Open Access. Powered by Scholars. Published by Universities.®
- Institution
-
- Chapman University (129)
- University of New Mexico (82)
- City University of New York (CUNY) (10)
- California State University, San Bernardino (7)
- Claremont Colleges (5)
-
- Rose-Hulman Institute of Technology (3)
- The University of Akron (3)
- University of Massachusetts Amherst (3)
- University of Nebraska - Lincoln (3)
- Boise State University (2)
- Colby College (2)
- Liberty University (2)
- Northern Michigan University (2)
- Olivet Nazarene University (2)
- The College of Wooster (2)
- University of Louisville (2)
- University of South Alabama (2)
- Utah State University (2)
- William & Mary (2)
- Bard College (1)
- Brigham Young University (1)
- California Polytechnic State University, San Luis Obispo (1)
- Central Washington University (1)
- East Tennessee State University (1)
- Florida International University (1)
- Illinois Math and Science Academy (1)
- Indian Statistical Institute (1)
- Louisiana State University (1)
- Missouri State University (1)
- Montclair State University (1)
- Keyword
-
- Neutrosophic logic (32)
- Mathematics (15)
- Coalgebra (13)
- Algebra (11)
- Reproducing kernels (8)
-
- Slice hyperholomorphic functions (8)
- Graph theory (7)
- White noise space (7)
- Modal logic (6)
- Realization (6)
- Wick product (6)
- Algebraic structures (5)
- Geometry (5)
- Problems (5)
- S-resolvent operators (5)
- Category theory (4)
- Gaussian processes (4)
- Mathematical problems (4)
- Number theory (4)
- S-spectrum (4)
- Abstract algebra (3)
- Coalgebraic logic (3)
- Coalgebras (3)
- Convolution algebra (3)
- Display calculus (3)
- Graph (3)
- Groupoid (3)
- Infinite products (3)
- Mathematics education (3)
- Matrices (3)
- Publication Year
- Publication
-
- Branch Mathematics and Statistics Faculty and Staff Publications (82)
- Mathematics, Physics, and Computer Science Faculty Articles and Research (81)
- Engineering Faculty Articles and Research (45)
- Electronic Theses, Projects, and Dissertations (7)
- Electronic Theses and Dissertations (4)
-
- Publications and Research (4)
- Dissertations, Theses, and Capstone Projects (3)
- Honors Theses (3)
- MPP Published Research (3)
- Open Educational Resources (3)
- Rose-Hulman Undergraduate Mathematics Journal (3)
- Williams Honors College, Honors Research Projects (3)
- All NMU Master's Theses (2)
- Doctoral Dissertations (2)
- Journal of Humanistic Mathematics (2)
- Paul Gunnells (2)
- Senior Honors Theses (2)
- Senior Independent Study Theses (2)
- Undergraduate Honors Theses (2)
- University Faculty and Staff Publications (2)
- Access*: Interdisciplinary Journal of Student Research and Scholarship (1)
- All Graduate Plan B and other Reports, Spring 1920 to Spring 2023 (1)
- All Graduate Reports and Creative Projects, Fall 2023 to Present (1)
- All HMC Faculty Publications and Research (1)
- Boise State University Theses and Dissertations (1)
- CMC Senior Theses (1)
- Department of Math & Statistics Faculty Publications (1)
- Department of Mathematics Facuty Scholarship and Creative Works (1)
- Department of Mathematics: Dissertations, Theses, and Student Research (1)
- FIU Electronic Theses and Dissertations (1)
Articles 31 - 60 of 294
Full-Text Articles in Other Mathematics
Mathematical Magic: A Study Of Number Puzzles, Nicasio M. Velez
Mathematical Magic: A Study Of Number Puzzles, Nicasio M. Velez
Rose-Hulman Undergraduate Mathematics Journal
Within this paper, we will briefly review the history of a collection of number puzzles which take the shape of squares, polygons, and polyhedra in both modular and nonmodular arithmetic. Among other results, we develop construction techniques for solutions of both Modulo and regular Magic Squares. For other polygons in nonmodular arithmetic, specifically of order 3, we present a proof of why there are only four Magic Triangles using linear algebra, disprove the existence of the Magic Tetrahedron in two ways, and utilizing the infamous 3-SUM combinatorics problem we disprove the existence of the Magic Octahedron.
Interdisciplinary Thinking: Financial Literacy Crosses Disciplinary Boundaries, Marla A. Sole
Interdisciplinary Thinking: Financial Literacy Crosses Disciplinary Boundaries, Marla A. Sole
Publications and Research
Financial literacy is ideally suited to be integrated into mathematics courses and taught in an interdisciplinary manner. Students learn best and are motivated when tackling real-world meaningful questions. This article shares how elementary mathematics was applied to better understand the debate about raising the minimum wage and the United States National Debt. To serve as a guide for other teachers who wish to incorporate financial literacy into their mathematics courses and take an interdisciplinary approach, this article suggests readings, data sets, and pedagogical practices. Students were engaged and enthusiastic to work on problems that challenged their thinking about financial issues.
Obstructive Wiring Patterns To Circular Planarity In Electrical Networks, Hannah Lebo
Obstructive Wiring Patterns To Circular Planarity In Electrical Networks, Hannah Lebo
Williams Honors College, Honors Research Projects
In order for an electrical network to be printed on a flat surface without changing the network’s input or output, it is important to consider if any wires will cross and if this problem can be avoided. If a circular network can be printed so that no wires cross, the network is said to be circular planar. In this paper, we identify a number of wiring patterns that make circular planarity impossible. We find exactly 3 wiring patterns using circular pairs with sets of two nodes, and we find exactly 78 wiring patterns using circular pairs with sets of three …
Sum Of Cubes Of The First N Integers, Obiamaka L. Agu
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. …
The Name Tag Problem, Christian Carley
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 …
Hamming Codes, Steve Mwangi, Sterling Quinn
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) …
Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder, Matthew Karlson, Bogdan Nita, Ashwin Vaidya
Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder, Matthew Karlson, Bogdan Nita, Ashwin Vaidya
Department of Mathematics Facuty Scholarship and Creative Works
We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which marks the …
Spectral Sequences For Almost Complex Manifolds, Qian Chen
Spectral Sequences For Almost Complex Manifolds, Qian Chen
Dissertations, Theses, and Capstone Projects
In recent work, two new cohomologies were introduced for almost complex manifolds: the so-called J-cohomology and N-cohomology [CKT17]. For the case of integrable (complex) structures, the former cohomology was already considered in [DGMS75], and the latter agrees with de Rham cohomology. In this dissertation, using ideas from [CW18], we introduce spectral sequences for these two cohomologies, showing the two cohomologies have natural bigradings. We show the spectral sequence for the J-cohomology converges at the second page whenever the almost complex structure is integrable, and explain how both fit in a natural diagram involving Bott-Chern cohomology and the Frolicher spectral sequence. …
Length Neutrosophic Subalgebras Of Bck/Bci-Algebras, Florentin Smarandache, Young Bae Jun, Madad Khan, Seok-Zun Song
Length Neutrosophic Subalgebras Of Bck/Bci-Algebras, Florentin Smarandache, Young Bae Jun, Madad Khan, Seok-Zun Song
Branch Mathematics and Statistics Faculty and Staff Publications
the notion of (i, j, k)-length neutrosophic subalgebras in BCK/BCI-algebras is introduced, and their properties are investigated. Characterizations of length neutrosophic subalgebras are discussed by using level sets of interval neutrosophic sets. Conditions for level sets of interval neutrosophic sets to be subalgebras are provided.
On Product Of Smooth Neutrosophic Topological Spaces, Florentin Smarandache, Kalaivani Chandran, Swathi Sundari Sundaramoorthy, Saeid Jafari
On Product Of Smooth Neutrosophic Topological Spaces, Florentin Smarandache, Kalaivani Chandran, Swathi Sundari Sundaramoorthy, Saeid Jafari
Branch Mathematics and Statistics Faculty and Staff Publications
In this paper, we develop the notion of the basis for a smooth neutrosophic topology in a more natural way. As a sequel, we define the notion of symmetric neutrosophic quasi-coincident neighborhood systems and prove some interesting results that fit with the classical ones, to establish the consistency of theory developed. Finally, we define and discuss the concept of product topology, in this context, using the definition of basis.
Exact And Strongly Exact Filters, M. A. Moshier, A. Pultr, A. L. Suarez
Exact And Strongly Exact Filters, M. A. Moshier, A. Pultr, A. L. Suarez
Mathematics, Physics, and Computer Science Faculty Articles and Research
A meet in a frame is exact if it join-distributes with every element, it is strongly exact if it is preserved by every frame homomorphism. Hence, finite meets are (strongly) exact which leads to the concept of an exact resp. strongly exact filter, a filter closed under exact resp. strongly exact meets. It is known that the exact filters constitute a frame FiltE(L) somewhat surprisingly isomorphic to the frame of joins of closed sublocales. In this paper we present a characteristic of the coframe of meets of open sublocales as the dual to the frame of strongly exact filters FiltsE(L).
Harmony Amid Chaos, Drew Schaffner
Harmony Amid Chaos, Drew Schaffner
Pence-Boyce STEM Student Scholarship
We provide a brief but intuitive study on the subjects from which Galois Fields have emerged and split our study up into two categories: harmony and chaos. Specifically, we study finite fields with elements where is prime. Such a finite field can be defined through a logarithm table. The Harmony Section is where we provide three proofs about the overall symmetry and structure of the Galois Field as well as several observations about the order within a given table. In the Chaos Section we make two attempts to analyze the tables, the first by methods used by Vladimir Arnold as …
On The Extension Of Positive Definite Kernels To Topological Algebras, Daniel Alpay, Ismael L. Paiva
On The Extension Of Positive Definite Kernels To Topological Algebras, Daniel Alpay, Ismael L. Paiva
Mathematics, Physics, and Computer Science Faculty Articles and Research
We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras and describe their associated reproducing kernel spaces. The case of entire functions is of special interest, and we give a precise meaning to some power series expansions of analytic functions that appears in many algebras.
Acoustic Versus Electromagnetic Field Theory: Scalar, Vector, Spinor Representations And The Emergence Of Acoustic Spin, Lucas Burns, Konstantin Y. Bliokh, Franco Nori, Justin Dressel
Acoustic Versus Electromagnetic Field Theory: Scalar, Vector, Spinor Representations And The Emergence Of Acoustic Spin, Lucas Burns, Konstantin Y. Bliokh, Franco Nori, Justin Dressel
Mathematics, Physics, and Computer Science Faculty Articles and Research
We construct a novel Lagrangian representation of acoustic field theory that describes the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach accounts for the recently-discovered nonzero spin angular momentum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian representation with a scalar potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement vector potential analogous to the electromagnetic vector potential, we derive the appropriate canonical momentum and spin densities as conserved Noether …
Structure Theorems For Idempotent Residuated Lattices, José Gil-Férez, Peter Jipsen, George Metcalfe
Structure Theorems For Idempotent Residuated Lattices, José Gil-Férez, Peter Jipsen, George Metcalfe
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we study structural properties of residuated lattices that are idempotent as monoids. We provide descriptions of the totally ordered members of this class and obtain counting theorems for the number of finite algebras in various subclasses. We also establish the finite embeddability property for certain varieties generated by classes of residuated lattices that are conservative in the sense that monoid multiplication always yields one of its arguments. We then make use of a more symmetric version of Raftery’s characterization theorem for totally ordered commutative idempotent residuated lattices to prove that the variety generated by this class has …
Ziplines And Stuntwork, Kelly W. Remijan
Ziplines And Stuntwork, Kelly W. Remijan
Teacher Resources
This activity involves an engineering activity which connects the work of stuntmen/stuntwomen working with ziplines to the concept of linear functions. Students create a physical model replicating a given situation and then model the zipline algebraically by writing the equation of the zipline.
Stationary Distribution Of Recombination On 4x4 Grid Graph As It Relates To Gerrymandering, Camryn Hollarsmith
Stationary Distribution Of Recombination On 4x4 Grid Graph As It Relates To Gerrymandering, Camryn Hollarsmith
Scripps Senior Theses
A gerrymandered political districting plan is used to benefit a group seeking to elect more of their own officials into office. This practice happens at the city, county and state level. A gerrymandered plan can be strategically designed based on partisanship, race, and other factors. Gerrymandering poses a contradiction to the idea of “one person, one vote” ruled by the United States Supreme Court case Reynolds v. Sims (1964) because it values one demographic’s votes more than another’s, thus creating an unfair advantage and compromising American democracy. To prevent the practice of gerrymandering, we must know how to detect a …
Neutro-Bck-Algebra, Florentin Smarandache, Mohammad Hamidi
Neutro-Bck-Algebra, Florentin Smarandache, Mohammad Hamidi
Branch Mathematics and Statistics Faculty and Staff Publications
This paper introduces the novel concept of Neutro-BCK-algebra. In Neutro-BCK-algebra, the outcome of any given two elements under an underlying operation (neutro-sophication procedure) has three cases, such as: appurtenance, non-appurtenance, or indeterminate. While for an axiom: equal, non-equal, or indeterminate. This study investigates the Neutro-BCK-algebra and shows that Neutro-BCK-algebra are different from BCK-algebra. The notation of Neutro-BCK-algebra generates a new concept of NeutroPoset and Neutro-Hass-diagram for NeutroPosets. Finally, we consider an instance of applications of the Neutro-BCK-algebra.
Extension Of Hypergraph To N-Superhypergraph And To Plithogenic N-Superhypergraph, And Extension Of Hyperalgebra To N-Ary (Classical-/Neutro-/Anti-)Hyperalgebra, Florentin Smarandache
Extension Of Hypergraph To N-Superhypergraph And To Plithogenic N-Superhypergraph, And Extension Of Hyperalgebra To N-Ary (Classical-/Neutro-/Anti-)Hyperalgebra, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
We recall and improve our 2019 concepts of n-Power Set of a Set, n-SuperHyperGraph, Plithogenic n-SuperHyperGraph, and n-ary HyperAlgebra, n-ary NeutroHyperAlgebra, n-ary AntiHyperAlgebra respectively, and we present several properties and examples connected with the real world.
On Neutro-Be-Algebras And Anti-Be-Algebras, Florentin Smarandache, Akbar Rezaei
On Neutro-Be-Algebras And Anti-Be-Algebras, Florentin Smarandache, Akbar Rezaei
Branch Mathematics and Statistics Faculty and Staff Publications
In this paper, the concepts of Neutro-BE-algebra and Anti-BE-algebra are introduced, and some related properties and four theorems are investigated. We show that the classes of Neutro-BE-algebra and Anti-BE-algebras are alternatives of the class of BE-algebras.
Generalizations And Alternatives Of Classical Algebraic Structures To Neutroalgebraic Structures And Antialgebraic Structures, Florentin Smarandache
Generalizations And Alternatives Of Classical Algebraic Structures To Neutroalgebraic Structures And Antialgebraic Structures, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
In this paper we present the development from paradoxism to neutrosophy, which gave birth to neutrosophic set and logic and especially to NeutroAlgebraic Structures (or NeutroAlgebras) and AntiAlgebraic Structures (or AntiAlgebras) that are generalizations and alternatives of the classical algebraic structures.
Codes, Cryptography, And The Mceliece Cryptosystem, Bethany Matsick
Codes, Cryptography, And The Mceliece Cryptosystem, Bethany Matsick
Senior Honors Theses
Over the past several decades, technology has continued to develop at an incredible rate, and the importance of properly securing information has increased significantly. While a variety of encryption schemes currently exist for this purpose, a number of them rely on problems, such as integer factorization, that are not resistant to quantum algorithms. With the reality of quantum computers approaching, it is critical that a quantum-resistant method of protecting information is found. After developing the proper background, we evaluate the potential of the McEliece cryptosystem for use in the post-quantum era by examining families of algebraic geometry codes that allow …
On The Bures–Wasserstein Distance Between Positive Definite Matrices, Rajendra Bhatia, T. Jain, Yongdo Lim
On The Bures–Wasserstein Distance Between Positive Definite Matrices, Rajendra Bhatia, T. Jain, Yongdo Lim
Journal Articles
The metric d(A,B)=trA+trB−2tr(A1∕2BA1∕2)1∕21∕2 on the manifold of n×n positive definite matrices arises in various optimisation problems, in quantum information and in the theory of optimal transport. It is also related to Riemannian geometry. In the first part of this paper we study this metric from the perspective of matrix analysis, simplifying and unifying various proofs. Then we develop a theory of a mean of two, and a barycentre of several, positive definite matrices with respect to this metric. We explain some recent work on a fixed point iteration for computing this Wasserstein barycentre. Our emphasis is on ideas natural to …
Analogues Between Leibniz's Harmonic Triangle And Pascal's Arithmetic Triangle, Lacey Taylor James
Analogues Between Leibniz's Harmonic Triangle And Pascal's Arithmetic Triangle, Lacey Taylor James
Electronic Theses, Projects, and Dissertations
This paper will discuss the analogues between Leibniz's Harmonic Triangle and Pascal's Arithmetic Triangle by utilizing mathematical proving techniques like partial sums, committees, telescoping, mathematical induction and applying George Polya's perspective. The topics presented in this paper will show that Pascal's triangle and Leibniz's triangle both have hockey stick type patterns, patterns of sums within shapes, and have the natural numbers, triangular numbers, tetrahedral numbers, and pentatope numbers hidden within. In addition, this paper will show how Pascal's Arithmetic Triangle can be used to construct Leibniz's Harmonic Triangle and show how both triangles relate to combinatorics and arithmetic through the …
Taking Notes: Generating Twelve-Tone Music With Mathematics, Nathan Molder
Taking Notes: Generating Twelve-Tone 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 twelve-tone 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 twelve-tone musical scores.
Understanding The Impact Of Peer-Led Workshops On Student Learning, Afolabi Ibitoye, Nadia Kennedy, Armando Cosme
Understanding The Impact Of Peer-Led Workshops On Student Learning, Afolabi Ibitoye, Nadia Kennedy, Armando Cosme
Publications and Research
As students we often wonder why some subjects are easy to understand and requires not much effort in terms of re-reading the material, for us to grasp what it entails. One subject seems to remain elusive and uneasy for a vast majority of learners at all levels of education; that subject is Mathematics, it is one subject that most learners finds difficult even after doubling the amount of time spent on studying the material. My intention is to explore ways to make Mathematics easier for other students using feedback from students enrolled in NSF mathematics peer leading workshops, and use …
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
Undergraduate 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
Rose-Hulman Undergraduate Mathematics Journal
We define the notion of superadjunction in the context of supercategories. In particular, we give definitions in terms of counit-unit superadjunctions and hom-space superadjunctions, and prove that these two definitions are equivalent. These results generalize well-known statements in the non-super 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.
Positive And Generalized Positive Real Lemma For Slice Hyperholomorphic Functions, Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz, Irene Sabadini
Positive And Generalized Positive Real Lemma For Slice Hyperholomorphic Functions, Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic functions. We consider the case of functions with positive real part in the half space of quaternions with positive real part, as well as the case of (generalized) Schur functions in the open unit ball.
Distribution Spaces And A New Construction Of Stochastic Processes Associated With The Grassmann Algebra, Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa
Distribution Spaces And A New Construction Of Stochastic Processes Associated With The Grassmann Algebra, Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
We associate with the Grassmann algebra a topological algebra of distributions, which allows the study of processes analogous to the corresponding free stochastic processes with stationary increments, as well as their derivatives.