Mathematics and Computer Science
Publication Record
Abi-Khuzam, F. F., and
B. Shayya. 2000. On a
singular integral estimate for the maximum modulus of a canonical product. Illinois
Journal of Mathematics 44:551–555.
Abu-Khuzam, H. 2000. A
note on rings with constraints involving potent and noncentral elements.
Mathematica Japonica 52 (3).
Beydoun, G., and A. Hoffmann. 2000. Search at the knowledge level.
International Journal of Human Computer Interactions 52 (3):493–530.
Beydoun, G. and A. Hoffmann. 2001. Theoretical framework of incremental
hierarchical knowledge acquisition. International Journal of Human
Computer Interactions 54 (3):407–452.
Haddad, J. N. 2000. On robust estimation in the
first-order autoregressive process. Communications in Statistics: Theory
and Methods 29:45–54.
———. Abraham, B.
Robust estimation in autoregressive processes. Statistical Methods 2
(2):123–135.
Haddad, J. N., and M. N. Nimah. 2001. Water quality monitoring of the
Litani river. Lebanese Science Journal.
Khuri-Makdisi, K. 2001.
On the curves associated to certain rings of automorphic forms. Canadian
Journal of Mathematics 53:98–121.
Nasri, A. 2001.
Interpolating meshes of boundary intersecting. The Visual Computer Journal
16 (1):3–14.
Nasri, A. H. 2001. Recursive
subdivision of polygonal complexes and their applications in computer aided
geometric design. Computer Aided Geometric Design.
Nasri, A., K. Overveld*,
and B. Wyvill*. 2001. A recursive subdivision
algorithm for piecemeal circular spline. Computer Graphics Forum.
Roddick*, J., L. Al-Jadir, L. Bertossi*, M.
Dumas*, F. Estrella*, H. Gregersen* et al. 2000. Evolution and change in data
management: Issues and directions. ACM SIGMOD Record 29 (1)
Abstracts, Conferences, and Proceedings
Abu-Khuzam, H. August 2000. On the structure of certain rings
with conditions on potent and noncentral elements. "Mathematical
Challenges of the 21 Century," American Mathematical Society Conference
held at UCLA, Los Angeles, California, USA.
Al-Jadir, L. April 2001. Encapsulating classification in an
OODBMS for data mining applications. IEEE Computer Society. Proc. of 7th
International Conference on Database Systems for Advanced Applications
(DASFAA'01), Hong Kong, China.
Al-Jadir, L., and M. Leonard*. August 1999. If we refuse the
inheritance. Lecture Notes in Computer Science 1677, Springer. Proc. of 10th
International Conference on Database and Expert Systems Applications
(DEXA'99), Florence, Italy.
———. November 1999. Transposed storage of an object database
to reduce the cost of schema changes. Lecture Notes in Computer Science 1727,
Springer. Proc. of 1st International Workshop on Evolution and Change
in Data Management (ECDM'99), Paris, France.
Beydoun, G., and A. Hoffmann. 2000.
Monitoring knowledge acquisition, instead of evaluating knowledge bases. In proceeding
of the 12th European Conference on Knowledge Acquisition, Modelling and
Management (EKAW2000), France, Springer Computer Science Lecture Notes
Series, pp. 387–402.
Beydoun, G., R. Kwok, and A.
Hoffmann. 2000. Towards order independent incremental knowledge acquisition.
in proceedings of Pacific Rim Knowledge Acquisition Workshop (PKAW2000), Sydney,
pp.71–88.
Drake, and G. Beydoun. Using Ripple Down Rules to Build
Predicates in Situation Semantics, in Proceedings of Pacific Rim Knowledge
Acquisition Workshop (PKAW2000), Sydney 12/2000, pp1-16.
Khuri-Makdisi, K. June 2000. On the curves associated to
certain rings of automorphic forms. Number Theory Seminar, Universite de
Paris XIII, Paris, France.
———. February 2001. Linear algebra algorithms for divisors on
algebraic curves. The Five Colleges Number Theory Seminar, Amherst,
Massachusetts, USA.
———. May 2001. Linear algebra algorithms for divisors on algebraic
curves. University of Rome II Number Theory Seminar, Rome, Italy.
Nahlus, N. January 2000. On extensions of representations of
Lie algebras, pro-algebraic groups, and analytic groups. First-Beit Mery
Workshop on Mathematical Sciences (organized by CAMS at AUB), Beit Mery,
Lebanon.
Nasri, A. August 1999. Curve generation by recursive
subdivision of polygonal strip complexes. ACM Siggraph 1999, Los Angeles,
USA.
———. April 2000. A polygon approach for interpolating meshes.
International Conference on Geometrical Modeling, Hong Kong, China.
Nasri, A., Adams, S.*, R. Jou*, A. Radimsky*, and B. Sy*.
October 1999. Integrating multimedia techniques into computer science
pedagogy. Web-Net 1999, Honolulu, Hawaii, USA.
Nasri , A., T. Kim*, and K. Lee*. May 2001. Smoothing
subdivision surfaces through meshes of curves. Shape Modeling International
2001, Genoa, Italy.
Graduate Theses and Projects
Ghandour, N. June 2000. Structure of certain weakly periodic rings
and other rings with conditions on elements. H. Abu-Khuzam.
Research Projects
A commutativity theorem for rings with conditions involving nilpotents
and the Jacobson radical
We have studied the commutativity and structure of certain
classes of rings and obtained results that generalize earlier results in this
area. In Proceedings of the International Conference on Algebra and its
Applications (2001), 1-8, in press. Abu-Khuzam, H.
Completed or in progress at AUB
On the structure of c*-rings
We introduce the notion of c*-rings which are
generalizations of rings having at most finitely many non-central elements
(in progress). Abu-Khuzam, H.
Completed or in progress at AUB
Structure of rings with a condition on zero divisors
We have studied the structure of certain rings that we
call D-rings in which every zero divisor is nilpotent (completed and accepted
for publication). Abu-Khuzam, H., H. Bell, and A. Yaqub.
Completed or in progress at AUB
Transposed storage of an object database for fast discovery of
association rules
Mining association rules are an important problem in data
mining (DM). One of the main challenges in DM is developing fast and
efficient algorithms that can handle large volumes of data. We propose an
algorithm based on the non-classical transposed storage of an object
database. The idea of transposed storage is to vertically partition the
objects of a class C according to each attribute of C. We already showed that
the transposed storage is efficient in the context of schema evolution since
it reduces the cost of schema changes. We show now that it is efficient for
generating association rules, too. Al-Jadir, L.
Supported by URB (October 1, 2000 - September 30, 2001)
Completed or in progress at AUB
Modeling water quality in time and space
We continue to monitor the chemical contamination of the
Litani river. In particular, the concentration of nitrate, acidity level, and
salinity has been constantly measured through time and space. A State-Space
model has been fitted to provide an on-line prediction for optimal
calibration of the monitoring network. Haddad, J. N., and M. N. Nimah.
Supported by LNCSR
Completed or in progress at AUB
Moments of the maximum likelihood estimator for the first-order
autoregressive process
The maximum likelihood estimator of the autocorrelation
parameter in a first-order autoregressive process is expressed in terms of
the Yule-Walker estimator. The moments of the latter are given in a form that
can be easily evaluated. The established relationship yields approximate
moments for the maximum likelihood estimator. The distribution of either one
of these estimators can then be approximated from their respective moments
under any assumed autocorrelation parameter, and any finite series length. Haddad,
J. N., S. B. Provost*, and E. M. Rudiuk*.
Completed or in progress at AUB
Linear algebra algorithms for divisors on algebraic curves
Abstract: We use an embedding of the symmetric d-th power
of any algebraic curve C of genus g into a Grassmannian space to give
algorithms for working with divisors on C, using only linear algebra in
vector spaces of dimension O(g), and matrices of size O(g^2) x O(g). When the
base field is finite, these give algorithms for working on the Jacobian of C
that require O(g^4) field operations. Our representation of points on the
Jacobian is fairly simple to work with, and is much better than using the
usual projective embedding of the Jacobian (using a multiple of the
theta-divisor) into a projective space of exponentially large
dimension. The algorithms are also a significant improvement on the
O(g^7) algorithms for Jacobians of general curves given in the work of
Volcheck. We note that for certain special classes of curves, such as
hyperelliptic curves (Cantor), superelliptic curves (Galbraith, Paulus, and
Smart), and C_ab curves (Harasawa and Suzuki), asymptotically better
algorithms are already known, with complexity O(g^2). Kamal Khuri-Makdisi.
Partially funded by Clay Mathematics Institute
Provarieties and observable subgroups of pro-affine algebraic groups
Abstract. We define a closed subgroup H of a
pro-affine algebraic group G to be
observable if every (finite-dimensional) rational H-module is an H sub-module
of a rational G-module. We show the equivalence to observability of a number
of other conditions on the pair (G, H), including the condition that the
provariety G/H be pro-quasi affine. To treat this latter, we also include
results on the foundations of provarieties.
Status: Accepted for publication in the Journal
of Group Theory. Magid, A. R., and N. Nahlus.
Completed or in progress at AUB
Representation of autoregressive processes
We have found a solution to the difference equation for an
autoregressive process.
This has led to an expression of the covariance matrix for the finite sample
process,
an expression for the inverse of the covariance matrix, and a representation
of any
pth order process in terms of p artificial first order processes. Monsour, M.
Completed or in progress at AUB
Schur functions
Using a different parametrization of Schur functions, have
obtained a recurrence relation for Schur functions. This has led to general
formulas for the coefficients or Kostka numbers for some Schur functions.
Monsour, M.
Completed or in progress at AUB
Lie algebras and separable morphisms in pro-affine algebraic groups
Abstract: Let K be an algebraically closed
field of arbitrary characteristics, and
let f:G->H be a surjective morphism of connected pro-affine
algebraic groups over K.
We show that, if f is bijective and separable, then f is an
isomorphism of pro-affine
algebraic groups. Moreover, f is separable if and only if (its
differential) fo is surjective.
Furthermore, if f is separable, then the Lie algebra
of Ker f coincides with Ker fo.
Status: Accepted for publication in the Proceedings of the American
Mathematical Society. Nahlus, N.
Completed or in progress at AUB
Lie algebras of pro-affine algebraic groups
Abstract: We extend the basic theory of Lie algebras
of affine algebraic groups to
the case of pro-affine algebraic groups over an algebraically closed field K
of characteristic 0.
However, some modifications are needed in some extensions. So we introduce
the
pro-discrete topology on the Lie algebra L(G) of the pro-affine algebraic
group G over K, which is discrete in the finite-dimensional case and linearly
compact in general. As an example, if L is any sub Lie algebra of
L(G), we show that the closure of [L, L] in L(G) is algebraic in
L(G).
We also discuss the Hopf algebra of representative
functions H(L) of a residually finite Lie algebra L. As an example, we show
that if L is a sub Lie algebra of L(G) and G is connected, then the
canonical Hopf algebra morphism from K[G] into H(L) is injective if and
only if L is algebraically dense in L(G).
Status: Accepted for publication in the Canadian Journal
of Mathematics. Nahlus, N.
Completed or in progress at AUB
Note on observable subgroups of linear algebraic groups and a theorem of
Chevalley
Abstract: Let H be an algebraic subgroup of a
linear algebraic group G over an
algebraically closed field K. We show that H is observable in G (if)
and only if there exists a finite-dimensional rational G-module V and an
element v of V such that H is the isotropy subgroup of v as well as the
isotropy subgroup of the line Kv. Moreover, we give a similar
result in the case where H contains a normal algebraic subgroup A which is
observable in G. In this case, we deduce that H is observable in G
whenever H/A has non non-trivial rational characters. We also give an example
from complex analytic groups.
Status: Accepted for publication in the Journal
of Lie Theory. Nahlus, N.
Completed or in progress at AUB
On extensions of representations of solvable Lie algebras of arbitrary
dimension
Abstract: Let A be a subLie algebra of a solvable Lie
algebra L over an algebraically closed field of characteristic 0. We are
interested in the problem of extending a finite-dimensional representation of
A to a finite-dimensional representation of L. In this paper, we show that
such an extension exists if and only if both
(i) the intersection of [L, L] with A acts nilpotently on
the given representation space, and
(ii) the kernel I of the given representation is admissible in L (with
respect to A) in the sense that there exists a cofinite-dimensional ideal J
in L whose intersection with A is contained in I.
Status: Submitted for publication. Nahlus, N.
Completed or in progress at AUB
On observable subgroups of complex analytic groups and algebraic
structures on analytic homogenous spaces
Abstract. Let L be a closed analytic subgroup
of a faithfully representable complex
analytic group G, let R(G) be the algebra of complex analytic representative
functions on G, and let G_0 be the universal algebraic subgroup
(or algebraic kernel) of G. In this paper, we show many characterizations of
the property that the homogeneous space G/L is (representationally)
separable, i.e., R(G)^L separates the points of G/L. This yields new
characterizations for the observability of L in G and new
characterizations for the existence of a quasi-affine structure
on G/L. For example, G/L is separable if and only if the
intersection X of G_0 with L is an observable algebraic subgroup of G_0.
Moreover, L is observable in G if and only if G/L is separable and L_0 =
X. Similarly, we discuss a weaker separability of G/L, and the existence
of a representative algebraic structure on G/L.
Status: Accepted for publication in the Journal of Lie Theory. Nahlus,
N.
Completed or in progress at AUB
Solid modeling by recursive subdivision surfaces
We discuss various issues related to modeling by recursive
subdivision. Issues related to curve interpolation and the design of
free-form surfaces from a given net of curves are described. Nasri, A.
Supported by AUB
Completed or in progress at AUB
Polygonal complexes in Catmull Clark subdivision surfaces
We discuss the use of polygonal complexes in the
interpolation of curve by Catmull-Clark subdivision surfaces. Nasri, A., and
A. Abbas.
Supported by LNCSR (expected)
Completed or in progress at AUB and Balamand University
Subdivision algorithm for rational curves
A subdivision algorithm for generating rational curves is
devised. From a square, this is the first subdivision algorithm that
generates a circle. From an arbitrary control polygon, a piecewise rational
curve is constructed. Nasri, A., and G. Farin*.
Supported by LNCSR
Completed or in progress at AUB
Fitting tirangular Bezier surfaces to clouds of data points
From given clouds of data points, we fit a triangular
Bezier surface. The generated surface interpolates the given data points, and
possibly normal conditions. Nasri, A., T. W. Kim, and G. Farin.
Supported by AUB, Arizona State University, and Seoul National University
(SNU)
Completed or in progress at AUB and SNU
Volume and higher order moments of solids enclosed by recursive
subdivision surfaces
We describe algorithms for computing various moments of
inertia of solids defined by recursive subdivision surfaces. Nasri, A., and
J. Peters*.
Supported by AUB
Completed or in progress at AUB
Interpolation constraints in recursive subdivision curves and surfaces
We discuss the various interpolation constraints for
practical use of subdivision curves and surfaces in computer graphics and
geometric modeling. Interpolating points, normal, tangents, etc. are
discussed, and open problems are outlined. Nasri, A., and M. Sabin*.
Supported by AUB, Royal Society, and LNCSR
Completed or in progress at AUB
Recursive subdivision in computer-aided geometric design
A book about the use of recursive subdivision in computer
aided geometric design and computer graphics. Nasri, A., and M. Sabin*.
Supported by AUB, LNSCR, and Numerical Geometry (UK)
Completed or in progress at AUB and Numerical Geometry (UK)
Nonisotropic strongly singular integral operators
To appear in the Transactions of the American
Mathematical Society. Shayya, B.
Completed or in progress at AUB
Singular integrals with nonhomogeneous oscillatory kernels
To appear in the Indiana University Mathematics Journal.
Shayya, B.
Completed or in progress at AUB
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