Physical Sciences and Mathematics Commons^™

Model Checks For Two-Sample Location-Scale, Atefeh Javidialsaadi

Dissertations

Two-sample location-scale refers to a model that permits a pair of standardized random variables to have a common distribution. This means that if X₁ and X₂ are two random variables with means µ₁ and µ₂ and standard deviations ?₁ and ?₂, then (X₁ - µ₁)/?₁ and (X₂ - µ₂)/?₂ have some common unspecified standard or base distribution F₀. Function-based hypothesis testing for these models refers to formal tests that would help determine whether or not two samples may have come from some location-scale …

Dependent Censoring In Survival Analysis, Zhongcheng Lin

Dissertations

This dissertation mainly consists of two parts. In the first part, some properties of bivariate Archimedean Copulas formed by two time-to-event random variables are discussed under the setting of left censoring, where these two variables are subject to one left-censored independent variable respectively. Some distributional results for their joint cdf under different censoring patterns are presented. Those results are expected to be useful in both model fitting and checking procedures for Archimedean copula models with bivariate left-censored data. As an application of the theoretical results that are obtained, a moment estimator of the dependence parameter in Archimedean copula models is …

Mathematical Model Of Cholera Spread Based On Sir: Optimal Control, Noer Hidayati, Eminugroho Ratna Sari, Nur Hadi Waryanto

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

The bacterium Vibrio cholerae is the cause of cholera. Cholera is spread through the feces of an infected individual in a population. From a mathematical point of view, this problem can be brought into a mathematical model in the form of Susceptible-Infected-Recovered (SIR), which considers the birth rate. Because outbreaks that occur easily spread if not treated immediately, it is necessary to control the susceptible individual population by vaccination. The vaccine used is Oral Vibrio cholera. For this reason, the purposes of this study were to establish a model for the spread of cholera without vaccination, analyze the stability of …

Penggunaan Goal Programming Dalam Perencanaan Menu Untuk Lansia Penderita Hipertensi, Diana Islamiyati, Dwi Lestari, Nur Insani

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Penelitian ini bertujuan untuk membangun suatu model goal programming untuk mengoptimalkan perencanaan menu harian lansia penderita hipertensi. Fungsi tujuan model ini yaitu untuk memaksimumkan kandungan gizi makanan lansia sesuai Angka Kecukupan Gizi (AKG), meminimumkan biaya pangan, memaksimumkan kuantitas pangan, dan meminimumkan konsumsi pangan yang mengandung natrium. Berdasarkan eksperimen komputasi yang dilakukan dengan menerapkan model weighted goal programming ini, dihasilkan solusi optimal kebutuhan gizi lansia penderita hipertensi yang sesuai dengan AKG. Adapun perencanaan optimal menu makanan untuk lima hari yaitu terdiri dari 12 jenis pangan dengan pengeluaran biaya sebesar Rp 11.236,- untuk hari pertama, 13 jenis pangan dengan pengeluaran biaya …

Drought-Prone Areas Mapping Using Fuzzy C-Means Method In Gunungkidul District, Kismiantini Kismiantini, Fajra Husniyah, Osval Antonio Montesinos-LンPez

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Gunungkidul district is one of the districts in the Special Region of Yogyakarta that is frequently affected by drought disasters. The purpose of this study is to map drought-prone areas in Gunungkidul district using the fuzzy c-means method, making it easier for the government to allocate water-dropping assistance to drought-affected areas. The research variables include rainfall, soil type, infiltration, slope, and land use. The type of variables is an ordinal scale, so they must be transformed using the successive interval method before being analyzed using the fuzzy c-means method. The cluster validity indexes of the Xie and Beni index, partition …

The Smooth 4-Genus Of (The Rest Of) The Prime Knots Through 12 Crossings, Mark Brittenham, Susan Hermiller

Department of Mathematics: Faculty Publications

We compute the smooth 4-genera of the prime knots with 12 crossings whose values, as reported on the KnotInfo website, were unknown. This completes the calculation of the smooth 4-genus for all prime knots with 12 or fewer crossings.

Decomposable Model Spaces And A Topological Approach To Curvature, Kevin M. Tully

Rose-Hulman Undergraduate Mathematics Journal

This research investigates a model space invariant known as k-plane constant vector curvature, traditionally studied when k=2, and introduces a new invariant, (m,k)-plane constant vector curvature. We prove that the sets of k-plane and (m,k)-plane constant vector curvature values are connected, compact subsets of the real numbers and establish several relationships between the curvature values of a decomposable model space and its component spaces. We also prove that every decomposable model space with a positive-definite inner product has k-plane constant vector curvature for some integer k>1. In …

Winning Strategy For Multiplayer And Multialliance Geometric Game, Jingkai Ye

Rose-Hulman Undergraduate Mathematics Journal

The Geometric Sequence with common ratio 2 is one of the most well-known geometric sequences. Every term is a nonnegative power of 2. Using this popular sequence, we can create a Geometric Game which contains combining moves (combining two copies of the same terms into the one copy of next term) and splitting moves (splitting three copies of the same term into two copies of previous terms and one copy of the next term). For this Geometric Game, we are able to prove that the game is finite and the final game state is unique. Furthermore, we are able to …

Hurwitz Actions On Reflection Factorizations In Complex Reflection Group G₆, Gaurav Gawankar, Dounia Lazreq, Mehr Rai, Seth Sabar

Rose-Hulman Undergraduate Mathematics Journal

We show that in the complex reflection group G₆, reflection factorizations of a Coxeter element that have the same length and multiset of conjugacy classes are in the same Hurwitz orbit. This confirms one case of a conjecture of Lewis and Reiner.

Lie-Derivations Of Three-Dimensional Non-Lie Leibniz Algebras, Emily H. Belanger

Rose-Hulman Undergraduate Mathematics Journal

The concept of Lie-derivation was recently introduced as a generalization of the notion of derivations for non-Lie Leibniz algebras. In this project, we determine the Lie algebras of Lie-derivations of all three-dimensional non-Lie Leibniz algebras. As a result of our calculations, we make conjectures on the basis of the Lie algebra of derivations of Lie-solvable non-Lie Leibniz algebras.

The Optimal Double Bubble For Density 𝑟ᵖ, Jack Hirsch, Kevin Li, Jackson Petty, Christopher Xue

Rose-Hulman Undergraduate Mathematics Journal

In 2008 Reichardt proved that the optimal Euclidean double bubble---the least-perimeter way to enclose and separate two given volumes---is three spherical caps meeting along a sphere at 120 degrees. We consider Rⁿ with density r^p, joining the surge of research on manifolds with density after their appearance in Perelman's 2006 proof of the Poincaré Conjecture. Boyer et al. proved that the best single bubble is a sphere through the origin. We conjecture that the best double bubble is the Euclidean solution with the singular sphere passing through the origin, for which we have verified equilibrium (first variation …

Locally Dependent Natural Image Priors For Non-Blind And Blind Image Deconvolution., Kaustav Nandy Dr.

Doctoral Theses

Degradation of photographic images is a common phenomenon that can occur due to several reasons. Astronomical images may be degraded due to atmospheric factors or telescope optics. Photographs taken using standard digital cameras may be blurred due to lack of focus, due to motion of the subject, due to low resolution, or due to camera shake during relatively long exposures. Often one wishes to correct for the effect of such degradation and recover the original image, and this has been a long-standing research problem in digital imaging. Effective solutions depend critically on the context of the problem and the type …

The Circle Of Life: The Mathematics Of Predator-Prey Dynamics, John Butler, Rebecca Brady

Articles

Some animals hunt other animals to feed themselves; these animals are called predators. Animals who are hunted and eaten are known as prey. What do you think would happen if a predator were introduced to an ecosystem where the prey previously lived without fear of being hunted? Would the new predator eat all the prey animals until they go extinct? Actually, the relationship between predator and prey is far more interesting than this. In this article, we show what the predator-prey relationship looks like over time and explain how scientists can make predictions about future population levels, all using basic …

A Proof Of A Generalization Of Niven's Theorem Using Algebraic Number Theory, Caroline Nunn

Rose-Hulman Undergraduate Mathematics Journal

Niven’s theorem states that the sine, cosine, and tangent functions are rational for only a few rational multiples of π. Specifically, for angles θ that are rational multiples of π, the only rational values of sin(θ) and cos(θ) are 0, ±½, and ±1. For tangent, the only rational values are 0 and ±1. We present a proof of this fact, along with a generalization, using the structure of ideals in imaginary quadratic rings. We first show that the theorem holds for the tangent function using elementary properties of Gaussian integers, before extending the approach to other imaginary quadratic rings. We …

Negative Order Kdv Equation With No Solitary Traveling Waves, Miguel Rodriguez, Jing Li, Zhijun Qiao

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We consider the negative order KdV (NKdV) hierarchy which generates nonlinear integrable equations. Selecting different seed functions produces different evolution equations. We apply the traveling wave setting to study one of these equations. Assuming a particular type of solution leads us to solve a cubic equation. New solutions are found, but none of these are classical solitary traveling wave solutions.

A Brief Treatise On Bayesian Inverse Regression., Debashis Chatterjee Dr.

Doctoral Theses

Inverse problems, where in a broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific disciplines. However, apart from the class of traditional inverse problems, there exists another class of inverse problems, which qualify as more authentic class of inverse problems, but unfortunately did not receive as much attention.In a nutshell, the other class of inverse problems can be described as the problem of predicting the covariates corresponding to given responses and the rest of the data. …

Secret Sharing And Its Variants, Matroids,Combinatorics., Shion Samadder Chaudhury Dr.

Doctoral Theses

The main focus of this thesis is secret sharing. Secret Sharing is a very basic and fundamental cryptographic primitive. It is a method to share a secret by a dealer among different parties in such a way that only certain predetermined subsets of parties can together reconstruct the secret while some of the remaining subsets of parties can have no information about the secret. Secret sharing was introduced independently by Shamir [139] and Blakely [20]. What they introduced is called a threshold secret sharing scheme. In such a secret sharing scheme the subsets of parties that can reconstruct a secret …

Existence Results For Nonlinear Schrodinger Equations Involving The Fractional (P, Q)-Laplacian And Critical Nonlinearities, Huilin Lv, Shenzhou Zheng, Zhaosheng Feng

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this article, we consider the existence of ground state positive solutions for nonlinear Schrodinger equations of the fractional (p, q)-Laplacian with Rabinowitz potentials defined in R-n,

(-Delta)(p)(s1) u + (-Delta)(q)(s2) q u+ V(epsilon x)(vertical bar u vertical bar(p-2)u+vertical bar u vertical bar(q-2)u) =lambda f(u) + sigma vertical bar u vertical bar q*(-2)(s2)u.

We prove existence by confining different ranges of the parameter lambda under the subcritical or critical nonlinearities caused by sigma = 0 or 1, respectively. In particular, a delicate calculation for the critical growth is provided so as to avoid the failure of a global Palais-Smale condition …

Sufficient Condition For The Possibility Of Completing The Pursuit, Nodirbek Umrzaqov

Scientific Bulletin. Physical and Mathematical Research

In this paper, the problem of chase is represented by a system of linear differential equations of motion dynamics. In this case, there is an integral limit to the control parameter of the evader, and a geometric limit to the control parameter of the pursuer. The pursuer is allowed to use the control that the fugitive has used so far to build his control. There are enough conditions for the game to end even if it starts from any starting point. An algorithm for constructing the control function of the pursuer is defined. It should also be noted that the …

Chromatic Quasisymmetric Class Functions For Combinatorial Hopf Monoids, Jacob A. White

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We study the chromatic quasisymmetric class function of a linearized combinatorial Hopf monoid. Given a linearized combinatorial Hopf monoid H, and an H-structure h on a set N, there are proper colorings of h, generalizing graph colorings and poset partitions. We show that the automorphism group of h acts on the set of proper colorings. The chromatic quasisymmetric class function enumerates the fixed points of this action, weighting each coloring with a monomial. For the Hopf monoid of graphs this invariant generalizes Stanley's chromatic symmetric function and specializes to the orbital chromatic polynomial of Cameron and Kayibi.

We also introduce …

A Continuous Wavelet Representation For Single And Bi-Parameter Calder\'On-Zygmund Operators, Tyler Williams

Arts & Sciences Electronic Theses and Dissertations

This thesis develops a novel approach to the representation of singular integral operators of Calder\'on-Zygmund type in terms of continuous model operators, in both the classical and the bi-parametric setting. The representation is realized as a finite sum of averages of wavelet projections of either cancellative or noncancellative type, which are themselves Calder\'on-Zygmund operators. Both properties are out of reach for the established dyadic-probabilistic technique. Unlike their dyadic counterparts, this new representation reflects the additional kernel smoothness of the operator being analyzed.

These representation formulas lead naturally to a new family of $T(1)$ theorems on weighted Sobolev spaces whose smoothness …

M-Subharmonic Functions On The Projective Space PN, Gokhan Gogus, Azimbay Sadullaev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We consider a class of quasi m-subharmonic functions in the projective space ℙⁿ. Similarly to the m-subharmonic functions, we will show a number of potential properties of quasi m-subharmonic functions. We introduce the concepts of Green’s function V_qm^*(z,K,ℙⁿ), ��_m-measure ω_qm^*(z,E,D) and study m-regularities of compact sets K ⊂ ℙⁿ. In contrast to the complex space ℂⁿ, we will prove that in the projective space ℙⁿ the locally …

Interpretation Of De Sitter Space Of Second Kind, Abdulaziz Artikbaev, Botirjon Mamadaliyev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In a five-dimensional pseudo-Euclidean space of index two, the geometry on its sphere is studied. The equivalence of the geometry on a sphere of imaginary radius on de Sitter space is shown. The interpretation of the geometry on a sphere of imaginary radius, inside the sphere of imaginary radius of the Minkowski four-dimensional space, is implemented. We study a curve in a five-dimensional pseudo-Euclidean space of index two and determine the membership condition of the curve to a sphere of imaginary radius.

Dirichlet Problem In The Class Of A(Z)-Harmonic Functions, Shohruh Khursanov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

This paper work is devoted to the study of the Dirichlet problem in the class of A(z)-harmonic functions.

An Intrinsic Proof Of An Extension Of Itô’S Isometry For Anticipating Stochastic Integrals, Hui-Hsiung Kuo, Pujan Shrestha, Sudip Sinha

Journal of Stochastic Analysis

No abstract provided.

Regularity Criteria For The Kuramoto-Sivashinsky Equation In Dimensions Two And Three, Adam Larios, Mohammad Mahabubur Rahman, Kazuo Yamazaki

Department of Mathematics: Faculty Publications

We propose and prove several regularity criteria for the 2D and 3D Kuramoto-Sivashinsky equation, in both its scalar and vector forms. In particular, we examine integrability criteria for the regularity of solutions in terms of the scalar solution ∅, the vector solution u ≜ ∇∅, as well as the divergence div(u) = Δ∅, and each component of u and ∇u. We also investigate these criteria computationally in the 2D case, and we include snapshots of solutions for several quantities of interest that arise in energy estimates.

Reduced-Order Dynamic Modeling And Robust Nonlinear Control Of Fluid Flow Velocity Fields, Anu Kossery Jayaprakash, William Mackunis, Vladimir Golubev, Oksana Stalnov

Publications

A robust nonlinear control method is developed for fluid flow velocity tracking, which formally addresses the inherent challenges in practical implementation of closed-loop active flow control systems. A key challenge being addressed here is flow control design to compensate for model parameter variations that can arise from actuator perturbations. The control design is based on a detailed reduced-order model of the actuated flow dynamics, which is rigorously derived to incorporate the inherent time-varying uncertainty in the both the model parameters and the actuator dynamics. To the best of the authors’ knowledge, this is the first robust nonlinear closed-loop active flow …

Entropy Analysis Of Boolean Network Reduction According To The Determinative Power Of Nodes, Matthew J. Pelz, Mihaela T. Velcsov

Mathematics Faculty Publications

Boolean networks are utilized to model systems in a variety of disciplines. The complexity of the systems under exploration often necessitates the construction of model networks with large numbers of nodes and unwieldy state spaces. A recently developed, entropy-based method for measuring the determinative power of each node offers a new method for identifying the most relevant nodes to include in subnetworks that may facilitate analysis of the parent network. We develop a determinative-power-based reduction algorithm and deploy it on 36 network types constructed through various combinations of settings with regards to the connectivity, topology, and functionality of networks. We …

Equisingular Approximation Of Analytic Germs, Aftab Yusuf Patel

Electronic Thesis and Dissertation Repository

This thesis deals with the problem of approximating germs of real or complex analytic spaces by Nash or algebraic germs. In particular, we investigate the problem of approximating analytic germs in various ways while preserving the Hilbert-Samuel function, which is of importance in the resolution of singularities. We first show that analytic germs that are complete intersections can be arbitrarily closely approximated by algebraic germs which are complete intersections with the same Hilbert-Samuel function. We then show that analytic germs whose local rings are Cohen-Macaulay can be arbitrarily closely approximated by Nash germs whose local rings are Cohen- Macaulay and …

Measuring Irregularity Via Approximate Entropy: How Does Perceived Human Instability Affect One's Own Stability?, Madi Braunersrither

Fall Student Research Symposium 2021

In a study performed at Utah State University, participants were prompted to evaluate the stability of pictured human postures while standing on a force plate. The force plate was used to collect the center of pressure of the subjects by recording measurements in the vertical and horizontal directions. The way these factors fluctuate over time and the irregularity in this fluctuation, specifically, can give insight into the subject’s postural stability. Rather than working with summary statistics such as means and variances of fitting parameters of a distribution as commonly done in statistics, we want to measure irregularity through analyzing the …