Applied Mathematics Commons^™

Metastability And Plasticity In A Conceptual Model Of Neurons, Bo Deng

Department of Mathematics: Faculty Publications

For a new class of neuron models we demonstrate here that typical membrane action potentials and spike-bursts are only transient states but appear to be asymptotically stable; and yet such metastable states are plastic — being able to dynamically change from one action potential to another with different pulse frequencies and from one spike-burst to another with different spike-per-burst numbers. The pulse and spike-burst frequencies change with individual ions’ pump currents while their corresponding metastable-plastic states maintain the same transmembrane voltage and current profiles in range. It is also demonstrated that the plasticity requires two one-way ion pumps operating in …

Advances And Applications Of Dsmt For Information Fusion (In Chinese), Florentin Smarandache, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Self-Authentication Of Audio Signals By Chirp Coding, Jonathan Blackledge, Eugene Coyle

Conference papers

This paper discusses a new approach to ‘watermarking’ digital signals using linear frequency modulated or ‘chirp’ coding. The principles underlying this approach are based on the use of a matched filter to provide a reconstruction of a chirped code that is uniquely robust in the case of signals with very low signal-to-noise ratios. Chirp coding for authenticating data is generic in the sense that it can be used for a range of data types and applications (the authentication of speech and audio signals, for example). The theoretical and computational aspects of the matched filter and the properties of a chirp …

A Computational Study Of The Effects Of Temperature Variation On Turtle Egg Development, Sex Determination, And Population Dynamics, Amy L. Parrott

Department of Mathematics: Dissertations, Theses, and Student Research

Climate change and its effects on ecosystems is a major concern. For certain animal species, especially those that exhibit what is known as temperature-dependent sex determination (TSD), temperature variations pose a possibly serious threat (Valenzuela and Lance, 2004). In these species, temperature, and not chromosomes, determines the sex of the animal (Valenzuela and Lance, 2004). It is conceivable therefore, that if the temperature changes to favor only one sex, then dire consequences for their populations could occur. In this dissertation, we examine possible effects that climate change may have upon Painted Turtles (Chrysemys picta), a species with TSD. We investigate …

Modeling And Analysis Of Biological Populations, Joan Lubben

Department of Mathematics: Dissertations, Theses, and Student Research

Asymptotic and transient dynamics are both important when considering the future population trajectory of a species. Asymptotic dynamics are often used to determine whether the long-term trend results in a stable, declining or increasing population and even provide possible directions for management actions. Transient dynamics are important for estimating invasion speed of non-indigenous species, population establishment after releasing biocontrol agents, or population management after a disturbance like fire. We briefly describe here the results in this thesis.

(1) We consider asymptotic dynamics using discrete time linear population models of the form n(t + 1) = An(t) where …

Ethnomathematics In The Dominican Republic: A Mathematics Education Approach To Knowledge And Emancipation, Sofia Pablo-Hoshino

Renée Crown University Honors Thesis Projects - All

This focus of this project was to look at the extent to which ethnomathematics is being used in the mathematics curriculum in theDominican Republic. Broadly described, ethnomathematics emphasizes that the culture, history, and experiences of the students are significant and therefore should be infused into the mathematics curriculum.

I read articles and books as well as traveled to theDominican Republicto conduct qualitative research. I interviewed 32 professionals consisting of mathematics teachers, mathematics professors, and mathematics education professors from theSantiagoandSanto Domingoareas. I then volunteered at the Dominican Republic Education and Mentoring (DREAM) Project where I was able to observe and participate …

Quantification Of Mandatory Sustainment Requirements, Joe M. Blackman

Theses and Dissertations

To emphasize the importance of sustainment, the DoD Joint Requirements Oversight Council addressed sustained Materiel readiness and established a mandatory Key Performance Parameter (KPP) for Materiel Availability; it also established supporting Key System Attributes (KSAs) for Materiel Reliability and Ownership Cost (Chairman of the Joint Chiefs of Staff Manual (CJCSM) 3170.01C, 2007). Current guidance requires two numbers: a threshold value and an objective value (Chairman of the Joint Chiefs of Staff Manual (CJCSM) 3170.01C, 2007). No distinction is made between the approaches in establishing these values for major system acquisitions, versus smaller, modification-focused efforts for existing systems. The Joint Staff …

Characterizing And Detecting Unrevealed Elements Of Network Systems, James A. Leinart

Theses and Dissertations

This dissertation addresses the problem of discovering and characterizing unknown elements in network systems. Klir (1985) provides a general definition of a system as “... a set of some things and a relation among the things" (p. 4). A system, where the `things', i.e. nodes, are related through links is a network system (Klir, 1985). The nodes can represent a range of entities such as machines or people (Pearl, 2001; Wasserman & Faust, 1994). Likewise, links can represent abstract relationships such as causal influence or more visible ties such as roads (Pearl, 1988, pp. 50-51; Wasserman & Faust, 1994; Winston, …

Probabilistic Estimation Of Rare Random Collisions In 3-Space, Timothy Holzmann

Theses and Dissertations

A study of risk assessment for artillery fire randomly colliding with fixed wing aircraft is presented. The research lends itself to a general study of collision models. Current models of object collisions fall under one of three categories: the historical model, the gas particle model, and the satellite model. These three vary in data requirements and mathematical representation of the impact event. The gas particle model is selected for its flexibility and robust estimation. However, current mathematical development in the literature does not include certain spatial and dynamic components necessary for a general encounter (collision) model. These are derived in …

Stability Of Traveling Waves In Thin Liquid Films Driven By Gravity And Surfactant, Ellen Peterson, Michael Shearer, Thomas P. Witelski, Rachel Levy

All HMC Faculty Publications and Research

A thin layer of fluid flowing down a solid planar surface has a free surface height described by a nonlinear PDE derived via the lubrication approximation from the Navier Stokes equations. For thin films, surface tension plays an important role both in providing a significant driving force and in smoothing the free surface. Surfactant molecules on the free surface tend to reduce surface tension, setting up gradients that modify the shape of the free surface. In earlier work [12, 13J a traveling wave was found in which the free surface undergoes three sharp transitions, or internal layers, and the surfactant …

Conceptual Circuit Models Of Neurons, Bo Deng

Department of Mathematics: Faculty Publications

A systematic circuit approach tomodel neurons with ion pump is presented here by which the voltage-gated current channels are modeled as conductors, the diffusion-induced current channels are modeled as negative resistors, and the one-way ion pumps are modeled as one-way inductors. The newly synthesized models are different from the type of models based on Hodgkin-Huxley (HH) approach which aggregates the electro, the diffusive, and the pump channels of each ion into one conductance channel. We show that our new models not only recover many known properties of the HH type models but also exhibit some new that cannot be extracted …

An Introduction To Dsmt, Florentin Smarandache, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or highly conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information systems involving artificial reasoning. In this introduction, we present a survey of our recent theory of plausible and paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT), developed for dealing with imprecise, uncertain and conflicting sources of information. We focus our presentation on the foundations of DSmT and on its most important rules of combination, rather than on browsing specific applications of DSmT available in literature. Several simple …

Mathematical Models: A Generalization From Population Biology And Time Scales, Martin Eggensperger

Theses and Dissertations

In this work, the theory of time scales calculus that we will employ is developed, as derivatives, integrals, and fundamental results are introduced. When necessary for subsequent discussion, other results are presented. The Hilger Complex Plane, the time scale exponential function, and its properties are given, as is a generalization of the variation of constants formula. The discrete and continuous Malthus population model, and the discrete and continuous Verhulst population models are investigated and analyzed. A unified and extended version of both models is developed and criteria for stability of critical solutions is presented. We investigate the relationship between both …

Gravity-Driven Thin Liquid Films With Insoluble Surfactant: Smooth Traveling Waves, Rachel Levy, Michael Shearer, Thomas P. Witelski

All HMC Faculty Publications and Research

The flow of a thin layer of fluid down an inclined plane is modified by the presence of insoluble surfactant. For any finite surfactant mass, traveling waves are constructed for a system of lubrication equations describing the evolution of the free-surface fluid height and the surfactant concentration. The one-parameter family of solutions is investigated using perturbation theory with three small parameters: the coefficient of surface tension, the surfactant diffusivity, and the coefficient of the gravity-driven diffusive spreading of the fluid. When all three parameters are zero, the nonlinear PDE system is hyperbolic/degenerateparabolic, and admits traveling wave solutions in which the …

Mathematical Methods In Composing Melodies, Thomas Brown

Undergraduate Theses and Capstone Projects

This thesis, “Mathematical Methods in Composing Melodies,” explores the different ways in which mathematics can be used to create music. Some research has been done in this field already. Richard F. Voss and John Clarke used fractals and different frequencies of noise to create music. The Greek composer Iannis Xenakis used Markovian Stochastic trees to create some of his compositions. Explored in this thesis are seven different methods to compose melodies. After compiling the different melodies, they were categorized by different musical periods based on the musical characteristics found in the melody. This thesis differs from other research that deals …

The Origin Of 2 Sexes Through Optimization Of Recombination Entropy Against Time And Energy, Bo Deng

Department of Mathematics: Faculty Publications

Sexual reproduction in nature requires two sexes, which raises the question why the reproductive scheme did not evolve to have three or more sexes. Here we construct a constrained optimization model based on the communication theory to analyze trade-offs among reproductive schemes with arbitrary number of sexes. More sexes on one hand lead to higher reproductive diversity, but on the other hand incur greater cost in time and energy for reproductive success. Our model shows that the two-sexes reproduction scheme maximizes the recombination entropy-to-cost ratio, and hence is the optimal solution to the problem.

A Unifying Field In Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability And Statistics - 6th Ed., Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

It was a surprise for me when in 1995 I received a manuscript from the mathematician, experimental writer and innovative painter Florentin Smarandache, especially because the treated subject was of philosophy - revealing paradoxes - and logics. He had generalized the fuzzy logic, and introduced two new concepts: a) “neutrosophy” – study of neutralities as an extension of dialectics; b) and its derivative “neutrosophic”, such as “neutrosophic logic”, “neutrosophic set”, “neutrosophic probability”, and “neutrosophic statistics” and thus opening new ways of research in four fields: philosophy, logics, set theory, and probability/statistics. It was known to me his setting up in …

Collected Papers Vol. 1, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Strings, Chains, And Ropes, Darryl H. Yong

All HMC Faculty Publications and Research

Following Antman [Amer. Math. Mon., 87 (1980), pp. 359–370], we advocate a more physically realistic and systematic derivation of the wave equation suitable for a typical undergraduate course in partial differential equations. To demonstrate the utility of this derivation, three applications that follow naturally are described: strings, hanging chains, and jump ropes.

Why Is The Number Of Dna Bases 4?, Bo Deng

Department of Mathematics: Faculty Publications

In this paper we construct a mathematical model for DNA replication based on Shannon’s mathematical theory for communication. We treatDNAreplication as a communication channel. We show that the mean replication rate is maximal with four nucleotide bases under the primary assumption that the pairing time of the G–C bases is between 1.65 and 3 times the pairing time of the A–T bases.

Sequences Of Numbers Involved In Unsolved Problems, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Here it is a long list of sequences, functions, unsolved problems, conjectures, theorems, relationships, operations, etc. Some of them are inter-connected. 1) Consecutive Sequence: 1,12,123,1234,12345,123456,1234567,12345678,123456789,12345678910, 1234567891011,123456789101112,12345678910111213,... How many primes are there among these numbers? In a general form, the Consecutive Sequence is considered in an arbitrary numeration base B.

References:

Student Conference, University of Craiova, Department of Mathematics, April 1979, "Some problems in number theory" by Florentin Smarandache.

Arizona State University, Hayden Library, "The Florentin Smarandache papers" special collection, Tempe, AZ 85287-1006, USA.

The Encyclopedia of Integer Sequences", by N. J. A. Sloane and S. Plouffe, Academic Press, San Diego, …

Reply To "Comment On ‘Atomic Spectral Line Free-Parameter Deconvolution Procedure’”, Vladimir Milosavljevic, Goran Poparic

Articles

We do not agree with the authors of the preceding Comment [X. Nikolic, X. Ojurovic, and X. Mijatovic, Phys. Rev. E, 67, 058401, 2003]. Our numerical procedure for the deconvolution of the theoretical asymmetric convolution integral of a Gaussian and a plasma broadened spectral line profile jA,R(λ) for spectral lines enables the determination of all broadening parameters. All broadening parameters can be determined directly from the recorded line profile of a single line, with minimal assumptions or prior knowledge. Additional experimental diagnostics are not required.

Thesis Digest: Mathematical Interpretation Of Political Power And The Arkansas State Government, Andrew King

Inquiry: The University of Arkansas Undergraduate Research Journal

On the whole, political power can he very difficult to quantify. A person may be powerful due to his or her personal charm, wealth, fame, credibility, or influential connections. Political bodies do not account for these qualities when creating voting procedures; they only assign voting rules to specific positions. For example, most would say that in the United States government that a Senator is more powerful than a Representative, but less powerful than the President, without knowing any way to quantify or verify those differences. Since the 1950's, mathematicians and political scientists have attempted to create mathematical models that partially …

Analysis Of The N-Card Version Of The Game Le Her, Arthur T. Benjamin, Alan J. Goldman

All HMC Faculty Publications and Research

We present a complete solution to a card game with historical origins. Our analysis exploits the convexity properties in the payoff matrix, allowing this discrete game to be resolved by continuous methods.

Modeling Control Of Hiv Infection Through Structured Treatment Interruptions With Recommendations For Experimental Protocol, Shannon Kubiak, Heather Lehr, Rachel Levy, Todd Moeller, Albert Parker, Edward Swim

All HMC Faculty Publications and Research

Highly Active Anti-Retroviral Therapy (HAART) of HIV infection has significantly reduced morbidity and mortality in developed countries. However, since these treatments can cause side effects and require strict adherence to treatment protocol, questions about whether or not treatment can be interrupted or discontinued with control of infection maintained by the host immune system remain to be answered. We present sensitivity analysis of a compartmental model for HIV infection that allows for treatment interruptions, including the sensitivity of the compartments themselves to our parameters as well as the sensitivity of the cost function used in parameter estimation. Recommendations are made about …

Cost Domination In Graphs, David John Erwin

Dissertations

Let G be a connected graph having order at least 2. A function f : V (G) —> {0 , 1 , . . . , diam G} for which f ( v ) < e(v) for every vertex v of G is a cost function on G. A vertex v with f ( v ) > 0 is an f-dominating vertex, and the set Vj~ = {v 6 V(G) : f(v) > 0} of f-dominating vertices is the f-dominating set. An /-dominating vertex v is said to f-dominate every vertex u with d(n, v) < f(u ), while …

Intractability And Undecidability In Small Sets Of Wang Tiles, Adam Delisse

Inquiry: The University of Arkansas Undergraduate Research Journal

Imagine a never-ending checkerboard, red and black squares alternating forever in every direction. Now close your eyes, wait for a second, and open them again. There is still the checkerboard, but is it different? Has somebody moved the checkerboard over two squares? Four squares? One million squares? It still looks the same. This is the nature of periodic tilings. Wang tiles are squares, much like the red and black ones used on a checkerboard, except Wang tiles have colors on their edges instead of on the whole square. Also, Wang tiles can only be put edge-to-edge with each other where …

An Analysis Of The Theory Of Functions Of One Real Variable, Robert J. Reed

Inquiry: The University of Arkansas Undergraduate Research Journal

Few undergraduates are aware that the Riemann integral taught in introductory calculus courses has only limited application-essentially this integral can be used only to integrate continuous functions over intervals. The necessity to integrate a broader class of functions over a wider range of sets that arises in many applications motivates the theory of abstract integration and functional analysis. The founder of this theory was the French mathematician Henri Lebesgue, who in 1902 defined the "Lebesgue measure" of subsets of the real line. The purpose of this project is to elucidate the theory of abstract measure spaces and of important spaces …

Collected Papers Vol. Iii, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Selection Of Curricular Topics Using Extensions Of Quality Function Deployment, Paul Kauffmann, Abel Fernandez, Charles Keating, Derya Jacobs, Resit Unal

Engineering Management & Systems Engineering Faculty Publications

Decision science can be an effective tool for enhancing organizational participation during strategic and complex decision making. This involvement develops a group consensus for relating organizational goals and the methods to achieve them. This paper describes an application of Quality Function Deployment (QFD) to define curricular topics that meet program objectives. Based on the ability of QFD to establish relationships, the model identifies the most important topics and quantifies their impact on meeting program goals. The model was developed to support restructuring of a Masters of Engineering Management degree program. The model supported decisions in selecting and prioritizing the required …