Physical Sciences and Mathematics Commons^™

Determinants Of Incidence And Hessian Matrices Arising From The Vector Space Lattice, Saeed Nasseh, Alexandra Seceleanu, Junzo Watanabe

Department of Mathematical Sciences Faculty Publications

We give explicit formulas for the determinants of the incidence and Hessian matrices arising from the interaction between the rank 1 and rank n−1 level sets of the subspace lattice of an n-dimensional finite vector space. Our exploration is motivated by the fact that both of these matrices arise naturally in the study of the combinatorial and algebraic Lefschetz properties for the vector space lattice and the graded Artinian Gorenstein algebra associated to it, respectively.

Building A Better Bijection Between Classes Of Compositions, James D. Diffenderfer

Department of Mathematical Sciences Faculty Publications

A bijective proof is given for the following theorem: The number of compositions of n into parts congruent to a (mod b) equals the number of compositions of n + b - a into parts congruent to b (mod a) that are greater than or equal to b. The bijection is then shown to preserve palindromicity.

Note On Rainbow Connection In Oriented Graphs With Diameter 2, Rebecca Holliday, Colton Magnant, Pouria Salehi Nowbandegani

Department of Mathematical Sciences Faculty Publications

In this note, we provide a sharp upper bound on the rainbow connection number of tournaments of diameter $2$. For a tournament $T$ of diameter $2$, we show $2 \leq \overrightarrow{rc}(T) \leq 3$. Furthermore, we provide a general upper bound on the rainbow $k$-connection number of tournaments as a simple example of the probabilistic method. Finally, we show that an edge-colored tournament of $k^{th}$ diameter $2$ has rainbow $k$-connection number at most approximately $k^{2}$.

Rainbow Generalizations Of Ramsey Theory - A Dynamic Survey, Shinya Fujita, Colton Magnant, Kenta Ozeki

Department of Mathematical Sciences Faculty Publications

In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs.

Causality Is Logically Definable-Toward An Equilibrium-Based Computing Paradigm Of Quantum Agents And Quantum Intelligence (Qaqi), Wen-Ran Zhang, Karl E. Peace

Biostatistics Faculty Publications

A survey on agents, causality and intelligence is presented and an equilibrium-based computing paradigm of quantum agents and quantum intelligence (QAQI) is proposed. In the survey, Aristotle’s causality principle and its historical extensions by David Hume, Bertrand Russell, Lotfi Zadeh, Donald Rubin, Judea Pearl, Niels Bohr, Albert Einstein, David Bohm, and the causal set initiative are reviewed; bipolar dynamic logic (BDL) is introduced as a causal logic for bipolar inductive and deductive reasoning; bipolar quantum linear algebra (BQLA) is introduced as a causal algebra for quantum agent interaction and formation. Despite the widely held view that causality is undefinable with …

Matrices From Vegetable Oils, Cashew Nut Shell Liquid, And Other Relevant Systems For Biocomposite Applications, Rafael Quirino, Thomas Garrison, Michael Kessler

Department of Chemistry and Biochemistry Faculty Publications

The partial replacement of petroleum-derived plastics and composites by novel bio-based materials from inexpensive, renewable, natural resources has the potential to greatly impact the plastics, coatings, and composites industries. Natural starting materials are usually abundant and renewable on a time scale many orders of magnitude smaller than petroleum. These characteristics, in combination with good mechanical properties, make the design of bio-based composites an interesting strategy for lowering the environmental impact of the plastics and composites industries while maintaining economical competitiveness. The present review will focus on the progress made over the last decade in the development of a select group …

Time-Dependent Regulation Of Apoptosis By Aen And Bax In Response To 2-Aminoanthracene Dietary Consumption, Worlanyo E. Gato, Dale B. Hales, Stacey R. Mcgee, Jay C. Means

Department of Chemistry and Biochemistry Faculty Publications

Background/Objective: The modulation of the toxic effects of 2-aminoanthracene (2AA) on the liver by apoptosis was investigated. Fisher-344 (F344) rats were exposed to various concentrations of 2AA for 14 and 28 days. The arylamine 2AA is an aromatic hydrocarbon employed in manufacturing chemicals, dyes, inks, and it is also a curing agent in epoxy resins and polyurethanes. 2AA has been detected in tobacco smoke and cooked foods.

Methods: Analysis of total messenger ribonucleic acid (mRNA) extracts from liver for apoptosis-related gene expression changes in apoptosis enhancing nuclease (AEN), Bcl2-associated X protein (BAX), CASP3, Jun proto-oncogene (JUN), murine double minute-2 p53 …