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Articles 1  30 of 1112
FullText Articles in Other Mathematics
Totally Positive Completable Matrix Patterns And Expansion, David Allen
Totally Positive Completable Matrix Patterns And Expansion, David Allen
Undergraduate Honors Theses
Though some special cases are now understood, the characterization of TPcompletable patterns is far from complete. Here, a new idea is developed: the \underline{expansion} of a pattern. It is used to explain some recent results, such as border patterns. The effects of expansion on certain cases of noncompletable and completable patterns is examined, as well as an attempt to characterize $3$by$n$ TPcompletable patterns. While many TPcompletable patterns remain so under expansion, a counterExample shows that this is not always so. In the process, some new results about TPcompletability are given.
Taking Notes: Generating TwelveTone Music With Mathematics, Nathan Molder
Taking Notes: Generating TwelveTone Music With Mathematics, Nathan Molder
Electronic Theses and Dissertations
There has often been a connection between music and mathematics. The world of musical composition is full of combinations of orderings of diﬀerent musical notes, each of which has diﬀerent sound quality, length, and em phasis. One of the more intricate composition styles is twelvetone music, where twelve unique notes (up to octave isomorphism) must be used before they can be repeated. In this thesis, we aim to show multiple ways in which mathematics can be used directly to compose twelvetone musical scores.
Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer
Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer
Undergraduate Theses and Capstone Projects
This research study used mathematical models to analyze and depicted specific battle situations and the outcomes of the zombie apocalypse. The original models that predicted warfare were the Lanchester models, while the zombie apocalypse models were fictional expansions upon mathematical models used to examine infectious diseases. In this paper, I analyzed and compared different mathematical models by examining each model’s set of assumptions and the impact of the change in variables on the population classes. The purpose of this study was to understand the basics of the discrete dynamical systems and to determine the similarities between imaginary and realistic ...
A More Powerful Unconditional Exact Test Of Homogeneity For 2 × C Contingency Table Analysis, Louis Ehwerhemuepha, Heng Sok, Cyril Rakovski
A More Powerful Unconditional Exact Test Of Homogeneity For 2 × C Contingency Table Analysis, Louis Ehwerhemuepha, Heng Sok, Cyril Rakovski
Mathematics, Physics, and Computer Science Faculty Articles and Research
The classical unconditional exact pvalue test can be used to compare two multinomial distributions with small samples. This general hypothesis requires parameter estimation under the null which makes the test severely conservative. Similar property has been observed for Fisher's exact test with Barnard and Boschloo providing distinct adjustments that produce more powerful testing approaches. In this study, we develop a novel adjustment for the conservativeness of the unconditional multinomial exact pvalue test that produces nominal type I error rate and increased power in comparison to all alternative approaches. We used a large simulation study to empirically estimate ...
Does Teaching The History Of Mathematics In High School Aid In Student Understanding?, Anne Campbell
Does Teaching The History Of Mathematics In High School Aid In Student Understanding?, Anne Campbell
Honors Thesis Projects
This research will study the effect teaching the history of mathematics in a high school classroom has on student understanding. To accomplish this, lessons both including and excluding historical background on different topics were taught in an Honors Algebra 2 class in the high school setting. This research aims to engage student learning and investigation of topics that normally do not draw a lot of student focus and spark a new or revived interest in mathematics for students by broadening lessons to include material of which students would not otherwise be exposed. The lessons themselves aim to engage other current ...
Monoidal Supercategories And Superadjunction, Dene Lepine
Monoidal Supercategories And Superadjunction, Dene Lepine
RoseHulman Undergraduate Mathematics Journal
We define the notion of superadjunction in the context of supercategories. In particular, we give definitions in terms of counitunit superadjunctions and homspace superadjunctions, and prove that these two definitions are equivalent. These results generalize wellknown statements in the nonsuper setting. In the super setting, they formalize some notions that have recently appeared in the literature. We conclude with a brief discussion of superadjunction in the language of string diagrams.
Heterogeneous Boolean Networks With Two Totalistic Rules, Katherine Toh
Heterogeneous Boolean Networks With Two Totalistic Rules, Katherine Toh
Student Research and Creative Activity Fair
Boolean Networks are being used to analyze models in biology, economics, social sciences, and many other areas. These models simplify the reality by assuming that each element in the network can take on only two possible values, such as ON and OFF. The node evolution is governed by its interaction with other nodes in its neighborhood, which is described mathematically by a Boolean function or rule. For simplicity reasons, many models assume that all nodes follow the same Boolean rule. However, real networks often use more than one Boolean rule and therefore are heterogeneous networks. Heterogeneous networks have not yet ...
Fourier Series Expansion Methods For The Heat And Wave Equations In Two And Three Dimensions On Spherical Domains, Matthew Eller
Fourier Series Expansion Methods For The Heat And Wave Equations In Two And Three Dimensions On Spherical Domains, Matthew Eller
Student Research and Creative Activity Fair
Description: The Fourier series expansion method is an invaluable approach to solving partial differential equations, including the heat and wave equations. For homogeneous heat and wave equations, the solution can readily be found through separation of variables and then expansion of the solution in terms of the eigenfunctions. Solutions to inhomogeneous heat and wave equations through Fourier series expansion methods were not readily available in the literature for two and threedimensional cases. In my previous paper, I developed an approach for solving inhomogeneous heat and wave equations on cubic domains using Fourier series expansion methods. I shall extend my general ...
Forensics Analysis For Bone Pair Matching Using Bipartite Graphs In Commingled Remains, Ryan Ernst
Forensics Analysis For Bone Pair Matching Using Bipartite Graphs In Commingled Remains, Ryan Ernst
Student Research and Creative Activity Fair
Identification of missing prisoners of war is a complex and time consuming task. There are many missing soldiers whose remains have yet to be returned to their families and loved ones. This nation has a solemn obligation to its soldiers and their families who have made the ultimate sacrifice for their country. There are currently over 82,000 unidentified prisoners of war which are identified at a rate of 100+ per year. At this rate it would take 300+ years to complete the identification process. Previously, anthropologists used excel spreadsheets to sort through skeletal data. This project aims to streamline ...
Operator Algebras Generated By Left Invertibles, Derek Desantis
Operator Algebras Generated By Left Invertibles, Derek Desantis
Dissertations, Theses, and Student Research Papers in Mathematics
Operator algebras generated by partial isometries and their adjoints form the basis for some of the most well studied classes of C*algebras. Representations of such algebras encode the dynamics of orthonormal sets in a Hilbert space.We instigate a research program on concrete operator algebras that model the dynamics of Hilbert space frames.
The primary object of this thesis is the normclosed operator algebra generated by a left invertible $T$ together with its MoorePenrose inverse $T^\dagger$. We denote this algebra by $\mathfrac{A}_T$. In the isometric case, $T^\dagger = T^*$ and $\mathfrac{A}_T$ is a representation ...
Brauer's Theorem And Nonnegative Matrices With Prescribed Diagonal Entries, Ricardo L. Soto, Ana I. Julio, Macarena A. Collao
Brauer's Theorem And Nonnegative Matrices With Prescribed Diagonal Entries, Ricardo L. Soto, Ana I. Julio, Macarena A. Collao
Electronic Journal of Linear Algebra
The problem of the existence and construction of nonnegative matrices with prescribed eigenvalues and diagonal entries is an important inverse problem, interesting by itself, but also necessary to apply a perturbation result, which has played an important role in the study of certain nonnegative inverse spectral problems. A number of partial results about the problem have been published by several authors, mainly by H. \v{S}migoc. In this paper, the relevance of a Brauer's result, and its implication for the nonnegative inverse eigenvalue problem with prescribed diagonal entries is emphasized. As a consequence, given a list of complex ...
Surjective Additive Rank1 Preservers On Hessenberg Matrices, Prathomjit Khachorncharoenkul, Sajee Pianskool
Surjective Additive Rank1 Preservers On Hessenberg Matrices, Prathomjit Khachorncharoenkul, Sajee Pianskool
Electronic Journal of Linear Algebra
Let $H_{n}(\mathbb{F})$ be the space of all $n\times n$ upper Hessenberg matrices over a field~$\mathbb{F}$, where $n$ is a positive integer greater than two. In this paper, surjective additive maps preserving rank$1$ on $H_{n}(\mathbb{F})$ are characterized.
Extending Set Functors To Generalised Metric Spaces, Adriana Balan, Alexander Kurz, Jiří Velebil
Extending Set Functors To Generalised Metric Spaces, Adriana Balan, Alexander Kurz, Jiří Velebil
Mathematics, Physics, and Computer Science Faculty Articles and Research
For a commutative quantale V, the category Vcat can be perceived as a category of generalised metric spaces and nonexpanding maps. We show that any type constructor T (formalised as an endofunctor on sets) can be extended in a canonical way to a type constructor T_{V} on Vcat. The proof yields methods of explicitly calculating the extension in concrete examples, which cover wellknown notions such as the PompeiuHausdorff metric as well as new ones.
Conceptually, this allows us to to solve the same recursive domain equation X ≅ TX in different categories (such as sets and metric spaces) and we ...
Exponential Inequalities For Exit Times For Stochastic NavierStokes Equations And A Class Of Evolutions, PoHan Hsu, Padamanbhan Sundar
Exponential Inequalities For Exit Times For Stochastic NavierStokes Equations And A Class Of Evolutions, PoHan Hsu, Padamanbhan Sundar
Communications on Stochastic Analysis
No abstract provided.
Composition Of Gaussian Noises From Successive Convex Integrations, Amites Dasgupta
Composition Of Gaussian Noises From Successive Convex Integrations, Amites Dasgupta
Communications on Stochastic Analysis
No abstract provided.
Random Matrices, Continuous Circular Systems And The Triangular Operator, Romuald Lenczewski
Random Matrices, Continuous Circular Systems And The Triangular Operator, Romuald Lenczewski
Communications on Stochastic Analysis
No abstract provided.
Global Strong Solutions Of The Stochastic Three Dimensional Inviscid Simplified Bardina Turbulence Model, Manil T. Mohan
Global Strong Solutions Of The Stochastic Three Dimensional Inviscid Simplified Bardina Turbulence Model, Manil T. Mohan
Communications on Stochastic Analysis
No abstract provided.
Limiting Means For Spherical Slices, Amy Peterson, Ambar Sengupta
Limiting Means For Spherical Slices, Amy Peterson, Ambar Sengupta
Communications on Stochastic Analysis
No abstract provided.
Normally Ordered Disentanglement Of MultiDimensional Schrödinger Algebra Exponentials, Luigi Accardi, Andreas Boukas
Normally Ordered Disentanglement Of MultiDimensional Schrödinger Algebra Exponentials, Luigi Accardi, Andreas Boukas
Communications on Stochastic Analysis
No abstract provided.
Generalized Stochastic Burgers' Equation With NonLipschitz Diffusion Coefficient, Vivek Kumar, Ankik Kumar Giri
Generalized Stochastic Burgers' Equation With NonLipschitz Diffusion Coefficient, Vivek Kumar, Ankik Kumar Giri
Communications on Stochastic Analysis
No abstract provided.
Call For Abstracts  Resrb 2019, July 89, Wrocław, Poland, Wojciech M. Budzianowski
Call For Abstracts  Resrb 2019, July 89, Wrocław, Poland, Wojciech M. Budzianowski
Wojciech Budzianowski
No abstract provided.
Exploring Flag Matroids And Duality, Zachary Garcia
Exploring Flag Matroids And Duality, Zachary Garcia
Electronic Theses, Projects, and Dissertations
Matroids capture an abstraction of independence in mathematics, and in doing so, connect discrete mathematical structures that arise in a variety of contexts. A matroid can be defined in several cryptomorphic ways depending on which perspective of a matroid is most applicable to the given context. Among the many important concepts in matroid theory, the concept of matroid duality provides a powerful tool when addressing difficult problems. The usefulness of matroid duality stems from the fact that the dual of a matroid is itself a matroid. In this thesis, we explore a matroidlike object called a flag matroid. In particular ...
Symmetric Presentations And Double Coset Enumeration, Charles Seager
Symmetric Presentations And Double Coset Enumeration, Charles Seager
Electronic Theses, Projects, and Dissertations
In this project, we demonstrate our discovery of original symmetric presentations and constructions of important groups, including nonabelian simple groups, and groups that have these as factor groups. The target nonabelian simple groups include alternating, linear, and sporadic groups. We give isomorphism types for each finite homomorphic image that has been found. We present original symmetric presentations of $M_{12}$, $M_{21}:(2 \times 2)$, $L_{3}(4):2^2$, $2:^{\cdot}L_{3}(4):2$, $S(4,3)$, and $S_{7}$ as homomorphism images of the progenitors $2^{*20}$ $:$ $A_{5}$, $2^{*10}$ $:$ $PGL(2,9)$, $2^{*10}$ $:$ $Aut ...
Commutators Involving Matrix Functions, Osman Kan, Süleyman Solak
Commutators Involving Matrix Functions, Osman Kan, Süleyman Solak
Electronic Journal of Linear Algebra
Some results are obtained for matrix commutators involving matrix exponentials $\left(\left[e^{A},B\right],\left[e^{A},e^{B}\right]\right)$ and their norms.
Determinants Of Interval Matrices, Jaroslav Horáček, Milan Hladík, Josef Matějka
Determinants Of Interval Matrices, Jaroslav Horáček, Milan Hladík, Josef Matějka
Electronic Journal of Linear Algebra
In this paper we shed more light on determinants of real interval matrices. Computing the exact bounds on a determinant of an interval matrix is an NPhard problem. Therefore, attention is first paid to approximations. NPhardness of both relative and absolute approximation is proved. Next, methods computing verified enclosures of interval determinants and their possible combination with preconditioning are discussed. A new method based on Cramer's rule was designed. It returns similar results to the stateoftheart method, however, it is less consuming regarding computational time. Other methods transferable from real matrices (e.g., the Gerschgorin circles, Hadamard's inequality ...
A Complete Characterization Of Near OuterPlanar Graphs, Tanya Allen Lueder Genannt Luehr
A Complete Characterization Of Near OuterPlanar Graphs, Tanya Allen Lueder Genannt Luehr
Doctoral Dissertations
A graph is outerplanar (OP) if it has a plane embedding in which all of the vertices lie on the boundary of the outer face. A graph is near outerplanar (NOP) if it is edgeless or has an edge whose deletion results in an outerplanar graph. An edge of a non outerplanar graph whose removal results in an outerplanar graph is a vulnerable edge. This dissertation focuses on near outerplanar (NOP) graphs. We describe the class of all such graphs in terms of a ﬁnite list of excluded graphs, in a manner similar to the wellknown Kuratowski Theorem for planar ...
Partial Sum Trigonometric Identities And Chebyshev Polynomials, Sarah Weller
Partial Sum Trigonometric Identities And Chebyshev Polynomials, Sarah Weller
RoseHulman Undergraduate Mathematics Journal
Using Euler’s theorem, geometric sums and Chebyshev polynomials, we prove trigonometric identities involving sums and multiplications of cosine.
Color Space Standardization And Image Analysis For HighThroughput Phenotyping Of Sorghum Bicolor, Alexandria A. Pokorny
Color Space Standardization And Image Analysis For HighThroughput Phenotyping Of Sorghum Bicolor, Alexandria A. Pokorny
Annual Symposium on Biomathematics and Ecology: Education and Research
No abstract provided.
A Decomposition Of A Space Of Multiple Wiener Integrals By The Difference Of Two Independent Lévy Processes In Terms Of The Lévy Laplacian, Atsushi Ishikawa
A Decomposition Of A Space Of Multiple Wiener Integrals By The Difference Of Two Independent Lévy Processes In Terms Of The Lévy Laplacian, Atsushi Ishikawa
Communications on Stochastic Analysis
No abstract provided.
A Stochastic Integral By A NearMartingale, Shinya Hibino, HuiHsiung Kuo, Kimiaki Saitô
A Stochastic Integral By A NearMartingale, Shinya Hibino, HuiHsiung Kuo, Kimiaki Saitô
Communications on Stochastic Analysis
No abstract provided.