Publications - 2008

Adjoint-based optimization of PDEs in moving domains

A generalization of projective covers

A new look at an old equation

A New Quantile Function Based Model for Modeling Price Behaviors in Financial Markets

ANOVA extensions for mixed discrete and continuous data

A simple grammar for generating cocompact Fuchsian groups, International Journal of Pure and Applied Mathematics:

Case Deletion Diagnostics in Multilevel Models

Controlling the dose distribution with gEUD-type constraints within the convex radiotherapy optimization framework

Covering a plane convex body by its negative homothets

Detection of Outliers in Multilevel Models

Formal paths, iterated integrals and the center problem for ODEs

Fundamental Number Theory with Applications

My tenth book is the second edition of Fundamental Number Theory with Applications, the first edition of which was published in 1998. This second edition is a radical rewriting of the first edition. Indeed, virtually all advanced material has been removed and there has been an addition of new material such as combinatorial number theory, partitions, and generating functions. There is also an expanded and more involved discussion of random number generation, more applications to cryptology, primality testing, and factoring. As well there is an expanded coverage of Diophantine equations from a more elementary point of view. This includes a section for Legendre''s Theorem on the equation ax^2+by^2+cz^2=0 and an expanded view of Bachet''s equation y^2=x^3+k. Moreover, the coverage of sums of two, three, and four squares has been revised completely. This edition concentrates on criteria for representation and more on the total number of primitive representations where the extensive coverage of the total number of imprimitive representations in the first edition has been deleted. On the topic of sums of two squares, applications from continued fraction theory which was not covered in the first edition, are discussed in detail. Sums of cubes is given a separate section, also not covered in the first edition. See below for the Table of Contents of the second edition. Thus, now the text is truly "fundamental".

Gaussian bounds for degenerate parabolic equations

Hartogs type theorems for CR L^2 functions on coverings of strongly pseudoconvex manifolds

Indivisible ultrametric spaces.

INTUITIVE GEOMETRY, Periodica Mathematica Hungarica,57(2),Intuitive Geometry Workshop, BIRS (2007), Intuitive Geometry Day in Calgary, U. of Calgary (2007)

Left quasi-morphic rings

Linearization of regular matrix polynomials

Nonparametric estimation of linear functionals of a bivariate distribution under univariate censoring

On braxtopes, a class of generalized simplices

On Factoring

On pseudospecrta of matrix polynomials and their boundaries.

On the decay of crossing numbers

On the weighted Kneser-Poulsen conjecture

On WHO and AIDS Deaths in India

Ordering of optimal portfolio allocations in a model with mixture of fundamental risks

Polynomial equation in radicals

Prime Factors of Consecutive Integers

Regularity of subelliptic Monge-Ampère equations

Report from the Ambassador to Cida-2

Robust empirical Bayes tests for discrete distributions

Small cycle double covers of products I: lexicographic product with paths and cycles

Stochastic orders of scalar products with applications

Taxonomy of Cryptographic Pairings

The number of bounded solutions of norm-form equations via Pell equations and ambiguous classes of solutions

The T(4) property of families of unit disks,

The virtues of a deliberately misspecified disease model in demonstrating a gene-environment interaction

Worst allocations of policy limits and deductibles