Mathematics Commons^™

2nd Annual Undergraduate Research Conference Abstract Book, University Of Missouri--Rolla

Undergraduate Research Conference at Missouri S&T

No abstract provided.

Stability Of The Gyroid Phase In Diblock Copolymers At Strong Segregation, Eric W. Cochran, Carlos J. Garcia-Cervera, Glenn H. Fredrickson

Eric W. Cochran

The gyroid phase in diblock copolymers at strong segregation was stabilized. The intriguing topology of the network structure has inspired a diverse array of potential applications ranging from high-performance separation membranes to photonic crystals. The pressure field enforces incompressibility, while the exchange field is conjugate to the composition pattern in the melt. The Laplacian operator is treated implicitly with a fourth-order backward differentiation formula (BDF4), whereas the source term is discretized explicitly using fourth-order accurate Adams-Bashford.

Multiple Lebesgue Integration On Time Scales, Gusein Sh. Guseinov, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We study the process of multiple Lebesgue integration on time scales. The relationship of the Riemann and the Lebesgue multiple integrals is investigated.

The Formal Laplace-Borel Transform Of Fliess Operators And The Composition Product, Yaqin Li, W. Steven Gray

Electrical & Computer Engineering Faculty Publications

The formal Laplace-Borel transform of an analytic integral operator, known as a Fliess operator, is defined and developed. Then, in conjunction with the composition product over formal power series, the formal Laplace-Borel transform is shown to provide an isomorphism between the semigroup of all Fliess operators under operator composition and the semigroup of all locally convergent formal power series under the composition product. Finally, the formal Laplace-Borel transform is applied in a systems theory setting to explicitly derive the relationship between the formal Laplace transform of the input and output functions of a Fliess operator. This gives a compact interpretation …

Melting And Solidification Study Of As-Deposited And Recrystallized Bi Thin Films, M. K. Zayed, H. E. Elsayed-Ali

Electrical & Computer Engineering Faculty Publications

Melting and solidification of as-deposited and recrystallized Bi crystallites, deposited on highly oriented 002-graphite at 423 K, were studied using reflection high-energy electron diffraction (RHEED). Films with mean thickness between 1.5 and 33 ML (monolayers) were studied. Ex situ atomic force microscopy was used to study the morphology and the size distribution of the formed nanocrystals. The as-deposited films grew in the form of three-dimensional crystallites with different shapes and sizes, while those recrystallized from the melt were formed in nearly similar shapes but different sizes. The change in the RHEED pattern with temperature was used to probe the melting …

Coalgebras And Their Logics, Alexander Kurz

Engineering Faculty Articles and Research

"Transition systems pervade much of computer science. This article outlines the beginnings of a general theory of specification languages for transition systems. More specifically, transition systems are generalised to coalgebras. Specification languages together with their proof systems, in the following called (logical or modal) calculi, are presented by the associated classes of algebras (e.g., classical propositional logic by Boolean algebras). Stone duality will be used to relate the logics and their coalgebraic semantics."

Advances And Applications Of Dezert-Smarandache Theory (Dsmt) For Information Fusion (Collected Works), Vol. 2, Florentin Smarandache, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

This second volume dedicated to Dezert-Smarandache Theory (DSmT) in Information Fusion brings in new fusion quantitative rules (such as the PCR1-6, where PCR5 for two sources does the most mathematically exact redistribution of conflicting masses to the non-empty sets in the fusion literature), qualitative fusion rules, and the Belief Conditioning Rule (BCR) which is different from the classical conditioning rule used by the fusion community working with the Mathematical Theory of Evidence.

Other fusion rules are constructed based on T-norm and T-conorm (hence using fuzzy logic and fuzzy set in information fusion), or more general fusion rules based on N-norm …