Mathematics Commons^™

Neutroalgebra Theory, Vol. I, Florentin Smarandache, Memet Şahin, Derya Bakbak, Vakkas Uluçay, Abdullah Kargın

Branch Mathematics and Statistics Faculty and Staff Publications

In general, in any field of knowledge, with respect to any structure, one has the following neutrosophic triplet . They were introduced by Smarandache in 2019 and 2020.

1) A classical Structure is a structure whose all elements are characterized by the same given Relationships and Attributes and Laws.

2) A NeutroStructure is a structure that has at least one NeutroRelation or one NeutroAttribute or one NeutroLaw, and no AntiRelation and no AntiAttribute and no AntiLaw.

3) An AntiStructure is a structure that has at least one AntiRelation or one AntiAttribute or one AntiLaw.

As a particular case, in the …

Neutrosophic Dynamic Set, A. A. Salama, K. F. Alhasan, H. A. Elagamy, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we introduced the concept of the dynamic set according to modern logic, is neutrosophic logic. We study the neutrosophic dynamic set according to time and random variable depended on dynamic set. Neutrosophic dynamic is a dynamic analysis of a sequence of data through of time. It used in many problems in life such as a mathematical statistic, philosophy, medicine, engineering. Some examples and notes are presented.

Comments On “A New Combination Of Evidence Based On Compromise” By K. Yamada, Jean Dezert, Arnaud Martin, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Yamada (2008) presents an interesting new model of combination of evidence called combination by compromise based on previous works published in Yamada (2006b,a). In the theory of belief functions, one of the most important problems is the one of reassigning the conflicting belief mass, as highlighted by the famous Zadeh’s example, see Zadeh (1979). To date, many combination rules have been developed, proposing a solution to this problem.

Hyers-Ulam Stability And Control Problem For Systems Governed By Impulsive Integro-Differential Equations In Banach Spaces, Adisorn Doodee

Chulalongkorn University Theses and Dissertations (Chula ETD)

This thesis is organized in two main parts. First, we study the Hyers-Ulam stability of impulsive integro-differential equations in Banach spaces. By using iterative methods, we establish sufficient conditions for existence of solutions and Hyers-Ulam stabilities. These conditions are based on the analysis of iterative methods. The second part deals with the control problems of impulsive integro-differential equations in Banach spaces. The iterative methods are used to investigate results and some examples are constructed to illustrate results. Moreover, we extend the scope of our study to the class of second order impulsive integro-differential equations in Banach spaces.

Regularity And Natural Partial Order On Invariant Transformation Semigroups, Hataiwit Palasak

Chulalongkorn University Theses and Dissertations (Chula ETD)

Let T(X) be the full transformation semigroup on a nonempty set X. For any nonempty subset Y of X, we denote by TY(X)={α ∈ T(X) : Y α ⊆ Y} the invariant subsemigroup of T(X), consisting of all transformations on X that map Y into itself. In this thesis, we characterize the regularity of certain subsemigroups of TY(X). In addition, we provide necessary and sufficient conditions for elements in those transformation subsemigroups of TY(X) to be related under the natural partial order.

Hexagon Tilings Of The Plane That Are Not Edge-To-Edge, D. Frettlöh, Alexey Glazyrin, Z. Lángi

School of Mathematical & Statistical Sciences Faculty Publications

An irregular vertex in a tiling by polygons is a vertex of one tile and belongs to the interior of an edge of another tile. In this paper we show that for any integer k≥3, there exists a normal tiling of the Euclidean plane by convex hexagons of unit area with exactly k irregular vertices. Using the same approach we show that there are normal edge-to-edge tilings of the plane by hexagons of unit area and exactly k many n-gons (n>6) of unit area. A result of Akopyan yields an upper bound for k depending on the maximal diameter …

Combining Assumptions And Graphical Network Into Gene Expression Data Analysis, Demba Fofana, E. O. George, Dale Brown

School of Mathematical & Statistical Sciences Faculty Publications

Background

Analyzing gene expression data rigorously requires taking assumptions into consideration but also relies on using information about network relations that exist among genes. Combining these different elements cannot only improve statistical power, but also provide a better framework through which gene expression can be properly analyzed.

Material and methods

We propose a novel statistical model that combines assumptions and gene network information into the analysis. Assumptions are important since every test statistic is valid only when required assumptions hold. So, we propose hybrid p-values and show that, under the null hypothesis of primary interest, these p-values are …

Estimation Of The Healthcare Waste Generation During Covid-19 Pandemic In Bangladesh, Tamal Chowdhury, Hemal Chowdhury, Md Salman Rahman, Nazia Hossain, Ashfaq Ahmed, Sadiq M. Sait

School of Mathematical & Statistical Sciences Faculty Publications

COVID-19 pandemic-borne wastes imposed a severe threat to human lives as well as the total environment. Improper handling of these wastes increases the possibility of future transmission. Therefore, immediate actions are required from both local and international authorities to mitigate the amount of waste generation and ensure proper disposal of these wastes, especially for low-income and developing countries where solid waste management is challenging. In this study, an attempt is made to estimate healthcare waste generated during the COVID-19 pandemic in Bangladesh. This study includes infected, ICU, deceased, isolated and quarantined patients as the primary sources of medical waste. Results …

Characterizations Of Student, Instructor, And Textbook Discourse Related To Basis And Change Of Basis In Quantum Mechanics, Kaitlyn Stephens Serbin, Megan Wawro, Rebecah Storms

School of Mathematical & Statistical Sciences Faculty Publications

Communities develop social languages in which utterances take on culturally specific situated meanings. As physics students interact in their classroom, they can learn the broader physics community’s social language by co-constructing meanings with their instructors. We provide an exposition of a systematic and productive use of idiosyncratic, socially acquired language in two classroom communities that we consider to be subcultures of the broader community of physicists. We perform a discourse analysis on twelve quantum mechanics students, two instructors, and the course text related to statements about basis and change of basis within a spin-½ probability problem. We classify the utterances’ …

Neutrosophic Sets And Systems, Vol. 41, 2021, Florentin Smarandache, Mohamed Abdel-Basset, Said Broumi

Neutrosophic Sets and Systems

No abstract provided.

The Influence Of The Psychophysical Assessment Paradigm On Pitch Discrimination For Adults (And A Pilot Sample Of Children), Ashley G. Flagge, Lucile Puranen, Madhuri S. Mulekar

Ashley Flagge Publications

Pitch discrimination ability has been of research interest due to its potential relationship to language and literacy. However, assessment protocols for pitch discrimination have varied widely. Prior studies with both children and adults have produced conflicting performance findings across different pitch discrimination research paradigms, though they have consistently shown that discrimination accuracy is based on the psychophysical assessment method applied. In the present study, we examined pitch discrimination performance among convenience samples of 19 adult women and ten female children across six different adaptive psychophysical measurement conditions. We found pitch discrimination performance in both groups to be impacted by the …

Amm Problem #12219, Brad Isaacson

Publications and Research

No abstract provided.

A Twisted Generalization Of The Classical Dedekind Sum, Brad Isaacson

Publications and Research

In this paper, we express three different, yet related, character sums in terms of generalized Bernoulli numbers. Two of these sums are generalizations of sums introduced and studied by Berndt and Arakawa–Ibukiyama–Kaneko in the context of the theory of modular forms. A third sum generalizes a sum already studied by Ramanujan in the context of theta function identities. Our methods are elementary, relying only on basic facts from algebra and number theory.

Analysis Of Intervention Effectiveness Using Early Outbreak Transmission Dynamics To Guide Future Pandemic Management And Decision-Making In Kuwait, Michael G. Tyshenko, Tamer Oraby, Joseph C. Longenecker, Harri Vainio, Janvier Gasana, Walid Q. Alali, Mohammad Alseaidan, Susie Elsaadany, Mustafa Al-Zoughool

School of Mathematical & Statistical Sciences Faculty Publications

Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) is a World Health Organization designated pandemic that can result in severe symptoms and death that disproportionately affects older patients or those with comorbidities. Kuwait reported its first imported cases of COVID-19 on February 24, 2020. Analysis of data from the first three months of community transmission of the COVID-19 outbreak in Kuwait can provide important guidance for decision-making when dealing with future SARS-CoV-2 epidemic wave management. The analysis of intervention scenarios can help to evaluate the possible impacts of various outbreak control measures going forward which aim to reduce the effective reproduction …

Majorization And Minimal Energy On Spheres, Oleg R. Musin

School of Mathematical & Statistical Sciences Faculty Publications

In the present paper, we consider the majorization theorem (also known as Karamata's inequality) and the respective minima of the majorization (the so-called M-sets) for f-energy potentials of m-point configurations on the unit sphere. In particular, we show the optimality of regular simplexes, describe some M-sets of small cardinality, define and discuss spherical f-designs.

Tri-Hamiltonian Duality System Of Merola-Ragnisco-Tu Equation, Mengxia Zhang, Bao-Feng Feng, Jiawen Liu

School of Mathematical & Statistical Sciences Faculty Publications

The tri-Hamiltonian method is applied to the Merola-Ragnisco-Tu equation. This enables us to construct a new integrable system, whose continuum limit is related to the AKNS system. Moreover, the system is proved to have linear spectral problems (Lax pair), bi-Hamiltonian structure and Darboux-Bäcklund transformation. Through the Darboux-Bäcklund transformation, we construct some exact solutions for the system.

Joint Modeling Of Rnaseq And Radiomics Data For Glioma Molecular Characterization And Prediction, Zeina A. Shboul, Norou Diawara, Arastoo Vossough, James Y. Chen, Khan M. Iftekharuddin

Electrical & Computer Engineering Faculty Publications

RNA sequencing (RNAseq) is a recent technology that profiles gene expression by measuring the relative frequency of the RNAseq reads. RNAseq read counts data is increasingly used in oncologic care and while radiology features (radiomics) have also been gaining utility in radiology practice such as disease diagnosis, monitoring, and treatment planning. However, contemporary literature lacks appropriate RNA-radiomics (henceforth, radiogenomics) joint modeling where RNAseq distribution is adaptive and also preserves the nature of RNAseq read counts data for glioma grading and prediction. The Negative Binomial (NB) distribution may be useful to model RNAseq read counts data that addresses potential shortcomings. …

Formal Power Series Approach To Nonlinear Systems With Static Output Feedback, G.S. Venkatesh, W. Steven Gray

Electrical & Computer Engineering Faculty Publications

The goal of this paper is to compute the generating series of a closed-loop system when the plant is described in terms of a Chen-Fliess series and static output feedback is applied. The first step is to reconsider the so called Wiener-Fliess connection consisting of a Chen-Fliess series followed by a memoryless function. Of particular importance will be the contractive nature of this map, which is needed to show that the closed-loop system has a Chen-Fliess series representation. To explicitly compute the generating series, two Hopf algebras are needed, the existing output feedback Hopf algebra used to describe dynamic output …

Acceleration Of Boltzmann Collision Integral Calculation Using Machine Learning, Ian Holloway, Aihua W. Wood, Alexander Alekseenko

Faculty Publications

The Boltzmann equation is essential to the accurate modeling of rarefied gases. Unfortunately, traditional numerical solvers for this equation are too computationally expensive for many practical applications. With modern interest in hypersonic flight and plasma flows, to which the Boltzmann equation is relevant, there would be immediate value in an efficient simulation method. The collision integral component of the equation is the main contributor of the large complexity. A plethora of new mathematical and numerical approaches have been proposed in an effort to reduce the computational cost of solving the Boltzmann collision integral, yet it still remains prohibitively expensive for …

An Algorithm To Compute Cvts For Finitely Generated Cantor Distributions, Carl P. Dettmann, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding Voronoi regions with respect to a given probability measure. CVT is a fundamental notion that has a wide spectrum of applications in computational science and engineering. In this paper, an algorithm is given to obtain the CVTs with n-generators to level m, for any positive integers m and n, of any Cantor set generated by a pair of self-similar mappings given by S1(x)=r1x and S2(x)=r2x+(1−r2) for x∈R, where r1,r2>0 and r1+r20 and p1+p2=1.