Physical Sciences and Mathematics Commons^™

On Orthogonally Additive Band Operators And Orthogonally Additive Disjointness Preserving Operators, Bahri̇ Turan, Demet Tülü

Turkish Journal of Mathematics

Let $M$ and $N$ be Archimedean vector lattices. We introduce orthogonally additive band operators and orthogonally additive inverse band operators from $M$ to $N$ and examine their properties. We investigate the relationship between orthogonally additive band operators and orthogonally additive disjointness preserving operators and show that under some assumptions on vector lattices $M$ or $N$, these two classes are the same. By using this relation, we show that if ${\mu }$ is a bijective orthogonally additive band operator (resp. orthogonally additive disjointness preserving operator) from $M$ into $N$ then ${\mu }^{-1}$:$N$${\rightarrow}$$M$ is an orthogonally additive band operator (resp. orthogonally additive …

Spectral And Topological Properties Of Linear Operators On A Hilbert Space, Salah Mecheri, Aissa Nasli Bakir

Turkish Journal of Mathematics

We introduce the class of $(M, k)$-quasi-$*$-paranormal operators on a Hilbert space $H$. This class extends the classes of $*$-paranormal and $k$-quasi-$*$-paranormal operators. An operator $T$ on a complex Hilbert space is called $(M, k)$-quasi-$*$-paranormal if there exists $M>0$ such that \begin{equation*} \sqrt{M}\left\Vert T^{k+2}x\right\Vert \left\Vert T^{k}x\right\Vert \geq \left\Vert T^{\ast }T^{k}x\right\Vert ^{2} \end{equation*} for all $x\in H.$ In the present article, we give operator matrix representation of a $(M, k)$-quasi-$*$-paranormal operator. The compactness, the invariant subspace, and some topological properties of this class of operators are studied. Several properties of this class of operators are also presented.

Left-Definite Hamiltonian Systems And Corresponding Nested Circles, Eki̇n Uğurlu

Turkish Journal of Mathematics

This work aims to construct the Titchmarsh-Weyl $M(\lambda )-$theory for an even-dimensional left-definite Hamiltonian system. For this purpose, we introduce a suitable Lagrange formula and selfadjoint boundary conditions including the spectral parameter $\lambda $. Then we obtain circle equations having nesting properties. Using the intersection point belonging to all the circles we share a lower bound for the number of Dirichlet-integrable solutions of the system.

Energy Decay And Blow-Up Of Solutions For A Class Of System Of Generalized Nonlinear Klein-Gordon Equations With Source And Damping Terms, Zeynep Sümeyye Çeli̇k, Şevket Gür, Erhan Pi̇şki̇n

Turkish Journal of Mathematics

In this work, we investigate generalized coupled nonlinear Klein-Gordon equations with nonlinear damping and source terms and initial-boundary value conditions, in a bounded domain. We obtain decay of solutions by use of Nakao inequality. The blow up of solutions with negative initial energy is also established.

A Study On Conformable Fractional Version Of Bullen-Type Inequalities, Fati̇h Hezenci̇, Hüseyi̇n Budak, Hasan Kara

Turkish Journal of Mathematics

In this paper, we give an equality for the case of differentiable convex functions involving conformable fractional integrals. Bullen-type inequalities for the conformable fractional integrals are established by using this equality. Some important inequalities are obtained by taking advantage of the convexity, the Hölder inequality and the power mean inequality. By using special choices, we present some known results in the literature. Furthermore, we give an example using a graph in order to show that our main results are correct.

The Inequalities On Dual Numbers And Their Topological Structures, Buşra Aktaş, Olgun Durmaz, Hali̇t Gündoğan

Turkish Journal of Mathematics

Inequalities are frequently used in various fields of mathematics to prove theorems. The existence of inequalities contributes significantly to the foundations of such branches. In this paper, we study the properties of order relations in the system of dual numbers, which is inspired by order relations defined on real numbers. Besides, some special inequalities that are used in various fields of mathematics, such as Cauchy-Schwarz, Minkowski, and Chebyshev are studied in this framework. An example is also provided to validate our research findings.

Atomic Systems In Krein Spaces, Osmin Ferrer Villar, Edilberto Arroyo Ortiz, José Naranjo Martínez

Turkish Journal of Mathematics

In the present article, we establish a definition of atomic systems in the Krein spaces, specifically, we establish the fundamental tools of the theory of atomic systems in the formalism of the Krein spaces and give a complete characterization of them. We also show that the atomic systems do not depend on the decomposition of the Krein space.

Between Graphical Zonotope And Graph-Associahedron, Marko Pesovic, Tanja Stojadinovic

Turkish Journal of Mathematics

This manuscript introduces a finite collection of generalized permutohedra associated to a simple graph. The first polytope of this collection is the graphical zonotope of the graph, and the last is the graph-associahedron associated to it. We describe the weighted integer points enumerators for polytopes in this collection as Hopf algebra morphisms of combinatorial Hopf algebras of decorated graphs. In the last section, we study some properties related to $\mathcal{H}$-polytopes.

Global Existence, Asymptotic Behavior And Blow Up Of Solutions For A Kirchhoff-Type Equation With Nonlinear Boundary Delay And Source Terms, Houria Kamache, Nouri Boumaza, Billel Gheraibia

Turkish Journal of Mathematics

The main goal of this work is to study an initial boundary value problem for a Kirchhoff-type equation with nonlinear boundary delay and source terms. This paper is devoted to prove the global existence, decay, and the blow up of solutions. To the best of our knowledge, there are not results on the Kirchhoff type-equation with nonlinear boundary delay and source terms.

Characterizations And Representations Of Weak Core Inverses And $M$-Weak Group Inverses, Wende Li, Jianlong Chen, Yukun Zhou

Turkish Journal of Mathematics

In a ring with an involution, we first present some necessary and sufficient conditions for the existence of the $m$-weak group inverse and expression. As an application, we prove that a regular element $a$ is $(m+1)$-weak group invertible if and only if $a^2a^{-}$ is $m$-weak group invertible, where $a^{-}$ is an inner inverse of $a$. The relevant results for weak core inverses and for pseudocore inverses are given. In addition, we present some new characterizations of weak core inverses, and also investigate maximal classes

Characterizations Of The Commutators Involving Idempotents In Certain Subrings Of $M_{2}(\Mathbb{Z})$, Tufan Özdi̇n, Günseli̇ Gümüşel

Turkish Journal of Mathematics

In this paper, we characterize the idempotency, cleanness, and unit-regularity of the commutator $[E_1, E_2]=E_1E_2-E_2E_1$ involving idempotents $E_1,E_2$ in certain subrings of $M_{2}(\mathbb{Z})$.

Boundary Value Problem For A Loaded Fractional Diffusion Equation, Arsen V. Pskhu, Murat I. Ramazanov, Minzilya Kosmakova

Turkish Journal of Mathematics

In this paper we consider a boundary value problem for a loaded fractional diffusion equation. The loaded term has the form of the Riemann-Liouville fractional derivative or integral. The BVP is considered in the open right upper quadrant. The problem is reduced to an integral equation that, in some cases, belongs to the pseudo-Volterra type, and its solvability depends on the order of differentiation in the loaded term and the behavior of the support line of the load in a neighborhood of the origin. All these cases are considered. In particular, we establish sufficient conditions for the unique solvability of …

Cavitation Erosion And Corrosion Resistance Of Hydrophobic Sol-Gel Coatings On Aluminium Alloy, Manasa Hegde, Joseph Mohan, Muhammad Qasim Mushtaq Warraich, Yvonne Kavanagh, Brendan Duffy, Edmond F. Tobin

Articles

Cavitation erosion and erosion-corrosion are the popular failure modes of hydronautics components namely propellers, valves, turbines etc which occurs due to mechanical destructions and electrochemical corrosion. Erosion corrosion is caused due to surge in the number of solid particles affecting the surfaces whereas cavitation erosion is caused due to steady collapse of cavities or bubbles. Aluminium alloys are widely used in marine renewable industries owing to its high strength, light weight and good corrosion resistance. Despite that, cavitation and erosion-corrosion are the limiting factors for these alloys. The aim of the present work is to produce a coating system capable …

The Biological Responses Of Vitamin K2: A Comprehensive Review, Quanxiang Yan, Tao Zhang, Christine O'Connor, James W. Barlow, John Walsh, Gaia Scalabrino, Feng Xu, Helan Sheridan

Articles

Vitamin K1 (VitK1) and Vitamin K2 (VitK2), two important naturally occurring micronutrients in the VitK family, found, respectively, in green leafy plants and algae (VitK1) and animal and fermented foods (VitK2). The present review explores the multiple biological functions of VitK2 from recently published in vitro and in vivo studies, including promotion of osteogenesis, prevention of calcification, relief of menopausal symptoms, enhancement of mitochondrial energy release, hepato-and neuro-protective effects, and possible use in treatment of coronavirus disease. The mechanisms of action associated with these biological effects are also explored. Overall, the findings presented here suggest that VitK, especially VitK2, is …

Design, Synthesis And Biological Evaluation Of A Novel Bioactive Indane Scaffold 2-(Diphenylmethylene)C-2,3-Dihydro-1h-Inden-1-One With Potential Anticancer Activity, Tao Zhang, Vilmar Bandero, Claire Corcoran, Ismael Obaidi, Manuel Ruether, John O'Brien, Lorraine O'Driscoll, Neil Frankish, Helen Sheridan

Articles

Over the past decades, designing of privileged structures has emerged as a useful approach to the discovery and optimisation of novel biologically active molecules, and many have been successfully exploited across and within different target families. Examples include indole, quinolone, isoquinoline, benzofuran and chromone, etc. In the current study, we focus on synthesising a novel hybrid scaffold constituting naturally occurring benzophenone (14) and indanone (22) ring systems, leading to a general structure of 2-(diphenylmethylene)-2,3-dihydro-1H-inden-1-one (23). It was hypothesised this new hybrid system would provide enhanced anti-cancer activity owing to the presence of the common features associated with the tubulin binding …

Microfluidic Flowmeter Based On Liquid Crystal Filled Nested Capillary, Zhe Wang, Zhuochen Wang, Anuradha Rout, Qiang Wu, Yuliya Semenova

Conference Papers

A novel flowmeter composed of a liquid crystal-filled nested capillary is proposed and experimentally demonstrated. Whispering gallery modes (WGMs) in the nested capillary are excited by a tapered fiber coupled perpendicularly to the nested capillary. The WGM transmission spectrum of the fiber taper was optimized to achieve the highest possible quality (Q) factor by moving the capillary along the axis of the fiber taper. The air flowing through the capillary cools it down, which leads to a temperature-induced change of the refractive index of the nematic liquid crystal. This change in turn leads to a spectral shift of the WGM …

Convolution Neural Networks For Phishing Detection, Arun D. Kulkarni

Computer Science Faculty Publications and Presentations

Phishing is one of the significant threats in cyber security. Phishing is a form of social engineering that uses e-mails with malicious websites to solicitate personal information. Phishing e-mails are growing in alarming number. In this paper we propose a novel machine learning approach to classify phishing websites using Convolution Neural Networks (CNNs) that use URL based features. CNNs consist of a stack of convolution, pooling layers, and a fully connected layer. CNNs accept images as input and perform feature extraction and classification. Many CNN models are available today. To avoid vanishing gradient problem, recent CNNs use entropy loss function …

Multispectral Image Analysis Using Convolution Neural Networks, Arun D. Kulkarni

Computer Science Faculty Publications and Presentations

Machine learning (ML) techniques are used often to classify pixels in multispectral images. Recently, there is growing interest in using Convolution Neural Networks (CNNs) for classifying multispectral images. CNNs are preferred because of high performance, advances in hardware such as graphical processing units (GPUs), and availability of several CNN architectures. In CNN, units in the first hidden layer view only a small image window and learn low level features. Deeper layers learn more expressive features by combining low level features. In this paper, we propose a novel approach to classify pixels in a multispectral image using deep convolution neural networks …

Prevention Research Center For Healthy Neighborhoods, Madeline Panus

Celebration of Scholarship 2023

No abstract provided.

The Effect Of S-Glutahionylation Of Keap-1/Nrf-2 And Caspase 3, Claire Greenless

Celebration of Scholarship 2023

S-glutathionylation is a form of post-translational modification where glutathione forms disulfide bonds with protein cysteine residues under oxidative conditions. The process of Sglutathionylation is important because it is a reversible process, regulates enzyme activity, and may link to disease development. In this work, under physiological conditions, KEAP-1 and NRF-2 bind together as a complex. Upon oxidative stress, NRF-2 dissociates from KEAP-1 and triggers an antioxidant response. However, the dissociation mechanism was not well studied. S-glutathionylation of KEAP-1 causes dissociation of NRF-2. This result demonstrates a possible dissociation mechanism of NRF-2. Caspase 3 is a cysteine containing protein and a key …

Mining Health Informatics Job Advertisements: Insights For Higher Education Programs And Job Seekers, Ahmed El Noshokaty, Mohammad A. Al-Ramahi, Omar El-Gayar, Abdullah Wahbeh, Tareq Nasralah

Computer Information Systems Faculty Publications

This paper used web scraping and data mining to analyze 831 health informatics job advertisements on indeed.com. Results showed that 87% of jobs explicitly required a college degree in a related field, 41% of jobs preferred a graduate degree, while 29% preferred or required professional certification. The analysis showed that preferred skills were analytics problem solving, communication skills, oral communication, interpersonal skills, project management, statistics, and critical thinking. The analysis also showed that college degrees, certifications, and the above-mentioned skill set are in high demand for working in the field of health informatics, especially in states with large populations and …

Conversational Agents For Mental Health And Well-Being: Discovering Design Recommendations Using Text Mining, Abdullah Wahbeh, Mohammad A. Al-Ramahi, Omar El-Gayar, Ahmed El Noshokaty, Tareq Nasralah

Computer Information Systems Faculty Publications

Conversational agents are increasingly being used by the general population due to shortages in healthcare providers and specialists, and limited access to treatments. They are also used by people to deal with loneliness and lack of companionship. As these apps are increasingly replacing real humans, there is a need to explore their design features and limitations for better design of conversational apps. Using text mining and topic modeling, this study analyzed a total of 126,610 reviews about Replika, a popular and well-established conversational agent mobile app. Our results emphasized current practices for designing conversational apps while at the same time …

Σ-Ary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Improving The Adelic Version Of The Minkowski-Hlawka Theorem, Fatmah Alnaser

Graduate Research Theses & Dissertations

In this dissertation we take a method developed by Schmidt to improve the classical version of the Minkowski-Hlawka Theorem and extend that to certain number fields. This leads to an analogous improvement to the adelic Minkowski-Hlawka Theorem in certain cases. We also demonstrate that the adelic version, even in the case where the number field is the field of rational numbers, is more general than the classical version.

Research@Smu: Sustainable Living, Singapore Management University

Research Collection Office of Research

Sustainable Living is one of the three key priorities of the SMU 2025 Strategy, and the University is committed to develop it into an area of cross-disciplinary strength. The articles in this booklet highlight impactful sustainability research accomplishments at SMU, which spans five broad pillars: Sustainable Business Operations; Sustainable Finance and Impact Assessment; Sustainable Ageing and Wellness; Sustainable Urban Infrastructure; and Sustainable Agro-business and Food Consumption.

Contents:

Sustainable Business Operations

• Managing the Load on Loading Bays
• Going the Last-mile
• Feeding a Growing World
• Pooling the Benefits of Sharing a Ride

Sustainable Finance and Impact Assessment

• When Going Green Becomes a …

Leading Toward Solutions To America’S Overcrowding And Underfunding Environmental Preservation Issues, James Seth Caudill

Theses, Dissertations and Capstones

This research aims to better comprehend how the environmental preservation issues of underfunding and overcrowding of America’s parks, recreation areas, and environmental surroundings are solved through quality leadership. These environmental issues are national, state, and community problems. Currently, there exists a wealth of literature on the environmental problems caused by overcrowding and underfunding. Unfortunately, the successful problem-solving ideas identified throughout these works often do not connect with an element of leadership. This research helps fill this identified gap in the currently available environmental preservation resources. This mixed methods study explored the perceptions, ideas, and successful solutions exhibited by environmental preservation …

On 2-Primitive Triangle Decompositions Of Cocktail Party Graphs, Ian P. Waddell

Theses, Dissertations and Capstones

A decomposition of a graph Γ is a collection C of subgraphs, perhaps nonisomorphic, that partition the edges of Γ. Analogously, consider a group of truck drivers whose non-overlapping routes jointly cover all of the roads between a set of cities; that is, each road is traversed by precisely one driver. In this scenario, the cities are the vertices of the graph, the roads are the edges between vertices, and the drivers’ routes are the subgraphs in the decomposition. Given a graph H, we call C an H-decomposition of Γ if each subgraph in C is isomorphic to …

A Path Planning Framework For Multi-Agent Robotic Systems Based On Multivariate Skew-Normal Distributions, Peter Estephan

Theses, Dissertations and Capstones

This thesis presents a path planning framework for a very-large-scale robotic (VLSR) system in an known obstacle environment, where the time-varying distributions of agents are applied to represent the multi-agent robotic system (MARS). A novel family of the multivariate skew-normal (MVSN) distributions is proposed based on the Bernoulli random field (BRF) referred to as the Bernoulli-random-field based skew-normal (BRF-SN) distribution. The proposed distributions are applied to model the agents’ distributions in an obstacle-deployed environment, where the obstacle effect is represented by a skew function and separated from the no-obstacle agents’ distributions. First, the obstacle layout is represented by a Hilbert …

Leveraging Explainable Artificial Intelligence (Xai) To Understand Performance Deviations In Load Tests Of Large Software Systems, Eric Shoemaker

Theses, Dissertations and Capstones

Performance testing generates vast amounts of data, making it challenging for human analysts to process within a reasonable timeframe. Therefore, black-box machine learning models are often used to determine pass/fail status, but these models lack transparency and cannot explain why a test has failed, leading to a time-consuming manual analysis process. To address this issue, this thesis proposes using Explainable Artificial Intelligence (XAI) to improve the trustworthiness of black-box and interpretable models in performance testing. The proposed approach leverages the Shapley Additive Explanation (SHAP) algorithm as a surrogate model to help performance analysts understand the decision-making process of black-box machine …

Eccentric Pairs: Analytic Gravitational Waves From Binary Black Holes In Elliptic Orbits, Dillon Buskirk, Maria Babiuc-Hamilton

Physics Faculty Research

Gravitational waves (GW) from eccentric binaries have intricate signals encoding important features about the location, creation and evolution of the sources. Eccentricity shortens the merger time, making the emitted GW statistically predominant in the observed data once detectors will reach the required sensitivity. We present a novel implementation of fully analytical GW templates from eccentric binary black hole (BBH) mergers within the Wolfram Mathematica software. We increase the accuracy by identifying and minimizing the possible source of errors. We start with an overview of the physics involved in eccentric mergers, then assemble the strain for the inspiral by employing up …