Operations On Submodules With The Multiplicative And Quotient Properties, 2024 University of New Mexico

#### Operations On Submodules With The Multiplicative And Quotient Properties, Jiekai Pang

*Mathematics & Statistics ETDs*

Inspired by the works of Petro, Epstein, Vassilev, and Morre, this thesis aims to study the generalized definitions of the semiprime operation, weakly prime operation, and standard closure operation on rings, that is, the multiplicative operation, weakly multiplicative operation, and standardly multiplicative operation on submodules. Then, we will use Matlis duality to induce the dual notions of these definitions on submodules of Matlis-dualizable Artinian modules. In order to understand the dual notion of the standardly multiplicative operation, that is, the standardly quotient operation, we will classify the operations on the injective hull of residue field of the ring K[[x,y]]/(xy) which …

Nestings Of Bibds With Block Size Four, 2024 Sapienza Università di Roma

#### Nestings Of Bibds With Block Size Four, Marco Buratti, Donald L. Kreher, Douglas R. Stinson

*Michigan Tech Publications, Part 2*

In a nesting of a balanced incomplete block design (or BIBD), we wish to add a point (the nested point) to every block of a (Formula presented.) -BIBD in such a way that we end up with a partial (Formula presented.) -BIBD. In the case where the partial (Formula presented.) -BIBD is in fact a (Formula presented.) -BIBD, we have a perfect nesting. We show that a nesting is perfect if and only if (Formula presented.). Perfect nestings were previously known to exist in the case of Steiner triple systems (i.e., (Formula presented.) -BIBDs) when (Formula presented.), as well as …

Shevtsov: Teaching Modeling To First-Year Life Science Students: The Ucsc Experience, 2024 University of California, Santa Cruz

#### Shevtsov: Teaching Modeling To First-Year Life Science Students: The Ucsc Experience, Martin H. Weissman

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

Modeling Opioid Addiction In Hand Surgery Patients, 2024 University of Portland

#### Modeling Opioid Addiction In Hand Surgery Patients, Eli Goldwyn, Grace Bowman, Kathryn Montovan, Julie Blackwood

*Annual Symposium on Biomathematics and Ecology Education and Research*

No abstract provided.

On The Work Of Cartan And Münzner On Isoparametric Hypersurfaces, 2024 College of the Holy Cross

#### On The Work Of Cartan And Münzner On Isoparametric Hypersurfaces, Thomas E. Cecil

*Mathematics and Computer Science Department Faculty Scholarship*

A hypersurface *M ^{n}* in a real space form

**R**

^{n+1},

*S*

^{n+1}, or

*H*

^{n+1}is isoparametric if it has constant principal curvatures. This paper is a survey of the fundamental work of Cartan and Münzner on the theory of isoparametric hypersurfaces in real space forms, in particular, spheres. This work is contained in four papers of Cartan published during the period 1938--1940, and two papers of Münzner that were published in preprint form in the early 1970's, and as journal articles in 1980--1981. These papers of Cartan and Münzner have been the foundation of …

Using Academic Librarians And The Academic Library: Survey Results From Mathematics Faculty In United States And Canada, 2024 University of Colorado, Boulder

#### Using Academic Librarians And The Academic Library: Survey Results From Mathematics Faculty In United States And Canada, Elizabeth Novosel, Daniel G. Kipnis, Jenni Burke, Rasitha Jayesekera

*Libraries Scholarship*

Presented at STEM Librarian South Conference, November 6, 2024

Despite our diligent outreach and relationship-building efforts, certain groups of faculty within STEM disciplines remain hesitant to engage with academic librarians and utilize library resources. This challenge raises a critical question: How can librarians effectively support a department when faculty members are unresponsive?

Our research team, composed of three frustrated mathematics librarians and one mathematics faculty member, recognized the need for a fresh approach. Mathematics, a department known for its independence, has received limited attention in scholarly Library and Information Science (LIS) literature. To address this gap, we embarked on a …

Book V Of The Mathematical Collection Of Pappus Of Alexandria, Translated By John B. Little, 2024 College of the Holy Cross

#### Book V Of The Mathematical Collection Of Pappus Of Alexandria, Translated By John B. Little, Pappus Of Alexandria, John B. Little

*Holy Cross Bookshelf*

John B. Little is the translator.

Book V of the Mathematical Collection is addressed to a certain Megethion, about whom we know nothing else. From the context he may have been a student or patron of Pappus in Alexandria. In a heading at the start, Pappus says that the general theme will be comparisons between different geometric figures. The overall structure brings interesting relations and connections to the fore. The book opens with a very well-known and charming discussion of how the importance of such comparisons can be seen by considering the structures built by non-human creatures such as bees. …

Algebraic Structures On Parallelizable Manifolds, 2024 The University of Texas Rio Grande Valley

#### Algebraic Structures On Parallelizable Manifolds, Sergey Grigorian

*School of Mathematical and Statistical Sciences Faculty Publications and Presentations*

In this paper we explore algebraic and geometric structures that arise on parallelizable manifolds. Given a parallelizable manifold L , there exists a global trivialization of the tangent bundle, which defines a map ρ p : l ⟶ T p L for each point p ∈ L , where l is some vector space. This allows us to define a particular class of vector fields, known as fundamental vector fields, that correspond to each element of l . Furthermore, flows of these vector fields give rise to a product between elements of l and L , which in turn induces …

Pricing Variance Swaps For The Discrete Bn-S Model, 2024 School of Computing and Data Science, Wentworth Institute of Technology, Boston MA, 02115, USA

#### Pricing Variance Swaps For The Discrete Bn-S Model, Semere Gebresilasie

*Journal of Stochastic Analysis*

No abstract provided.

A Phenomenological Study Of Persistence For Black Women In Mathematics Doctoral Programs, 2024 Liberty University

#### A Phenomenological Study Of Persistence For Black Women In Mathematics Doctoral Programs, Shushannah Marie Smith

*Doctoral Dissertations and Projects*

The purpose of this phenomenological study was to describe the doctoral persistence experiences of Black women mathematicians. Guided by McGee’s fragile and robust mathematical identity framework, the research design followed Moustakas’ qualitative transcendental phenomenological approach. The researcher explored the contributing factors to the phenomenon guided by the central research question, “What are the doctoral persistence experiences of Black women mathematicians?” The study involved 11 Black women participants who hold or were within one year of holding a doctoral degree in mathematics and were selected to ensure diversity and representativeness. Data collection encompassed three methods: a mathematical identity development timeline, one-on-one …

Uniqueness Of Maximum Points Of A Sequence Of Functions Arising From An Adapted Algorithm For ‘The Secretary Problem’, 2024 Old Dominion University

#### Uniqueness Of Maximum Points Of A Sequence Of Functions Arising From An Adapted Algorithm For ‘The Secretary Problem’, Boning Wang, Giang Vu Thanh Nguyen

*OUR Journal: ODU Undergraduate Research Journal*

This paper is aimed at a sequence of functions that is extended from an adaptive algorithm of the classical ‘secretary problem’. It was proved in Nguyen et al. (2024) the uniqueness of maximizers of a function sequence that represents the expected score of an element in a ‘candidate’ sequence. This function sequence is indeed considered as a special case of an extended function sequence that corresponds to the case α = 0. More specifically, we are motivated to prove the uniqueness of maximizers for this extended function sequence in the case α = 1. Nevertheless, the corresponding proof is rather …

Scaled Global Operators And Fueter Variables On Non-Zero Scaled Hypercomplex Numbers, 2024 Chapman University

#### Scaled Global Operators And Fueter Variables On Non-Zero Scaled Hypercomplex Numbers, Daniel Alpay, Ilwoo Choo, Mihaela Vajiac

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

In this paper we describe the rise of global operators in the scaled quaternionic case, an important extension from the quaternionic case to the family of scaled hypercomplex numbers H_{t}, t ∈ R^{∗} , of which the H_{−1} = H is the space of quaternions and H_{1} is the space of split quaternions.We also describe the scaled Fueter-type variables associated to these operators, developing a coherent theory in this field. We use these types of variables to build different types of function spaces on H_{t}. Counterparts of the Hardy space and of the …

Counting The Classes Of Projectively-Equivalent Pentagons On Finite Projective Planes Of Prime Order, 2024 Rose-Hulman Institute of Technology

#### Counting The Classes Of Projectively-Equivalent Pentagons On Finite Projective Planes Of Prime Order, Maxwell Hosler

*Rose-Hulman Undergraduate Mathematics Journal*

In this paper, we examine the number of equivalence classes of pentagons on finite projective planes of prime order under projective transformations. We are interested in those pentagons in general position, meaning that no three vertices are collinear. We consider those planes which can be constructed from finite fields of prime order, and use algebraic techniques to characterize them by their symmetries. We are able to construct a unique representative for each pentagon class with nontrivial symmetries. We can then leverage this fact to count classes of pentagons in general. We discover that there are (1/10)((*p*+3)(*p*-3)+4 …

Nano Topology And Decision Making In Medical Applications, 2024 Tanta University - Faculty of Engineering

#### Nano Topology And Decision Making In Medical Applications, Samir Mukhtar, Mohamed Shokry, Manar Omran

*Journal of Engineering Research*

**Nano Topology** **is one of the essential topics that receive special attention from some athletes in the field of General Topology, Operations Research, and Computer Science, because it has a vital role in the generalizing most of the various mathematical concepts. Recently, many efforts have been made to study many types of Nano Topology, as the previous studies lacked real applications in Engineering, Medicine, Pharmacy, and Social Sciences. In this paper, we present some different applications of these studies. The paper is divided into two parts: Firstly, we study the theory of The Nano Topology and investigate its relation with …**

New Operation Defined Over Dual-Hesitant Fuzzy Set And Its Application In Diagnostics In Medicine, 2024 Tanta University - Faculty of Engineering

#### New Operation Defined Over Dual-Hesitant Fuzzy Set And Its Application In Diagnostics In Medicine, Manar Mohamed Omran, Reham Abdel-Aziz Abo-Khadra

*Journal of Engineering Research*

In recent decades, several types of sets, such as fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type 2 fuzzy sets, type *n* fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multi-sets as special cases. Then we investigate the basic operations and properties of DHFSs. We also discuss the relationships among the sets mentioned above, and then propose an extension principle of DHFSs. Additionally, we give an example to illustrate …

Decision-Making In Diagnosing Heart Failure Problems Using Dual Hesitant Fuzzy Sets, 2024 Universityof Tanta, Faculty of Engineering

#### Decision-Making In Diagnosing Heart Failure Problems Using Dual Hesitant Fuzzy Sets, Manar Mohamed Omran, Reham Abdel-Aziz Abo-Khadra

*Journal of Engineering Research*

In recent decades, several types of sets, such as fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type 2 fuzzy sets, type *n* fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multi-sets as special cases. Then we investigate the basic operations and properties of DHFSs. We also discuss the relationships among the sets mentioned above, and then propose an extension principle of DHFSs. Additionally, we give an example to illustrate …

Discrete Time Series Forecasting Of Hive Weight, In-Hive Temperature, And Hive Entrance Traffic In Non-Invasive Monitoring Of Managed Honey Bee Colonies: Part I, 2024 Utah State University

#### Discrete Time Series Forecasting Of Hive Weight, In-Hive Temperature, And Hive Entrance Traffic In Non-Invasive Monitoring Of Managed Honey Bee Colonies: Part I, Vladimir A. Kulyukin, Daniel Coster, Aleksey V. Kulyukin, William Meikle, Milagra Weiss

*Computer Science Faculty and Staff Publications*

From June to October, 2022, we recorded the weight, the internal temperature, and the hive entrance video traffic of ten managed honey bee (*Apis mellifera*) colonies at a research apiary of the Carl Hayden Bee Research Center in Tucson, AZ, USA. The weight and temperature were recorded every five minutes around the clock. The 30 s videos were recorded every five minutes daily from 7:00 to 20:55. We curated the collected data into a dataset of 758,703 records (208,760–weight; 322,570–temperature; 155,373–video). A principal objective of Part I of our investigation was to use the curated dataset to investigate …

(Si13-07) Optimal Range For Value Of Two-Person Zero-Sum Game Models With Uncertain Payoffs, 2024 VIT Bhopal University, India

#### (Si13-07) Optimal Range For Value Of Two-Person Zero-Sum Game Models With Uncertain Payoffs, Sana Afreen, Ajay Kumar Bhurjee

*Applications and Applied Mathematics: An International Journal (AAM)*

Game theory deals with the decision-making of individuals in conflicting situations with known payoffs. However, these payoffs are imprecisely known, which means they have uncertainty due to vagueness in the data set of most real-world problems. Therefore, we consider a two-person zero-sum game model on a larger scale where the payoffs are imprecise and lie within a closed interval. We define the pure and mixed strategy as well as value for the game models. The proposed method computes the optimal range for the value of the game model using interval analysis. To derive some important results, we establish some lemmas …

(Si13-06) Analysis Of Some Unified Integral Equations Of Fredholm Type Associated With Multivariable Incomplete H And I-Functions, 2024 University of Engineering and Management, India

#### (Si13-06) Analysis Of Some Unified Integral Equations Of Fredholm Type Associated With Multivariable Incomplete H And I-Functions, Rahul Sharma, Vinod Gill, Naresh Kumar, Kanak Modi, Yudhveer Singh

*Applications and Applied Mathematics: An International Journal (AAM)*

In this research paper, we examine various effective methods for addressing the problem of solving Fredholm-type integral equations. Our investigation commences by applying the principles of fractional calculus theory. We employ series representations and products of multivariable incomplete H-functions and multivariable incomplete I-functions to solve these integrals. The outcomes derived from our analysis possess a general nature and hold the potential to yield numerous results.

Zermelo's Theorem: How To Reach A Standard Of Perfect Play In Chess, 2024 DePauw University

#### Zermelo's Theorem: How To Reach A Standard Of Perfect Play In Chess, Elisha Amadasu '26

*Annual Student Research Poster Session*

Zermelo’s theorem establishes that in any two player zero-sum game with perfect information (without the element of chance), either one side can force a win regardless of how the other side plays, or both sides can force a draw (if allowed in the rules). This theorem encouraged me to see how I could better my chess to see if I could exploit the existence of this perfect standard. I considered how chess engines play, as they are currently the strongest at playing chess. I understood that they often look 60-70 moves deep from the opening stage of the game, which …