Yang Wang, MS Candidate in Applied Mathematics, University of Dayton: Compound orthogonal array
ABSTRACT: Factorial experiments focus on determining the level combinations with a desirable mean response, often as well as a desirable variance. In this talk, we will introduce compound orthogonal arrays for factorial analysis. Compound orthogonal arrays carry some attractive properties that Taguchi's direct product arrays do not share.
We will firstly introduce Taguchi's direct product arrays, orthogonal arrays, compound orthogonal arrays, complete/fractional factorial arrays, and then focus on discussing four cases in compound orthogonal arrays, Complete & Complete, Fractional & Complete, Complete & Fractional, and Fractional & Fractional.The motivation of maximizing the strengths of the control-factor array, error-factor array, and overall array, and methods of maximization for CC and FC cases will be explained.
Refreshments will be served at 2:45 in SH 108.
Below are seminars held earlier this semester.
ABSTRACT: We find necessary and sufficient conditions for the existence of a 6-cycle system of K_n-E(F) for any spanning forest F and K_n-E(R) for any 2-regular subgraph R of the complete graph K_n.
Refreshments will be served at 2:50 in SH 106.
ABSTRACT: We discuss the structure of some special types of regular graphs satisfying some stronger property. We give upper bounds on the order of such graphs along with examples of the so-called "extremal graphs" for this bound. Finally, we give a conjecture on the lower bound of such graphs along with examples.
Refreshments will be served at 2:50 in SH 106.
ABSTRACT:
Refreshments will be served at 2:50 in SH 106.
ABSTRACT: The use of statistical methods based on ranked set sampling can lead to a substantial improvement over analog methods associated with simple random sampling schemes. In this talk, I will discuss a rank based estimator and testing procedures for multiple linear regression models for the ranked set samples. The estimator is defined as the minimizer of the rank dispersion function with Wilcoxon scores. It is shown that the estimator of the regression parameter is asymptotically normal and it has higher Pitman asymptotic efficiency than simple random sample rank regression estimator. I will also introduce three testing procedures in order to test a general linear hypothesis. Testing procedures include dispersion, Wald and aligned rank test. It is shown that all these test statistics converge to a chi-square distribution and the aligned rank test reduces to simple random sample analog of the Kruskal-Wallis test for one way analysis of variance. Under the assumption of perfect judgment ranking, I will construct an optimal allocation design of order statistics for set sizes less than seven. The optimal allocation design quantifies middle observation(s) for symmetric unimodal distributions and smallest (largest)observation for right (left) skewed distributions.
Refreshments will be served at 2:50 in SH 108.
ABSTRACT: Nested changeover designs are described for experiments in which subjects are required to perform a series of tasks (levels of a factor B) under a given set of experimental conditions in any one session. The conditions (levels of a factor A) are changed from one session to another. Within each session, carryover effects may occur. This talk defines a class of nested changeover designs which are universally optimal for estimating the direct effects of the treatment combinations and the carryover effects of factors B.
Refreshments will be served at 2:50 in SH 108.
SHERMAN HALL ROOM 105
ABSTRACT: In standard regression models, statisticians usually assume the type of the distribution of the response variable is known prior to data analysis, for example, normal distribution, with only parameters unspecified. In that case, data were mainly used to determined the unspecified parameters, not the type of the distribution.
It is believed that data represents more than just determining the parameters within a given distribution. Data can be used to determine the type of the distribution along with the parameters within it, if properly used.
In this talk, we will study the case when the distribution of the response variable is assumed to have the general form of distributions of exponential family, with the concrete type of distributions unspecified. It is well know that exponential family covers various of distributions: Normal, Binomial, Multinomial, Possion, Gamma, Inverse Gaussian, etc.. Data were used to determine its own distribution shape along with its parameters. Especially, we study the case when the number of parameters goes to infinity as the observation number goes to infinity. The proof of the large sample properties of the parameters fills out the gap in statistical theory in this area and it shows that the maximum likelihood estimates of the parameters are consistent and follow asymptotically normal distribution.
Refreshments will be served at 2:50 in SH 108.
ABSTRACT: The Kronecker-Weber theorem tells us that every abelian extension K of Q is a subfield of some cyclotomic field Q(zetan). Moreover, we can determine a suitable value of n using only knowledge about the ramification of primes in K. The situation is more complicated for non-abelian extensions. Serre's conjecture asserts that number fields whose Galois groups are subgroups of GL_2(Z/pZ) and which satisfy a mild parity condition arise from certain modular forms via a construction of Deligne. As in the abelian case, Serre's conjecture allows us to pinpoint the modular form corresponding to a field K based on number theoretic invariants of K. We will discuss this correspondence, and touch on some generalizations of Serre's conjecture.
Refreshments will be served at 2:45 in SH 108.
ABSTRACT: A function f is in the class V2p iff f(z)=e-az^(2p+2)g(z) where a is less than or equal to 0, and g is a constant multiple of a real entire function of genus less than or equal to 2p+1 with only real zeros. The class U2p is defined as follows: U0=V0, U2p=V2p-V2p-2. Functions in the class U2p* are represented as g(z)=c(z)f(z) where f is in U2p and c is a real polynomial with no real zeros. Every real entire function g, of finite order with at most finitely many non-real zeros satisfies g is in U2p* for a unique p.
We will examine functions in U2p* of the form f(z)=P(z)eQ(z). We will count the non-real zeros of f" and discuss the "extraordinary zeros" of f". Then we will show, for a subclass of all f in U2p, necessary and sufficient conditions for f" to have exactly 2p non-real zeros. For a subclass of U2p* we show that if f' has only real zeros, then f" has exactly 2p non-real zeros. For all f in U2p* we show that 2p is a lower bound for the number of non-real zeros of f(k) for k greater than or equal to 2.
Refreshments will be served at 2:45 in SH 108.
ABSTRACT: Descent theory involves the study of what happens when one changes the base field (or base ring) of an algebraic structure. Extending the field is not usually a problem. If K, a subset of E is a field extension, and if H is some "K-object" (like a vector space, associative algebra, or Lie algebra over K), then we can make ExH an "E-object". However, there is often a challenge when you have an E-object and want to restrict the field (or "descend" to a smaller field), and many interesting questions arise. In this talk we will discuss descent theory when applied to the algebraic structures coalgebras and Hopf algebras.
Refreshments will be served at 2:45 in SH 108.
ABSTRACT: This talk is concerned with a new conservative finite difference method for solving the generalized nonlinear Schrödinger (GNLS) equation. The equation has been playing an important role in the nonlinear wave theory and its applications. The numerical scheme is constructed through the semidiscretization and an application of the quartic spline approximation. Central difference and extrapolation formulae are used for approximating the Neumann boundary conditions introduced. Both continuous and discrete energy conservation and the stability property are investigated. The numerical method provides an efficient and reliable way for computing long time solitary solutions given by the GNLS equation. A number of the results discussed in our talk will be published in volume 166 of the Journal of Computational Physics.
Refreshments will be served at 2:45 in SH 108.
Todd Eisworth, Northern Iowa University: Canonical Approximations
ABSTRACT: This is joint work with Lucia Junqueira of the University of Sao Paolo, Doug Mupasiri and Adrienne Stanley of the University of Northern Iowa, and Frank Tall of the University of Toronto.
When one thinks of "approximation theory" in a general sense, the picture that usually comes to mind is that of a complex structure being obtained from simpler structures by passing to some sort of limit. The Stone--Weierstrass theorem, for example, tells us that continuous functions on the unit interval can be viewed as uniform limits of polynomials. Does this sort of thing make sense in the context of topological spaces? How well is a complex space approximated by simpler spaces, and in what sense?
We will show how tools of mathematical logic and set theory allow us to give positive answers to these questions, and also give a few applications.
Refreshments will be served at 2:45 in SH 108.
Bogdana Georgieva, Oregon State University: The Generalized Variational Principle, contact transformations, and conservation laws
ABSTRACT: In the study of systems of differential equations, the concept of a conservation law, which is a mathematical description of the familiar laws of conservation of energy, conservation of momentum , and so on, plays an important role in the analysis of properties of the solutions. In 1918, Emmy Noether proved the remarkable result that for systems arising from the classical variational principle, every conservation law of the system comes from a corresponding symmetry property. Noether's method is the principle systematic procedure for constructing conservation laws for complicated systems of partial differential equations.
However, Noether's theorem does not apply to functionals defined by differential equations. The generalized variational principle, proposed by G. Herglotz, defines the functional whose extrema are sought by a differential equation, rather than an integral. This variational principle is important for a number of reasons including the fact that the corresponding generalized Euler-Lagrange equations define families of contact transformations.
A Noether-type theorem was proved for functionals defined by differential equations. It gives a systematic way of calculating conservation laws in non-conservative systems described by the generalized variational principle.
Refreshments will be served at 2:45 in SH 108.
Peter Hovey, University of Dayton Research Institute: Probabilistic Risk Assessment in the Aerospace Industry: A Comparison of Methods Used for Engines and for Aging Airframes
ABSTRACT: The aerospace engine manufacturers are being driven to design engines with better performance, higher reliability and lower weight. The high cost of new aircraft has driven the Air Force and commercial airlines to investigate the possibility of continuing to use aircraft beyond their original design lives. Probabilistic risk assessments have become an important tool to both engine manufacturers and the users of aging aircraft. This talk will discuss the uses of probabilistic risk analyses for both aerospace engines and aging aircraft and the types of computational tools that have been used.
Refreshments will be served at 2:45 in SH 108.
Jeong-gun Park, University of Georgia: Optimal Estimation Equations for Mixed Effects Models with dependent Observations
ABSTRACT: Estimating functions are a popular and useful method to conduct inferences when the specific form of the likelihood is unknown. Under this approach, we show the methods to derive optimal estimating functions for models containing mixed effects via an extended Godambe's optimality criterion. Two alternative methods, joint and marginal, to obtain optimal estimating functions are discussed. Applications to stochastic processes are discussed when mixed effects are involved. Results from a brief simulation study compare the performance of the estimates from the two methods.
Refreshments will be served at 2:45 in SH 108.
John Zimmerman, Ohio University: E. B. Seitz, 19th Century Ohio Pioneer Mathematician
ABSTRACT: Enoch Beery Seitz, an Ohio native, was a prominent mathematician in the 19th century. Testimony to his "greatness" was recorded in numerous news media of the time. In fact, the first article in the first issue of the American Mathematical Monthly was a biographical memorial written by his admirer B.F. Finkel, founder of the MAA. An early death cut short a very promising career; this talk will focus on his early years in Ohio and some haunting new developments.
Refreshments will be served at 2:45 in SH 108.
Yang Gao, University of Dayton graduate student: The method of quasilinearization and a three-point boundary value problem
This talk is given in partial fulfillment of the mathematics clinic project.
ABSTRACT: The method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand. In this paper, we show the method applies to two families of three-point boundary value problems for second order ordinary differential equations; linear boundary conditions and nonlinear conditions are addressed independently.
Refreshments will be served at 2:45 in SH 108.
Joan Hart, University of Dayton: Bohr Topologies and Compact Function Spaces
ABSTRACT: We consider (discrete) structures for a countable language, and their associated Bohr topologies. A compact Hausdorff space Y is homeomorphic to a subspace of some such structure with its Bohr topology iff Y is Talagrand compact. Furthermore, a compact Hausdorff space Y is Eberlein compact iff Y is homeomorphic to a closed subspace of some nice structure with its Bohr topology.
Atif Abueida, University of Dayton: Multidecomposition of the complete graph
ABSTRACT: We say that a subgraph G divides Km if the edges of Km can be partitioned into copies of G. Such a partition is called a G-decomposition or G-design. Let G and H be a pair of non-isomorphic graphs on fewer than m vertices. We introduce the idea of (G,H)-multidecomposition of Km. We also explore the problem of multidesigns for graph-pairs of order 5. This is joint work with Mike Daven of Mount Saint Mary College.