Publications - 2005

A Generalization of the Discrete Isoperimetric Inequality for Piecewise Smooth Curves of Constant Geodesic Curvature

A hierarchical 3-{D} direct {H}elmholtz solver by domain decomposition and modified {F}ourier method

Algorithms for hyperbolic quadratic eigenvalue problems.

An algorithm for minimal number of intersection points of curves on surfaces

A New Multivariate Control Chart for Monitoring Both Location and Dispersion

A note on the Diophantine equation D_1x^2+D_2=ak^n

Binary space partition of orthogonal subdivisions

B-Spline Estimation in a Semiparametric Regression Model With Nonlinear Time Series Errors

Canonical forms for symmetric/skewsymsmetric real matrix pairs under strict equivalence and congruence.

Censored multiple regression by the method of average derivatives

Chromatic numbers and products

Let $f(n)$ be the smallest number so that there are two $n$ chromatic graphs whose product has chromatic number $f(n)$. Under the assumption that a certain sharper result than one obtained by Duffus, Sands and Woodrow \cite{DSW}, and Welzl \cite{W}, holds we will prove that $f(n)\geq {n/2}$.

Classification of Singularities and Bifurcations of Critical Points of Even Functions

Codes; The Guide to Secrecy from Ancient to Modern Times

From the Preface: "This book has been written with a broad spectrum of readers in minnd, which includes anyone interested in "secrecy" and related issues. Thus, this is a tome for the merely curious, as well as the history-minded reader, the amateur mathematician, engineers, bankers, academics, students, those practitioners working incryptography, specialists in the field, and instructors wanting to use the book for a text in a course on a variety of topics related to"codes". We will look at this topic from all aspects including not only those related to cryptography (the study of methods for sending messages in secret), but also the notion of"codes" as removal of noise from telephone channels, satellite signals, CDs and the like." It starts with two chapters on the history of the subject, beginning with the Minoan civilization on the island of Crete 4,000 years ago and moves through the modern day. Subsequent chapters provide explicit descriptions of the most up-to-date ciphers, including Blowfish, Rijndael, RC4, and other stream ciphers. There is also a full accounting of public-key cryptography including, RSA, ElGamal, and digital signatures. There is a chapter on cryptographic protocols including, identification, commitment, secret sharing, electronic voting, protocol layers and SSL, as well as digital cash schemes. Key management in detail is covered with attention to authentication, exchange, distribution, and an overview of PKI. Message authentication is covered with an eye to authentication functions, authentication codes, encryption functions, and applications. E-Mail topics are covered such as, PGP, S/MIME, IPSec, Firewalls, Client-Server models and cookies, as well as a history of the Internet and the World Wide Web. Modern-day concerns are covered, such as cyber-crime, hackers, computer viruses, copyright issues including music downloads, and modern technology such as in smart cards, wireless phones, and biometrics. E-commerce is covered in great detail with SET, SSL, RC4, and other protocols, which have become standards on the Internet. The concluding eleventh chapter is devoted to Information Theory, and Error-Correcting Codes. There are seven appendices with topics including, background on mathematical facts: sets, relations and functions, basic and modular arithmetic, groups, fields, modules, rings, vector spaces, basic matrix theory, continued fractions, elliptic curves, and complexity theory in Appendix A. There is pseudo-random number generation in Appendix B including: ANSI X9.17 and the Blum-Blum-Shub generator. Appendix C covers factoring including: classical methods, the continued fraction algorithm, Pollard''s p-1 algorithm, as well as his rho method, the quadratic sieve, and the multipolynomial quadratic sieve, the elliptic curve method, and the general number field sieve. Appendix D covers technical and advanced details: AES, Silver-Pohlig-Hellman, Baby-Step Giant-Step and the index-calculus algorithm, Brand''s digital cash scheme, and radix-64 encoding. Probability theory is the topic of Appendix E including: basic methods, random variables, expectation and variance, binomial distribution, the law of large numbers, and error-detection. Appendix F is devoted to recognizing primes: primality and compositness tests, Miller-Selfridge-Rabin, Primes is in P, and generation of random primes. The last appendix has just under 400 exercises for all chapters so an instructor may use the book as a text in a course or variety of courses. It also serves as a mechanism for an individual to test their understanding of the topics covered, including many puzzles to be solved for sheer interest. The index has nearly 5,000 entries for easy access to any topic, and the extensive bibliography, with nearly 300 entries for further reading, ensures the reader will have the best of all possible references. Moreover, the bibliography has the page reference of each and every entry --- exactly where it is cited in text. This is a feature not often seen in the literature, but is very useful for the reader. At roughly 700 pages, it will be the only source book you need, with virtually any topic you want on the subject covered.

Complete integrability beyond {L}iouville-{A}rnol\cprime d

Delay differential equations with {H}ill's type growth rate and linear harvesting

Edge-antipodal 3-polytopes

Eisenstein equations and central norms

Estimation of parameters for a Birnbaum-Saunders regression model with censored data

Fast Elliptic Curve Point Multiplication Using Double Base Chains

Finding the best face on a Voronoi polyhedron - the strong dodecahedral conjecture revisited

Generalized separation theorems for singular values of a matrix and their applications in canonical correlation analysis

Holomorphic functions of slow growth on coverings of strongly pseudoconvex manifolds

Indefinite Linear Algebra with Applications

Indivisible homogeneous directed graphs and a game for vertex partitions

Let $\mathcal T$ be a set of finite tournaments. We will give a necessary and sufficient condition for the $\mathcal T$-free homogeneous directed graph $\Ha_{\mathcal T}$ to be {\sl divisible}; that is, that there is a partition of $\Ha_{\mathcal T}$ into two sets neither of which contains an isomorphic copy of $\Ha_{\mathcal T}$.

Inverse problems for damped vibrating systems.

Isospectral vibrating systems. Part I: The spectral method.

Jackknifing in Partially Linear Regression Models With Serially Correlated Errors

Modeling and Pricing of Variance Swaps for Stochastic Volatilities with Delay

Necessary and Sufficient Conditions for the Central Norm to Equal 2^h in the Simple Continued Fraction Expansion of (2^h)^(1/2) for Any Odd c>1

Norm form equations and continued fractions

On antipodal 3-polytopes.

On Estimating HIV Prevalence in Canada and in the United States

On exponential dichotomy, {B}ohl-{P}erron type theorems and stability of difference equations

On the completeness of pseudo-Riemannian metrics

On the pseudospectra of matrix polynomials.

Optimal stopping behavior of equity-linked investment products with regime switching

Point counting on Picard curves in large characteristic.

Riemann and his zeta function

Simultaneous Lipschitz extensions

Strong lifting

Testing Herterocedasticity in Partially Linear Regression

Total Energy Singular Vectors for Atmospheric Chemical Transport Models