Digital Commons Network^™

Optimal Experimental Design To Characterize A Wave Source Using Dosimeter Measurements, Renee L. Gooding

Mathematics & Statistics ETDs

When modeling physical phenomena we want to solve the inverse problem by estimating the parameters that characterize the source model that we are interested in. In this thesis, we focus on the optimal placement of a finite number of individual sensors, called dosimeters, in two and three dimensions with a time dependent Gaussian wave source. Using a computational model along with experimental data, we design an iterative process to determine the optimal placement of an additional sensor such that the noise in the measurements has a minimal effect on the parameter estimation. First, we estimate the parameters that characterize the …

Deterministic And Probabilistic Methods For Seismic Source Inversion, Juan Pablo Madrigal Cianci

Mathematics & Statistics ETDs

The national Earthquake Information Center (NEIC) reports an occurrence of about 13,000 earthquakes every year, spanning different values on the Richter scale from very mild (2) to "giant earthquakes'' (8 and above). Being able to study these earthquakes provides useful information for a wide range of applications in geophysics. In the present work we study the characteristics of an earthquake by performing seismic source inversion; a mathematical problem that, given some recorded data, produces a set of parameters that when used as input in a mathematical model for the earthquake generates synthetic data that closely resembles the measured data. There …

Cancer Modeling: From Optimal Cell Renewal To Immunotherapy, Cesar L. Alvarado

Mathematics & Statistics ETDs

Cancer is a disease caused by mutations in normal cells. According to the National Cancer Institute, in 2016, an estimated 1.6 million people were diagnosed and approximately 0.5 million people died from the disease in the United States. There are many factors that shape cancer at the cellular and organismal level, including genetic, immunological, and environmental components. In this thesis, we show how mathematical modeling can be used to provide insight into some of the key mechanisms underlying cancer dynamics. First, we use mathematical modeling to investigate optimal homeostatic cell renewal in tissues such as the small intestine with an …

Modeling Trait Evolutionary Processes With More Than One Gene, Huan Jiang

Mathematics & Statistics ETDs

Phylogenetic comparative methods have been used to test evolutionary signals through trait evolutionary processes. Traditionally, biologists use one phylogenetic tree as a tool to handle dependent data for the traits of interest and hence utilize one gene only. However, it is more informative if the evolutionary processes of a trait are presented by phylogenetic trees reconstructed by the DNA alignments from more than one gene. In this work, we explain and develop two methods involving modeling the trait evolutionary processes: (a) two gene trees via the Brownian motion (BM) model; and (b) two gene trees via the Ornstein-Uhlenbeck (OU) model. …

The Effects Of Different Teaching Methods On Student Attitude And Achievement In Calculus Recitations, Jocelyn Noelle Rios

Mathematics & Statistics ETDs

Many universities offer recitation sections in their calculus sequences; however, little research has been conducted on TA best practices in the recitations.This study first aimed to observe the different teaching methods that TAs employed in their recitations and then measure their efficacy in improving student course attitudes and achievement, focusing on student-centered and concept-based instruction. In addition, this study aimed to assess the quality of professional development offered to recitation leaders. Using a quantitative-dominant mixed methods design, 12 TAs were observed throughout the semester and TAs and calculus students were surveyed. This study found that student-centered instruction was positively correlated …

From Acoustic Analog Of Space, Cancer Therapy, To Acoustic Sachs-Wolfe Theorem: A Model Of The Universe As A Guitar, Victor Christianto, Florentin Smarandache, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such an acoustic model of cosmology is rarely developed fully into a complete framework from the notion of space, cancer therapy up to the sky. This paper may be the first attempt towards such a complete description of the Universe based on classical wave equation of sound. It is argued that one can arrive at a consistent description of space, elementary particles, Sachs-Wolfe acoustic theorem, up to a novel approach for cancer …

Numerical Solution Of Master Equation Corresponding To Schumann Waves, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Following a hypothesis by Marciak-Kozlowska, 2011, we consider one-dimensional Schumann wave transfer phenomena. Numerical solution of that equation was obtained by the help of Mathematica.

Neutrosophic Quadruple Algebraic Hyperstructures, A. A. A. Agboola, B. Davvaz, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The objective of this paper is to develop neutrosophic quadruple algebraic hyperstructures. Specifically, we develop neutrosophic quadruple semihypergroups, neutrosophic quadruple canonical hypergroups and neutrosophic quadruple hyperrings and we present elementary properties which characterize them.

Neutrosophic Operational Research - Vol. 1, Florentin Smarandache, Mohamed Abdel Basset, Yongquan Zhou

Branch Mathematics and Statistics Faculty and Staff Publications

This book is an excellent exposition of the use of Data Envelopment Analysis (DEA) to generate data analytic insights to make evidence-based decisions, to improve productivity, and to manage cost-risk and benefitopportunity in public and private sectors. The design and the content of the book make it an up-to-date and timely reference for professionals, academics, students, and employees, in particular those involved in strategic and operational decisionmaking processes to evaluate and prioritize alternatives to boost productivity growth, to optimize the efficiency of resource utilization, and to maximize the effectiveness of outputs and impacts to stakeholders. It is concerned with the …

Complex Valued Graphs For Soft Computing, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce in a systematic way the notion of complex valued graphs, strong complex valued graphs and complex neutrosophic valued graphs. Several interesting properties are defined, described and developed. Most of the conjectures which are open in case of usual graphs continue to be open problems in case of both complex valued graphs and strong complex valued graphs. We also give some applications of them in soft computing and social networks. At this juncture it is pertinent to keep on record that Dr. Tohru Nitta was the pioneer to use complex valued graphs …

Neutrosophic Triplet Groups And Their Applications To Mathematical Modelling, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K.

Branch Mathematics and Statistics Faculty and Staff Publications

The innovative notion of neutrosophic triplet groups, introduced by Smarandache and Ali in 2014-2016, happens to yield the anti-element and neutral element once the element is given. It is established that the neutrosophic triplet group collection forms the classical group under product for Zn, for some specific n. However the collection is not even closed under sum. These neutrosophic triplet groups are built using only modulo integers or Cayley tables. Several interesting properties related with them are defined. It is pertinent to record that in Zn, when n is a prime number, we cannot get a neutral element which can …

Nidus Idearum. Scilogs, Iii: Viva La Neutrosophia!, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Welcome into my scientific lab! My lab[oratory] is a virtual facility with noncontrolled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings "ground", "opinion", "expectation"), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). * In this third book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, referring to topics on NEUTROSOPHY – email …

Special Issue: Neutrosophic Theories Applied In Engineering, Florentin Smarandache, Jun Ye

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic sets and logic are generalizations of fuzzy and intuitionistic fuzzy sets and logic. Neutrosophic sets and logic are gaining significant attention in solving many real life decision making problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. They have been applied in computational intelligence, multiple criteria decision making, image processing, medical diagnoses, etc. This Special Issue presents original research papers that report on state-of-the-art and recent advancements in neutrosophic sets and logic in soft computing, artificial intelligence, big and small data mining, decision making problems, and practical achievements.

An Operational View In Computational Construction Of Information, Florentin Smarandache, Stefan Vladutescu, Constantin Dima, Valeriu Voinea

Branch Mathematics and Statistics Faculty and Staff Publications

The paper aims to explain the technology of emergence of information. Our research proves that information as communicational product is the result of processing within some operations, actions, mechanisms and strategies of informational material meanings. Are determined eight computational-communicative operations of building information. Information occurs in two communication phases, syncretic and the segregation-synthetic. The syncretic phase consists of four operations: referral of significant field, primary delimitation of information, detection-looking information and an anticipative-draft constitution (feedforward). The segregation-synthetic phase also includes four operations: discrimination, identification, interpretation and confrontation (feedback). In the future we will investigate informational actions, mechanisms and strategies.

A Lattice Theoretic Look: A Negated Approach To Adjectival (Intersective, Neutrosophic And Private) Phrases, Florentin Smarandache, Selcuk Topal

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Curiozităţi Ale Funcţiilor Supermatematice, Florentin Smarandache, Mircea Eugen Selariu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

The Use Of The Pivot Pairwise Relative Criteria Importance Assessment Method For Determining The Weights Of Criteria, Florentin Smarandache, Dragisa Stanujkic, Edmundas Kazimieras Zavadskas, Darjan Karabasevic, Zenonas Turskis

Branch Mathematics and Statistics Faculty and Staff Publications

The weights of evaluation criteria could have a significant impact on the results obtained by applying multiple criteria decision-making methods. Therefore, the two extensions of the SWARA method that can be used in cases when it is not easy, or even is impossible to reach a consensus on the expected importance of the evaluation criteria are proposed in this paper. The primary objective of the proposed extensions is to provide an understandable and easy-to-use approach to the collecting of respondents’ real attitudes towards the significance of evaluation criteria and to also provide an approach to the checking of the reliability …

P-Union And P-Intersection Of Neutrosophic Cubic Sets, Florentin Smarandache, Young Bae Jun, Chang Su Kim

Branch Mathematics and Statistics Faculty and Staff Publications

Conditions for the P-intersection and P-intersection of falsity-external (resp. indeterminacy-external and truth-external) neutrosophic cubic sets to be an falsity-external (resp. indeterminacy-external and truthexternal) neutrosophic cubic set are provided. Conditions for the Punion and the P-intersection of two truth-external (resp. indeterminacyexternal and falsity-external) neutrosophic cubic sets to be a truthinternal (resp. indeterminacy-internal and falsity-internal) neutrosophic cubic set are discussed.

Multicriteria Decision Making Using Double Refined Indeterminacy Neutrosophic Cross Entropy And Indeterminacy Based Cross Entropy, Ilanthenral Kandasamy, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Double Refined Indeterminacy Neutrosophic Set (DRINS) is an inclusive case of the refined neutrosophic set, defined by Smarandache [1], which provides the additional possibility to represent with sensitivity and accuracy the uncertain, imprecise, incomplete, and inconsistent information which are available in real world.

More precision is provided in handling indeterminacy; by classifying indeterminacy (I) into two, based on membership; as indeterminacy leaning towards truth membership (IT ) and indeterminacy leaning towards false membership (IF ). This kind of classification of indeterminacy is not feasible with the existing Single Valued Neutrosophic Set (SVNS), but it is a particular case of the …

Special Types Of Bipolar Single Valued Neutrosophic Graphs, Ali Hassan, Muhammad Aslam Malik, Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic theory has many applications in graph theory, bipolar single valued neutrosophic graphs (BSVNGs) is the generalization of fuzzy graphs and intuitionistic fuzzy graphs, SVNGs. In this paper we introduce some types of BSVNGs, such as subdivision BSVNGs, middle BSVNGs, total BSVNGs and bipolar single valued neutrosophic line graphs (BSVNLGs), also investigate the isomorphism, co weak isomorphism and weak isomorphism properties of subdivision BSVNGs, middle BSVNGs, total BSVNGs and BSVNLGs.

Introducing A Theory Of Neutrosophic Evolution: Degrees Of Evolution, Indeterminacy, And Involution, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

During the process of adaptation of a being (plant, animal, or human), to a new environment or conditions, the being partially evolves, partially devolves (degenerates), and partially is indeterminate i.e. neither evolving nor devolving, therefore unchanged (neutral), or the change is unclear, ambiguous, vague, as in neutrosophic logic. Thank to adaptation, one therefore has: evolution, involution, and indeterminacy (or neutrality), each one of these three neutrosophic components in some degree. The degrees of evolution/indeterminacy/involution are referred to both: the structure of the being (its body parts), and functionality of the being (functionality of each part, or inter-functionality of the parts …

Neutrosophic Operational Research - Vol. 2, Florentin Smarandache, Mohamed Abdel Basset, Victor Chang

Branch Mathematics and Statistics Faculty and Staff Publications

Foreword John R. Edwards This book is an excellent exposition of the use of Data Envelopment Analysis (DEA) to generate data analytic insights to make evidence-based decisions, to improve productivity, and to manage cost-risk and benefitopportunity in public and private sectors. The design and the content of the book make it an up-to-date and timely reference for professionals, academics, students, and employees, in particular those involved in strategic and operational decisionmaking processes to evaluate and prioritize alternatives to boost productivity growth, to optimize the efficiency of resource utilization, and to maximize the effectiveness of outputs and impacts to stakeholders. It …

An Outline Of Cellular Automaton Universe Via Cosmological Kdv Equation, Florentin Smarandache, Victor Christianto, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such a sound wave model of cosmology is rarely developed fully into a complete framework. This paper can be considered as our second attempt towards such a complete description of the Universe based on soliton wave solution of cosmological KdV equation. Then we advance further this KdV equation by virtue of Cellular Automaton method to solve the PDEs. We submit wholeheartedly Robert Kuruczs hypothesis that Big Bang should be replaced with a …

A Bipolar Single Valued Neutrosophic Isolated Graphs: Revisited, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Mohsin Khan

Branch Mathematics and Statistics Faculty and Staff Publications

In this research paper, the graph of the bipolar single-valued neutrosophic set model (BSVNS) is proposed. The graphs of single valued neutrosophic set models is generalized by this graph. For the BSVNS model, several results have been proved on complete and isolated graphs. Adding, an important and suitable condition for the graphs of the BSVNS model to become an isolated graph of the BSVNS model has been demonstrated.

Generalized Interval Valued Neutrosophic Graphs Of First Type, Florentin Smarandache, Said Broumi, Mohamed Talea, Assia Bakali, Ali Hassan

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, motivated by the notion of generalized single valued neutrosophic graphs of first type, we defined a new neutrosophic graphs named generalized interval valued neutrosophic graphs of first type (GIVNG1) and presented a matrix representation for it and studied few properties of this new concept. The concept of GIVNG1 is an extension of generalized fuzzy graphs (GFG1) and generalized single valued neutrosophic of first type (GSVNG1).

Computation Of Shortest Path Problem In A Network With Sv-Triangular Neutrosophic Numbers, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea

Branch Mathematics and Statistics Faculty and Staff Publications

In this article, we present an algorithm method for finding the shortest path length between a paired nodes on a network where the edge weights are characterized by single valued triangular neutrosophic numbers. The proposed algorithm gives the shortest shortest path length from source node to destination node based on a ranking method. Finally, a numerical example is also presented to illustrate the efficiency of the proposed approach.

Numbers In Base B That Generate Primes With Help The Luhn Function Of Order Ω, Florentin Smarandache, Octavian Cira

Branch Mathematics and Statistics Faculty and Staff Publications

We put the problem to determine the sets of integers in base b ≥ 2 that generate primes with using a function.

Neutrosophic Perspectives: Triplets, Duplets, Multisets, Hybrid Operators, Modal Logic, Hedge Algebras. And Applications (Second Extended And Improved), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This book is part of the book-series dedicated to the advances of neutrosophic theories and their applications, started by the author in 1998. Its aim is to present the last developments in the field. For the first time, we now introduce:

— Neutrosophic Duplets and the Neutrosophic Duplet Structures;

— Neutrosophic Multisets (as an extension of the classical multisets);

— Neutrosophic Spherical Numbers;

— Neutrosophic Overnumbers / Undernumbers / Offnumbers;

— Neutrosophic Indeterminacy of Second Type;

— Neutrosophic Hybrid Operators (where the heterogeneous t-norms and t-conorms may be used in designing neutrosophic aggregations);

— Neutrosophic Triplet Loop;

— Neutrosophic Triplet …

Easier To Break From Inside Than From Outside / Mai Ușor Să Distrugi Din Interior Decât Din Exterior, Florentin Smarandache, Andrusa R. Vatuiu

Branch Mathematics and Statistics Faculty and Staff Publications

Abstract in English:

This book contains concrete examples from history, economy, biology, digital world, nuclear physics, agriculture and so on about breaking a neutrosophic dynamic system (i.e. a dynamic system that has indeterminacy) from inside.

We define a neutrosophic mathematical model using a system of ordinary differential equations and the neutrosophic probability in order to approximate the process of breaking from inside a neutrosophic complex dynamic system.

It shows that for breaking from inside it is needed a smaller force than for breaking from outside the neutrosophic complex dynamic system.

Methods that have been used in the past for breaking …