Digital Commons Network^™

P-37 Self And Mixed Delta Moves On Algebraically Split Links, Justyce Goode, Davielle Smith, Yamil Kas-Danouche, Devin Garcia, Anthony Bosman

Celebration of Research and Creative Scholarship

A link is an embedding of circles into 3-dimensional space. A Delta-move is a local move on a link diagram. The Delta-Gordian distance between links measures the minimum number of Delta-moves needed to move between link diagrams. We place restrictions on the Delta-move by either requiring the move to only involve a single component of the link, called a self Delta-move, or multiple components of the link, called a mixed Delta-move. We prove a number of results on how (mixed/self) Delta-moves relate to classical link invariants including the Arf invariant and crossing number. This allows us to produce a graph …

P-36 The Delta-Crossing Number For Links, Zachary Duah

Celebration of Research and Creative Scholarship

An m-component link is an embedding of m circles into 3-dimensional space; a 1-component link is called a knot. The diagram for a link may be drawn so that all crossings occur within delta tangles, collections of three crossings as appear in a delta move. The delta crossing number is defined to be the minimal number of delta tangles in such a diagram. The delta crossing number has been well-studied for knots but not for links with multiple components. Using bounds we determine the delta crossing number for several 2-component links with up to 8 crossings as well as for …

Embrace Cultural Relevance With Mathematical Decision-Making, Jordan Moreno, Eryn M. Maher

College of Science & Mathematics: Faculty Presentations

We share and implement a multi-step strategy for adapting tasks by opening contexts to student decisionmaking and exploration

A Sharp Rate Of Convergence In The Functional Central Limit Theorem With Gaussian Input, S.V. Lototsky

Journal of Stochastic Analysis

No abstract provided.

Mathematical Musings On The External Anatomy Of The Novel Coronavirus. Part 4: Models Of N-Cov, Jyotirmoy Sarkar, Mamunur Rashid

Mathematics Faculty Publications

What is the shape of the novel coronavirus (n-CoV) which has turned our world upside down? Even though under a microscope, it looks dull, unattractive, and even disgusting, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathematician contribute to this effort? We take a purist’s point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from reality but still constrained by the rules of mathematics, anyone can enjoy this ethereal beauty of the mind’s creation, …

Classifications Of Dupin Hypersurfaces In Lie Sphere Geometry, Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

This is a survey of local and global classification results concerning Dupin hypersurfaces in Sⁿ (or Rⁿ) that have been obtained in the context of Lie sphere geometry. The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres. Along with these classification results, many important concepts from Lie sphere geometry, such as curvature spheres, Lie curvatures, and Legendre lifts of submanifolds of Sⁿ (or Rⁿ), are described in detail. The paper also contains several important constructions of Dupin hypersurfaces with certain special properties.

Determining The Idealizers Of Principal Monomial Ideals Over A Rational Normal Curve, Perla A. Maldonado Cortez

Mathematics & Statistics ETDs

Given an ideal J generated by an element of the form sm1 tm2 , where
m1 ≥ 2 and m2 ≥ 0, we illustrate how to compute the idealizer I(J) over the ring
of the rational normal curve of degree n and we give a formula for it using the
graded pieces of the sets of differential operators.

Symplectic Reduction Along A Submanifold, Peter Crooks, Maxence Mayrand

Mathematics and Statistics Faculty Publications

We introduce the process of symplectic reduction along a submanifold as a uniform approach to taking quotients in symplectic geometry. This construction holds in the categories of smooth manifolds, complex analytic spaces, and complex algebraic varieties, and has an interpretation in terms of derived stacks in shifted symplectic geometry. It also encompasses Marsden-Weinstein-Meyer reduction, Mikami-Weinstein reduction, the pre-images of Poisson transversals under moment maps, symplectic cutting, symplectic implosion, and the Ginzburg-Kazhdan construction of Moore-Tachikawa varieties in topological quantum field theory. A key feature of our construction is a concrete and systematic association of a Hamiltonian G-space 𝔐_𝐺,𝑆 to …

Optimal Quantization For Some Triadic Uniform Cantor Distributions With Exact Bounds, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Let {Sj:1≤j≤3} be a set of three contractive similarity mappings such that Sj(x)=rx+j−12(1−r) for all x∈R, and 1≤j≤3, where 0

Let {Sj:1≤j≤3}">{Sj:1≤j≤3}{Sj:1≤j≤3} be a set of three contractive similarity mappings such that Sj(x)=rx+j−12(1−r)">Sj(x)=rx+j−12(1−r)Sj(x)=rx+j−12(1−r) for all x∈R">x∈Rx∈R, and 1≤j≤3">1≤j≤31≤j≤3, where 0Phas support the Cantor set generated by the similarity mappings Sj">SjSj for 1≤j≤3">1≤j≤31≤j≤3. Let r0=0.1622776602">r0=0.1622776602r0=0.1622776602, and r1=0.2317626315">r1=0.2317626315r1=0.2317626315 (which are ten digit rational approximations of two real numbers). In this paper, for 00n-means and the nth quantization errors for the triadic uniform Cantor distribution P for all positive integers n≥2">n≥2n≥2. Previously, Roychowdhury …

Alpha Labeling Of Amalgamated Cycles, Christian Barrientos

Theory & Applications of Graphs

A graceful labeling of a bipartite graph is an α-labeling if it has the property that the labels assigned to the vertices of one stable set of the graph are smaller than the labels assigned to the vertices of the other stable set. A concatenation of cycles is a connected graph formed by a collection of cycles, where each cycle shares at most either two vertices or two edges with other cycles in the collection. In this work we investigate the existence of α-labelings for this kind of graphs, exploring the concepts of vertex amalgamation to produce a …

Quantization Of The Free Poisson Central Limit Theorem, Yungang Lu

Journal of Stochastic Analysis

No abstract provided.

Gender Disparities In Nlsy97: Educational Attainment And Income Level, Ngan Tran, Naima Shifa

Annual Student Research Poster Session

This paper is designed to examine gender differences in education and their impact on education and occupation status, following the research Economic Rationale for Sex Differences in Education conducted by Janice Fanning Madden. Data was collected from the NLSY97 (National Longitudinal Survey) on American youth born between 1980-84. The sample originally included 8,984 respondents when first interviewed in 1997.

Extended Duration Studies Of Energetic Particles In The Stratosphere, Ian Kuhl, Ashna Coondiah, Howard L. Brooks

Annual Student Research Poster Session

The Balloon Assisted Stratospheric Experiments (BASE) program aims to measure atmospheric muon concentration at the Pfotzer Maximum with Geiger Counters carried by weather balloons. The most intense radiation is found at the Pfotzer Maximum 18 - 22 km (11 - 13 mi) above ground level. During this summer, seven flights were conducted to attain maximum time in the Pfotzer Maximum using different strategies like underfilling and multiple balloon systems.

High-Risk Behavior Of Students Carrying Weapon To School, Nan Lin Wah Sin Htoo, Naima Shifa

Annual Student Research Poster Session

The rise of personal and mental issues in students has been accompanied by an increase in the number of students carrying guns and the frequency of mass shootings at schools in the US. A recent study (Dong, 2021) pointed out that future researchers should focus on recognizing high-risk youths and tackle their issues early on in life most appropriately according to individual differences such as age and personal circumstances.This research discusses the contributing factors to youths carrying guns to schools and analyzes the high-risk behaviors of students. It was hypothesized that their personal issues such as their mental wellness, high-risk …

On Equivariant Flag F-Vectors For Balanced Relative Simplicial Complexes, Jacob A. White

School of Mathematical & Statistical Sciences Faculty Publications

We study the equivariant flag f-vector and equivariant flag h-vector of a balanced relative simplicial complex with respect to a group action. When the complex satisfies Serre's condition (Sℓ), we show that the equivariant flag h-vector, the equivariant h-vector, and the equivariant f-vector satisfy several inequalities.
We apply these results to the study of P-partitions of double posets, and weak colorings of mixed graphs.

(Si10-063) Number Of Automorphisms Of Some Non-Abelian P-Groups Of Order P^4, Muniya ., Harsha Arora, Mahender Singh

Applications and Applied Mathematics: An International Journal (AAM)

The automorphism of a group is a way of mapping the object to itself while preserving all of its structure, and the set of automorphisms of an object forms a group called the automorphism group. It is simply a bijective homomorphism. One of the earliest group automorphism was given by Irish mathematician William Rowan Hamilton in 1856, in his icosian calculus where he discovered an order two automorphism. In this paper, we compute the automorphisms of some non-Abelian groups of order p⁴, where p is an odd prime and GAP (Group Algorithm Programming) software has been used for …

(Si10-089) Integer Cordial Labeling Of Alternate Snake Graph And Irregular Snake Graph, Pratik Shah, Dharamvirsinh Parmar

Applications and Applied Mathematics: An International Journal (AAM)

If a graph G admits integer cordial labeling, it is called an integer cordial graph. In this paper we prove that Alternate m-triangular Snake graph, Quadrilateral Snake graph, Alternate m- quadrilateral Snake graph, Pentagonal Snake graph, Alternate m-pentagonal Snake graph, Irregular triangular Snake graph, Irregular quadrilateral Snake graph, and Irregular pentagonal Snake graphs are integer cordial graphs.

(Si10-115) Controllability Results For Nonlinear Impulsive Functional Neutral Integrodifferential Equations In N-Dimensional Fuzzy Vector Space, Murugesan Nagarajan, Kumaran Karthik

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we concentrated to study the controllability of fuzzy solution for nonlinear impulsive functional neutral integrodifferential equations with nonlocal condition in n-dimensional vector space. Moreover, we obtained controllability of fuzzy result for the normal, convex, upper semi-continuous and compactly supported interval fuzzy number. Finally, an example was provided to reveal the application of the result.

Why 1/(1+D) Is An Effective Distance-Based Similarity Measure: Two Explanations, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Most of our decisions are based on the notion of similarity: we use a decision that helped in similar situations. From this viewpoint, it is important to have, for each pair of situations or objects, a numerical value describing similarity between them. This is called a similarity measure. In some cases, the only information that we can use to estimate the similarity value is some natural distance measure d(a,b). In many such situations, empirical data shows that the similarity measure 1/(1+d) is very effective. In this paper, we provide two explanations for this effectiveness.

How To Describe Variety Of A Probability Distribution: A Possible Answer To Yager's Question, Vladik Kreinovich

Departmental Technical Reports (CS)

Entropy is a natural measure of randomness. It progresses from its smallest possible value 0 -- when we have a deterministic case in which one alternative i occurs with probability 1 (pi = 1), to the largest possible value which is attained at a uniform distribution p1 = ... = pn = 1/n. Intuitively, both in the deterministic case and in the uniform distribution case, there is not much variety in the distribution, while in the intermediate cases, when we have several different values pi, there is a strong variety. Entropy does not seem to capture this notion of variety. …

How The Pavement Strength Changes With Time: Ai Ideas Help To Explain Semi-Empirical Formulas, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we use AI ideas to provide a theoretical explanation for semi-empirical formulas that describe how the pavement strength changes with time, and how we can predict the pavement lifetime.

College Algebra Slide Decks, Bader Abukhodair, Michelle Zeng

All Open Educational Resources

This collection of slide decks is designed to be used in concert with the following Open Eduational Resources:

- OpenStax College Algebra 2e Open Texbook

- Department of Mathematics Video Playlist

- Homework questions from myOpenMath

Concepts include are: A study of equations, graphs, and inequalities for linear, quadratic, polynomial, rational, logarithmic, exponential, and absolute value functions. Transformations on graphs, complex numbers, circles, systems of inequalities, and systems of equations including matrices.

(Si10-068) Performance Analysis Of Cosine Window Function, Vikas Misra, Narendra Singh, M. Shukla

Applications and Applied Mathematics: An International Journal (AAM)

This paper reviews the mathematical functions called the window functions which are employed in the Finite Impulse Response (FIR) filter design applications as well as spectral analysis for the detection of weak signals. The characteristic properties of the window functions are analyzed and parameters are compared among the known conventional cosine window (CW) functions (Rectangular, Hamming, Hanning, and Blackman) and the variable Kaiser window function. The window function expressed in the time domain can be transformed into the frequency domain by taking the Discrete Fourier Transform (DFT) of the time domain window function. The frequency response of the window function …

Implicit Surface Reconstruction With A Curl-Free Radial Basis Function Partition Of Unity Method, Kathryn P. Drake, Edward J. Fuselier, Grady B. Wright

Mathematics Faculty Publications and Presentations

Surface reconstruction from a set of scattered points, or a point cloud, has many applications ranging from computer graphics to remote sensing. We present a new method for this task that produces an implicit surface (zero-level set) approximation for an oriented point cloud using only information about (approximate) normals to the surface. The technique exploits the fundamental result from vector calculus that the normals to an implicit surface are curl-free. By using curl-free radial basis function (RBF) interpolation of the normals, we can extract a potential for the vector field whose zero-level surface approximates the point cloud. We use curl-free …

Bounds On Cohomological Support Varieties, Benjamin Briggs, Eloisa Grifo, Josh Pollitz

Department of Mathematics: Faculty Publications

Over a local ring R, the theory of cohomological support varieties attaches to any bounded complex M of finitely generated R-modules an algebraic variety VR(M) that encodes homological properties of M. We give lower bounds for the dimension of VR(M) in terms of classical invariants of R. In particular, when R is Cohen-Macaulay and not complete intersection we find that there are always varieties that cannot be realized as the cohomological support of any complex. When M has finite projective dimension, we also give an upper bound for dimVR(M) in terms of the dimension of the radical of the homotopy …

Machine Learning To Predict Warhead Fragmentation In-Flight Behavior From Static Data, Katharine Larsen

Doctoral Dissertations and Master's Theses

Accurate characterization of fragment fly-out properties from high-speed warhead detonations is essential for estimation of collateral damage and lethality for a given weapon. Real warhead dynamic detonation tests are rare, costly, and often unrealizable with current technology, leaving fragmentation experiments limited to static arena tests and numerical simulations. Stereoscopic imaging techniques can now provide static arena tests with time-dependent tracks of individual fragments, each with characteristics such as fragment IDs and their respective position vector. Simulation methods can account for the dynamic case but can exclude relevant dynamics experienced in real-life warhead detonations. This research leverages machine learning methodologies to …

(Si10-054) Nonsplit Edge Geodetic Domination Number Of A Graph, P. Arul Paul Sudhahar, J. Jeba Lisa

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we have defined an inventive parameter called the nonsplit edge geodetic domination number of a graph, and some of its general properties are studied. The nonsplit edge geodetic domination number of some standard graph is obtained. In this work, we also determine the realization results of the nonsplit edge geodetic domination number and the edge geodetic number of a graph.

(Si10-123) Comparison Between The Homotopy Perturbation Method And Variational Iteration Method For Fuzzy Differential Equations, P. Chandru, B. Radhakrishnan

Applications and Applied Mathematics: An International Journal (AAM)

In this article, the authors discusses the numerical simulations of higher-order differential equations under a fuzzy environment by using Homotopy Perturbation Method and Variational Iteration Method. The fuzzy parameter and variables are represented by triangular fuzzy convex normalized sets. Comparison of the results are obtained by the homotopy perturbation method with those obtained by the variational iteration method. Examples are provided to demonstrate the theory.

(Si10-130) On Regular Inverse Eccentric Fuzzy Graphs, N. Meenal, J. Jeromi Jovita

Applications and Applied Mathematics: An International Journal (AAM)

Two new concepts of regular inverse eccentric fuzzy graphs and totally regular inverse eccentric fuzzy graphs are established in this article. By illustrations, these two graphs are compared and the results are derived. Equivalent condition for the existence of these two graphs are found. The exact values of Order and Size for some standard inverse eccentric graphs are also derived.

(Si10-062) Comprehensive Study On Methodology Of Orthogonal Interleavers, Priyanka Agarwal, Shivani Dixit, M. Shukla, Gaurish Joshi

Applications and Applied Mathematics: An International Journal (AAM)

Interleaving permutes the data bits by employing a user defined sequence to reduce burst error which at times exceeds the minimum hamming distance. It serves as the sole medium to distinguish user data in the overlapping channel and is the heart of Interleave Division Multiple Access (IDMA) scheme. Versatility of interleavers relies on various design parameters such as orthogonality, correlation, latency and performance parameters like bit error rate (BER), memory occupancy and computation complexity. In this paper, a comprehensive study of interleaving phenomenon and discussion on numerous interleavers is presented. Also, the BER performance of interleavers using IDMA scheme is …