Mathematics Commons^™

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.

Efficient Time-Stepping Approaches For The Dispersive Shallow Water Equations, Linwan Feng

Dissertations

This dissertation focuses on developing efficient and stable (high order) time-stepping strategies for the dispersive shallow water equations (DSWE) with variable bathymetry. The DSWE extends the regular shallow water equations to include dispersive effects. Dispersion is physically important and can maintain the shape of a wave that would otherwise form a shock in the shallow water system.

In some cases, the DSWE may be simplified when the bathymetry length scales are small (or large) in relation to other length scales in the shallow water system. These simplified DSWE models, which are related to the full DSWEs, are also considered in …

Hybrid Deep Neural Networks For Mining Heterogeneous Data, Xiurui Hou

Dissertations

In the era of big data, the rapidly growing flood of data represents an immense opportunity. New computational methods are desired to fully leverage the potential that exists within massive structured and unstructured data. However, decision-makers are often confronted with multiple diverse heterogeneous data sources. The heterogeneity includes different data types, different granularities, and different dimensions, posing a fundamental challenge in many applications. This dissertation focuses on designing hybrid deep neural networks for modeling various kinds of data heterogeneity.

The first part of this dissertation concerns modeling diverse data types, the first kind of data heterogeneity. Specifically, image data and …

Resonant Triad Interactions In One And Two-Layer Systems, Malik Chabane

Dissertations

This dissertation is a study of the weakly nonlinear resonant interactions of a triad of gravity-capillary waves in systems of one and two fluid layers of arbitrary depth, in one and two-dimentions. For one-layer systems, resonant triad interactions of gravity-capillary waves are considered and a region where resonant triads can be always found is identified, in the two-dimensional wavevector angles-space. Then a description of the variations of resonant wavenumbers and wave frequencies over the resonance region is given. The amplitude equations correct to second order in wave slope are used to investigate special resonant triads that, providing their initial amplitude …

Arithmetical Structures On Paths With A Doubled Edge, Darren B. Glass, Joshua R. Wagner

Math Faculty Publications

An arithmetical structure on a graph is given by a labeling of the vertices that satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical structures for graphs in these families.

An Approach To Neutrosophic Dialogue And A Response To Wef's Great Reset: How Dialogue Is Required In Order To Preserve Social Justice With Anger Management, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In recent debates, there are arguments on the role of anger in order to preserve social justice. For instance, in open democracy net, there is promoted phrase: "anger is the language of social justice." Others call for anger fueled with love (Sisonke Msimangs). Is that true? Is it achievable, the so-called "anger with love?"

Nonparametric Recursive Method For Kernel-Type Function Estimators For Censored Data, Salim Bouzebda, Yousri Slaoui

Journal of Stochastic Analysis

No abstract provided.

Get The News Out Loudly And Quickly: Modeling The Influence Of The Media On Limiting Infectious Disease, Anna Mummert, Howard Weiss

Mathematics Faculty Research

During outbreaks of infectious diseases with high morbidity and mortality, individuals closely follow media reports of the outbreak. Many will attempt to minimize contacts with other individuals in order to protect themselves from infection and possibly death. This process is called social distancing. Social distancing strategies include restricting socializing and travel, and using barrier protections. We use modeling to show that for short-term outbreaks, social distancing can have a large influence on reducing outbreak morbidity and mortality. In particular, public health agencies working together with the media can significantly reduce the severity of an outbreak by providing timely accounts of …

Research On The Logistics Development Model Of Shanghai Free Trade Zone, Yuhong Xie

World Maritime University Dissertations

No abstract provided.

Research On The Economic Viability Of Mega Container Ships, Guozhen Peng

World Maritime University Dissertations

No abstract provided.

Research On Concentration Force Of Goods In Ports Across The Taiwan Strait, Yucong Xie

World Maritime University Dissertations

No abstract provided.

Evaluation Of China Shipping Hub-And-Spoke Network Based On Herfindahl-Hirschmann Index (Hhi), Wenjin Sun

World Maritime University Dissertations

No abstract provided.

Application Of Harvard Analytical Framework In Shipping Enterprises Under Influence Of Covid-19 Pandemic A Case Of Shanghai International Port Group, Lei Wang

World Maritime University Dissertations

No abstract provided.

Research On The Regulation Problem Of The Integration Of Inland Shipping In The Yangtze River Delta, Yiyang Xiong

World Maritime University Dissertations

No abstract provided.

From Emission Trade Sysytem To Carbon Offset : Status And Progress Of Emission Control In Shipping Industry, Zhili Yao

World Maritime University Dissertations

No abstract provided.

Research On Quantity Discount Pricing By Container Liner Shipping, Runzhe Zhao

World Maritime University Dissertations

No abstract provided.

Diagrams Of ⋆-Trisections, José Román Aranda, Jesse Moeller

Department of Mathematics: Faculty Publications

In this note we provide a generalization for the definition of a trisection of a 4-manifold with boundary. We demonstrate the utility of this more general definition by finding a trisection diagram for the Cacime Surface, and also by finding a trisection-theoretic way to perform logarithmic surgery. In addition, we describe how to perform 1-surgery on closed trisections. The insight gained from this description leads us to the classification of an infinite family of genus three trisections. We include an appendix where we extend two classic results for relative trisections for the case when the trisection surface is closed.

“Playing The Whole Game”: A Data Collection And Analysis Exercise With Google Calendar, Albert Y. Kim, Johanna Hardin

Statistical and Data Sciences: Faculty Publications

We provide a computational exercise suitable for early introduction in an undergraduate statistics or data science course that allows students to “play the whole game” of data science: performing both data collection and data analysis. While many teaching resources exist for data analysis, such resources are not as abundant for data collection given the inherent difficulty of the task. Our proposed exercise centers around student use of Google Calendar to collect data with the goal of answering the question “How do I spend my time?” On the one hand, the exercise involves answering a question with near universal appeal, but …

General Product Formula Of Multiple Integrals Of Lévy Process, Nishant Agrawal, Yaozhong Hu, Neha Sharma

Journal of Stochastic Analysis

No abstract provided.

Continuous Dependence On The Coefficients For Mean-Field Fractional Stochastic Delay Evolution Equations, Brahim Boufoussi, Salah Hajji

Journal of Stochastic Analysis

No abstract provided.

Inverse Limits And Atomic Projections, Włodzimierz J. Charatonik, Faruq A. Mena, Robert Paul Roe

Mathematics and Statistics Faculty Research & Creative Works

We consider generalized inverse limits of continua with bonding functions Fn that have the projection of Graph (Fn) onto the second (first) factor atomic and images (pre-image) of points are zero-dimensional. For such bonding functions we show that under some easily verified conditions that if the first (all) factor space(s) has a certain property then the inverse limit space must have this property. The properties considered include hereditary decomposability, hereditary indecomposability, hereditary unicoherence, arc-likeness, and tree-likeness. We illustrate the theorems by several examples.

Wavelet Coherence Analysis With An Application Of Brain Images, Yiqian Fang

Arts & Sciences Graduate Student Theses and Dissertations

Wavelet analysis has become an emerging method in a wide range of applications with non-stationary data. In this work, we apply wavelets to tackle the problem of estimating dynamic association in a collection of multivariate non-stationary time series. Coherence is a common metric for linear dependence across signals. However, it assumes static dependence and does not sufficiently model many biological processes with time-evolving dependence structures. We explore continuous wavelet analysis for modeling and estimating such dynamic dependence under the replicated multivariate time series settings. Wavelet transformation provides a decomposition of signals that localizes in both time and frequency domains, hence …

The Value Of Information Under Partial Information For Exponential Utility, Farai Julius Mhlanga, Mbakisi Dube

Journal of Stochastic Analysis

No abstract provided.

A Theory Of Preimage Complexity: Data-Structures, Complexity Measures And Applications To Endofunctions And Associated Digraphs, Bradford M. Fournier-Eaton

LSU New Orleans Theses and Dissertations

This dissertation develops a new theory of finite function complexity. This novel approach is based on the structure of preimage sets generated under repeat application of the inverse. We encode this information in our primary data-structure, an square matrix called the sigma matrix. This matrix allows us to easily encode information about the functional digraph and cycle structure of the associated endofunction. Additionally, the sigma matrix is of interest in its own right. The columns of sigma matrices are integer partitions of the domain size n, the size of the domain is always an eigenvalue of the sigma matrix, and …

Modeling Braids With Space-Varying And Time-Varying Stranded Cellular Automata, Brian Chan

Mathematical Sciences Technical Reports (MSTR)

Braids in a traditional sense and braids in a mathematical sense are wildly different outlooks on the same concept. Using cellular automata to represent and analyze braids is a way to bridge the gap between them. Joshua and Lana Holden and Hao Yang have previously worked on developing and expanding upon a Stranded Cellular Automata (SCA) model capable of representing many different braids and weaves. Continuing their work, we were able to devise a more user-friendly method for interacting with the model such that even those without a mathematical background can construct and analyze braids of their own. This paper …

The Künneth Formula And Applications, Melissa Sugimoto

SURF Posters and Papers

The de Rham cohomology of a manifold is a homotopy invariant that expresses basic topological information about smooth manifolds. The q-th de Rham cohomology of the n-dimensional Euclidean space is the vector space defined by the closed q-forms over the exact q-forms. Furthermore, the support of a continuous function f on a topological space X is the closure of the set on which f is nonzero. The result of restricting the definition of the de Rham cohomology to functions with compact support is called the de Rham cohomology with compact support, or the compact cohomology. The concept of cohomology can …

The Poincaré Duality Theorem And Its Applications, Natanael Alpay, Melissa Sugimoto, Mihaela Vajiac

SURF Posters and Papers

In this talk I will explain the duality between the deRham cohomology of a manifold M and the compactly supported cohomology on the same space. This phenomenon is entitled “Poincaré duality” and it describes a general occurrence in differential topology, a duality between spaces of closed, exact differentiable forms on a manifold and their compactly supported counterparts. In order to define and prove this duality I will start with the simple definition of the dual space of a vector space, with the definition of a positive definite inner product on a vector space, then define the concept of a manifold. …

A Psychometric Investigation Of A Mathematics Placement Test At A Science, Technology, Engineering, And Mathematics (Stem) Gifted Residential High School, Hannah Ruth Anderson

Publications & Research

Educational institutions, at all levels, must justify their use of placement testing and confront questions of their impact on students’ educational outcomes to assure all stakeholders that students are being enrolled in courses appropriate with their ability in order to maximize their chances of success (Linn, 1994; Mattern & Packman, 2009; McFate & Olmsted III, 1999; Norman, Medhanie, Harwell, Anderson, & Post, 2011; Wiggins, 1989). The aims of this research were to (1) provide evidence of Content Validity, (2) provide evidence of Construct Validity and Internal Consistency Reliability, (3) examine the item characteristics and potential bias of the items between …

Energy Stable Numerical Schemes For Ternary Cahn-Hilliard System, Wenbin Chen, Cheng Wang, Shufen Wang, Xiaoming Wang, Steven M. Wise

Mathematics and Statistics Faculty Research & Creative Works

We present and analyze a uniquely solvable and unconditionally energy stable numerical scheme for the ternary Cahn-Hilliard system, with a polynomial pattern nonlinear free energy expansion. One key difficulty is associated with presence of the three mass components, though a total mass constraint reduces this to two components. Another numerical challenge is to ensure the energy stability for the nonlinear energy functional in the mixed product form, which turns out to be non-convex, non-concave in the three-phase space. to overcome this subtle difficulty, we add a few auxiliary terms to make the combined energy functional convex in the three-phase space, …

Why Cutting Trajectories Into Small Pieces Helps To Learn Dynamical Systems Better: A Seemingly Counterintuitive Empirical Result Explained, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In general, the more information we use in machine learning, the more accurate predictions we get. However, recently, it was observed that for prediction of the behavior of dynamical systems, the opposite effect happens: when we replace the original trajectories with shorter pieces -- thus ignoring the information about the system's long-term behavior -- the accuracy of machine learning predictions actually increases. In this paper, we provide an explanation for this seemingly counterintuitive result.