Mathematics Commons^™

Inverse Problems For Polynomial And Rational Matrices, Richard Allen Hollister

Dissertations

Inverse problems have long been studied in mathematics not only because there are many applications in science and engineering, but also because they yield new insight into the beauty of mathematics. Central to the subject of linear algebra is the eigenvalue problem: given a matrix, and its eigenvalues (numerical invariants). Eigenvalue problems play a key role in almost every field of scientific endeavor from calculating the vibrational modes of a molecule to modeling the spread of an infectious disease, and so have been studied extensively since the time of Euler in the 18th century.

If a typical matrix eigenvalue problem …

Math Active Learning Lab: Math 107 Precalculus Notebook, Gwennie Byron, Department Of Mathematics, University Of North Dakota

Open Educational Resources

This course notebook has been designed for students of Math 107 (Precalculus) at the University of North Dakota. It has been designed to help you get the most out of the ALEKS resources and your time.

• Topics in the Notebook are organized by weekly learning module.
• Space for notes from ALEKS learning pages, e-book and videos directs you to essential concepts.
• Examples and “You Try It” problems have been carefully chosen to help you focus on these essential concepts.
• Completed Notebook is an invaluable tool when studying for exams.

Math Active Learning Lab: Math 98 Notebook, Gwennie Byron, Michele Iiams, Department Of Mathematics, University Of North Dakota

Open Educational Resources

This course notebook has been designed for students of Math 98 (Intermediate Algebra) at the University of North Dakota. It has been designed to help you get the most out of the ALEKS resources and your time.

• Topics in the Notebook are organized by weekly learning module.
• Space for notes from ALEKS learning pages, e-book and videos directs you to essential concepts.
• Examples and “You Try It” problems have been carefully chosen to help you focus on these essential concepts.
• Completed Notebook is an invaluable tool when studying for exams.

Analyzing Network Topology For Ddos Mitigation Using The Abelian Sandpile Model, Bhavana Panchumarthi, Monroe Ame Stephenson

altREU Projects

A Distributed Denial of Service (DDoS) is a cyber attack, which is capable of triggering a cascading failure in the victim network. While DDoS attacks come in different forms, their general goal is to make a network's service unavailable to its users. A common, but risky, countermeasure is to blackhole or null route the source, or the attacked destination. When a server becomes a blackhole, or referred to as the sink in the paper, the data that is assigned to it "disappears" or gets deleted. Our research shows how mathematical modeling can propose an alternative blackholing strategy that could improve …

Trisections Of Flat Surface Bundles Over Surfaces, Marla Williams

Department of Mathematics: Dissertations, Theses, and Student Research

A trisection of a smooth 4-manifold is a decomposition into three simple pieces with nice intersection properties. Work by Gay and Kirby shows that every smooth, connected, orientable 4-manifold can be trisected. Natural problems in trisection theory are to exhibit trisections of certain classes of 4-manifolds and to determine the minimal trisection genus of a particular 4-manifold.

Let $\Sigma_g$ denote the closed, connected, orientable surface of genus $g$. In this thesis, we show that the direct product $\Sigma_g\times\Sigma_h$ has a $((2g+1)(2h+1)+1;2g+2h)$-trisection, and that these parameters are minimal. We provide a description of the trisection, and an algorithm to generate a …

Complete Integrability And Discretization Of Euler Top And Manakov Top, Austin Marstaller

Theses and Dissertations

The Euler top is a completely integrable system with physical system implications and the Manakov top is its four-dimensional extension. We are concerned about their complete integrability and the preservation of this property under a specific discretization known as the Hirota-Kimura Discretization. Surprisingly, it is not guaranteed that under any discretization the conserved quantities are preserved and therefore they must be discovered. In this work we construct the Poisson bracket and Lax pair for each system and provide the Lie algebra background needed to do such such constructions.

The Period Of The Coefficients Of The Gaussian Polynomial[N+33], Arturo J. Martinez

Theses and Dissertations

Definition 1. For any N, the central coefficient(s) of [N+33] is denoted by C0(N) and the coefficient that is x ''away" from the central coefficient(s) of [N+33] is denoted by Cx(N).

In [1] the following result is proved:

Theorem 2. The central coefficient(s) of the Gaussian polynomial [N+33] are described by the generating function

[Special characters omitted]

This generating function has period 4.

The main goal of this thesis is to generalize Theorem 0.2 by way of proving the following conjecture:

Conjecture 3. For any x the …

Learning Dynamics From Large Biological Data Sets: Machine Learning Meets Systems Biology, William Gilpin, Yitong Huang, Daniel B. Forger

Mathematics Sciences: Faculty Publications

In the past few decades, mathematical models based on dynamical systems theory have provided new insight into diverse biological systems. In this review, we ask whether the recent success of machine learning techniques for large-scale biological data analysis provides a complementary or competing approach to more traditional modeling approaches. Recent applications of machine learning to the problem of learning biological dynamics in diverse systems range from neuroscience to animal behavior. We compare the underlying mechanisms and limitations of traditional dynamical models with those of machine learning models. We highlight the unique role that traditional modeling has played in providing predictive …

Faktor Yang Mempengaruhi Kebolehan Perwakilan Ikonik Dan Simbolik Murid Tahun Empat Dalam Nombor Pecahan Di Sekolah Jenis Kebangsaan Cina, Wee Pu Lim

Student Works (2020-2029)

Perwakilan matematik telah mula diberi perhatian lalu menjadi salah satu proses utama yang perlu dikuasai oleh murid. Hal ini kerana perwakilan merupakan satu elemen baharu dalam Kurikulum Standard Sekolah Rendah (KSSR). Kajian ini bertujuan untuk menentukan sama ada faktor jantina murid dan tahap pencapaian matematik murid mempengaruhi kebolehan murid tahun empat dalam perwakilan ikonik dan simbolik tentang nombor pecahan serta interaksi antara kedua-dua faktor tersebut. Untuk menjawab tiga soalan kajian ini, reka bentuk kajian perbandingan punca dan kajian faktorial telah digunakan. 596 orang murid tahun 4 (293 lelaki, 303 perempuan) daripada 5 buah sekolah dengan menggunakan pensampelan kluster dua tahap …

New Bounds On The Real Polynomial Roots, Emil M. Prodanov

Articles

The presented analysis determines several new bounds on the roots of the equation $a_n x^n + a_{n−1} x^{n−1} + · · · + a_0 = 0$ (with $a_n > 0$). All proposed new bounds are lower than the Cauchy bound max $\{ 1, sum_{j=0}^{n-1} | a_j / a_n | \}$. Firstly, the Cauchy bound formula is derived by presenting it in a new light — through a recursion. It is shown that this recursion could be exited at earlier stages and, the earlier the recursion is terminated, the lower the resulting root bound will be. Following a separate analysis, it is …

Drug Delivery In Catheterized Arterial Blood Flow With Atherosclerosis, Saulo Orizaga, Daniel N. Riahi, Jose R. Soto

School of Mathematical & Statistical Sciences Faculty Publications

We study the problem of drug delivery in a catheterized artery in the presence of atherosclerosis. The problem is modeled in the context of a two-phase flow system which consists of red blood cells and blood plasma. The coupled differential equations for fluid (plasma) and particles (red cells) are solved for the relevant quantities in the reasonable limits. The drug delivery problem is modeled with a partial differential equation that is developed in terms of the drug concentration, blood plasma velocity, hematocrit value and the diffusion coefficient of the drug/fluid. A conservative-implicit finite difference scheme is develop in order to …

Pipe Flow Of Newtonian And Non-Newtonian Fluids, Erick Sanchez

Theses and Dissertations

We consider an incompressible, viscous fluid in a cylindrical pipe. We obtain velocity profile for both Newtonian fluid and non-Newtonian fluids such as shear-thinning, shear- thickening and Bingham plastic fluids. The flow is governed by the equation of continuity (conservation of mass) and the momentum equation. After presenting the governing system in the cylindrical coordinate system and assuming that the flow is due to the pressure drop and wall shear stress, we derive the expressions for the velocity component in the axial direction for these cases. Some computational results of the velocity profiles for various cases are presented. We will …

An Efficient Method Based On Framelets For Solving Fractional Volterra Integral Equations, Mutaz Mohammad, Alexander Trounev, Carlo Cattani

All Works

© 2020 by the authors. This paper is devoted to shedding some light on the advantages of using tight frame systems for solving some types of fractional Volterra integral equations (FVIEs) involved by the Caputo fractional order derivative. A tight frame or simply framelet, is a generalization of an orthonormal basis. A lot of applications are modeled by non-negative functions; taking this into account in this paper, we consider framelet systems generated using some refinable non-negative functions, namely, B-splines. The FVIEs we considered were reduced to a set of linear system of equations and were solved numerically based on a …

Decompositions Of The Complete Mixed Graph By Mixed Stars, Chance Culver

Electronic Theses and Dissertations

In the study of mixed graphs, a common question is: What are the necessary and suffcient conditions for the existence of a decomposition of the complete mixed graph into isomorphic copies of a given mixed graph? Since the complete mixed graph has twice as many arcs as edges, then an obvious necessary condition is that the isomorphic copies have twice as many arcs as edges. We will prove necessary and suffcient conditions for the existence of a decomposition of the complete mixed graphs into mixed stars with two edges and four arcs. We also consider some special cases of decompositions …

A General Model Of Neutrosophic Ideals In Bck/Bci-Algebras Based On Neutrosophic Points, Florentin Smarandache, Hashem Bordbar, Rajab Ali Borzooei, Young Bae Jun

Branch Mathematics and Statistics Faculty and Staff Publications

More general form of (∈, ∈∨q)-neutrosophic ideal is introduced, and their properties are investigated.

The Polar Form Of A Neutrosophic Complex Number, Florentin Smarandache, Riad K. Al-Hamido, Mayas Ismail

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we will define the exponential form of a neutrosophic complex number. We have proven some characteristics and theories, including the conjugate of the exponential form of a neutrosophic complex number, division of the exponential form of a neutrosophic complex numbers, multiplication of the exponential form of a neutrosophic complex numbers. In addition, we have given the method of changing from the exponential to the algebraic form of a complex number.

A Review Of Fuzzy Soft Topological Spaces, Intuitionistic Fuzzy Soft Topological Spaces And Neutrosophic Soft Topological Spaces, Florentin Smarandache, M. Parimala, M. Karthika

Branch Mathematics and Statistics Faculty and Staff Publications

The notion of fuzzy sets initiated to overcome the uncertainty of an object. Fuzzy topological space, intuitionistic fuzzy sets in topological structure space, vagueness in topological structure space, rough sets in topological space, theory of hesitancy and neutrosophic topological space, etc. are the extension of fuzzy sets. Soft set is a family of parameters which is also a set. Fuzzy soft topological space, intuitionistic fuzzy soft and neutrosophic soft topological space are obtained by incorporating soft sets with various topological structures. This motivates to write a review and study on various soft set concepts. This paper shows the detailed review …

An Expanded Model Of Unmatter From Neutrosophic Logic Perspective: Towards Matter-Spirit Unity View, Florentin Smarandache, Victor Christianto, Robert Neil Boyd

Branch Mathematics and Statistics Faculty and Staff Publications

In Neutrosophic Logic, a basic assertion is that there are variations of about everything that we can measure; the variations surround three parameters called T, I, F (truth, indeterminacy, falsehood) which can take a range of values. A previous paper in IJNS, 2020 shortly reviews the links among aether and matter creation from the perspective of Neutrosophic Logic. In any case, matter creation process in nature stays a major puzzle for physicists, scientists and other science analysts. To this issue neutrosophic logic offers an answer: "unmatter." This paper examines an extended model of unmatter, to incorporate issue soul solidarity. So, …

Combination Of The Single-Valued Neutrosophic Fuzzy Set And The Soft Set With Applications In Decision-Making, Florentin Smarandache, Ahmed Mostafa Khalil, Dunqian Chao, A. A. Azzam, W. Alharby

Branch Mathematics and Statistics Faculty and Staff Publications

In this article, we propose a novel concept of the single-valued neutrosophic fuzzy soft set by combining the single-valued neutrosophic fuzzy set and the soft set. For possible applications, five kinds of operations (e.g., subset, equal, union, intersection, and complement) on single-valued neutrosophic fuzzy soft sets are presented. Then, several theoretical operations of single-valued neutrosophic fuzzy soft sets are given. In addition, the first type for the fuzzy decision-making based on single-valued neutrosophic fuzzy soft set matrix is constructed. Finally, we present the second type by using the AND operation of the single-valued neutrosophic fuzzy soft set for fuzzy decision-making …

A Neutrosophic Clinical Decision-Making System For Cardiovascular Diseases Risk Analysis, Florentin Smarandache, Shaista Habib, Wardat-Us- Salam, M. Arif Butt, Muhammad Akram

Branch Mathematics and Statistics Faculty and Staff Publications

Cardiovascular diseases are the leading cause of death worldwide. Early diagnosis of heart disease can reduce this large number of deaths so that treatment can be carried out. Many decision-making systems have been developed, but they are too complex for medical professionals. To target these objectives, we develop an explainable neutrosophic clinical decision-making system for the timely diagnose of cardiovascular disease risk. We make our system transparent and easy to understand with the help of explainable artificial intelligence techniques so that medical professionals can easily adopt this system. Our system is taking thirtyfive symptoms as input parameters, which are, gender, …