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.

Major Index Over Descent Distributions Of Standard Young Tableaux, Emily Anible

Dissertations, Master's Theses and Master's Reports

This thesis concerns the generating functions $f_{\lambda, k}(q)$ for standard Young tableaux of shape $\lambda$ with precisely $k$ descents, aiming to find closed formulas for a general form given by Kirillov and Reshetikhin in 1988. Throughout, we approach various methods by which further closed forms could be found. In Chapter 2 we give closed formulas for tableaux of any shape and minimal number of descents, which arise as principal specializations of Schur functions. We provide formulas for tableaux with three parts and one more than minimal number of descents, and demonstrate that the technique is extendable to any number of …

Diagrams In Intra-Configurational Analysis, Marco Panza, Gianluca Longa

MPP Published Research

In this paper we would like to attempt to shed some light on the way in which diagrams enter into the practice of ancient Greek geometrical analysis. To this end, we will first distinguish two main forms of this practice, i.e., trans-configurational and intra-configurational. We will then argue that, while in the former diagrams enter in the proof essentially in the same way (mutatis mutandis) they enter in canonical synthetic demonstrations, in the latter, they take part in the analytic argument in a specific way, which has no correlation in other aspects of classical geometry. In intra-configurational analysis, diagrams represent …

Analysis, Constructions And Diagrams In Classical Geometry, Marco Panza

MPP Published Research

Greek ancient and early modern geometry necessarily uses diagrams. Among other things, these enter geometrical analysis. The paper distinguishes two sorts of geometrical analysis and shows that in one of them, dubbed “intra-confgurational” analysis, some diagrams necessarily enter as outcomes of a purely material gesture, namely not as result of a codifed constructive procedure, but as result of a free-hand drawing.

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.

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.

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.

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 …

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’ …

Calabi-Yau Products: Graded Quivers For General Toric Calabi-Yaus, Sebastián Franco, Azeem Hasan

Publications and Research

The open string sector of the topological B-model on CY (m + 2)-folds is described by m-graded quivers with superpotentials. This correspondence generalizes the connection between CY (m + 2)-folds and gauge theories on the worldvolume of D(5 − 2m)-branes for m = 0, . . . , 3 to arbitrary m. In this paper we introduce the Calabi-Yau product, a new algorithm that starting from the known quiver theories for a pair of toric CY_m+2 and CY_n+2 produces the quiver theory for a related CY_{m+n+3 …}

Dimers, Orientifolds And Anomalies, Riccardo Argurio, Matteo Bertolini, Sebastían Franco, Eduardo Garcia-Valdecasas, Shani Meynet, Antoine Pasternak, Valdo Tatitscheff

Publications and Research

We study 4d N = 1 gauge theories engineered via D-branes at orientifolds of toric singularities, where gauge anomalies are cancelled without the introduction of non-compact flavor branes. Using dimer model techniques, we derive geometric criteria for establishing whether a given singularity can admit anomaly-free D-brane configurations purely based on its toric data and the type of orientifold projection. Our results therefore extend the dictionary between geometric properties of singularities and physical properties of the corresponding gauge theories.

Light-Ray Moments As Endpoint Contributions To Modular Hamiltonians, Daniel Kabat, Gilad Lifschytz, Phuc Nguyen, Debajyoti Sarkar

Publications and Research

We consider excited states in a CFT, obtained by applying a weak unitary perturbation to the vacuum. The perturbation is generated by the integral of a local operator J⁽ⁿ⁾ of modular weight n over a spacelike surface passing through x = 0. For |n| ≥ 2 the modular Hamiltonian associated with a division of space at x = 0 picks up an endpoint contribution, sensitive to the details of the perturbation (including the shape of the spacelike surface) at x = 0. The endpoint contribution is a sum of light-ray moments of the perturbing operator …

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

Neutrosophic Sets and Systems

No abstract provided.

Cross-Model Parameter Estimation In Epidemiology, Julia R. Fitzgibbons

Honors Theses and Capstones

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.