Mathematics Commons^™

Domain Decomposition Methods For The Solution Of Multiple Scattering Problems, Michael Pedneault

Dissertations

This presents a Schur complement Domain Decomposition (DD) algorithm for the solution of frequency domain multiple scattering problems. Just as in the classical DD methods,(1) the ensemble of scatterers is enclosed in a domain bounded by an artificial boundary, (2) this domain is subdivided into a collection of nonoverlapping subdomains so that the boundaries of the subdomains do not intersect any of the scatterers, and (3) the solutions of the subproblems are connected via Robin boundary conditions matching on the common interfaces between subdomains. Subdomain Robin-to-Robin maps are used to recast the DD problem as a sparse linear system whose …

Fwer Controlling Procedures In Simultaneous And Selective Inference, Li Yu

Dissertations

With increasing complexity of research objectives in clinical trials, a variety of relatively complex and less intuitive multiple testing procedures (MTPs) have been developed and applied in clinical data analysis. In order to make testing strategies more explicit and intuitive to communicate with non-statisticians, several flexible and powerful graphical approaches have recently been introduced in the literature for developing and visualizing newer MTPs. Nevertheless, some theoretical as well as methodological issues still remain to be fully addressed. This dissertation addresses several important issues arising in graphical approaches and related selective inference problems. It consists of three parts.

In the first …

Optimasi Perencanaan Produksi Bahan Bakar Minyak Dengan Fungsi Kendala Fuzzy Menggunakan Metode Goal Programming, Wiwiet Widyaningsih, Sri Andayani

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Dalam perencanaan produksi PT. Pertamina (Persero) TBBM Boyolali, perusahaan tersebut hanya mendistribusikan BBM sesuai dengan permintaan SPBU tanpa melakukan perhitungan matematis apakah pendapatan yang diperoleh sudah optimal dengan semua faktor dan kendala yang ada, seperti harga setiap jenis BBM, jam kerja mesin pengisian BBM di New Gantry System (NGS), moda transport mobil tangki, dan tingkat keselamatan mobil tangki. Untuk itu, penelitian ini bertujuan untuk melakukan optimasi perencanaan produksi BBM menggunakan metode goal programming agar perusahaan dapat memperoleh pendapatan yang maksimal dengan memperhatikan faktor-faktor dan kendala yang ada. Metode goal programming merupakan perluasan dari linear programming yang dapat menyelesaikan optimasi dengan …

Model Matematis Predator-Prey Tanaman Padi, Hama Penggerek Batang, Tikus, Dan Wereng Batang Coklat Di Karawang, Tesa Nur Padilah, Betha Nurina Sari, Hannie Hannie

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Karawang merupakan salah satu pusat penanaman padi di Pulau Jawa. Keberhasilan panen dapat terganggu oleh adanya organisme pengganggu tumbuhan (OPT) sehingga dapat mengancam target swasembada beras. Hubungan antara tanaman padi dengan OPT dapat dibentuk menjadi suatu model matematis yaitu model predator-prey. Untuk itu, penelitian ini bertujuan untuk menganalisis model matematis predator-prey tanaman padi dan OPT. Predator (pemangsa) adalah makhluk hidup yang memakan mangsa (prey). Model predator-prey antara tanaman padi dengan OPT yang dibahas adalah model tiga predator yaitu hama penggerek batang, tikus, dan wereng batang coklat dengan prey yaitu padi. Pertumbuhan padi mengikuti …

Nonparametric Collective Spectral Density Estimation With An Application To Clustering The Brain Signals, Mehdi Maadooliat, Ying Sun, Tianbo Chen

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this paper, we develop a method for the simultaneous estimation of spectral density functions (SDFs) for a collection of stationary time series that share some common features. Due to the similarities among the SDFs, the log‐SDF can be represented using a common set of basis functions. The basis shared by the collection of the log‐SDFs is estimated as a low‐dimensional manifold of a large space spanned by a prespecified rich basis. A collective estimation approach pools information and borrows strength across the SDFs to achieve better estimation efficiency. Moreover, each estimated spectral density has a concise representation using the …

Find, Process, And Share: An Optimal Control In The Vidale-Wolfe Marketing Model, Michael C. Barg

CODEE Journal

The Vidale-Wolfe marketing model is a first-order, linear, non-homogeneous ordinary differential equation (ODE) where the forcing term is proportional to advertising expenditure. With an initial response in sales as the initial condition, the solution of the initial value problem is straightforward for a first undergraduate ODE course. The model serves as an excellent example of many relevant topics for those students whose interests lie in economics, finance, or marketing. Its inclusion in the curriculum is particularly rewarding at an institution without a physics program. The model is not new, but it was novel to us when a group of students …

Lozenge Tilings Of A Halved Hexagon With An Array Of Triangles Removed From The Boundary, Part Ii, Tri Lai

Department of Mathematics: Faculty Publications

Proctor's work on staircase plane partitions yields an exact enumeration of lozenge tilings of a halved hexagon on the triangular lattice. Rohatgi later ex- tended this tiling enumeration to a halved hexagon with a triangle cut o from the boundary. In his previous paper, the author proved a common generalization of Proctor's and Rohatgi's results by enumerating lozenge tilings of a halved hexagon in the case an array of an arbitrary number of triangles has been removed from a non-staircase side. In this paper we consider the other case when the array of tri- angles has been removed from the …

Power In Pairs: Assessing The Statistical Value Of Paired Samples In Tests For Differential Expression, John R. Stevens, Jennifer S. Herrick, Roger K. Wolff, Martha L. Slattery

Mathematics and Statistics Faculty Publications

Background: When genomics researchers design a high-throughput study to test for differential expression, some biological systems and research questions provide opportunities to use paired samples from subjects, and researchers can plan for a certain proportion of subjects to have paired samples. We consider the effect of this paired samples proportion on the statistical power of the study, using characteristics of both count (RNA-Seq) and continuous (microarray) expression data from a colorectal cancer study.

Results: We demonstrate that a higher proportion of subjects with paired samples yields higher statistical power, for various total numbers of samples, and for various strengths of …

Numerical Simulation Of Dropped Cylindrical Objects Into Water In Two Dimensions (2d), Yi Zhen

University of New Orleans Theses and Dissertations

The dropped objects are identified as one of the top ten causes of fatalities and serious injuries in the oil and gas industry. It is of importance to understand dynamics of dropped objects under water in order to accurately predict the motion of dropped objects and protect the underwater structures and facilities from being damaged. In this thesis, we study nondimensionalization of dynamic equations of dropped cylindrical objects. Nondimensionalization helps to reduce the number of free parameters, identify the relative size of effects of parameters, and gain a deeper insight of the essential nature of dynamics of dropped cylindrical objects …

Limit Properties Of Order Statistics, А. Madraximov, S. Kukieva

Scientific journal of the Fergana State University

The paper studies the question of estimating the concentration function for the sums of minima of positive random variables.

Substantiation The Parameters Of The Cotton Cleaners’ Polyhedral Vibrating Fire-Bars, A. Djuraev, R.Kh. Maksudov, Sh. Shukhratov

Scientific journal of the Fergana State University

The article describes the principle of operation of the recommended multifaceted grate on elastic supports, as well as the results of the analysis of the grate oscillations, and the parameters are justified. The results of comparative production tests.

Mathematical Models For The Numerical Solution Of Boundary Value Problems Nonstationary Three-Phase Filtering, А. Abdukodirov, G. Аkramova

Scientific journal of the Fergana State University

The construction of an explicit / implicit scheme for the numerical solution of regional problems of non-stationary three-phase filtration is considered in the article.

Recommendations For Developing Modern Electronic Educational Resources, S. Abdurakhmonov, I. Bilolov

Scientific journal of the Fergana State University

The article discusses the use of AutoPlay Media Studio in creating e-learning resources, and also studies the technology of creating electronic resources. Based on the examples, recommendations for use in the education system are developed and provided,

The Way Of Obtaining Of Polyfunctional Haemosorbent, Х. Eshjanov, А. Sarimsakov, М., Baltayeva, М. Nurmatova

Scientific journal of the Fergana State University

In the article the facts about separation fibroin fibers from waste matter of silk fibers and the properties of haemosorbent vitamin-B12 sorbtion are given.

Logarithmic Hennings Invariants For Restricted Quantum Sl (2), Anna Beliakova, Christian Blanchet, Alexandra Tebbs

Mathematics and Statistics Faculty Publications

We construct a Hennings-type logarithmic invariant for restricted quantum sl (2) at a 2p^th root of unity. This quantum group U is not quasitriangular and hence not ribbon, but factorizable. The invariant is defined for a pair: a 3–manifold M and a colored link L inside M. The link L is split into two parts colored by central elements and by trace classes, or elements in the 0^th Hochschild homology of U, respectively. The two main ingredients of our construction are the universal invariant of a string link with values in tensor powers of U, and the modified …

Gizmos Computer Simulations In The Mathematics Classroom, Bethany L. Inman

Morehead State Theses and Dissertations

A capstone submitted in partial fulfillment of the requirements for the degree of Doctor of Education in the College of Education at Morehead State University by Bethany L. Inman on December 6, 2018

Equations Of Motion In A Rotating Noninertial Reference Frame, Nicholas L. Sponsel

Essential Studies UNDergraduate Showcase

Measurement is an essential part of empirical research. As such, understanding whether the frame of reference in which a measurement occurs is inertial is essential for accurate data. As a rotating sphere, Earth is a non-inertial frame of reference and gives rise to fictitious forces. These forces are derived through vector algebra and further solved through matrix differential equations. The final solution for how velocity evolves over time results in sinusoidal functions with a period of 24 hours for Earth. To test the equations further, rational scenarios are proposed for different locations on the surface of Earth involving different initial …

Modeling The Spread Of Disease, James Hollister

Essential Studies UNDergraduate Showcase

Mathematically modeling the spread of disease in a population is a focus among epidemiologists. Using an SIR model (susceptible, infected, and recovered), we can create a system of differential equations to help better understand how a disease spreads in a simple environment. However, if we are to create a more realistic environment, computer simulations may be necessary. We can use the results from these simulations to try and find ways to eradicate the disease as efficiently as possible. In this poster, we will present the SIR model, present a system of differential equations that describe the movement of disease in …

A New Trend In Human Reproduction - Women In The Usa, Abby Rokke

Essential Studies UNDergraduate Showcase

The control a woman is allowed to have over her own reproductive system has been a recent popular topic of debate. Since the 1950's, women have made up over half of the total United States population. With women making up the majority of the country's citizens, it would be quite the contradiction for them to not have the right to make decisions about their own bodies. Over the last two decades many contraceptive and medical advances have assisted in a woman's ability to make her own choice. An interesting trend in childbearing has occurred from this new wave of technologies. …

Subsets Of Vertices Of The Same Size And The Same Maximum Distance, Maria Axenovich, Dominik Duerrschnabel

Theory & Applications of Graphs

For a simple connected graph G=(V,E) and a subset X of its vertices, let

d*(X) = max {dist}_G(x,y): x,y ∈ X}

and let h*(G) be the largest k such that there are disjoint vertex subsets A and B of G, each of size k such that d*(A) = d*(B). Let h*(n) = min {h*(G): |V(G)|=n}. We prove that h*(n) =⌊(n+1)/3 ⌋, for n ≥ 6. This solves the homometric set problem restricted to the largest distance exactly. In addition we compare h*(G) with a respective function h_diam(G), where …

Control Theory: The Double Pendulum Inverted On A Cart, Ian J P Crowe-Wright

Mathematics & Statistics ETDs

In this thesis the Double Pendulum Inverted on a Cart (DPIC) system is modeled using the Euler-Lagrange equation for the chosen Lagrangian, giving a second-order nonlinear system. This system can be approximated by a linear first-order system in which linear control theory can be used. The important definitions and theorems of linear control theory are stated and proved to allow them to be utilized on a linear version of the DPIC system. Controllability and eigenvalue placement for the linear system are shown using MATLAB. Linear Optimal control theory is likewise explained in this section and its uses are applied to …

Invariant Subspaces Of Compact Operators And Related Topics, Weston Mckay Grewe

Mathematics

The invariant subspace problem asks if every bounded linear operator on a Banach space has a nontrivial closed invariant subspace. Per Enflo has shown this is false in general, however it is known that every compact operator has an invariant subspace. The purpose of this project is to explore introductory results in functional analysis. Specifically we are interested in understanding compact operators and the proof that all compact operators on a Hilbert space have an invariant subspace. In the process of doing this we build up many examples and theorems relating to operators on a Hilbert or Banach space. Continuing …

Another Characterization Of Warped Product Submanifolds Of Nearly Cosymplectic Manifolds, Ali H. Alkhaldi, Abid Kamal

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study warped product pseudo-slant submanifolds of nearly cosymplectic manifolds. First, we derive the integrability conditions of the distributions and then, we investigate the geometry of the leaves of both distributions. Also, we prove a characterization theorem for a pseudo-slant submanifold to be locally a warped product manifold.

Almost Periodic Functions In Quantum Calculus, Martin Bohner, Jaqueline Godoy Mesquita

Mathematics and Statistics Faculty Research & Creative Works

In this article, we introduce the concepts of Bochner and Bohr almost periodic functions in quantum calculus and show that both concepts are equivalent. Also, we present a correspondence between almost periodic functions defined in quantum calculus and N₀, proving several important properties for this class of functions. We investigate the existence of almost periodic solutions of linear and nonlinear q-difference equations. Finally, we provide some examples of almost periodic functions in quantum calculus.

Properties Of The Secondary Hochschild Homology, Jacob Laubacher

Faculty Creative and Scholarly Works

Abstract. In this paper we study properties of the secondary Hochschild homology of the triple (A, B, ε) with coefficients in M. We establish a type of Morita equivalence between two triples and show that H•((A, B, ε);M) is invariant under this equivalence. We also prove the existence of an exact sequence which connects the usual and the secondary Hochschild homologies in low dimension, allowing one to perform easy computations. The functoriality of H•((A, B, ε);M) is also discussed.

Fibonacci And Lucas Differential Equations, Esra Erkus-Duman, Hakan Ciftci

Applications and Applied Mathematics: An International Journal (AAM)

The second-order linear hypergeometric differential equation and the hypergeometric function play a central role in many areas of mathematics and physics. The purpose of this paper is to obtain differential equations and the hypergeometric forms of the Fibonacci and the Lucas polynomials. We also write again these polynomials by means of Olver’s hypergeometric functions. In addition, we present some relations between these polynomials and the other well-known functions.

Approximate Analytical Solutions Of Space-Fractional Telegraph Equations By Sumudu Adomian Decomposition Method, Hasib Khan, Cemil Tunç, Rahmat A. Khan, Akhtyar G. Shirzoi, Aziz Khan

Applications and Applied Mathematics: An International Journal (AAM)

The main goal in this work is to establish a new and efficient analytical scheme for space fractional telegraph equation (FTE) by means of fractional Sumudu decomposition method (SDM). The fractional SDM gives us an approximate convergent series solution. The stability of the analytical scheme is also studied. The approximate solutions obtained by SDM show that the approach is easy to implement and computationally very much attractive. Further, some numerical examples are presented to illustrate the accuracy and stability for linear and nonlinear cases.

Η-Ricci Soliton On 3-Dimensional F-Kenmotsu Manifolds, S. K. Hui, S. K. Yadav, S. K. Chaubey

Applications and Applied Mathematics: An International Journal (AAM)

The object of the present paper is to carry out η-Ricci soliton on 3-dimensional regularf-Kenmotsu manifold and we turn up some geometrical results. Furthermore we bring out the curvature conditions for which η-Ricci soliton on such manifolds are shrinking, steady or expanding. We wind up by considering examples of existence of shrinking and expanding η-Ricci soliton on 3-dimensional regularf-Kenmotsu manifolds.

Non-Existence Of Hopf Real Hypersurfaces In Complex Quadric With Recurrent Ricci Tensor, Pooja Bansal, Mohammad H. Shahid

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we first introduce the notion of recurrent Ricci tensor which is the generalization of parallel Ricci tensor in the complex quadric Q^m = SO_m+2 /SO_m SO₂. After then, we investigate real hypersurfaces of the complex quadric Q^m with the condition of recurrent Ricci tensor and give the glimpse of full classification with this condition.

An Investigatiozn On Prime And Semiprime Fuzzy Hyperideals In Po-Ternary Semihypergroups, Aakif F. Talee, M. Y. Abbasi, S. A. Khan

Applications and Applied Mathematics: An International Journal (AAM)

The aim of this paper is to apply the concept of fuzzification on prime hyperideals and semiprime hyperideals in po-ternary semihypergroups and look for some of their related characteristics. Moreover, a number of characterizations for intra-regular po-ternary semihypergroups had been given by using the concept of fuzzy hyperideals.