Physical Sciences and Mathematics Commons^™

All About 1089, Lara Pudwell

Lara K. Pudwell

No abstract provided.

A Mathematical Regression Of The U.S. Gross Private Domestic Investment 1959-2001, Byron E. Bell

Byron E. Bell

SUMMARY OF PROJECT What did I do? A study of the role the U.S. stock markets and money markets have possibly played in the Gross Private Domestic Investment (GPDI) of the United States from the year 1959 to the year 2001 and I created a Multiple Linear Regression Model (MLRM).

Sequences, Series, And Function Approximation, Lawrence Stout

Lawrence N. Stout

Sequences are important in approximation: the usual representation of real numbers using decimals is in fact the process of giving a sequence of rational numbers approximation the real number in question successively better as more decimal places are given. These decimal approximation sequences are actually rather special: successive decimal approximations never get smaller (so the sequence is monotone nondecreasing) and two approximations which agree to the kth decimal place differ by at most 10-k (so the sequence is a Cauchy sequence: to make two values in the sequence close to each other all you need to do is take them …

Bayesian Wavelet Estimation Of Partially Linear Models, Leming Qu

Leming Qu

A Bayesian wavelet approach is presented for estimating a partially linear model (PLM). A PLM consists of a linear part and a nonparametric component. The nonparametric component is represented with a wavelet series where the wavelet coefficients have assumed prior distributions. The prior for each coefficient consists of a mixture of a normal distribution and a point mass at 0. The linear parameters are assumed to have a normal prior. The hyperparameters are estimated by the marginal maximum likelihood estimator using the direct maximization. The model selection and model averaging methods give different estimates of the model parameters. MCMC computation …

Fun With Fractals, Borbala Mazzag

Borbala Mazzag

No abstract provided.

Implementing Standards-Based Mathematics Curricula Into The Teaching Of Mathematics And Education Courses For Prospective Teachers, Shannon Driskell, J. Herrelko

Shannon O.S. Driskell

Driskell, S. (Co-PI), & Herrelko, J. (Co-PI), University of Dayton Learning Teaching Center Innovation Grants, $7,500, Year: 2006 - 2007.

The Tablet Pc For Faculty: A Pilot Project, Rob Weitz, Bert Wachsmuth, Danielle Mirliss

Bert Wachsmuth

This paper describes a pilot project with the purpose of evaluating the usefulness of tablet PCs for university professors. The focus is on the value of tablets primarily with respect to teaching and learning (and not for research or administrative work). Sixty-four professors, distributed across the various schools of a university, were provided with tablet PCs and were trained in their use.

Multivariate Expansion Associated With Sheffer-Type Polynomials And Operators, Tian-Xiao He, Leetsch Hsu, Peter Shiue

Tian-Xiao He

With the aid of multivariate Sheffer-type polynomials and differential operators, this paper provides two kinds of general expansion formulas, called respectively the first expansion formula and the second expansion formula, that yield a constructive solution to the problem of the expansion of A(ˆt)f([g(t)) (a composition of any given formal power series) and the expansion of the multivariate entire functions in terms of multivariate Sheffer-type polynomials, which may be considered an application of the first expansion formula and the Sheffer-type operators. The results are applicable to combinatorics and special function theory.

Construction Of Rational Points On Elliptic Curves Over Finite Fields, Andrew Shallue, Christiaan E. Van De Woestijne

Andrew Shallue

A New Type Of Orthogonality In Banach Spaces, Abeer Hasan

Abeer Hasan

On The Convergence Of The Summation Formulas Constructed By Using A Symbolic Operator Approach, Tian-Xiao He, Leetsch C. Hsu, Peter J.-S. Shiue

Tian-Xiao He

This paper deals with the convergence of the summation of power series of the form Σ_{a ≤ k ≤ b}f(k)x^k, where 0 ≤ a ≤ b < ∞, and {f(k)} is a given sequence of numbers with k ∈ [a, b) or f(t) a differentiable function defined on [a, b). Here, the summation is found by using the symbolic operator approach shown in [1]. We will give a different type of the remainder of the summation formulas. The convergence of the corresponding power series will be determined consequently. Several examples such as the generalized Euler's transformation series will also be given. In addition, we will compare the convergence of the given series transforms.

Absolute Equal Distribution Of The Eigenvalues Of Discrete Sturm-Liouville Problems, William F. Trench

William F. Trench

No abstract provided.

Numerical Approximation To Ζ(2n+1), Tian-Xiao He, Michael J. Dancs

Tian-Xiao He

In this short paper, we establish a family of rapidly converging series expansions ζ(2n +1) by discretizing an integral representation given by Cvijovic and Klinowski [3] in Integral representations of the Riemann zeta function for odd-integer arguments, J. Comput. Appl. Math. 142 (2002) 435–439. The proofs are elementary, using basic properties of the Bernoulli polynomials.

Functional Perturbations Of Nonoscillatory Second Order Difference Equations, William F. Trench

William F. Trench

No abstract provided.

On The Generalized Möbius Inversion Formulas, Tian-Xiao He, Peter J. S. Shiue3, Leetsch C. Hsu

Tian-Xiao He

We provide a wide class of M¨obius inversion formulas in terms of the generalized M¨obius functions and its application to the setting of the Selberg multiplicative functions.

An Euler-Type Formula For Ζ(2k +1), Tian-Xiao He, Michael J. Dancs

Tian-Xiao He

In this short paper, we give several new formulas for ζ(n) when n is an odd positive integer. The method is based on a recent proof, due to H. Tsumura, of Euler’s classical result for even n. Our results illuminate the similarities between the even and odd cases, and may give some insight into why the odd case is much more difficult.

Universal Series By Trigonometric System In Weighted Spaces, Sergo Armenak Episkoposian (Yepiskoposyan)

Sergo Armenak Episkoposian (Yepiskoposyan)

No abstract provided.

An Euler-Type Formula For Zeta (2k+1), Tian-Xiao He

Tian-Xiao He

No abstract provided.

Combinatorial Stochastic Processes , Jim Pitman

Jim Pitman

This is a set of lecture notes for a course given at the St. Flour summer school in July 2002. The theme of the course is the study of various combinatorial models of random partitions and random trees, and the asymptotics of these models related to continuous parameter stochastic processes. Following is a list of the main topics treated: models for random combinatorial structures, such as trees, forests, permutations, mappings, and partitions; probabilistic interpretations of various combinatorial notions e.g. Bell polynomials, Stirling numbers, polynomials of binomial type, Lagrange inversion; Kingman's theory of exchangeable random partitions and random discrete distributions; connections …