University of Calgary

# Publications - 2005

## A Continuous-time GARCH model for stochastic volatility with delay

Swishchuk, Anatoliy and Kazmerchuk, Yuriy and Wu, Jianhong

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

Balazs, Csikos, Langi, Zsolt and Naszodi, Marton

## A generalized Mahalanobis distance for mixed data

de Leon, Alexander and Carriere, KC

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

Braverman, Elena, Israeli, M. and Averbuch, A.

## A higher-dimensional partial Legendre transform, and regularity of degenerate Monge-Ampère equations

Rios, Cristian, Sawyer, Eric and Wheeden, Richard

## Algorithms for hyperbolic quadratic eigenvalue problems.

Guo, Chun-Hua and Lancaster, Peter

## Allocating vertex Ï-guards in simple polygons via pseudo-triangulations

Speckmann, Bettina and Toth, Csaba

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

Goncalves, Daciberg L., Kudryavtseva, Elena and Zieschang, Heiner

## An Asymptotic Theory for Semiparametric Generalized Least Squares Estimation in Partially Linear Regression Models

Chen, Gemai and You, Jinhong

## A New Multivariate Control Chart for Monitoring Both Location and Dispersion

Chen, Gemai and S.W. Cheng, H. Xie

## An Extended EWMA Mean Chart

Chen, Gemai and L. Zhang

Mollin, Richard

## Approximation of positive matrices by transitive matrices.

Farkas, A., Lancaster, Peter and Rozsa, P.

## Binary space partition of orthogonal subdivisions

Hershberger, John, Suri, Subhash and Toth, Csaba

## Binary space partitions: recent developments

Toth, Csaba in Combinatorial and Computational Geometry, vol. 52 of MSRI Publications

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

Chen, Gemai and J. You, X. Zhou

## Canonical forms for hermitian matrix pairs under strict equivalence and congruence.

Lancaster, Peter and Rodman, L.

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

Lancaster, Peter and Rodman, L.

## Cell Shape Analysis, A Statistical Approcah

Nettel-Aguirre, Alberto

## Censored multiple regression by the method of average derivatives

Lu, Xuewen and Burke, Murray

Bisztriczky, Ted

## Chromatic numbers and products

Duffus, Dwight and Sauer, Norbert

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 $f(n)\geq {n/2}$.

Mollin, Richard

## Classification of Singularities and Bifurcations of Critical Points of Even Functions

Kudryavtseva, Elena and Lakshtanov, Evgeny L.

## Clean general rings

Nicholson, W. Keith and Zhou, Y.

## Codes; The Guide to Secrecy from Ancient to Modern Times

Mollin, Richard

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.

## Comparison of stereoscopic digital imaging to film in the identification of macular degeneration

Somani, R, Tennant, M, Rudnisky, CJ, Weis, E, Ting, A, Greve, M, Hinz, B and de Leon, Alexander

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

Bates, Larry and Cushman, Richard

Brudnyi, Alex

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

Berezansky, L., Braverman, Elena and Idels, L.

## Development of a global stochastic model describing the relationship between the distribution of individual cell physiological states and population physiological state

McKellar, R.C. and Lu, Xuewen

## Edge-antipodal 3-polytopes

Bezdek, Karoly, Bisztriczky, Ted and Boroczky, Karoly

Mollin, Richard

## Endomorphisms that are the sum of a unit and a root of a fixed polynomial

Nicholson, W. Keith and Zhou, Y.

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

Desmond, A.F., Rodriguez-Yam, G.A. and Lu, Xuewen

Bezdek, Karoly

Mollin, Richard

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

Xie, C., Singh, R.S., Smith, B. and Lu, Xuewen

Brudnyi, Alex

Brudnyi, Alex

## Improved Estimation of Regression Parameters in Measurement Error Models

Kim, Hyang Mi and Saleh, A.K.Md.E

## Indefinite Linear Algebra with Applications

Gohberg, Israel, Lancaster, Peter and Rodman, Leiba

## Indivisible homogeneous directed graphs and a game for vertex partitions

Sauer, Norbert and El-Zahar

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 $\Ha_{\mathcal T}$.

## Indivisible homogeneous directed graphs and a game for vertex partitions

Sauer, Norbert and M. El-Zahar

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 Modeling of Aerosol Dynamics using Adjoints - Theoretical and Numerical Considerations

Sandu, Adrian, Liao, Wenyuan, Carmichael, G.R., Henze, D.K. and Seinfeld, J.H.

## Inverse problems for damped vibrating systems.

Lancaster, Peter and Prells, U.

## Isospectral vibrating systems. Part II: Structure preserving transformations.

Prells, U. and Lancaster, Peter

Lancaster, Peter

## Iterative Weighted Semiparametric Least Squares Estimation in Repeated Measurement Partially Linear Regression Models

Chen, Gemai and J. You

## Jackknifing in Partially Linear Regression Models With Serially Correlated Errors

Chen, Gemai and J. You, X. Zhou

Mollin, Richard

## Modeling and Pricing of Variance Swaps for Stochastic Volatilities with Delay

Swishchuk, Anatoliy

## Morphic modules

Nicholson, W. Keith and Sanchez Campos, E.

Mollin, Richard

## New Developments in Chemical Data Assimilation: Computational Tools

A. Sandu, GR Charmichael, T. Chai, E. Constantinescu and Liao, Wenyuan

Mollin, Richard

Mollin, Richard

## On antipodal 3-polytopes.

Boroczky, Karoly and Bisztriczky, Ted

## On coincidence points of mappings of torus to a surface

Bogatyi, Semeon A., Kudryavtseva, Elena and Zieschang, Heiner

Aggarwala, Ben

## On Eulerian and regular perfect path double covers of graphs

Seyffarth, Karen and Wang, Chengde

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

Berezansky, L. and Braverman, Elena

## On persistence of a delay differential equation with positive and negative coefficients

Berezansky, L. and Braverman, Elena

Bates, Larry

Bezdek, Karoly

## On the pseudospectra of matrix polynomials.

Lancaster, Peter and Psarrakos, P.

## On the relative distances of six points in a plane convex body

Langi, Zsolt and Böröczky, Károly

Let $C$ be a convex body in the Euclidean plane. By the relative distance of points $p$ and $q$ we mean the ratio of the Euclidean distance of $p$ and $q$ to the half of the Euclidean length of a longest chord of $C$ parallel to $pq$. In this note we find the least upper bound of the minimum pairwise relative distance of six points in a plane convex body.

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

Cheung, Ka Chun and Yang, Hailiang

## Pairwise likelihood approach to grouped continuous model and its extension

de Leon, Alexander

## Point counting on Picard curves in large characteristic.

Bauer, Mark, Teske, Edlyn and Weng, Annegret

## Removing the cocycle in a momentum map

Bates, Larry and Cushman, Richard

## Riemann and his zeta function

Kudryavtseva, Elena, Saidak, Filip and Zvengrowski, Peter

## Scaling Ozone Responses of Forest Trees to the Ecosystem Level in a Changing Climate

Karnosky, D. F., Pregitzer, K. S., Zak, D. R., Kubiske, M. E., Hendrey, G. R., Weinstein, D. and Nosal, Miloslav

## Simultaneous Lipschitz extensions

Brudnyi, Alex and Brudnyi, Yuri

Nosal, Miloslav

## Strong lifting

Nicholson, W. Keith and Zhou, Y.

## Sufficient conditions for the global stability of nonautonomous higher order difference equations

Berezansky, Leonid, Braverman, Elena and Liz, Eduardo

## Testing Herterocedasticity in Partially Linear Regression

Chen, Gemai and J. You

## The rotation number and the herpolhode angle in {E}uler's top

Bates, Larry, Cushman, Richard and Savev, Emil