Mathematics Commons^™

N-Refined Neutrosophic Vector Spaces, Florentin Smarandache, Mohammad Abobala

Branch Mathematics and Statistics Faculty and Staff Publications

This paper introduces the concept of n-refined neutrosophic vector spaces as a generalization of neutrosophic vector spaces, and it studies elementary properties of them. Also, this work discusses some corresponding concepts such as weak/strong n-refined neutrosophic vector spaces, and n-refined neutrosophic homomorphisms.

N-Refined Neutrosophic Rings, Florentin Smarandache, Mohammad Abobala

Branch Mathematics and Statistics Faculty and Staff Publications

The aim of this paper is to introduce the concept of n-refined neutrosophic ring as a generalization of refined neutrosophic ring. Also, we present concept of n-refined polynomial ring. We study some basic concepts related to these rings such as AH-subrings, AH-ideals, AH-factors, and AH-homomorphisms.

How We Can Extend The Standard Deviation Notion With Neutrosophic Interval And Quadruple Neutrosophic Numbers, Victor Christianto, Florentin Smarandache, Muhammad Aslam

Branch Mathematics and Statistics Faculty and Staff Publications

During scientific demonstrating of genuine specialized framework we can meet any sort and rate model vulnerability. Its reasons can be incognizance of modelers or information mistake. In this way, characterization of vulnerabilities, as for their sources, recognizes aleatory and epistemic ones. The aleatory vulnerability is an inalienable information variety related with the researched framework or its condition. Epistemic one is a vulnerability that is because of an absence of information on amounts or procedures of the framework or the earth [7]. Right now, we examine fourfold neutrosophic numbers and their potential application for practical displaying of physical frameworks, particularly in …

A Short Remark On Vortex As Fluid Particle From Neutrosophic Logic Perspective, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In a previous paper in this journal (IJNS), it is mentioned about a possible approach to re-describe QED without renormalization route. As it is known that in literature, there are some attempts to reconcile vortex-based fluid dynamics and particle dynamics. Some attempts are not quite as fruitful as others. As a follow up to previous paper, the present paper will discuss two theorems for developing unification theories, and then point out some new proposals including by Simula (2020) on how to derive Maxwell equations in superfluid dynamics setting; this could be a new alternative approach towards “fluidicle” or “vorticle” model …

A Short Remark On Bong Han Duct System (Pvs) As A Neutrosophic Bridge Between Eastern And Western Medicine Paradigms, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In a previous paper in this journal (IJNS), it is mentioned about a possible approach of “curemony” as a middle way in order to reconcile Eastern and Western’s paradigms of medicine [1]. Although it is known in literature that there are some attempts to reconcile between Eastern and Western medicine paradigms, known as “integrative medicine,” here a new viewpoint is submitted, i.e. Bong Han duct system (PVS), which is a proof of Meridian system, can be a bridge between those two medicine paradigms in neutrosophic sense. This can be considered as a Neutrosophic Logic way to bridge or reconcile the …

A Review On Superluminal Physics And Superluminal Communication In Light Of The Neutrosophic Logic Perspective, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In a recent paper, we describe a model of quantum communication based on combining consciousness experiment and entanglement, which can serve as impetus to stop 5G-network-caused diseases. Therefore, in this paper we consider superluminal physics and superluminal communication as a bridge or intermediate way between subluminal physics and action-at-a-distance (AAAD) physics, especially from neutrosophic logic perspective. Although several ways have been proposed to bring such a superluminal communication into reality, such as Telluric wave or Telepathy analog of Horejev and Baburin, here we also review two possibilities: quaternion communication and also quantum communication based on quantum noise. Further research is …

Neutrosophic In Latin America, Advances And Perspectives (Neutrosofía En Latinoamérica, Avances Y Perspectivas), Maykel Leyva-Vazquez, Jesus Estupinan, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophy has given way to its own research method by constituting a unified field of logic for a transdisciplinary study that crosses the borders between the sciences. This paper analyzes the impact of neutrosophic theory in Latin America, its main drivers and the state of the research. The increase in publications since the creation of the Latin American Association of Neutrosophic Sciences is noteworthy. The most approached areas are found in the interrelation of the social sciences and neutrosophy, presenting outstanding results in these areas of research. The most outstanding university and institutions are the Autonomous Regional University of the …

Neutrosophic Local Function And Generated Neutrosophic Topology, A. A. Salama, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we introduce the notion of ideals on neutrosophic set which is considered as a generalization of fuzzy and fuzzy intuitionistic ideals studies. The concept of neutrosophic local function is also introduced for a neutrosophic topological space. These concepts are discussed with a view to find new neutrosophic topology. The basic structure, especially a basis for such generated neutrosophic topologies and several relations between different topological neutrosophic ideals and neutrosophic topologies are also studied here. Possible application to GIS topology rules are touched upon.

Explicit Determinantal Formula For A Class Of Banded Matrices, Yerlan Amanbek, Zhibin Du, Yogi Erlangga, Carlos M. Da Fonseca, Bakytzhan Kurmanbek, António Pereira

All Works

© 2020 Yerlan Amanbek et al., published by De Gruyter 2020. In this short note, we provide a brief proof for a recent determinantal formula involving a particular family of banded matrices.

Neutroalgebra Is A Generalization Of Partial Algebra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019 research referred to NeutroAlgebras and AntiAlgebras (also called NeutroAlgebraic Structures and respectively AntiAlgebraic Structures). Let be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosphication, we split the nonempty space we work on into three regions {two opposite ones corresponding to and , and one corresponding to neutral (indeterminate) (also denoted ) between the opposites}, which may or may not be disjoint – depending on the application, but they are exhaustive (their union equals the whole space). A NeutroAlgebra …

The Geometry Of The Orthological Triangles, Florentin Smarandache, Ion Patrascu

Branch Mathematics and Statistics Faculty and Staff Publications

Plants and trees grow perpendicular to the plane tangent to the soil surface, at the point of penetration into the soil; in vacuum, the bodies fall perpendicular to the surface of the Earth - in both cases, if the surface is horizontal. Starting from the property of two triangles to be orthological, the two authors have designed this work that seeks to provide an integrative image of elementary geometry by the prism of this "filter". Basically, the property of orthology is the skeleton of the present work, which establishes many connections of some theorems and geometric properties with it. The …

The Subconstituent Algebra Of A Hypercube, Jared B. Billet

UNF Graduate Theses and Dissertations

We study the hypercube and the associated subconstituent algebra. Let Q_D denote the hypercube with dimension D and let X denote the vertex set of Q_D. Fix a vertex x in X. We denote by A the adjacency matrix of Q_D and by A* = A*(x) the diagonal matrix with yy-entry equal to D − 2i, where i is the distance between x and y. The subconstitutent algebra T = T(x) of Q_D with respect to x is generated by A and A* . We show that A 2A* − 2AA*A + A*A 2 = 4A* A*2A − 2A*AA* + …

Harmonic Morphisms With One-Dimensional Fibres And Milnor Fibrations, Murphy Griffin

UNF Graduate Theses and Dissertations

We study a problem at the intersection of harmonic morphisms and real analytic Milnor fibrations. Baird and Ou establish that a harmonic morphism from G: \mathbb{R}^m \setminus V_G \rightarrow \mathbb{R}^n\setminus \{0\} defined by homogeneous polynomials of order p retracts to a harmonic morphism \psi|: S^{m-1} \setminus K_\epsilon \rightarrow S^{n-1} that induces a Milnor fibration over the sphere. In seeking to relax the homogeneity assumption on the map G, we determine that the only harmonic morphism $\varphi: \mathbb{R}^m \setminus V_G \rightarrow S^{m-1}\K_\epsilon$ that preserves \arg G is radial projection. Due to this limitation, we confirm Baird and Ou's result, yet establish …

Maximality And Applications Of Subword-Closed Languages, Rhys Davis Jones

UNF Graduate Theses and Dissertations

Characterizing languages D that are maximal with the property that D^* ⊆ S^⊗ is an important problem in formal language theory with applications to coding theory and DNA codewords. Given a finite set of words of a fixed length S, the constraint, we consider its subword closure, S^⊗, the set of words whose subwords of that fixed length are all in the constraint. We investigate these maximal languages and present characterizations for them. These characterizations use strongly connected components of deterministic finite automata and lead to polynomial time algorithms for generating such languages. We prove that …

Improvement Of Error Bounds Of Local Limit Theorems For Sums Of Independent Integer-Valued Random Variables, Tatpon Siripraparat

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Poisson Approximation For Locally Dependent Collateralized Debt Obligation, Nat Yonghint

Chulalongkorn University Theses and Dissertations (Chula ETD)

A collateralized debt obligation (CDO) is a type of structured asset-backed security. The assets are pooled together and divided into tranches to be sold to investors. Each tranche has a substantially different credit quality and risk level. Jaio and Kaouri (2009), Neammanee and Yonghint (2020) used Poisson approximation to approximate a percentage loss for each tranche in CDO where all reference assets are independent. However, in the real world, each asset may not have the independent structure. In this thesis, we consider reference assets without assuming independence. If a default of reference asset may affect to some asset then we …

Smooth Approximations Of Continuous Functions Definable In D-Minimal Structures, Phaphontee Yamchote

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Fuzzy Logistic Regression For Detecting Differential Dna Methylation Regions, Tarek M. Bubaker Bennaser

Doctoral Dissertations

“Epigenetics is the study of changes in gene activity or function that are not related to a change in the DNA sequence. DNA methylation is one of the main types of epigenetic modifications, that occur when a methyl chemical group attaches to a cytosine on the DNA sequence. Although the sequence does not change, the addition of a methyl group can change the way genes are expressed and produce different phenotypes. DNA methylation is involved in many biological processes and has important implications in the fields of biomedicine and agriculture.

Statistical methods have been developed to compare DNA methylation at …

Uniform Three-Class Regular Partial Steiner Triple Systems With Uniform Degrees, Prangya Rani Parida

Dissertations, Master's Theses and Master's Reports

A Partial Steiner Triple system (X, T) is a finite set of points C and a collection T of 3-element subsets of C that every pair of points intersect in at most 1 triple. A 3-class regular PSTS (3-PSTS) is a PSTS where the points can be partitioned into 3 classes (each class having size m, n and p respectively) such that no triple belongs to any class and any two points from the same class occur in the same number of triples (a, b and c respectively). The 3-PSTS is said to be uniform if m = n = …

Pseudo-Contractions, Rigidity, Fixed Points And Related Questions, Daniel Alpay, Vladimir Bolotnikov, David Shoikhet

Mathematics, Physics, and Computer Science Faculty Articles and Research

The class of holomorphic self-mappings of the open unit disk (which are contractions with respect to the Poincaré metric) admits a natural extension to the class of holomorphic pseudo-contractions. In this paper, we study various inequalities involving the values of derivatives of holomorphic pseudo-contractions at fixed points (particularly, at the Denjoy–Wolff fixed point).

Visualizing The Mean And The Standard Deviation Using R/Rstudio Shiny Package, Rachel Hufnagel, Ziyi Chen, Mamunur Rashid, Jyotirmoy Sarkar

Student Research

Many of us have experienced an unpleasant situation in which only the mean and the standard deviation of a data set are reported, but we are expected to know everything about the dataset as if those two values were all we needed to know. We would learn so much more if there were easy ways to create and share graphical representations and interpretations of the entire raw data. In this paper, we not only explain what the mean and the standard deviation tell us about a data set, but also describe how to include additional information on the data. We …

Forced (2 + 1)-Dimensional Discrete Three-Wave Equation, Junyi Zhu, Sishou Zhou, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

We generalize the ∂-dressing method to investigate a (2 + 1)-dimensional lattice, which can be regarded as a forced (2 + 1)-dimensional discrete three-wave equation. The soliton solutions to the (2 + 1)-dimensional lattice are given through constructing different symmetry conditions. The asymptotic analysis of one-soliton solution is discussed. For the soliton solution, the forces are zero.

Decomposition Of 2-Soliton Solutions For The Good Boussinesq Equations, Vesselin Vatchev

School of Mathematical & Statistical Sciences Faculty Publications

We consider decompositions of two-soliton solutions for the good Boussinesq equation obtained by the Hirota method and the Wronskian technique. The explicit forms of the components are used to study the dynamics of 2-soliton solutions. An interpretation in the context of eigenvalue problems arising from KdV type equations and transport equations is considered. Numerical examples are included.

Professional Development For Mathematics Teacher Education Faculty: Need And Design, Billy Jackson, Shandy Hauk, Jenq Jong Tsay, Alma Ramirez

School of Mathematical & Statistical Sciences Faculty Publications

The purpose of this report is to share a conceptual model useful in the design of professional learning about teaching for university mathematics faculty. The model is illustrated by examples from a particular design effort: the development of an online shortcourse for faculty new to teaching mathematics courses for prospective primary school teachers. How novice mathematics teacher educators grow as instructors is an emerging area of research and development in the United States. At the same time, it is well established that effective instructional design of any course, including a course for faculty, requires breadth first: understanding and anticipating the …

Flows Of Co-Closed G_{2}-Structures, Sergey Grigorian

School of Mathematical & Statistical Sciences Faculty Publications

We survey recent progress in the study of G_{2}-structure Laplacian coflows, that is, heat flows of co-closed G_{2}-structures. We introduce the properties of the original Laplacian coflow of G_{2}-structures as well as the modified coflow, reviewing short-time existence and uniqueness results for the modified coflow and well as recent Shi-type estimates that apply to a more general class of G_{2}-structure flows.

Bayesian Modelling Of Nonlinear Poisson Regression With Artificial Neural Networks, Hansapani Rodrigo, Chris P. Tsokos

School of Mathematical & Statistical Sciences Faculty Publications

Modelling and prediction of count and rate responses have substantial usage in many fields, including health, finance, social, etc. Conventionally, linear Poisson regression models have been widely used to model these responses. However, the linearity assumption of the systematic component of linear Poisson regression models restricts their capability of handling complex data patterns. In this regard, it is important to develop nonlinear Poisson regression models to capture the inherent variability within the count data. In this study, we introduce a probabilistically driven nonlinear Poisson regression model with Bayesian artificial neural networks (ANN) to model count and rate data. This new …

Effect Of Hydraulic Resistivity On A Weakly Nonlinear Thermal Flow In A Porous Layer, Dambaru Bhatta, Daniel N. Riahi

School of Mathematical & Statistical Sciences Faculty Publications

Heat and mass transfer through porous media has been a topic of research interest because of its importance in various applications. The flow system in porous media is modelled by a set of partial differential equations. The momentum equation which is derived from Darcy’s law contains a resistivity parameter. We investigate the effect of hydraulic resistivity on a weakly nonlinear thermal flow in a horizontal porous layer. The present study is a realistic study of nonlinear convection flow with variable resistivity whose rate of variation is arbitrary in general. This is a first step for considering more general problems in …

Screening Potential Citrus Rootstocks For Phytophthora Nicotianae Tolerance, Madhurababu Kunta, Sandy Chavez, Zenaida Viloria, Hilda S. Del Rio, Madhavi Devanaboina, George Yanev, Jong-Won Park, Eliezer S. Louzada

School of Mathematical & Statistical Sciences Faculty Publications

Seeds from four citrus rootstocks including sour orange, Bitters-C22 citrandarin, Sarawak pummelo 3 Rio Red grapefruit, and Sarawak pummelo 3Bower mandarin were exposed to high inoculum levels of Phytophthora nicotianae to screen for tolerance. Inoculation of pregerminated seeds (PGIS) and non-PGIS was carried out. The average P. nicotianae propagule counts from the soil samples where these seedlings were raised ranged from 424 to 1361 colony forming units/cm3. The proportion of live to dead plants was recorded at 11months postinoculation, which showed that Sarawak3Bower performed significantly better than other rootstocks. Evaluation of the rootstocks 18 months postinoculation resulted in only one …

Finite Lifespan Of Solutions Of The Semilinear Wave Equation In The Einstein–De Sitter Spacetime, Anahit Galstian, Karen Yagdjian

School of Mathematical & Statistical Sciences Faculty Publications

We examine the solutions of the semilinear wave equation, and, in particular, of the φq model of quantum field theory in the curved space-time. More exactly, for 1 < q < 4 we prove that the solution of the massless self-interacting scalar field equation in the Einstein-de Sitter universe has finite lifespan.

The Quantization Of The Standard Triadic Cantor Distribution, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. For a given k ≥ 2, let {Sj : 1 ≤ j ≤ k} be a set of k contractive similarity mappings such that Sj(x) = 1 2k−1x + 2(j−1) 2k−1 for all x ∈ R, and let P = 1 k Pk j=1 P ◦ S−1 j . Then, P is a unique Borel probability measure on R such that P has support the Cantor set generated by the similarity mappings …