Department of Mathematics
Headlines
Academic Year 2000-01

  Two research presentations of Griff Elder in France.

[Posted:  Thu Jun 7 00:37:09 CDT 2001 ]

Dr. Griff Elder will spend this Summer in Europe on a research trip partially supported by UNO-UCR. He will give two research talks during prestigious conferences in France:
During the meeting Journees Arithmetiques in Lille on July 2-6, 2001, Dr. Elder will talk on Galois structure of the integers in cyclic extensions of local number fields⁴
Next Dr. Elder will attend the conference Galois Modules in Arithmetic Geometry (GaMAG) (July 9-13, 2001) during which he will give a presentation on Wild Extensions, Tame Group Rings and a Twist⁵
 

  Aaron Becker and Jennifer Waldren are the awardees of James Earl Scholarships.

[Posted:  Thu Jun 7 00:03:55 CDT 2001]

Upon the recommendation of the James Earl Scholarship Committee, Aaron Becker and Jennifer Waldren were awarded the 2001-2002 James Earl Scholarships. The Scholarship was established by Margaret Earl in honor of Dr. James M. Earl, Professor and Chair of Mathematics at the Municipal University of Omaha from 1932 to 1962. The Scholarship supports outstanding undergraduate mathematics students at UNO. You may read more on Dr. Earl on page 3 of Fall'1999 Newsletter.
 

  A mini-course in Beer Sheva, Israel.

[Posted:  Tue May 15 16:04:59 CDT 2001 ]

Dr. Andrzej Roslanowski will give a mini-series of lectures Forcing with norms during Conference and Workshop in honor of Professor Saharon Shelah, winner of Bolyai and Wolf Prizes . The meeting will be held in Ben-Gurion University of the Negev, Beer-Sheva, Israel, from Sunday, May 20, through Friday, May 25, 2001.
 

  A research talk in Las Vegas.

[Posted:  Mon Apr 23 17:49:31 CDT 2001 ]

Dr. Andrzej Roslanowski gave a research talk Consistently, every sup-measurable function is measurable in Special Session on Set Theory during 2001 Spring Western Sectional Meeting of the American Mathematical Society, which was held in Las Vegas, NV, on April 21-22, 2001.
 

  Larry Stephens honored with the Alumni Outstanding Teaching Award!

[Posted:  Mon Apr 2 17:12:41 CDT 2001 ]

Dr. Larry Stephens is among the nine faculty members who will be honored with the Alumni Outstanding Teaching Award, UNOmaha Notes reported on April 02, 2000. The ceremony, UNOmaha Faculty Honors Convocation, will take place on April 05.
 

  Two research presentations of our faculty at Lawrence.

[Posted:  Mon Apr 2 13:44:47 CDT 2001 ]

Two our faculty members were invited to give talks at Special Sessions during 2001 Spring Central Section Meeting of the American Mathematical Society which was held in Lawrence, KS, on March 30-31, 2001. Dr. Valentin Matache gave a lecture on Numerical Ranges of Some Special Classes of Operators in Special Session on C*-Algebras and Crossed Products. Dr. Andrzej Roslanowski gave presentation Possibly every real function is continuous on a non-null set in Special Session on Set Theoretic Topology and Boolean Algebra.
 

  New Results in the Renewal Theory

[Posted:  Fri Mar 23 23:45:01 CST 2001]

A research paper Some New Approximations for the Renewal Function ³ by Dr. Steve From has been accepted for publication in the journal Communications in Statistics - Simulation and Computation.
 

  Andrew Gacek scores extremely well on Putnam Exam !

[Posted:  Tue Mar 13 20:57:39 CST 2001]

It was recently announced that Andrew Gacek , a double major at UNO - Mathematics/CS, placed 86th out of the 2818 participants from Canada and the US who took the Sixty-First Annual William Lowell Putnam Mathematical Competition on Saturday December 2, 2000. He did this with a score of 40 points. Aaron Becker's performance was also noteworthy. He, also a double major Mathematics/CS, placed among the top 40% of contestants.
Putnam Exam is a very prestigious mathematical competition open only to regularly enrolled undergraduates in colleges and universities of the United States and Canada. Each year several UNO students participate.
 

  Intradepartmental Collaboration flourish

[Posted:   Thu Mar 8 13:36:08 CST 2001]

Research cooperation of Dr. Yi-Hsin Liu and Dr. Valentin Matache gave first fruits. Together with Dr. Han-lin Li and Dr. Po-Lung Yu they wrote a research article A Necessary and Sufficient Condition for Minimizing a Convex Frechet Differentiable Function on a Certain Hyperplane ² which now has been published in Journal of Mathematical Analysis and Applications.
 

  International Collaboration Pays Off

[Posted:   Wed Mar 7 18:17:09 CST 2001]

Supported by a grant from the UNO University Committee on Research, Dr. N. P. Byott of the School of Mathematical Sciences, University of Exeter (England), visited Dr. G. Griffith Elder in the Fall of 1999 to investigate a question in Algebraic Number Theory. The flurry of activity that followed this visit resulted in a research article, Biquadratic Extensions with One Break ¹, that now has been accepted for the Canadian Mathematical Bulletin. Elder and Byott will continue their collaboration this Summer when Elder will visit Exeter (supported by UNO-UCR).
 

  Matt Culek earns an NSF sponsored Research Experience for Undergraduates

[Posted:  Wed Mar 7 18:16:55 CST 2001]

Matt Culek, a double major at UNO - Mathematics/Physics, a Regents Scholar and a James Earl Scholar, is one of eight students selected nationally to participate in this summer's intensive 7 week REU program at the Rose-Hulman Institute of Technology. This prestigious program has produced international caliber mathematical break-throughs in previous summers. It is an exciting opportunity and a well deserved honor for Matt. His research will concern an important problem in Number Theory, the Partitions of the Integers. Besides paying his travel and housing expenses, the program pays a stipend of $3000.
 

  Headlines - news from our Department: one click from you!

[Posted:  Wed Mar 7 18:16:00 CST 2001]

The first Headlines are posted on March 07, 2001. There is a lot of news (good and bad) that should be reported here - please help your Webmaster in collecting that info!

Footnotes

Biquadratic Extensions with One Break ¹, Canadian Mathematical Bulletin, accepted.

Abstract:  We explicitly describe, in terms of indecomposable -modules, the Galois module structure of ideals in totally ramified biquadratic extensions of local number fields with only one break in their ramification filtration. This paper completes work [Elder: Canad. J. Math. 50 (5), 1998 pp. 1007-1047].

 

 

 

A Necessary and Sufficient Condition for Minimizing a Convex Frechet Differentiable Function on a Certain Hyperplane ², Journal of Mathematical Analysis and Applications, 253, 2001:290-296.

Abstract:  A convex Frechet differentiable function is minimized subject to a certain hyperplane at a point if the function is minimized in all directions which are defined by a finite set of vectors. The proposed approach is different from the Lagrange multiplier approach. At the end of this paper, a linear program is formulated to solve the case when the above given convex function is quadratic.

 

 

 

Some New Approximations for the Renewal Function, Communications in Statistics - Simulation and Computation³, accepted.

Abstract:  In this paper, an approximation for computing the (renewal function) solution of renewal-type integral equations is presented. This approximation is a modified rational function near the origin and switches to an asymptotic linear function for larger values of the time variable. This approach is similar to that of Garg and Kalagnanam (IEEE Trans. Reliability, 47:66-72 (1998)) but differs near the origin and has a different switch-over-point in general. Examples are presented for the truncated normal and Weibull distributions. Some alternative models are also discussed.

 

 

 

Galois structure of the integers in cyclic extensions of local number fields ⁴.

Abstract:  The ring of integers in a Galois extension provides us with a natural integral representation of the Galois group to study - although, under wild ramification, a general description of this object currently appears to be out of reach. In this talk, I will restrict my attention to cyclic, fully ramified p-extensions, L/K, themselves finite extensions of the p-adic numbers, Q_p. I will consider O_L, the ring of integers of L, as a module over the group ring O_k[G] for G=Gal(L/K) and O_k the ring of integers of a certain subfield k of K. After discussing some relevant integral representation theory and an extreme situation, almost maximal ramification, I will present some recent progress. By bounding the first ramification number (of L/K) from below, a restriction that includes one-half of its possible values, I am able to provide an explicit description of this integral representation. In a natural way, this description is determined by properties of the lower ramification numbers, the absolute ramification degree and inertia index alone.

 

 

 

Wild Extensions, Tame Group Rings and a Twist ⁵.

Abstract:  This talk will report on the Z[Gal(N/K)]-structure of the ring of integers (as well as other ambiguous ideals) in wildly ramified extensions N/K of number fields for which the group ring Z[Gal(N/K)] is of tame representation type. As there is no local-global problem to contend with, the results are essentially local.