Mathematics Commons^™

Analysis Of A Time-Delayed Hiv/Aids Epidemic Model With Education Campaigns, Sedar Ngoma, Dawit Denu, Rachidi B. Salako

Mathematics

We consider a time-delayed HIV/AIDS epidemic model with education dissemination and study the asymptotic dynamics of solutions as well as the asymptotic behavior of the endemic equilibrium with respect to the amount of information disseminated about the disease. Under appropriate assumptions on the infection rates, we show that if the basic reproduction number is less than or equal to one, then the disease will be eradicated in the long run and any solution to the Cauchy problem converges to the unique disease-free equilibrium of the model. On the other hand, when the basic reproduction number is greater than one, we …

A Consistent Estimator Of Nontrivial Stationary Solutions Of Dynamic Neural Fields, Eddy Kwessi

Mathematics Faculty Research

Dynamics of neural fields are tools used in neurosciences to understand the activities generated by large ensembles of neurons. They are also used in networks analysis and neuroinformatics in particular to model a continuum of neural networks. They are mathematical models that describe the average behavior of these congregations of neurons, which are often in large numbers, even in small cortexes of the brain. Therefore, change of average activity (potential, connectivity, firing rate, etc.) are described using systems of partial different equations. In their continuous or discrete forms, these systems have a rich array of properties, among which is the …

A Continuous-Time Mathematical Model And Discrete Approximations For The Aggregation Of Β-Amyloid, A. S. Ackleh, Saber Elaydi, G. Livadiotis, A. Veprauskas

Mathematics Faculty Research

Alzheimer's disease is a degenerative disorder characterized by the loss of synapses and neurons from the brain, as well as the accumulation of amyloid-based neuritic plaques. While it remains a matter of contention whether β-amyloid causes the neurodegeneration, β-amyloid aggregation is associated with the disease progression. Therefore, gaining a clearer understanding of this aggregation may help to better understand the disease. We develop a continuous-time model for β-amyloid aggregation using concepts from chemical kinetics and population dynamics. We show the model conserves mass and establish conditions for the existence and stability of equilibria. We also develop two …

Pancyclicity And Vertex Pancyclicity For Some Products Of Graphs, Artchariya Muaengwaeng

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Global Analysis Of A Discrete Sirs Epidemic Model With Nonlinear Incidence Rate, Butsayapat Chaihao

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we prove some behaviors of a discrete SIRS epidemic model with a nonlinear incidence rate and a distributed time-delay. This model is constructed from the discretization of the corresponding continuous model by using a nonstandard finite difference method. The basic properties including the positivity and the boundedness of the solutions are established. We derive the existence of the disease-free equilibrium and the endemic equilibrium of the model. In addition, by applying Lyapunov function techniques, we prove that the disease-free equilibrium is globally attractive. Moreover, we give a sufficient condition for the permanence of the model. In order …

Hamiltonian Decompositions Of Hypergraphs, Chutima Saengchampa

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this dissertation, we first discuss four versions of Hamiltonicity in hypergraphs. We mainly study the existence problem of Hamiltonian decompositions of uniform hypergraphs based on two versions of Hamiltonian cycles, so called ``KK-definition" and ``WJ-definition". For KK-definition, we create a recursive construction of KK-Hamiltonian decomposition of complete 3-uniform hypergraphs. Our construction method uses a KK-Hamiltonian decomposition of the complete 3-uniform hypergraph, Kt(3), and some well-known graph decompositions to obtain a KK-Hamiltonian decomposition of the complete t-partite 3-uniform hypergraph, Kt(n)(3), when t=4,8 (mod12), n>=2, as well as a KK-Hamiltonian decomposition of K2t(3). Therefore, together with the current results in …

Algebraic Degree Of Spectra Of Cayley Hypergraphs, Naparat Sripaisan

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Local Limit Theorems For Sums Of Independent Integer-Valued Lattice Random Variables, Punyapat Kammoo

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Hamiltonian Cycles Of Equational Graphs Over Finite Fields, Wachirawit Chaifongsri

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Closed-Form Formulas For Conditional Moments Of Generalized Cox-Ingersoll-Ross Processes, Phiraphat Sutthimat

Chulalongkorn University Theses and Dissertations (Chula ETD)

Cox-Ingersoll-Ross (CIR) process, introduced in 1985, is a one factor model used to describe the evolution of interest rate and pricing the financial derivatives. It was later extended to have time-dependent parameters called the extended CIR (ECIR) process, which is more widely studied and used in a variety of applications. The generalized versions of CIR process are also studied and investigated for more applications in finance. However, most of these applications rely on the knowledge and properties of conditional expectations and moments, which most of them are not yet fully developed into closed form. In this work, we propose closed-form …

Enhanced Heterogeneous Network Model With Ensemble Similarities For Identifying Protein Targets Of Drugs, Piyanut Tangmanussukum

Chulalongkorn University Theses and Dissertations (Chula ETD)

Currently, computational identification of drug target proteins is widely used to help saving cost and time for drug discovery and development. One of the most efficient approaches is a prediction of drug-target interactions based on similarity scores between drugs and target proteins. Despite various data about drugs and targets extensively available, only chemical structures and protein sequences are mostly used to compute drug-drug and target-target similarity scores, respectively. In this thesis, the Forward similarity integration (FSI) Framework is proposed for systematically integrating multiple similarity measures to construct a heterogeneous network propagation model with a suitable similarity integration. Seven drug-similarity measures, …

Newton Iterative Algorithm For Polynomial Modular Inversion Modulo Xn±1 For Some Patterns Of N, Samakorn Sripatthanakul

Chulalongkorn University Theses and Dissertations (Chula ETD)

This thesis presents an algorithm for computing the modular inverse of a polynomial in a ring of polynomials over a finite field $\mathbb{F}_q$ with a characteristic $p$. Given a polynomial $f$ and a natural number $r$, by applying the idea of the Newton iteration algorithm, the fast division algorithm used to find the inverse of $f$ under modulo $x^{p^r}-1$, $x^{p^r}+1$, $x^{2p^r}-1$ and $x^n-1$ where $n=2^r d$ for some $r,d\in\mathbb{N}$, is established. The cost analysis for these cases show that the algorithm has the computational complexity of $\mathcal{O}(n \log n)$ which is more efficient than the Half-GCD algorithm in terms of …

Scheduling Of Pressing Process In Multi-Layer Printed Circuit Board Manufacturing Via Milp And Heuristic, Teeradech Laisupannawong

Chulalongkorn University Theses and Dissertations (Chula ETD)

The pressing process aims to press the panel which is the stack of materials to form a multi-layer printed circuit board (PCB). This process is a part of multi-layer PCB fabrication and can be considered as a scheduling problem with the objective of minimizing the makespan. In this dissertation, two mixed-integer linear programming models (Models 1 and 2) and a three-phase-PCB-pressing heuristic (3P-PCB-PH) algorithm for scheduling the pressing process are presented. Model 2 is an improvement of Model 1 in terms of the model size and the dimensionality of some decision variables. Both models and the 3P-PCB-PH algorithm are used …

Acceleration Of Boltzmann Collision Integral Calculation Using Machine Learning, Ian Holloway, Aihua W. Wood, Alexander Alekseenko

Faculty Publications

The Boltzmann equation is essential to the accurate modeling of rarefied gases. Unfortunately, traditional numerical solvers for this equation are too computationally expensive for many practical applications. With modern interest in hypersonic flight and plasma flows, to which the Boltzmann equation is relevant, there would be immediate value in an efficient simulation method. The collision integral component of the equation is the main contributor of the large complexity. A plethora of new mathematical and numerical approaches have been proposed in an effort to reduce the computational cost of solving the Boltzmann collision integral, yet it still remains prohibitively expensive for …

Characterizations Of The Discrete Lindley And Discrete Poisson-Lindley Distributions, Gholamhossein G. Hamedani, Mahrokh Najaf

Mathematical and Statistical Science Faculty Research and Publications

Certain characterizations of the discrete Lindley and discrete Poisson-Lindley distributions, originally introduced by Bakouch, Jazi and Nadarjah (2014) and Sankaran (1970), respectively, are presented. Al-Babtain, Gemeay and Afify (2020) revisited these distributions and provided estimation methods and actuarial measures as well as their applications in medicine. This short note is intended to complete, in some way, Al-Babtain, Gemeay and Afify (2020)’s work. It should be mentioned that the probability mass functions reported in the two papers mentioned above are not correct. In this note, it will be explained why they are not correct.

A New Extended Alpha Power Transformed Family Of Distributions: Properties, Characterizations And An Application To A Data Set In The Insurance Sciences, Zubair Ahmad, Eisa Mahmoudi, Gholamhossein Hamedani

Mathematical and Statistical Science Faculty Research and Publications

Heavy tailed distributions are useful for modeling actuarial and financial risk management problems. Actuaries often search for finding distributions that provide the best fit to heavy tailed data sets. In the present work, we introduce a new class of heavy tailed distributions of a special sub-model of the proposed family, called a new extended alpha power transformed Weibull distribution, useful for modeling heavy tailed data sets. Mathematical properties along with certain characterizations of the proposed distribution are presented. Maximum likelihood estimates of the model parameters are obtained. A simulation study is provided to evaluate the performance of the maximum likelihood …

Solutions For Fermi Questions, November 2021: Question 1: Chess Moves, Question 2: Cat Litter, Larry Weinstein

Physics Faculty Publications

Answers to the questions: How many chess moves are made by Americans each year? How much cat litter did Americans scoop last year?

Solutions For Fermi Questions, September 2021: Question 1: Cell Phone Gold, Question 2: Food For Thought, Larry Weinstein

Physics Faculty Publications

Answers to the questions: "How much gold is in a cell phone? Is it worth mining cell phones for gold?"

Solutions For Femi Questions, October 2021: Rising Water Level: Popping Many Pimples, Larry Weinstein

Physics Faculty Publications

[Introduction] How much would sea levels rise if everyone jumped in the ocean? (Thanks to Bob Friedhoffer for suggesting the problem.)

To estimate this, we need to know the number of people, the average volume of a person, and the area of the oceans. This is the kind of estimation problem where the inputs are relatively well known, and we are calculating the answer to see its order of magnitude.

There are about 7 X 10⁹ people in the world. If each person has a mass of 100 kg (in round numbers), then they each have a volume …

Geometric Properties Of Representation Varieties For An Elementary Abelian Group Of Rank 2 In Positive Characteristic, Eric Johnson

Graduate Research Theses & Dissertations

This dissertation’s motivation is the exploration of the irreducible components of Repn(kG), the affine variety whose points are n-dimensional representations of a finite group G over a field k. We let G = Z/pZ×Z/pZ and assume k is algebraically closed with char(k) = p > 0. In this case there is an isomorphism of affine varieties φ : Repn (kG) → C nil 1 (n) where C nil 1 (n) = {(x, y) Mn(k)×Mn(k) | x p = y p = xy−yx = 0}. Hence, for an irreducible component X of Repn (kG), φ(X) is an irreducible component of C nil …

Optimization Of Dynamic Objective Functions Using Path Integrals, Paramahansa Pramanik

Graduate Research Theses & Dissertations

Path integrals are used to find an optimal strategy for a firm under a Walrasian system. We define dynamic optimal strategies and develop an integration method to capture all non-additive non-convex strategies. We also show that the method can solve the non-linear case, for example Merton-Garman-Hamiltonian system, which the traditional Pontryagin maximum principle cannot solve in closed form. Furthermore, we assume that the strategy space and time are inseparable with respect to a contract. Under this assumption we show that the strategy spacetime is a dynamic curved Liouville-like 2-brane quantum gravity surface under asymmetric information and that traditional Euclidean geometry …

The Zorich Transform And Generalizing Koenigs Linearization Theorem To Quasiregular Maps, Jacob A. Pratscher

Graduate Research Theses & Dissertations

This dissertation investigates the role that a new tool called the Zorich transform plays in quasiregular dynamics as a generalization of the logarithmic transform in complex dynamics. In particular we use the Zorich transform to construct analogues of the logarithmic spiral maps and interpolation between radial stretch maps. These constructions are then used to completely classify the orbit space of a quasiregular map. Also, conditions are given in which a quasiregular map $f:D\to\R^n$, where $D\subset\R^n$ is a domain, that is quasiconformal in a neighborhood of a geometrically attracting fixed point can be conjugated by a quasiconformal map to the asymptotic …

Cheeger Constants Of Two Related Hyperbolic Riemann Surfaces, Ronald E. Hoagland

Masters Theses

This thesis concerns the study of the Cheeger constant of two related hyperbolic Riemann surfaces. The first surface R is formed by taking the quotient U²/Γ(4), where U² is the upper half-plane model of the hyperbolic plane and Γ(4) is a congruence subgroup of PSL2(Z), an isometry group of U² . This quotient is shown to form a Riemann surface which is constructed by gluing sides of a fundamental domain for Γ(4) together according to certain specified side pairings. To form the related Riemann surface R' , we follow a similar procedure, this time taking the …

An Extension Of Maximum Principle With Some Applications, Ali Parsian

Turkish Journal of Mathematics

Let $U\subseteq R^{n}$ (res. $D\subset R^{n}$) be an open (res. a compact) subset, and let $L$ be an elliptic operator defined on $C^{2}(U, R)$ (res. $C^{2}(D, R)$). In the present paper, we are going to extend the maximum principle for the function $f \in C^{2}(U, R)$ (res. $f \in C^{2}(D, R)$) satisfying the equation $Lf=\varepsilon$, where $\varepsilon$ is a real everywhere nonzero continuous function on $U$ (res. $D$). Finally, we obtain some applications in mathematics and physics.

Modularly Equidistant Numerical Semigroups, José Carlos Rosales, Manuel Baptista Branco, Márcio Andre Traesel

Turkish Journal of Mathematics

IfS is a numerical semigroup and s ∈ S , we denote by next$_{S}$(s) = min {x ∈ S s < x}. Leta be an integer greater than or equal to two. A numerical semigroup is equidistant modulo a if next$_{S}$((s) - s - 1 is a multiple of a for every s ∈ S . In this note, we give algorithms for computing the whole set of equidistant numerical semigroups modulo a with fixed multiplicity, genus, and Frobenius number. Moreover, we will study this kind of semigroups with maximal embedding dimension.

Good Components Of Curves In Projective Spaces Outside The Brill-Noether Range, Edoardo Ballico

Turkish Journal of Mathematics

For all integers $n, d, g$ such that $n\ge 4$, $d\ge n+1$, and $(n+2)(d-n-1)\ge n(g-1)$, we define a good (i.e. generically smooth of dimension $(n+1)d+(3-n)(g-1)$ and with the expected number of moduli) irreducible component $A(d,g;n)$ of the Hilbert scheme of smooth and nondegenerate curves in $\mathbb{P}^n$ with degree $d$ and genus $g$. For most of these $(d,g)$, we prove that a general $X\in A(d,g;n)$ has maximal rank. We cover, in this way, a range of $(d,g,n)$ outside the Brill-Noether range.

Near-Rings On Nearness Approximation Spaces, Mustafa Uçkun, Abdurrahman Genç

Turkish Journal of Mathematics

In this study, nearness near-ring, subnearness near-ring, nearness M-group and nearness ideal are introduced. By considering operations on the set of all near left weak cosets, nearness near-ring of all near left weak cosets and nearness near-ring homomorphism are also presented. Moreover, some properties of these structures are investigated.

T$_{4}$, Urysohn's Lemma, And Tietze Extension Theorem For Constant Filter Convergence Spaces, Tesni̇m Meryem Baran, Ayhan Erci̇yes

Turkish Journal of Mathematics

In this paper, we characterize various local forms of T$_{4}$ constant filter convergence spaces and investigate the relationships among them as well as showing that the full subcategories of the category of constant filter convergence spaces consisting of local T$_{4}$ constant filter convergence spaces that are hereditary. Furthermore, we examine the relationship between local T$_{4}$ and general T$_{4}$ constant filter convergence spaces. Finally, we present Urysohn's lemma and Tietze extension theorem for constant filter convergence spaces.

Oscillation Tests For Nonlinear Differential Equations With Nonmonotone Delays, Nurten Kiliç

Turkish Journal of Mathematics

In this paper, our aim is to investigate a class of first-order nonlinear delay differential equations with several deviating arguments. In addition, we present some sufficient conditions for the oscillatory solutions of these equations. Differing from other studies in the literature, delay terms are not necessarily monotone. Finally, we give examples to demonstrate the results.

Some Soft Topological Properties And Fixed Soft Element Results In Soft Complex Valued Metric Spaces, İzzetti̇n Demi̇r

Turkish Journal of Mathematics

In this paper, first, by using the idea of soft complex numbers as in Das and Samanta [8], we introduce the notion of soft complex valued metric spaces and investigate some of their topological aspects. Next, we establish some fixed soft element theorems for various soft mappings on soft complex valued metric spaces, which are the main results of our paper.