Engaging Students In The Practice Of Statistics Through Undergraduate Research,
2018
University of Mary Washington
Engaging Students In The Practice Of Statistics Through Undergraduate Research, Debra L. Hydorn
Mathematics Articles
As statisticians, we engage in a variety of activities, some of which are regularly integrated into our undergraduate courses. However, the individual courses that comprise a mathematics or statistics degree program might not provide students with experiences in the broader range of activities that define the practice of statistics. To remedy this situation, faculty can consider developing and mentoring undergraduate research projects. This article briefly discusses the skills that comprise statistical practice along with some course and program options for helping students to develop these skills. Then, types of undergraduate research projects in statistics are described to help faculty generate …
On The Efficacy Of High-Dose Ascorbic Acid As Anticancer Treatment: A Literature Survey,
2018
University of New Mexico
On The Efficacy Of High-Dose Ascorbic Acid As Anticancer Treatment: A Literature Survey, Florentin Smarandache, Victor Christianto
Branch Mathematics and Statistics Faculty and Staff Publications
Vitamin C (ascorbic acid, ascorbate) has a controversial history in cancer treatment. Emerging evidence indicates that ascorbate in cancer treatment deserves re-examination. As research results concerning ascorbate pharmacokinetics and its mechanisms of action against tumor cells have been published, and as evidence from case studies has continued to mount that ascorbate therapy could be effective if the right protocols were used, interest among physicians and scientists has increased.
Analysis Of A Vector-Borne Diseases Model With A Two-Lag Delay Differential Equation,
2018
Swarthmore College
Analysis Of A Vector-Borne Diseases Model With A Two-Lag Delay Differential Equation, Y. Qaddura, Nsoki Mavinga
Mathematics & Statistics Faculty Works
We are concerned with the stability analysis of equilibrium solutions for a two-lag delay differential equation which models the spread of vector-borne diseases, where the lags are incubation periods in humans and vectors. We show that there are some values of transmission and recovery rates for which the disease dies out and others for which the disease spreads into an endemic. The proofs of the main stability results are based on the linearization method and the analysis of roots of transcendental equations. We then simulate numerical solutions using MATLAB. We observe that the solution could possess chaotic and sometimes unbounded …
The Impact Of Spike-Frequency Adaptation On Balanced Network Dynamics,
2018
Swarthmore College
The Impact Of Spike-Frequency Adaptation On Balanced Network Dynamics, Victor J. Barranca, Han Huang , '19, Sida Li , '18
Mathematics & Statistics Faculty Works
A dynamic balance between strong excitatory and inhibitory neuronal inputs is hypothesized to play a pivotal role in information processing in the brain. While there is evidence of the existence of a balanced operating regime in several cortical areas and idealized neuronal network models, it is important for the theory of balanced networks to be reconciled with more physiological neuronal modeling assumptions. In this work, we examine the impact of spike-frequency adaptation, observed widely across neurons in the brain, on balanced dynamics. We incorporate adaptation into binary and integrate-and-fire neuronal network models, analyzing the theoretical effect of adaptation in the …
Intensity Inhomogeneity Correction Of Sd-Oct Data Using Macular Flatspace,
2018
Johns Hopkins University
Intensity Inhomogeneity Correction Of Sd-Oct Data Using Macular Flatspace, Andrew Lang, Aaron Carass, Bruno M. Jedynak, Sharon D. Solomon, Peter A. Calabresi, Jerry L. Prince
Mathematics and Statistics Faculty Publications and Presentations
Images of the retina acquired using optical coherence tomography (OCT) often suffer from intensity inhomogeneity problems that degrade both the quality of the images and the performance of automated algorithms utilized to measure structural changes. This intensity variation has many causes, including off-axis acquisition, signal attenuation, multi-frame averaging, and vignetting, making it difficult to correct the data in a fundamental way. This paper presents a method for inhomogeneity correction by acting to reduce the variability of intensities within each layer. In particular, the N3 algorithm, which is popular in neuroimage analysis, is adapted to work for OCT data. N3 works …
On The Density Of The Odd Values Of The Partition Function,
2018
Michigan Technological University
On The Density Of The Odd Values Of The Partition Function, Samuel Judge
Dissertations, Master's Theses and Master's Reports
The purpose of this dissertation is to introduce a new approach to the study of one of the most basic and seemingly intractable problems in partition theory, namely the conjecture that the partition function $p(n)$ is equidistributed modulo $2$. We provide a doubly-indexed, infinite family of conjectural identities in the ring of series $\Z_2[[q]]$, which relate $p(n)$ with suitable $t$-multipartition functions, and show how to, in principle, prove each such identity. We will exhibit explicit proofs for $32$ of our identities. However, the conjecture remains open in full generality. A striking consequence of these conjectural identities is that, under suitable …
Dynamical Analysis Of An N−H−T Cosmological Quintessence Real Gas Model With A General Equation Of State,
2018
Technological University Dublin
Dynamical Analysis Of An N−H−T Cosmological Quintessence Real Gas Model With A General Equation Of State, Emil Prodanov, Rossen Ivanov
Articles
The cosmological dynamics of a quintessence model based on real gas with general equation of state is presented within the framework of a three-dimensional dynamical system describing the time evolution of the number density, the Hubble parameter, and the temperature. Two global first integrals are found and examples for gas with virial expansion and van der Waals gas are presented. The van der Waals system is completely integrable. In addition to the unbounded trajectories, stemming from the presence of the conserved quantities, stable periodic solutions (closed orbits) also exist under certain conditions and these represent models of a cyclic Universe. …
Distribution Of Zeros Of Nondegenerate Functions On Short Cuttings Ii,
2018
Institute of Mathematics of National Academy of Sciences of Belarus.
Distribution Of Zeros Of Nondegenerate Functions On Short Cuttings Ii, Vasili Ivanovich Bernik, Natalia Viktorovna Budarina, Artyom Vadimovich Lunevich, Hugh O’Donnell
Articles
No abstract provided.
Catalogue Of Extreme Wave Events In Ireland: Revised And Updated For 14 680 Bp To 2017,
2018
Technological University Dublin
Catalogue Of Extreme Wave Events In Ireland: Revised And Updated For 14 680 Bp To 2017, Laura Cooke, Emiliano Renzi, John M. Dudley, Colm Clancy, FréDéRic Dias
Articles
This paper aims to extend and update the survey of extreme wave events in Ireland that was previously carried out by O’Brien et al. (2013). The original catalogue high- lighted the frequency of such events dating back as far as the turn of the last ice age and as recent as 2012. Ireland’s marine territory extends far beyond its coastline and is one of the largest seabed territories in Europe. It is therefore not surprising that extreme waves have continued to occur reg- ularly since 2012, particularly considering the severity of weather during the winters of 2013–2014 and 2015–2016. In …
Resale Value Of Individual Sets Of Magic The Gathering,
2018
University of Northern Iowa
Resale Value Of Individual Sets Of Magic The Gathering, Nichole Bolas Mlodzik
Honors Program Theses
Magic: the Gathering is a strategy-based fantasy card game developed by Richard Garfield in 1993. The appeal of playing the game is found in using cardboard printed cards to cast spells to achieve a victory over one or more opponents. This thesis will provide an analysis of six MTG sets, calculating the average value of one pack of fourteen cards. The relationships between the average resale value for each set will be evaluated using statistical graphical analysis. Conclusions will be drawn regarding the average resale value of a pack of fourteen cards in each of six sets
Symmetry Of Numerical Range And Semigroup Generation Of Infinite Dimensional Hamiltonian Operators,
2018
TÜBİTAK
Symmetry Of Numerical Range And Semigroup Generation Of Infinite Dimensional Hamiltonian Operators, Junjie Huang, Jie Liu, Alatancang Chen
Turkish Journal of Mathematics
This paper deals with the infinite dimensional Hamiltonian operator with unbounded entries. Using the core of its entries, we obtain the conditions under which the numerical range of such an operator is symmetric with respect to the imaginary axis. Based on the symmetry above, a necessary and sufficient condition for generating $C_0$ semigroups is further given.
An Operational Matrix Method For Solving Linear Fredholm‒Volterra Integro-Differential Equations,
2018
TÜBİTAK
An Operational Matrix Method For Solving Linear Fredholm‒Volterra Integro-Differential Equations, Şuayi̇p Yüzbaşi, Nurbol Ismailov
Turkish Journal of Mathematics
The aim of this paper is to propose an efficient method to compute approximate solutions of linear Fredholm‒Volterra integro-differential equations (FVIDEs) using Taylor polynomials. More precisely, we present a method based on operational matrices of Taylor polynomials in order to solve linear FVIDEs. By using the operational matrices of integration and product for the Taylor polynomials, the problem for linear FVIDEs is transformed into a system of linear algebraic equations. The solution of the problem is obtained from this linear system after the incorporation of initial conditions. Numerical examples are presented to show the applicability and the efficiency of the …
An Effective Application Of Differential Quadrature Method Based Onmodified Cubic B-Splines To Numerical Solutions Of The Kdv Equation, Ali̇ Başhan
Turkish Journal of Mathematics
In this study, numerical solutions of the third-order nonlinear Korteweg--de Vries (KdV) equation are obtained via differential quadrature method based on modified cubic B-splines. Five different problems are solved. To show the accuracy of the proposed method, $L_{2}$ and $L_{\infty }$ error norms of the problem, which has an analytical solution, and three lowest invariants are calculated and reported. The obtained solutions are compared with some earlier works. Stability analysis of the present method is also given.
Applications Of Extended Watson's Summation Theorem,
2018
TÜBİTAK
Applications Of Extended Watson's Summation Theorem, Young Sup Kim, Sebastien Gaboury, Arjun Kumar Rathie
Turkish Journal of Mathematics
In this research paper, several interesting applications of the extended classical summation theorem are given. As special cases, we recover several known results available in the literature.
Joint Densities Of Hitting Times For Finite State Markov Processes,
2018
TÜBİTAK
Joint Densities Of Hitting Times For Finite State Markov Processes, Tomasz R. Bielecki, Monique Jeanblanc, Ali̇ Devi̇n Sezer
Turkish Journal of Mathematics
For a finite state Markov process $X$ and a finite collection $\{ \Gamma_k, k \in K \}$ of subsets of its state space, let $\tau_k$ be the first time the process visits the set $\Gamma_k$. In general, $X$ may enter some of the $\Gamma_k$ at the same time and therefore the vector $\bm\tau :=(\tau_k, k \in K)$ may put nonzero mass over lower dimensional regions of ${\mathbb R}_+^{ K }$; these regions are of the form $R_s=\{{\bm t} \in {\mathbb R}_+^{ K }: t_i = t_j, ~~i,j \in s(1) \} \cap \bigcap_{l=2}^{ s } \{{\bm t}:t_m < t_i = t_j,~~ i,j \in s(l), m \in s(l-1) \}$ where $s$ is any ordered partition of the set $K$ and $s(j)$ denotes the $j^{th}$ subset of $K$ in the partition $s$. When $ s < K $, the density of the law of $\bm\tau$ over these regions is said to be ``singular'' because it is with respect to the $ s $-dimensional Lebesgue measure over the region $R_s.$ We derive explicit/recursive and simple to compute formulas for these singular densities and their corresponding tail probabilities over all $R_s$ as $s$ ranges over ordered partitions of $K$. We give a numerical example and indicate the relevance of our results to credit risk modeling.
The Natural Brackets On Couples Of Vector Fields And $1$-Forms,
2018
TÜBİTAK
The Natural Brackets On Couples Of Vector Fields And $1$-Forms, Miroslav Doupovec, Jan Kurek, Wlodzimierz Mikulski
Turkish Journal of Mathematics
All natural bilinear operators transforming pairs of couples of vector fields and $1$-forms into couples of vector fields and $1$-forms are found. All natural bilinear operators as above satisfying the Leibniz rule are extracted. All natural Lie algebra brackets on couples of vector fields and $1$-forms are collected.
On The Exponential Diophantine Equation $(18m^2+1)^X+(7m^2-1)^Y=(5m)^Z$,
2018
TÜBİTAK
On The Exponential Diophantine Equation $(18m^2+1)^X+(7m^2-1)^Y=(5m)^Z$, Murat Alan
Turkish Journal of Mathematics
Let $m$ be a positive integer. We show that the exponential Diophantine equation $ (18m^2+1)^x+(7m^2-1)^y=(5m)^z $ has only the positive integer solution $(x,y,z)=(1,1,2)$ except for $m \equiv 23,47,63, 87 \pmod {120}$. For $m\not\equiv 0 \pmod5$ we use some elementary methods and linear forms in two logarithms. For $m \equiv 0 \pmod 5$ we apply a result for linear forms in $p$-adic logarithms.
Existence And Uniqueness Of Solution Fordifferential Equation Of Fractional Order $2,
2018
TÜBİTAK
Existence And Uniqueness Of Solution Fordifferential Equation Of Fractional Order $2, Ghazala Akram, Fareeha Anjum
Turkish Journal of Mathematics
This paper is devoted to the study of nonlinear fractional differential equation involving Caputo fractional derivative of order $2
The Density Theorem For Hermitian K-Theory,
2018
TÜBİTAK
The Density Theorem For Hermitian K-Theory, Mohamed Elamine Talbi
Turkish Journal of Mathematics
Karoubi's density theorem was first proved in Benayat's thesis and then cited and used in several books and articles. As K-theory is a special case of hermitian $_{\varepsilon }L$-theory, a natural question is whether such a theorem is still true in the latter theory. The purpose of this article is to show that it is indeed the case.
Equivalence Problem For Compatible Bi-Hamiltonian Structures On Three-Dimensional Orientable Manifolds,
2018
TÜBİTAK
Equivalence Problem For Compatible Bi-Hamiltonian Structures On Three-Dimensional Orientable Manifolds, Tuna Bayrakdar, Abdullah Azi̇z Ergi̇n
Turkish Journal of Mathematics
We solve the equivalence problem for compatible bi-Hamiltonian structures on three-dimensional orientable manifolds via Cartan's method of equivalence. The problem separates into two branches on total space, one of which ends up with the intransitive involutive structure equations. For the transitive case, we obtain an $\{e\}$-structure on both total and base spaces.
