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On Rugina’S System Of Thought, Florentin Smarandache 2018 University of New Mexico

On Rugina’S System Of Thought, Florentin Smarandache

Mathematics and Statistics Faculty and Staff Publications

This article investigates Rugina's orientation table and gives particular examples for several of its seven models. Leon Walras's Economics of Stable Equilibrium and Keynes's Economics of Disequilibrium are combined in Rugina's orientation table in systems which are s percent stable and 100 ÿ s percent unstable, where s may be 100, 95, 65, 50, 35, 5, and 0. Classical logic and modern logic are united in Rugina's integrated logic, and then generalized in neutrosophic logic.


Quantum Attacks On Modern Cryptography And Post-Quantum Cryptosystems, Zachary Marron 2018 Liberty University

Quantum Attacks On Modern Cryptography And Post-Quantum Cryptosystems, Zachary Marron

Senior Honors Theses

Cryptography is a critical technology in the modern computing industry, but the security of many cryptosystems relies on the difficulty of mathematical problems such as integer factorization and discrete logarithms. Large quantum computers can solve these problems efficiently, enabling the effective cryptanalysis of many common cryptosystems using such algorithms as Shor’s and Grover’s. If data integrity and security are to be preserved in the future, the algorithms that are vulnerable to quantum cryptanalytic techniques must be phased out in favor of quantum-proof cryptosystems. While quantum computer technology is still developing and is not yet capable of breaking commercial ...


Pgl2(FL) Number Fields With Rational Companion Forms, David P. Roberts 2018 University of Minnesota - Morris

Pgl2(FL) Number Fields With Rational Companion Forms, David P. Roberts

Mathematics Publications

We give a list of PGL2(Fl) number fields for ℓ ≥ 11 which have rational companion forms. Our list has fifty-three fields and seems likely to be complete. Some of the fields on our list are very lightly ramified for their Galois group.


Number Theory: Niven Numbers, Factorial Triangle, And Erdos' Conjecture, Sarah Riccio 2018 Sacred Heart University

Number Theory: Niven Numbers, Factorial Triangle, And Erdos' Conjecture, Sarah Riccio

Mathematics Undergraduate Publications

In this paper, three topics in number theory will be explored: Niven Numbers, the Factorial Triangle, and Erdos's Conjecture . For each of these topics, the goal is for us to find patterns within the numbers which help us determine all possible values in each category. We will look at two digit Niven Numbers and the set that they belong to, the alternating summation of the rows of the Factorial Triangle, and the unit fractions whose sum is the basis of Erdos' Conjecture.


Some Aggregation Operators For Bipolar-Valued Hesitant Fuzzy Information, Florentin Smarandache, Tahir Mahmood, Kifayat Ullah, Qaisar Khan 2018 University of New Mexico

Some Aggregation Operators For Bipolar-Valued Hesitant Fuzzy Information, Florentin Smarandache, Tahir Mahmood, Kifayat Ullah, Qaisar Khan

Mathematics and Statistics Faculty and Staff Publications

In this article we define some aggregation operators for bipolar-valued hesitant fuzzy sets. These operations include bipolar-valued hesitant fuzzy ordered weighted averaging (BPVHFOWA) operator, bipolar-valued hesitant fuzzy ordered weighted geometric (BPVHFOWG) operator and their generalized forms. We also define hybrid aggregation operators and their generalized forms and solved a decision-making problem on these operation.


Monomial Progenitors And Related Topics, Madai Obaid Alnominy 2018 California State University - San Bernardino

Monomial Progenitors And Related Topics, Madai Obaid Alnominy

Electronic Theses, Projects, and Dissertations

The main objective of this project is to find the original symmetric presentations of some very important finite groups and to give our constructions of some of these groups. We have found the Mathieu sporadic group M11, HS × D5, where HS is the sporadic group Higman-Sim group, the projective special unitary group U(3; 5) and the projective special linear group L2(149) as homomorphic images of the monomial progenitors 11*4 :m (5 :4), 5*6 :m S5 and 149*2 :m D37. We have also discovered 24 : S3 × C2, 2 ...


Neutrosophic Soft Rough Graphs With Application, Florentin Smarandache, Muhammad Akram, Hafsa M. Malik, Sundas Shahzadi 2018 University of New Mexico

Neutrosophic Soft Rough Graphs With Application, Florentin Smarandache, Muhammad Akram, Hafsa M. Malik, Sundas Shahzadi

Mathematics and Statistics Faculty and Staff Publications

Neutrosophic sets (NSs) handle uncertain information while fuzzy sets (FSs) and intuitionistic fuzzy sets (IFs) fail to handle indeterminate information. Soft set theory, neutrosophic set theory, and rough set theory are different mathematical models for handling uncertainties and they are mutually related. The neutrosophic soft rough set (NSRS) model is a hybrid model by combining neutrosophic soft sets with rough sets. We apply neutrosophic soft rough sets to graphs. In this research paper, we introduce the idea of neutrosophic soft rough graphs (NSRGs) and describe different methods of their construction. We consider the application of NSRG in decision-making problems. In ...


Nn-Harmonic Mean Aggregation Operators-Based Mcgdm Strategy In A Neutrosophic Number Environment, Florentin Smarandache, Kalyan Mondal, Surapati Pramanik, Bibhas C. Giri 2018 University of New Mexico

Nn-Harmonic Mean Aggregation Operators-Based Mcgdm Strategy In A Neutrosophic Number Environment, Florentin Smarandache, Kalyan Mondal, Surapati Pramanik, Bibhas C. Giri

Mathematics and Statistics Faculty and Staff Publications

A neutrosophic number (a + bI) is a significant mathematical tool to deal with indeterminate and incomplete information which exists generally in real-world problems, where a and bI denote the determinate component and indeterminate component, respectively. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine the unknown weight of the criteria. We define the neutrosophic number harmonic mean operators and prove their basic properties. Then, we develop two novel multi-criteria group decision-making (MCGDM) strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility, applicability, and effectiveness ...


Equidimensional Adic Eigenvarieties For Groups With Discrete Series, Daniel Robert Gulotta '03 2018 Illinois Mathematics and Science Academy

Equidimensional Adic Eigenvarieties For Groups With Discrete Series, Daniel Robert Gulotta '03

Doctoral Dissertations

We extend Urban's construction of eigenvarieties for reductive groups G such that G(R) has discrete series to include characteristic p points at the boundary of weight space. In order to perform this construction, we define a notion of "locally analytic" functions and distributions on a locally Qp-analytic manifold taking values in a complete Tate Zp-algebra in which p is not necessarily invertible. Our definition agrees with the definition of locally analytic distributions on p-adic Lie groups given by Johansson and Newton.


An Algorithm To Determine All Odd Primitive Abundant Numbers With D Prime Divisors, Jacob Liddy 2018 The University of Akron

An Algorithm To Determine All Odd Primitive Abundant Numbers With D Prime Divisors, Jacob Liddy

Williams Honors College, Honors Research Projects

An abundant number is said to be primitive if none of its proper divisors are abundant. Dickson proved that for an arbitrary positive integer d there exists only finitely many odd primitive abundant numbers having exactly d prime divisors. In this paper we describe a fast algorithm that finds all primitive odd numbers with d unique prime divisors. We use this algorithm to find all the number of odd primitive abundant numbers with 6 unique Divisors. We use this algorithm to prove that an odd weird number must have at least 6 prime divisors.


Fuzzy And Neutrosophic Sets In Semigroups, Florentin Smarandache, Young Bae Jun, Madad Khan 2018 University of New Mexico

Fuzzy And Neutrosophic Sets In Semigroups, Florentin Smarandache, Young Bae Jun, Madad Khan

Mathematics and Statistics Faculty and Staff Publications

The first chapter, Characterizations of regular and duo semigroups based on int-soft set theory, investigates the relations among int-soft semigroup, int-soft (generalized) bi-ideal, int-soft quasi-ideal and int-soft interior ideal. Using int-soft left (right) ideal, an int-soft quasi-ideal is constructed. We show that every int-soft quasi-ideal can be represented as the soft intersection of an int-soft left ideal and an int-soft right ideal. Using int-soft quasiideal, an int-soft bi-ideal is established. Conditions for a semigroup to be regular are displayed.


Neutrosophic Logic: The Revolutionary Logic In Science And Philosophy -- Proceedings Of The National Symposium, Florentin Smarandache, Huda E. Khalid, Ahmed K. Essa 2018 University of New Mexico

Neutrosophic Logic: The Revolutionary Logic In Science And Philosophy -- Proceedings Of The National Symposium, Florentin Smarandache, Huda E. Khalid, Ahmed K. Essa

Mathematics and Statistics Faculty and Staff Publications

The first part of this book is an introduction to the activities of the National Symposium, as well as a presentation of Neutrosophic Scientific International Association (NSIA), based in New Mexico, USA, also explaining the role and scope of NSIA - Iraqi branch. The NSIA Iraqi branch presents a suggestion for the international instructions in attempting to organize NSIA's work. In the second chapter, the pivots of the Symposium are presented, including a history of neutrosophic theory and its applications, the most important books and papers in the advancement of neutrosophics, a biographical note of Prof. Florentin Smarandache in Arabic ...


Special Issue: Algebraic Structures Of Neutrosophic Triplets, Neutrosophic Duplets, Or Neutrosophic Multisets, Vol. I, Florentin Smarandache, Xiaohong Zhang, Mumtaz Ali 2018 University of New Mexico

On The Density Of The Odd Values Of The Partition Function, Samuel Judge 2018 Michigan Technological University

On The Density Of The Odd Values Of The Partition Function, Samuel Judge

Dissertations, Master's Theses and Master's Reports

The purpose of this dissertation is to introduce a new approach to the study of one of the most basic and seemingly intractable problems in partition theory, namely the conjecture that the partition function $p(n)$ is equidistributed modulo $2$. We provide a doubly-indexed, infinite family of conjectural identities in the ring of series $\Z_2[[q]]$, which relate $p(n)$ with suitable $t$-multipartition functions, and show how to, in principle, prove each such identity. We will exhibit explicit proofs for $32$ of our identities. However, the conjecture remains open in full generality. A striking consequence of these conjectural identities ...


Mod Rectangular Natural Neutrosophic Numbers, Florentin Smarandache, K. Ilanthenral, W.B. Vasantha Kandasamy 2018 University of New Mexico

Mod Rectangular Natural Neutrosophic Numbers, Florentin Smarandache, K. Ilanthenral, W.B. Vasantha Kandasamy

Mathematics and Statistics Faculty and Staff Publications

In this book authors introduce the new notion of MOD rectangular planes. The functions on them behave very differently when compared to MOD planes (square). These are different from the usual MOD planes. Algebraic structures on these MOD rectangular planes are defined and developed. However we have built only MOD interval natural neutrosophic products


The Rsa Cryptosystem, Rodrigo Iglesias 2018 The University of Akron

The Rsa Cryptosystem, Rodrigo Iglesias

Williams Honors College, Honors Research Projects

This paper intends to present an overview of the RSA cryptosystem. Cryptosystems are mathematical algorithms that disguise information so that only the people for whom the information is intended can read it. The invention of the RSA cryptosystem in 1977 was a significant event in the history of cryptosystems. We will describe in detail how the RSA cryptosystem works and then illustrate the process with a realistic example using fictional characters. In addition, we will discuss how cryptosystems worked prior to the invention of RSA and the advantage of using RSA over any of the previous cryptosystems. This will help ...


Algebraic Number Theory And Simplest Cubic Fields, Jianing Yang 2018 Colby College

Algebraic Number Theory And Simplest Cubic Fields, Jianing Yang

Honors Theses

The motivation behind this paper lies in understanding the meaning of integrality in general number fields. I present some important definitions and results in algebraic number theory, as well as theorems and their proofs on cyclic cubic fields. In particular, I discuss my understanding of Daniel Shanks' paper on the simplest cubic fields and their class numbers.


Distributive Lattice Models Of The Type C One-Rowed Weyl Group Symmetric Functions, William Atkins 2018 Murray State University

Distributive Lattice Models Of The Type C One-Rowed Weyl Group Symmetric Functions, William Atkins

Murray State Theses and Dissertations

We present two families of diamond-colored distributive lattices – one known and one new – that we can show are models of the type C one-rowed Weyl symmetric functions. These lattices are constructed using certain sequences of positive integers that are visualized as filling the boxes of one-rowed partition diagrams. We show how natural orderings of these one-rowed tableaux produce our distributive lattices as sublattices of a more general object, and how a natural coloring of the edges of the associated order diagrams yields a certain diamond-coloring property. We show that each edge-colored lattice possesses a certain structure that is associated with ...


Parametric Polynomials For Small Galois Groups, Claire Huang 2018 Colby College

Parametric Polynomials For Small Galois Groups, Claire Huang

Honors Theses

Galois theory, named after French mathematician Evariste Galois in 19th-century, is an important part of abstract algebra. It brings together many different branches of mathematics by providing connections among fields, polynomials, and groups.

Specifically, Galois theory allows us to attach a finite field extension with a finite group. We call such a group the Galois group of the finite field extension. A typical way to attain a finite field extension to compute the splitting field of some polynomial. So we can always start with a polynomial and find the finite group associate to the field extension on its splitting field ...


Neutrosophic Hough Transform, Florentin Smarandache, Umit Budak, Yanhui Guo, Abdulkadir Sengur 2017 University of New Mexico

Neutrosophic Hough Transform, Florentin Smarandache, Umit Budak, Yanhui Guo, Abdulkadir Sengur

Mathematics and Statistics Faculty and Staff Publications

Hough transform (HT) is a useful tool for both pattern recognition and image processing communities. In the view of pattern recognition, it can extract unique features for description of various shapes, such as lines, circles, ellipses, and etc. In the view of image processing, a dozen of applications can be handled with HT, such as lane detection for autonomous cars, blood cell detection in microscope images, and so on. As HT is a straight forward shape detector in a given image, its shape detection ability is low in noisy images. To alleviate its weakness on noisy images and improve its ...


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