Mathematics Commons^™

Soft Sets Extensions Used In Bioinformatics, Florentin Smarandache, Daniela Gifu

Branch Mathematics and Statistics Faculty and Staff Publications

This comprehensive review delves into the intricate realm of Soft Sets and their extensions, including HyperSoft Set, IndetermSoft Set, IndetermHyperSoft Set, and TreeSoft Set, within the context of biomedical data analysis. Soft Sets serve as a foundational framework for managing the inherent uncertainty and imprecision inherent in biological data, thereby facilitating informed decision-making and knowledge discovery. The exploration of Soft Set Products, particularly in the context of multiple soft sets, underscores their pivotal role in advancing biomedical research. By extending these concepts to HyperSoft Sets, researchers can unlock deeper insights into complex biological phenomena, enabling more accurate predictions and classification.

Logical Pluralism And Neutrosophy: Reflections On The Nature Of Truth, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The article explores the shift from classical binary logic (true and false) to a more complex landscape of logical frameworks. It introduces logical pluralism, which suggests that no single, universally accepted system of logic exists. The paper connects this idea to neutrosophy, a framework that extends fuzzy logic by incorporating a third value: indeterminacy. This triadic approach, where every proposition has a degree of truth (T), falsity (F), and indeterminacy (I), is particularly useful for managing incomplete or contradictory information. The author argues that different logical systems, like different tools, are suited for different problems, and that the …

Optimizing Energy Consumption In Smart Homes Using Ga-Lstm, Akibor Junior Chukwuka, Bakare-Bolaji Moyosoreoluwa, Baboucarr Dibba

School of Mathematical & Statistical Sciences Faculty Publications

The need to optimize energy consumption arises from the inadequate energy supply many homes face. However, to optimize energy consumption in a home, one must be equipped with the knowledge of the energy consumption rate and energy supply rate in the home. This paper proposed the use of a Long Short-Term Memory (LSTM) model optimized by Genetic Algorithm (GA) to optimize the energy consumption in a smart home. The model was designed using 8 input variables, which were observed weather information of a given region over a span of 350 days. The data set was split into a training data …

Analyzing A Smartphone Battle Using Bass Competition Model, Maila Hallare, Alireza Hosseinkhan, Hasala Senpathy K. Gallolu Kankanamalage

CODEE Journal

Many examples of 2x2 nonlinear systems in a first-course in ODE or a mathematical modeling class come from physics or biology. We present an example that comes from the business or management sciences, namely, the Bass diffusion model. We believe that students will appreciate this model because it does not require a lot of background material and it is used to analyze sales data and serve as a guide in pricing decisions for a single product. In this project, we create a 2x2 ODE system that is inspired by the Bass diffusion model; we call the resulting system the Bass …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Modeling The Population Dynamics And Movement Of Zebra Mussels, Alexanderia Lacy, Yu Jin, David Strayer, Suzanne Lenhart

Department of Mathematics: Faculty Publications

Zebra mussels have caused significant damage in many lakes and rivers. By using a hybrid population model with discrete-time equations and ordinary differential equations, we represent the zebra mussel’s life cycle, growth, and population movement. The dynamics of the larvae (unsettled and settled larvae) are represented during the summer months in a system of two ordinary differential equations, while the juvenile, small adult, and large adult stages are represented by a discrete model with yearly time steps. The goal is to investigate the effects of zebra mussel movement between three different spatial locations and possible control measures. Zebra mussel data …

Regular Ideals, Ideal Intersections, And Quotients, Jonathan H. Brown, Adam H. Fuller, David R. Pitts, Sarah A. Reznikoff

Department of Mathematics: Faculty Publications

Let B ⊆ A be an inclusion of C^∗ -algebras. We study the relationship between the regular ideals of B and regular ideals of A.We show that if B ⊆ A is a regular C^∗ -inclusion and there is a faithful invariant conditional expectation from A onto B, then there is an isomorphism between the lattice of regular ideals of A and invariant regular ideals of B. We study properties of inclusions preserved under quotients by regular ideals. This includes showing that if D ⊆ A is a Cartan inclusion and J is a regular ideal in A, …

A Mathematical Model For Frogeye Leaf Spot Epidemics In Soybean, Chayu Yang, Jin Wang

Department of Mathematics: Faculty Publications

We propose a new mathematical model based on differential equations to investigate the transmission and spread of frogeye leaf spot, a major soybean disease caused by the fungus Cercospora sojina. The model incorporates the primary and secondary transmission routes of the disease as well as the intrinsic dynamics of the pathogen in the contaminated soil. We conduct detailed equilibrium and stability analyses for this model using theories of dynamical systems. We additionally conduct numerical simulations to verify the analytical predictions and to implement the model for a practical application.

Renormalized Stress-Energy Tensor For Scalar Fields In Hartle-Hawking, Boulware, And Unruh States In The Reissner-Nordström Spacetime, Julio Arrechea, Cormac Breen, Adrian Ottewill, Peter Taylor

Articles

In this paper, we consider a quantum scalar field propagating on the Reissner-Nordström black hole spacetime. We compute the renormalized stress-energy tensor for the field in the Hartle-Hawking, Boulware and Unruh states. When the field is in the Hartle-Hawking state, we renormalize using the recently developed “extended coordinate” prescription. This method, which relies on Euclidean techniques, is very fast and accurate. Once, we have renormalized in the Hartle-Hawking state, we compute the stress-energy tensor in the Boulware and Unruh states by leveraging the fact that the difference between stress-energy tensors in different quantum states is already finite. We consider a …

Applications Of Survival Estimation Under Stochastic Order To Cancer: The Three Sample Problem, Sage Vantine

Honors Program Theses and Research Projects

Stochastic ordering of probability distributions holds various practical applications. However, in real-world scenarios, the empirical survival functions extracted from actual data often fail to meet the requirements of stochastic ordering. Consequently, we must devise methods to estimate these distribution curves in order to satisfy the constraint. In practical applications, such as the investigation of the time of death or the progression of diseases like cancer, we frequently observe that patients with one condition are expected to exhibit a higher likelihood of survival at all time points compared to those with a different condition. Nevertheless, when we attempt to fit a …

(R2061) Differential Equations Involving A New Definition Of Complex Number Derivatives, Mehmet Pakdemirli

Applications and Applied Mathematics: An International Journal (AAM)

The recently proposed complex number differential operator is used in formulating ordinary differential equations for the first time. The differential operator definition is totally different than the real number differentiation of complex valued functions. The basic definitions and properties of the differential operator are given first. Various linear differential equations are treated containing the new differential operator. Associated theorems with the differential equations are given. Then the nonlinear differential equations of complex valued functions are treated. In separated form, the complex differential operator equations lead to nonlinear coupled real valued equations. Various nonlinear differential equations with complex number derivatives are …

Convolution And Autoencoders Applied To Nonlinear Differential Equations, Noah Borquaye

Electronic Theses and Dissertations

Autoencoders, a type of artificial neural network, have gained recognition by researchers in various fields, especially machine learning due to their vast applications in data representations from inputs. Recently researchers have explored the possibility to extend the application of autoencoders to solve nonlinear differential equations. Algorithms and methods employed in an autoencoder framework include sparse identification of nonlinear dynamics (SINDy), dynamic mode decomposition (DMD), Koopman operator theory and singular value decomposition (SVD). These approaches use matrix multiplication to represent linear transformation. However, machine learning algorithms often use convolution to represent linear transformations. In our work, we modify these approaches to …

An Exposition Of The Curvature Of Warped Product Manifolds, Angelina Bisson

Electronic Theses, Projects, and Dissertations

The field of differential geometry is brimming with compelling objects, among which are warped products. These objects hold a prominent place in differential geometry and have been widely studied, as is evident in the literature. Warped products are topologically the same as the Cartesian product of two manifolds, but with distances in one of the factors in skewed. Our goal is to introduce warped product manifolds and to compute their curvature at any point. We follow recent literature and present a previously known result that classifies all flat warped products to find that there are flat examples of warped products …

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

All Dissertations

In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …

Stochastic Optimal Control Of Conditional Mckean-Vlasov Equations With Jump And Markovian Switching, Charles Samuel Conly Sharp

Theses and Dissertations

This thesis obtains a number of results in stochastic optimal control for conditional McKean-Vlasov equations with jump and Markovian switching. First, we prove the uniqueness of the solutions and derive a relevant version of Itô's formula. We provide the dynamic programming principle and prove the associated verification theorem. A stochastic maximum principle is established. Further, we derive the relationship between dynamic programming and the stochastic maximum principle. Additionally, we utilize our stochastic maximum principle result for a mean-variance portfolio selection problem.

Differentiating By Prime Numbers, Jack Jeffries

Department of Mathematics: Faculty Publications

It is likely a fair assumption that you, the reader, are not only familiar with but even quite adept at differentiating by x. What about differentiating by 13? That certainly didn’t come up in my calculus class! From a calculus perspective, this is ridiculous: are we supposed to take a limit as 13 changes? One notion of differentiating by 13, or any other prime number, is the notion of p-derivation discovered independently by Joyal [Joy85] and Buium [Bui96]. p-derivations have been put to use in a range of applications in algebra, number theory, and arithmetic geometry. Despite the wide range …

Understanding Impact Of Educational Awareness And Vaccines As Optimal Control Mechanisms For Changing Human Behavior In Disease Epidemics, Manal Badgaish, Dr. Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Modeling Framework For Minimizing Spread Of Mathematics Anxiety In College Students, Sara Sony, Majid Bani-Yaghoub

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Msis-Kadelka: On The Uniqueness Of Network Identification, Alan Veliz-Cuba, Elena Dimitrova

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Fibonacci Differential Equation And Associated Spiral Curves, Mehmet Pakdemirli

CODEE Journal

The Fibonacci differential equation is defined with analogy from the Fibonacci difference equation. The linear second order differential equation is solved for suitable initial conditions. The solutions constitute spirals in the polar coordinates. The properties of the spirals with respect to the Fibonacci numbers and the differences between the new spirals and classical spirals are discussed.

Nuclear Dimension Of Graph C∗-Algebras With Condition (K), Gregory Faurot, Christopher Schafhauser

Department of Mathematics: Faculty Publications

We prove that for any countable directed graph E with Condition (K), the associated graph C^*-algebra C^*(E) has nuclear dimension at most 2. Furthermore, we provide a sufficient condition producing an upper bound of 1.

Is Math Real? How Simple Questions Lead Us To Mathematics' Deepest Truths, Eugenia Cheng

Dalrymple Lecture Series

Where does math come from: from rules in a textbook? From logic and deduction? Not quite. In this talk Eugenia Cheng will argue that math comes from human curiosity - most importantly, from asking questions. Many people are discouraged from asking these questions in school, thinking they’re too simple to be taken seriously, or being told that their questions are stupid. But often, these simple-sounding questions lead to wondrous mathematical revelations. Dr Cheng will take us on a journey of discovery starting with questions like "Why does 2x3 = 3x2?" and "What's the point of maths?", leading us into research-level …

Are The Cans In The Store “Volume Optimized”? [Mathematics], Bukurie Gjoci

Open Educational Resources

This is one of LaGuardia’s Project Connexion STEM Team’s experiential learning activities. Project Connexion's purpose is to promote creative thinking on how to engage students in the classroom. As part of this, the STEM team developed Experiential/co-curricular activities that demonstrated to students how their work in class connects to the world around them. These activities were embedded into the syllabus to ensure the participation of all students. Each professor designed a Co-curricular activity for their courses, ensuring that the Co-curricular activity directly linked course material to the outside world.

This Calculus I Experiential Learning Project aligns with one of the …

Rigid Body Constrained Motion Optimization And Control On Lie Groups And Their Tangent Bundles, Brennan S. Mccann

Doctoral Dissertations and Master's Theses

Rigid body motion requires formulations where rotational and translational motion are accounted for appropriately. Two Lie groups, the special orthogonal group SO(3) and the space of quaternions H, are commonly used to represent attitude. When considering rigid body pose, that is spacecraft position and attitude, the special Euclidean group SE(3) and the space of dual quaternions DH are frequently utilized. All these groups are Lie groups and Riemannian manifolds, and these identifications have profound implications for dynamics and controls. The trajectory optimization and optimal control problem on Riemannian manifolds presents significant opportunities for theoretical development. Riemannian optimization is an attractive …

On Subset Labelings Of Trees, Gary Chartrand, Ebrahim Salehi, Ping Zhang

Mathematical Sciences Faculty Research

For a nontrivial graph G, a subset labeling of G is a labeling of the vertices of G with nonempty subsets of the set [r]={1, 2, ... , r} for a positive integer r such that two vertices of G have disjoint labels if and only if the vertices are adjacent. The subset index ρ(G) of G is the minimum positive integer r for which G has such a subset labeling from the set [r]. If T is a tree of diameter d, then ρ(Pd+1) ≤ ρ(T). It is shown that there are several classes of trees T of diameter …

Forecasting Economic Growth And Movements With Wavelet Transform And Arima Model, Omar Alsinglawi, Omar Alsinglawi, Mohammad Aladwan, Mohammad Aladwan, Saddam Alwadi, Saddam Alwadi

Applied Mathematics & Information Sciences

This study uses historical data and modern statistical models to forecast future Gross Domestic Product (GDP) in Jordan. The Wavelet Transformation model (WT) and Autoregressive Integrated Moving Average (ARIMA) model were applied to the time series data and yielded a best-fitting result of (2,1,1) for estimating GDP between 2022-2031. The study concludes that GDP is expected to increase with a positive growth rate of around 3.22%, and recommends government agencies to monitor GDP, strengthen existing policies, and adopt necessary economic reforms to support growth. Additionally, the private sector is encouraged to enhance production tools to achieve economic growth that benefits …

Neutrosophic Adaptive Lsb And Deep Learning Hybrid Framework For Ecg Signal Classification, Abdallah Rezk, Ahmed S. Sakr, H. M. Abdulkader

Applied Mathematics & Information Sciences

This paper proposes a novel hybrid framework for ECG signal classification and privacy preservation. The framework includes two phases: the first phase uses LSTM+CNN with attention gate for ECG classification, while the second phase utilizes adaptive least signal bit with neutrosophic for hiding important data during transmission. The proposed framework converts data into three sets of degrees (true, false, and intermediate) using neutrosophic and passes them to an embedding layer. In the sender part, the framework hides important data in ECG signal as true and false degrees, using the intermediate set as a shared dynamic key between sender and receiver. …

Compatibility Of Clique Clustering Algorithm With Dimensionality Reduction, Ug ̆Ur Madran, Duygu Soyog ̆Lu

Applied Mathematics & Information Sciences

In our previous work, we introduced a clustering algorithm based on clique formation. Cliques, the obtained clusters, are constructed by choosing the most dense complete subgraphs by using similarity values between instances. The clique algorithm successfully reduces the number of instances in a data set without substantially changing the accuracy rate. In this current work, we focused on reducing the number of features. For this purpose, the effect of the clique clustering algorithm on dimensionality reduction has been analyzed. We propose a novel algorithm for support vector machine classification by combining these two techniques and applying different strategies by differentiating …

The Influence Of Supply Chain Management Strategies On Organizational Performance In Hospitality Industry, Omar Jawabreh, Abdullah Mahfoud Baadhem, Basel J. A. Ali, Anas Ahmad Bani Atta, Anis Ali, Fahmi Fadhl Al- Hosaini

Applied Mathematics & Information Sciences

The studys primary goal is to analyze the connection between SCM practices and organizational performance, and it also aims to evaluate the moderating role of management type. Quantitative data collected from Jordans hotel and restaurant workers via questionnaire. Structural equation modeling is used to examine the hypothesized relationships. Organizational Performance is positively impacted by effective information sharing. Information Quality (IQ) positively affects Organizational Performance (OP), and Strategic Supplier Partnerships (SSP) play a crucial role. Customer Relationship Management (CRM) had no discernible effect on OP, according to the study. OP is positively impacted by Postponement (POS) techniques. When implemented, postponement increases …

The Effect Of System Quality And User Quality Of Information Technology On Internal Audit Effectiveness In Jordan, And The Moderating Effect Of Management Support, Ahmad Yahiya Ahmad Bani Ahmad (Ayassrah), Anas Ahmad Mahmoud Bani Atta, Hanan Ali Alawawdeh, Nawaf Abdallah Aljundi, Amer Morshed, Saleh Amin Dahbour

Applied Mathematics & Information Sciences

The goal of this study is to ascertain the moderating role that management support has in internal audit effectiveness in Jordan, as well as the impact of system quality and user quality of information technology. There were 172 responders in all, and they were split across Jordanian auditors. In the data analysis process, the quantitative analysis test— which consists of the validity test, reliability test, test of conventional assumptions, and hypothesis test—is applied. Information technology system and user quality are independent variables in this study. The dependent variable in this study is internal audit effectiveness, and the moderating variable is …