Mathematics Commons^™

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 …

New Perspectives On Semi-Primal Varieties, Alexander Kurz, Wolfgang Poiger, Bruno Teheux

Engineering Faculty Articles and Research

We study varieties generated by semi-primal lattice-expansions by means of category theory. We provide a new proof of the Keimel-Werner topological duality for such varieties and, using similar methods, establish its discrete version. We describe multiple adjunctions between the variety of Boolean algebras and the variety generated by a semi-primal lattice-expansion, both on the topological side and explicitly algebraic. In particular, we show that the Boolean skeleton functor has two adjoints, both defined by taking certain Boolean powers, and we identify properties of these adjunctions which fully characterize semi-primality of an algebra. Lastly, we give a new characterization of canonical …

Individual Difference Correlates Of Being Sexually Unrestricted Yet Declining An Hiv Test, Nicholas S. Holtzman, Stephen W. Carden, Stacy W. Smallwood, Janice Steirn, S. Mason Garrison

Mathematical Sciences: Faculty Publications

Which individual differences accurately predict one’s decision to get tested for human immunodeficiency virus (HIV), and do individuals who have regular short-term sex get tested at higher rates? Two studies—one lab study (total valid N = 69, with n = 20 who were tested) and one involving a student health center (valid N = 250, n = 4 who were tested)—involved participants (total valid N = 319, with n = 24 who got tested) taking a number of personality and individual difference measures, including the dark triad (Machiavellianism, narcissism, and psychopathy). Then, in both studies, participants had the opportunity to …

The Mean Sum Of Squared Linking Numbers Of Random Piecewise-Linear Embeddings Of $K_N$, Yasmin Aguillon, Xingyu Cheng, Spencer Eddins, Pedro Morales

Rose-Hulman Undergraduate Mathematics Journal

DNA and other polymer chains in confined spaces behave like closed loops. Arsuaga et al. \cite{AB} introduced the uniform random polygon model in order to better understand such loops in confined spaces using probabilistic and knot theoretical techniques, giving some classification on the mean squared linking number of such loops. Flapan and Kozai \cite{flapan2016linking} extended these techniques to find the mean sum of squared linking numbers for random linear embeddings of complete graphs $K_n$ and found it to have order $\Theta(n(n!))$. We further these ideas by inspecting random piecewise-linear embeddings of complete graphs and give introductory-level summaries of the ideas …

Haar Multipliers In The Context Of Weighted Spaces And Bilinear Operators, Weiyan Huang

Arts & Sciences Graduate Student Theses and Dissertations

This thesis offers a deep dive into Haar multipliers, focusing on their behavior in weighted spaces, two-weight inequalities, and spaces of homogeneous type. Chapter 1 introduces the main themes and summarises subsequent chapters. Chapter 2 provides necessary background information and notation, building a strong foundation for the core discussions that follow. In Chapter 3, the focus is on a Haar multiplier, $T_w^v$, defined on a pair of weights. The result is a characterization of the conditions under which this Haar multiplier is bounded in Lebesgue spaces. Chapter 4 extends the previous discussions into the realm of $t$-Haar multipliers, establishing a …

Roots Of Polynomials And Umbilics Of Surfaces, Brendan Guilfoyle, Wilhelm Klingenberg

Department of Mathematics Publications

For certain polynomials we relate the number of roots inside the unit circle with the index of a non-degenerate isolated umbilic point on a real analytic surface in Euclidean 3-space. In particular, for N>0" role="presentation" style="box-sizing: inherit; display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">��>0 we prove that for a certain (N+2" role="presentation" style="box-sizing: inherit; display: inline-block; line-height: normal; font-size-adjust: none; word-spacing: normal; overflow-wrap: normal; text-wrap: nowrap; float: none; direction: ltr; max-width: none; …

Normalized Solutions For Sobolev Critical Schrödinger-Bopp-Podolsky Systems, Yuxin Li, Xiaojun Chang, Zhaosheng Feng

School of Mathematical & Statistical Sciences Faculty Publications

We study the Sobolev critical Schr¨odinger-Bopp-Podolsky system −∆u + φu = λu + µ|u|p−2u + |u|4u in R3, −∆φ + ∆2φ = 4πu2 in R3, under the mass constraint u2 dx = c R3 for some prescribed c > 0, where 2 < p < 8/3, µ > 0 is a parameter, and λ ∈ R is a Lagrange multiplier. By developing a constraint minimizing approach, we show that the above system admits a local minimizer. Furthermore, we establish the existence of normalized ground state solutions.

Multi-Symplectic Simulation On Soliton-Collision For Nonlinear Perturbed Schrödinger Equation, Peijun Zhang, Weipeng Hu, Zhen Wang, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

Seeking solitary wave solutions and revealing their interactional characteristics for nonlinear evolution equations help us lot to comprehend the motion laws of the microparticles. As a local nonlinear dynamic behavior, the soliton-collision is difficult to be reproduced numerically. In this paper, the soliton-collision process in the nonlinear perturbed Schrödinger equation is simulated employing the multi-symplectic method. The multi-symplectic formulations are derived including the multi-symplectic form and three local conservation laws of the nonlinear perturbed Schrödinger equation. Employing the implicit midpoint rule, we construct a multi-symplectic scheme, which is equivalent to the Preissmann box scheme, for the nonlinear perturbed Schrödinger equation. …

Many-Valued Coalgebraic Logic: From Boolean Algebras To Primal Varieties, Alexander Kurz, Wolfgang Poiger

Engineering Faculty Articles and Research

We study many-valued coalgebraic logics with primal algebras of truth-degrees. We describe a way to lift algebraic semantics of classical coalgebraic logics, given by an endofunctor on the variety of Boolean algebras, to this many-valued setting, and we show that many important properties of the original logic are inherited by its lifting. Then, we deal with the problem of obtaining a concrete axiomatic presentation of the variety of algebras for this lifted logic, given that we know one for the original one. We solve this problem for a class of presentations which behaves well with respect to a lattice structure …

Reversibility Of Stranded Cellular Automata, Allyn Loyd

Mathematical Sciences Technical Reports (MSTR)

Cellular automata, such as the Stranded Cellular Automaton (SCA) model created by Joshua and Lana Holden, can be used to model weaving patterns. Similar models can be constructed to model macrame patterns, where strands are knotted together. If a rule is injective, then it is reversible. If a rule is surjective, then every configuration has at least one predecessor. In this paper, we will discuss the injectivity and surjectivity of several new SCA models in order to find reversible rules. We will also analyze the number of configurations with no predecessors and the number of configurations that map to the …

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 …

Optimal Control Analysis Of The Dynamics Of Covid-19 With Application To Ethiopian Data, Temesgen Duresa Keno, Fekadu Mosisa Legesse, Ebisa Olana Bajira

Applied Mathematics & Information Sciences

In this paper, we proposed an optimal control of the COVID-19 transmission dynamics. First, we investigated system features such as solution boundedness, positivity, disease-free and endemic equilibrium, and the local and global stability of equilibrium points. Besides, a disease-free equilibrium point is globally asymptotically stable if the basic reproduction number is less than one, and an endemic equilibrium point exists otherwise. Secondly, we have shown the sensitivity analysis of the basic reproduction number. Also the model is then fitted using COVID-19 infected reported in Ethiopia from February 1,2023 to March 2,2023. The values of model parameters are then estimated from …

Nexus Between Intellectual Capital And Financial Performance Sustainability: Evidence From Listed Jordanian Firms, Ali M. Alrabei, Leqaa N. Al-Othman, Thaer A. Abutaber, Mustafa S. Alathamneh, Tareq M. Almomani, Mohammed H. Qeshta

Applied Mathematics & Information Sciences

Purpose: The authors observe the effect of exploring the reality of Intellectual Capital (IC) and its impact on the financial performance of Jordanian industrial firms in Amman Stock Exchange. This empirical research explores the effect of intellectual capital on financial performance using data from 36 Jordanian industrial firms listed in Amman Stock Exchange for the period 2016-2020. The Value-Added Intellectual coefficient (VAIC) was adopted to measure the intellectual capital, while the return on assets (ROA), return on equity (ROE), and earnings per share (EPS) were adopted as measures of the companys financial performance. The effect of IC was tested by …

Assessing The Moderating Effect Of Innovation On The Relationship Between Information Technology And Supply Chain Management: An Empirical Examination, Heba Hatamlah, Mahmoud Allahham, Ibrahim A. Abu-Alsondos, Alaa S. Mushtaha, Ghadeer M. Al-Anati, Mustafa Al-Shaikh

Applied Mathematics & Information Sciences

This study examines how innovation (INN) influences the relationship between supply chain management and information technology in Jordan. 211 employees of Jordanian industrial enterprises who work in the Operations Department provided information for the study, which examines this subject. The findings indicate a close connection between information technology and supply chain management. Innovation also dramatically modifies the interaction between supply chain management and information technology. Management help may be the subject of future research.

The Role Of Business Intelligence Adoption As A Mediator Of Big Data Analytics In The Management Of Outsourced Reverse Supply Chain Operations, Heba Hatamlah, Mahmoud Allahham, Ibrahim A. Abu-Alsondos, Alaa Al-Junaidi, Ghadeer M. Al-Anati, Mustafa Al-Shaikh

Applied Mathematics & Information Sciences

The fluctuating and disorganized state of todays global markets is the result of several factors. COVID-19 is an illustration. Supply chain managers should re-evaluate their competitive strategy and leverage big data analytics in light of the rising volatility in demand and supply, rivalry among supply chain partners, and the requirement to deliver tailored goods and services (BDA). Supply chain firms require sophisticated BDA processes and procedures to provide useful insights from big data to better decision-making and supply chain operations, as many leaders in the sector have acknowledged the necessity for improving with data" (SCO). This research gives theoretical justification …

The Artificial Intelligence As A Decision-Making Instrument For Modeling And Predicting Small Cities’ Attractiveness: Evidence From Morocco, Sohaib Khalid, Driss Effina, Khaoula Rihab Khalid, Mohamed Salem Chaabane

Applied Mathematics & Information Sciences

This study analyzes residential attractiveness in small Moroccan cities using statistical models. Net migration rates are commonly used to assess attractiveness. The study estimated net migration rates for each city and employed a structural econometric model with logistic regression to identify influential variables that affect the net migration rate. These variables were then used in a predictive model with an artificial neural network algorithm. The logistic model revealed insights, highlighting the complexity of residential attractiveness influenced by factors like job supply, accessibility, and housing conditions. The artificial neural network model provided accurate predictions (over 80%), aiding policymakers in decision-making and …

Improving The Performance Of A Series-Parallel System Based On Lindley Distribution, Abdelfattah Mustafa, M. I. Khan, Maher. A. Alraddadi

Applied Mathematics & Information Sciences

In this article, the performance of a series-parallel system is improved. The system components are assumed to follows independently and identically Lindley distributed with three parameters. The system reliability for the given system will be improved by using reduction method, hot, cold and imperfect duplication method. Some reliability measures are derived. Two types of reliability equivalence factors and gamma fractiles are calculated. A numerical example is introduced to explain the theoretical results.

Quantization Of Fractional Constrained Systems With Wkb Approximation, Ola A. Jarabah

Applied Mathematics & Information Sciences

In this paper the constrained systems with two primary first class constraints are studied using fractional Lagrangian, after that we find the fractional Hamiltonian and the corresponding Hamilton Jacobi equation. Using separation of variables technique, we can find the action function S this function helps us to formulate the wave function which describe the behavior of our systems also from the action function S we can find the equations of motion and the corresponding momenta in fractional form. This work is illustrated using one example.

Applications Of The Ara-Residual Power Series Technique To Physical Phenomena, Aliaa Burqan

Applied Mathematics & Information Sciences

In this paper, a new analytical method called the ARA-Residual power series method (ARA- RPSM) is implemented to solve some fractional physical equations. The methodology of the proposed method based on applying the ARA-transform to the given fractional differential equations, followed by the creation of approximate series solutions using Taylor’s expansion. Then the series solution is transformed using the inverse of the ARA-transform to get the solution in the original space. Accuracy, effectiveness, and validity of the suggested method are demonstrated through the discussion of three attractive applications. The solution obtained using ARA-RPSM demonstrates good agreement when compared to the …

Generalization Of Renyi’S Entropy And Its Application In Source Coding, Ashiq Hussain Bhat, Niyamat Ali Siddiqui, Ismail A Mageed, Shawkat Alkhazaleh, Vidyanand Rabi Das, M. A. K Baig

Applied Mathematics & Information Sciences

In this paper, we introduce a new generalization of Renyis entropy β(P) and the most important feature of this generalized entropy Rαβ (P) is that it derives most important entropies that are well known and influence information theory and applied mathematics. Some significant properties of Rαβ (P) has been undertaken in this article. In addition, we introduce a new generalized exponentiated mean codeword length Lβα (P) in this article then determine how Rβα (P) and Lβα (P) are related in terms of source coding theorem.

Linear Regression Under Partial Information, Tho M. Nguyen, Saeid Tizpaz-Niari, Vladik Kreinovich

Departmental Technical Reports (CS)

Often, we need to know how to estimate the value of a difficult-to-directly estimate quantity y -- e.g., tomorrow's temperature -- based on the known values of several quantities x1, ..., xn. In many practical situations, we know that the relation between y and xi can be accurately described by a linear function. So, to find this dependence, we need to estimate the coefficients of this linear dependence based on the known cases in which we know both y and xi; this is known as linear regression. In the ideal situation, when in each case, we know all the inputs …

Pappus Of Alexandria, Book Viii Of The Mathematical Collection, Pappus Of Alexandria, John B. Little

Holy Cross Bookshelf

John B. Little is the translator.

This is a Greek-to-English translation of one section or chapter of a larger ancient Greek work called the Mathematical Collectionby Pappus of Alexandria (ca. 290 - 350 CE). Specifically, this is “Book VIII”' of that work. To date and to the translator’s knowledge, no complete English translation of Book VIII has been published.

Pappus was very influential as a bridge between the knowledge that had been preserved from ancient mathematics and European mathematicians in the Renaissance. This specific part of Pappus' work deals with applications of geometry to questions in mechanics.

The format …

When Is It Beneficial To Merge Two Companies? When Is It Beneficial To Start A Research Collaboration?, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Merging two companies or splitting a company into two, teaming of two researchers or two research groups -- or splitting a research group into two -- these are frequent occurrences. Sometimes these actions lead to increased effectiveness, but sometimes, contrary to the optimistic expectations, the overall effectiveness decreases. To minimize the possibility of such failures, it is desirable to replace the current semi-intuitive way of making the corresponding decisions with a more objective approach. In this paper, we propose such an approach.

Fuglede's Conjecture In Some Finite Abelian Groups, Thomas Fallon

Dissertations, Theses, and Capstone Projects

This dissertation thoroughly examines Fuglede's Conjecture within some discrete settings, shedding light on its intricate details. Fuglede's Conjecture establishes a profound connection between the geometric property of being a tiling set and the analytical attribute of being a spectral set. By exploring the conjecture on various discrete settings, this thesis delves into the implications and ramifications of the conjecture, unraveling its implications within the field.

Constrained Quantization For A Uniform Distribution With Respect To A Family Of Constraints, Megha Pandey, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, with respect to a family of constraints for a uniform probability distribution we determine the optimal sets of n-points and the nth constrained quantization errors for all positive integers n. We also calculate the constrained quantization dimension and the constrained quantization coefficient. The work in this paper shows that the constrained quantization dimension of an absolutely continuous probability measure depends on the family of constraints and is not always equal to the Euclidean dimension of the underlying space where the support of the probability measure is defined.

On The Spectrum Of Quaquaversal Operators, Josiah Sugarman

Dissertations, Theses, and Capstone Projects

In 1998 Charles Radin and John Conway introduced the Quaquaversal Tiling. A three dimensional hierarchical tiling with the property that the orientations of its tiles approach a uniform distribution faster than what is possible for hierarchical tilings in two dimensions. The distribution of orientations is controlled by the spectrum of a certain Hecke operator, which we refer to as the Quaquaversal Operator. For example, by showing that the largest eigenvalue has multiplicity equal to one, Charles Radin and John Conway showed that the orientations of this tiling approach a uniform distribution. In 2008, Bourgain and Gamburd showed that this operator …