. If all elements of a matrix are zero, then the matrix is represented by an empty tree; otherwise it is represented by a tree consisting of four subtrees, each representing, recursively, a quadrant of the matrix. Using four-way block decomposition, algorithms on

ACM SIGSAM Bulletin, 1992

IEEE Transactions on Computers, 1971

ACM SIGSAM Bulletin, 1986

This paper is concerned with the problem of generalizing theorems about recursively defined funct... more This paper is concerned with the problem of generalizing theorems about recursively defined functions, so as to make these theorems amenable to proof by induction. Some generalization heuristics are presented for certain special forms of theorems about functions specified by certain recursive schemas. The heuristics are based upon the analysis of computational sequences associated with the schemas. If applicable, the heuristics produce generalizations that are guaranteed to be theorems. INTRODUCTION This paper deals with the generalization of theorems arising from the analysis of recursive definitions. The theorems of concern here express the properties of functions computed by instances of certain recursive program w<hern&:: To prove these theorems, one usually needs to invoke some form of induction. However, one often encounters cases when induction fails. That is, it turns out that, as originally posed, a given theorem is too weak to be useable in the induction hypothesis for ...

A book[21] published recently by Nachef and Kadi argues that for North America the qibla (i.e., t... more A book[21] published recently by Nachef and Kadi argues that for North America the qibla (i.e., the direction of Mecca) is to the southeast. As proof of this claim, they quote from a number of classical Islamic jurisprudents. In further support of their view, they append testimonials from several living Muslim religious scholars as well as from several Canadian and US scientists. The consulted scientists—mainly geographers—suggest that the qibla should be identified with the rhumb line to Mecca, which is in the southeastern quadrant for most of North America. The qibla adopted by Nachef and Kadi (referred to as NK this direction is not the same as the rhumb line from the place to Mecca, but the two directions lie in the same quadrant. In their preliminary remarks, N&K state that North American Muslim communities used the southeast direction for the qibla without exception until the publication of a book[1] about 20 years ago. N&K imply that the use of the great circle for computing ...

Recreational Mathematics Magazine, 2016

The dominant part in the mental calculation of the day of the week for any given date is to deter... more The dominant part in the mental calculation of the day of the week for any given date is to determine the year share, that is, the contribution of the two-digit year part of the date. This paper describes a number of year share computation methods, some well-known and some new. The “Parity Minus 3” method, in particular, is a new alternative to the popular “Odd+11” method. The paper categorizes the methods of year share computation, and presents simpler proofs of their correctness than usually provided.