Other Mathematics Commons^™

A Nonstandard Proof Of De Finetti’S Theorem For Bernoulli Random Variables, Irfan Alam

Journal of Stochastic Analysis

No abstract provided.

L_P_ Approximation By Relu Neural Networks, Eman Samir Bhaya, Zainab Abdulmunim Sharba

Karbala International Journal of Modern Science

We know that we can use the neural networks for the approximation of functions for many types of activation functions. Here, we treat only neural networks with simple and particular activation function called rectified linear units (ReLU). The main aim of this paper is to introduce a type of constructive universal approximation theorem and estimate the error of the universal approximation. We will obtain optimal approximation if we have a basis independent of the target function. We prove a type of Debao Chen's theorem for approximation.

The Boundedness Of General Alternative Singular Integrals With Respect To The Gaussian Measure, Eduard Navas, Ebner Pineda, Wilfredo O. Urbina

Journal of Stochastic Analysis

No abstract provided.

Martingales And Cocycles In Quantum Probability, Kalyan B. Sinha

Journal of Stochastic Analysis

No abstract provided.

Rényi Entropy On C*-Algebras, Farrukh Mukhamedov, Kyouhei Ohmura, Noboru Watanabe

Journal of Stochastic Analysis

No abstract provided.

R(P,Q) Analogs Of Discrete Distributions: General Formalism And Applications, Mahouton Norbert Hounkonnou, Fridolin Melong

Journal of Stochastic Analysis

No abstract provided.

The Yang-Mills Heat Equation On Three-Manifolds With Boundary, Nelia Charalambous

Journal of Stochastic Analysis

No abstract provided.

Emergence Of Quantum Theories From Classical Probability: Historical Origins, Developments, And Open Problems, Luigi Accardi, Yun-Gang Lu

Journal of Stochastic Analysis

No abstract provided.

Quantitatively Hyper-Positive Real Functions, Daniel Alpay, Izchak Lewkowicz

Mathematics, Physics, and Computer Science Faculty Articles and Research

Hyper-positive real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related through nested inclusions, are introduced. Structurally, this family of functions turns out to be matrix-convex and closed under inversion.

A state-space characterization of these functions through a corresponding Kalman-Yakubovich-Popov Lemma, is given. Technically, the classical Linear Matrix Inclusions, associated with passive systems, are here substituted by Quadratic Matrix Inclusions.

An Asymptotic Formula For Integrals Of Products Of Jacobi Polynomials, Maxim Derevyagin, Nicholas Juricic

Journal of Stochastic Analysis

No abstract provided.

Introduction To Neutrosophic Genetics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Genetics is the study of genetics using neutrosophic logic, set, probability, statistics, measure and other neutrosophic tools and procedures. In this paper, based on the Neutrosophic Theory of Evolution (that includes degrees of Evolution, Neutrality (or Indeterminacy), and Involution) – as extension of Darwin’s Theory of Evolution, we show the applicability of neutrosophy in genetics, and we present within the frame of neutrosophic genetics the following concepts: neutrosophic mutation, neutrosophic speciation, and neutrosophic coevolution.

Structure, Neutrostructure, And Antistructure In Science, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In any science, a classical Theorem, defined on a given space, is a statement that is 100% true (i.e. true for all elements of the space). To prove that a classical theorem is false, it is sufficient to get a single counter-example where the statement is false. Therefore, the classical sciences do not leave room for partial truth of a theorem (or a statement). But, in our world and in our everyday life, we have many more examples of statements that are only partially true, than statements that are totally true. The NeutroTheorem and AntiTheorem are generalizations and alternatives of …

Sum Of Cubes Of The First N Integers, Obiamaka L. Agu

Electronic Theses, Projects, and Dissertations

In Calculus we learned that 􏰅Sum^{n}_{k=1} k = [n(n+1)]/2 , that Sum^{􏰅n}_{k=1} k^2 = [n(n+1)(2n+1)]/6 , and that Sum^{n}_{k=1} k^{3} = (n(n+1)/2)^{2}. These formulas are useful when solving for the area below quadratic or cubic function over an interval [a, b]. This tedious process, solving for areas under a quadratic or a cubic, served as motivation for the introduction of Riemman integrals. For the overzealous math student, these steps were replaced by a simpler method of evaluating antiderivatives at the endpoints a and b. From my recollection, a former instructor informed us to do the value of memorizing these formulas. …

Covariant Quantum White Noise From Light-Like Quantum Fields, Radhakrishnan Balu

Journal of Stochastic Analysis

No abstract provided.

Grim Under A Compensation Variant, Aaron Davis, Aaron Davis

Honors College Theses

Games on graphs are a well studied subset of combinatorial games. Balance and strategies for winning are often looked at in these games. One such combinatorial graph game is Grim. Many of the winning strategies of Grim are already known. We note that many of these winning strategies are only available to the first player. Hoping to develop a fairer Grim, we look at Grim played under a slighlty different rule set. We develop winning strategies and known outcomes for this altered Grim. Throughout, we discuss whether our altered Grim is a fairer game then the original.

Deformed Gaussian Operators On Weighted Q-Fock Spaces, Nobuhiro Asai, Hiroaki Yoshida

Journal of Stochastic Analysis

No abstract provided.

Subproduct Systems And Cartesian Systems: New Results On Factorial Languages And Their Relations With Other Areas, Malte Gerhold, Michael Skeide

Journal of Stochastic Analysis

No abstract provided.

An Analysis Of Preservice Elementary Teachers’ Professional Noticing Skills In A Mathematics Education Setting, Liza Bondurant, Lisa Poling, Diana Moss

Journal of Practitioner Research

Prospective elementary mathematics teachers (PTs) were asked to analyze 28 videos of cognitive interviews. The purpose of this study was to determine if experiences analyzing videos would lead to improvements in PTs’ professional noticing skills. Using a coding schema that reflected three levels of understanding (periphery, transitional, and accomplished), a frequency table was constructed that allowed PTs’ use and understanding of a noticing framework to be analyzed. Findings indicate that experiences analyzing videos leads to improvements in PTs’ professional noticing skills.

Ethnomathematics: Art, Culture, And Social Justice, John R. Jungck

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Community-Based Curriculum: A Novel Approach In Collaborative Teaching, Christopher Hay-Jahans

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Testing The Effect Of Acetaminophen Overdose On The Liver And The Role Of Biomarkers To Predict Death Or Survival, Christine Brasic

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Name Tag Problem, Christian Carley

Rose-Hulman Undergraduate Mathematics Journal

The Name Tag Problem is a thought experiment that, when formalized, serves as an introduction to the concept of an orthomorphism of $\Zn$. Orthomorphisms are a type of group permutation and their graphs are used to construct mutually orthogonal Latin squares, affine planes and other objects. This paper walks through the formalization of the Name Tag Problem and its linear solutions, which center around modular arithmetic. The characterization of which linear mappings give rise to these solutions developed in this paper can be used to calculate the exact number of linear orthomorphisms for any additive group Z/nZ, which is demonstrated …

On The Equitable Total (𝑘+1)-Coloring Of 𝑘-Regular Graphs, Bryson Stemock

Rose-Hulman Undergraduate Mathematics Journal

A graph is considered to be totally colored when one color is assigned to each vertex and to each edge so that no adjacent or incident vertices or edges bear the same color. The \textit{total chromatic number} of a graph is the least number of colors required to totally color a graph. This paper focuses on $k$-regular graphs, whose symmetry and regularity allow for a closer look at general total coloring strategies. Such graphs include the previously defined M\"obius ladder, which has a total chromatic number of 5, as well as the newly defined bird's nest, which is shown to …

Hamming Codes, Steve Mwangi, Sterling Quinn

Access*: Interdisciplinary Journal of Student Research and Scholarship

We will be looking into the application of Matrix Algebra in forming Hamming Codes. Hamming Codes are essential not just in the detection of errors, but also in the linear concurrent correction of these errors. The matrices we will use, will have entries that are binary units. Binary units are mathematically convenient, and their simplicity permits the representation of many open and closed circuits used in communication systems. The entries in the matrices will represent a message that is meant for transmission or reception, akin to the contemporary application of Hamming Codes in wireless communication. We will use Hamming (7,4) …

Quantum Markov Chains Associated With Unitary Quantum Walks, Chul Ki Ko, Hyun Jae Yoo

Journal of Stochastic Analysis

No abstract provided.

Invariant Projections For Covariant Quantum Markov Semigroups, Franco Fagnola, Emanuela Sasso, Veronica Umanità

Journal of Stochastic Analysis

No abstract provided.

Pauli Matrices: A Triple Of Accardi Complementary Observables, Stephen Bruce Sontz

Journal of Stochastic Analysis

No abstract provided.

Preface, Julius Esunge, Brian C. Hall, Ambar N. Sengupta, Aurel Stan

Journal of Stochastic Analysis

No abstract provided.

Spatial Training And Calculus Ability: Investigating Impacts On Student Performance And Cognitive Style, Lindsay J. Mccunn, Emily Cilli-Turner

Journal of Educational Research and Practice

Undergraduate calculus is a foundational mathematics sequence that previews the sophistication students will need to succeed in higher-level courses. However, students often struggle with concepts in calculus because they are more abstract and visual than those in other foundational mathematics courses. Additionally, women continue to be underrepresented in the STEM fields. This study builds on previous work indicating a malleability in spatial ability by testing whether improvement occurs in students’ spatial and mathematics ability after implementing spatial training in calculus courses. The researchers also measured associations between spatial training and self-reported cognitive style. While spatial training did not significantly improve …

True-False Set Is A Particular Case Of The Refined Neutrosophic Set, Florentin Smarandache, Said Broumi

Branch Mathematics and Statistics Faculty and Staff Publications

Borzooei, Mohseni Takallo, and Jun recently proposed a new type of set, called True-False Set [1], and they claimed it is a generalization of Neutrosophic Set [2]. We prove that this assertion is untrue. Actually it’s the opposite, the True-False Set is a particular case of the Refined Neutrosophic Set.