Mathematics Commons^™

3. Derivatives Of Exponential Functions, Ruth Dover

More on Derivatives

Exploring the derivative of exponential functions.

Series 03, Ruth Dover

Series

Considers the creation of a general Maclaurin series.

Free Energies For Singleton Minimal States, John Murrough Golden

Articles

It is assumed that any free energy funcuon exhibits strict periodic benav10r tor histories that have been periodic for all past times. This is not the case for the work function, which, however, has the usual defining properties of a free energy. Fonns given m fairly recent years for the minimum and related free energies of linear materials with memory have this property. Materials for which the minimal states are all singletons are those for which at least some of the singularities of the Fourier transfonn of the relaxation function are not isolated. For such materials, the maximum free energy …

Application Of Virtual Reality Head Mounted Display For Investigation Of Movement: A Novel Effect Of Orientation Of Attention, Brendan Quinlivan, John Butler, Ines Beiser, Laura Williams, Eavan Mcgovern, Sean O'Riordan, Michael Hutchinson, Richard Reilly

Articles

Objective. To date human kinematics research has relied on video processing, motion capture and magnetic search coil data acquisition techniques. However, the use of head mounted display virtual reality systems, as a novel research tool, could facilitate novel studies into human movement and movement disorders. These systems have the unique ability of presenting immersive 3D stimulus while also allowing participants to make ecologically valid movement-based responses. Approach. We employed one such system (Oculus Rift DK2) in this study to present visual stimulus and acquire head-turn data from a cohort of 40 healthy adults. Participants were asked to complete head movements …

Using Ciliate Operations To Construct Chromosome Phylogenies, Jacob L. Herlin, Anna Nelson, Marion Scheepers

Mathematics Faculty Publications and Presentations

Whole genome sequencing has revealed several examples where genomes of different species are related by permutation. The number of certain types of rearrangements needed to transform one permuted list into another can measure the distance between such lists. Using an algorithm based on three basic DNA editing operations suggested by a model for ciliate micronuclear decryption, this study defines the distance between two permutations to be the number of ciliate operations the algorithm performs during such a transformation. Combining well-known clustering methods with this distance function enables one to construct corresponding phylogenies. These ideas are illustrated by exploring the phylogenetic …

Voting Aggregation Leads To (Interval) Median, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When we have several results of measuring or estimating the same quantities, it is desirable to aggregate them into a single estimate for the desired quantities. A natural requirement is that if the majority of estimates has some property, then the aggregate estimate should have the same property. It turns out that it is not possible to require this forall possible properties -- but we can require it for bounds, i.e., for properties that the value of the quantity is in between given bounds a and b. In this paper, we prove that if we restrict the …

Why Superellipsoids: A Probability-Based Explanation, Pedro Barragan Olague, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, it turns out that the set of possible values of the deviation vector is (approximately) a super-ellipsoid. In this paper, we provide a theoretical explanation for this empirical fact -- an explanation based on the natural notion of scale-invariance.

On Geometry Of Finsler Causality: For Convex Cones, There Is No Affine-Invariant Linear Order (Similar To Comparing Volumes), Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Some physicists suggest that to more adequately describe the causal structure of space-time, it is necessary to go beyond the usual pseudo-Riemannian causality, to a more general Finsler causality. In this general case, the set of all the events which can be influenced by a given event is, locally, a generic convex cone, and not necessarily a pseudo-Reimannian-style quadratic cone. Since all current observations support pseudo-Riemannian causality, Finsler causality cones should be close to quadratic ones. It is therefore desirable to approximate a general convex cone by a quadratic one. This cane be done if we select a hyperplane, and …

A Model For Spheroid Versus Monolayer Response Of Sk-N-Sh Neuroblastoma Cells To Treatment With 15-Deoxy-Pgj2, Dorothy I. Wallace, Ann Dunham, Paula X. Chen, Michelle Chen, Milan Huynh, Evan Rheingold, Olivia F. Prosper

Mathematics Faculty Publications

Researchers have observed that response of tumor cells to treatment varies depending on whether the cells are grown in monolayer, as in vitro spheroids or in vivo. This study uses data from the literature on monolayer treatment of SK-N-SH neuroblastoma cells with 15-deoxy-PGJ₂ and couples it with data on growth rates for untreated SK-N-SH neuroblastoma cells grown as multicellular spheroids. A linear model is constructed for untreated and treated monolayer data sets, which is tuned to growth, death, and cell cycle data for the monolayer case for both control and treatment with 15-deoxy-PGJ₂. The monolayer …

Multilinear And Multiparameter Pseudo-Differential Operators And Trudinger-Moser Inequalities, Lu Zhang

Wayne State University Dissertations

Pseudo-differential operators play important roles in harmonic analysis, several complex variables, partial differential equations and other branches of modern mathematics. We studied some types of multilinear and multiparameter Pseudo-differential operators. They include a class of trilinear Pseudo-differential operators, where the symbols are in the forms of products of Hormander symbols defined on lower dimensions, and we established the Holder type Lp estimate for these operators. They derive from the trilinear Coifman-Meyer type operators with flag singularities. And we also studied a class of bilinear bi-parameter Pseudo-differential operators, where the symbols are taken from the general Hormander class, and we studied …

Multiple Problem-Solving Strategies Provide Insight Into Students’ Understanding Of Open-Ended Linear Programming Problems, Marla A. Sole

Publications and Research

Open-ended questions that can be solved using different strategies help students learn and integrate content, and provide teachers with greater insights into students’ unique capabilities and levels of understanding. This article provides a problem that was modified to allow for multiple approaches. Students tended to employ high-powered, complex, familiar solution strategies rather than simpler, more intuitive strategies, which suggests that students might need more experience working with informal solution methods. During the semester, by incorporating open-ended questions, I gained valuable feedback, was able to better model real-world problems, challenge students with different abilities, and strengthen students’ problem solving skills.

Risk And Safety Of Complex Network Systems, Xiao-Bing Hu, Adrian V. Gheorghe, Mark S. Leeson, Supeng Leng, Julien Bourgeois, Xiaobo Qu

Engineering Management & Systems Engineering Faculty Publications

No abstract provided.

A Hierarchical Statistical Engineering Modeling Methodology, Teddy Steven Cotter

Engineering Management & Systems Engineering Faculty Publications

In the ASEM-IAC 2015, Cotter (2015) proposed a systemic joint deterministic-stochastic dynamic causal Bayesian statistical engineering model that addressed the knowledge gap needed to integrate deterministic mathematical engineering models within a stochastic framework. However, Cotter did not specify the modeling methodology through which statistical engineering models could be developed, diagnosed, and applied to predict systemic mission performance. This paper updates research into the development a hierarchical statistical engineering modeling methodology and sets forth the initial theoretical foundation for the methodology.

Variational Analysis And Stability In Optimization, M. Ebrahim Sarabi

Wayne State University Dissertations

The dissertation is devoted to the study of the so-called full Lipschitzian stability of local solutions to finite-dimensional parameterized problems of constrained optimization, which has been well recognized as a very important property from both viewpoints of optimization theory and its applications. Employing second-order subdifferentials of variational analysis, we obtain necessary and sufficient conditions for fully stable local minimizers in general classes of constrained optimization problems including problems of composite optimization as well as problems of nonlinear programming with twice continuously differentiable data. Based on our recent explicit calculations of the second-order subdifferential for convex piecewise linear functions, we establish …

Nonlinear Stochastic Systems And Controls: Lotka-Volterra Type Models, Permanence And Extinction, Optimal Harvesting Strategies, And Numerical Methods For Systems Under Partial Observations, Ky Quan Tran

Wayne State University Dissertations

This dissertation focuses on a class of stochastic models formulated using stochastic differential equations with regime switching represented by a continuous-time Markov chain, which also known as hybrid switching diffusion processes. Our motivations for studying such processes in this dissertation stem from emerging and existing applications in biological systems, ecosystems, financial engineering, modeling, analysis, and control and optimization of stochastic systems under the influence of random environments, with complete observations or partial observations.

The first part is concerned with Lotka-Volterra models with white noise and regime switching represented by a continuous-time Markov chain. Different from the existing literature, the Markov …

The Maximum Multiplicity Of An Eigenvalue Of Symmetric Matrices With A Given Graph, Keivan Hassani Monfared, Sudipta Mallik

Mathematics Faculty Research

For a graph G, M(G) denotes the maximum multiplicity occurring of an eigenvalue of a symmetric matrix whose zero-nonzero pattern is given by edges of G. We introduce two combinatorial graph parameters T^-(G) and T^+(G) that give a lower and an upper bound for M(G) respectively, and we show that these bounds are sharp.

Photo Of Euler Semimagic Square With Exercises., Jeremiah Farrell

Scholarship and Professional Work - LAS

A submission to the Gardner Birthday Celebration on the occasion of his 102nd birthday in October 2016.

A Special Tribute To Martin Gardner, Jeremiah Farrell

Scholarship and Professional Work - LAS

There are exactly 12 different letters in the phrase GATHERING FOR MARTIN GARDNER. We use each of the 12 letters three times each in 18 different two-letter words that are to be placed on the nodes of the graph so adjoining nodes have a letter in common.

You Like Japan, Jeremiah Farrell, Kate Jones

Scholarship and Professional Work - LAS

Jeremiah's puzzle "You Like Japan", which was exchanged at the 2016 International Puzzle Party in Kyoto, Japan, alongside Kate Jone's "You Like Japan" 12x12 Challenge. 100 puzzle designers create 100 copies of their puzzle and pass it out at the party and exchange them. This puzzle is manufacured by Kadon Enterprises, Inc. as "You Like Japan".

Hidden Symmetries And Commensurability Of 2-Bridge Link Complements, Christian Millichap, William Worden

Faculty Publications

In this paper, we show that any nonarithmetic hyperbolic 2-bridge link complement admits no hidden symmetries. As a corollary, we conclude that a hyperbolic 2-bridge link complement cannot irregularly cover a hyperbolic 3-manifold. By combining this corollary with the work of Boileau and Weidmann, we obtain a characterization of 3-manifolds with nontrivial JSJ-decomposition and rank-two fundamental groups. We also show that the only commensurable hyperbolic 2-bridge link complements are the figure-eight knot complement and the 6²₂ link complement. Our work requires a careful analysis of the tilings of R² that come from lifting the canonical triangulations of …