Open Access. Powered by Scholars. Published by Universities.®
- Institution
-
- University of New Mexico (58)
- California State University, San Bernardino (8)
- Rose-Hulman Institute of Technology (7)
- Bard College (6)
- Prairie View A&M University (6)
-
- City University of New York (CUNY) (5)
- University of Kentucky (5)
- University of Tennessee, Knoxville (5)
- Claremont Colleges (4)
- Western University (4)
- Clemson University (3)
- Colby College (3)
- Liberty University (2)
- Olivet Nazarene University (2)
- SelectedWorks (2)
- Arkansas Tech University (1)
- Augustana College (1)
- Boise State University (1)
- Cedarville University (1)
- East Tennessee State University (1)
- Georgia Southern University (1)
- Gettysburg College (1)
- Jacksonville State University (1)
- Lawrence University (1)
- Louisiana State University (1)
- Michigan Technological University (1)
- Missouri State University (1)
- Montclair State University (1)
- Murray State University (1)
- Old Dominion University (1)
- Keyword
-
- Neutrosophic logic (26)
- Number theory (16)
- Algebra (9)
- Mathematics (9)
- Algebraic structures (6)
-
- Problems (6)
- Mathematical problems (5)
- Number Theory (5)
- Combinatorics (4)
- Factorization (4)
- Geometry (4)
- Group Theory (4)
- Modular arithmetic (4)
- Abstract Algebra (3)
- Abstract algebra (3)
- Algebraic number theory (3)
- Cryptography (3)
- Elliptic curves (3)
- Finite fields (3)
- Galois Theory (3)
- Group theory (3)
- P-adic fields (3)
- Polynomials (3)
- Trigonometry (3)
- Algebraic Number Theory (2)
- Analysis (2)
- Elementary Type Conjecture (2)
- Elliptic Curves (2)
- Factoring (2)
- Finite field (2)
- Publication Year
- Publication
-
- Branch Mathematics and Statistics Faculty and Staff Publications (58)
- Electronic Theses, Projects, and Dissertations (7)
- Rose-Hulman Undergraduate Mathematics Journal (7)
- Applications and Applied Mathematics: An International Journal (AAM) (6)
- Doctoral Dissertations (5)
-
- Theses and Dissertations--Mathematics (5)
- Electronic Thesis and Dissertation Repository (4)
- Honors Theses (4)
- Dissertations, Theses, and Capstone Projects (3)
- Electronic Theses and Dissertations (3)
- All Theses (2)
- CMC Senior Theses (2)
- Senior Honors Theses (2)
- Senior Projects Spring 2019 (2)
- ATU Research Symposium (1)
- All Dissertations (1)
- All Graduate Plan B and other Reports, Spring 1920 to Spring 2023 (1)
- All HMC Faculty Publications and Research (1)
- Celebration of Learning (1)
- Channels: Where Disciplines Meet (1)
- Cybersecurity Undergraduate Research Showcase (1)
- Department of Mathematics Facuty Scholarship and Creative Works (1)
- Dissertations (1)
- Dissertations, Master's Theses and Master's Reports (1)
- Frederick F Harrop (1)
- Graduate Student Publications and Research (1)
- HMC Senior Theses (1)
- Honors Program Projects (1)
- Honors Scholar Theses (1)
- Idaho Conference on Undergraduate Research (1)
- Publication Type
- File Type
Articles 61 - 90 of 147
Full-Text Articles in Number Theory
Algebraic Number Theory And Simplest Cubic Fields, Jianing Yang
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.
Mod Rectangular Natural Neutrosophic Numbers, Florentin Smarandache, K. Ilanthenral, W.B. Vasantha Kandasamy
Mod Rectangular Natural Neutrosophic Numbers, Florentin Smarandache, K. Ilanthenral, W.B. Vasantha Kandasamy
Branch 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
Neutrosophic Logic: The Revolutionary Logic In Science And Philosophy -- Proceedings Of The National Symposium, Florentin Smarandache, Huda E. Khalid, Ahmed K. Essa
Neutrosophic Logic: The Revolutionary Logic In Science And Philosophy -- Proceedings Of The National Symposium, Florentin Smarandache, Huda E. Khalid, Ahmed K. Essa
Branch 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 …
On The Density Of The Odd Values Of The Partition Function, Samuel Judge
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 is that, under suitable …
Neutrosophic Commutative N-Ideals In Bck-Algebras, Florentin Smarandache, Seok-Zun Song, Young Bae Jun
Neutrosophic Commutative N-Ideals In Bck-Algebras, Florentin Smarandache, Seok-Zun Song, Young Bae Jun
Branch Mathematics and Statistics Faculty and Staff Publications
The notion of a neutrosophic commutative N -ideal in BCK-algebras is introduced, and several properties are investigated. Relations between a neutrosophic N -ideal and a neutrosophic commutative N -ideal are discussed. Characterizations of a neutrosophic commutative N -ideal are considered.
On A Frobenius Problem For Polynomials, Ricardo Conceição, R. Gondim, M. Rodriguez
On A Frobenius Problem For Polynomials, Ricardo Conceição, R. Gondim, M. Rodriguez
Math Faculty Publications
We extend the famous diophantine Frobenius problem to a ring of polynomials over a field~k. Similar to the classical problem we show that the n = 2 case of the Frobenius problem for polynomials is easy to solve. In addition, we translate a few results from the Frobenius problem over ℤ to k[t] and give an algorithm to solve the Frobenius problem for polynomials over a field k of sufficiently large size.
Efficiently Representing The Integer Factorization Problem Using Binary Decision Diagrams, David Skidmore
Efficiently Representing The Integer Factorization Problem Using Binary Decision Diagrams, David Skidmore
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Let p be a prime positive integer and let α be a positive integer greater than 1. A method is given to reduce the problem of finding a nontrivial factorization of α to the problem of finding a solution to a system of modulo p polynomial congruences where each variable in the system is constrained to the set {0,...,p − 1}. In the case that p = 2 it is shown that each polynomial in the system can be represented by an ordered binary decision diagram with size less than 20.25log2(α)3 + 16.5log2(α)2 + …
On Circulant-Like Rhotrices Over Finite Fields, P. L. Sharma, Shalini Gupta, Mansi Rehan
On Circulant-Like Rhotrices Over Finite Fields, P. L. Sharma, Shalini Gupta, Mansi Rehan
Applications and Applied Mathematics: An International Journal (AAM)
Circulant matrices over finite fields are widely used in cryptographic hash functions, Lattice based cryptographic functions and Advanced Encryption Standard (AES). Maximum distance separable codes over finite field GF2 have vital a role for error control in both digital communication and storage systems whereas maximum distance separable matrices over finite field GF2 are used in block ciphers due to their properties of diffusion. Rhotrices are represented in the form of coupled matrices. In the present paper, we discuss the circulant- like rhotrices and then construct the maximum distance separable rhotrices over finite fields.
On P-Adic Fields And P-Groups, Luis A. Sordo Vieira
On P-Adic Fields And P-Groups, Luis A. Sordo Vieira
Theses and Dissertations--Mathematics
The dissertation is divided into two parts. The first part mainly treats a conjecture of Emil Artin from the 1930s. Namely, if f = a_1x_1^d + a_2x_2^d +...+ a_{d^2+1}x^d where the coefficients a_i lie in a finite unramified extension of a rational p-adic field, where p is an odd prime, then f is isotropic. We also deal with systems of quadratic forms over finite fields and study the isotropicity of the system relative to the number of variables. We also study a variant of the classical Davenport constant of finite abelian groups and relate it to the isotropicity of diagonal …
Mathematics Education From A Mathematicians Point Of View, Nan Woodson Simpson
Mathematics Education From A Mathematicians Point Of View, Nan Woodson Simpson
Masters Theses
This study has been written to illustrate the development from early mathematical learning (grades 3-8) to secondary education regarding the Fundamental Theorem of Arithmetic and the Fundamental Theorem of Algebra. It investigates the progression of the mathematics presented to the students by the current curriculum adopted by the Rhea County School System and the mathematics academic standards set forth by the State of Tennessee.
P-Adic L-Functions And The Geometry Of Hida Families, Joseph Kramer-Miller
P-Adic L-Functions And The Geometry Of Hida Families, Joseph Kramer-Miller
Dissertations, Theses, and Capstone Projects
A major theme in the theory of $p$-adic deformations of automorphic forms is how $p$-adic $L$-functions over eigenvarieties relate to the geometry of these eigenvarieties. In this talk we explain results in this vein for the ordinary part of the eigencurve (i.e. Hida families). We address how Taylor expansions of one variable $p$-adic $L$-functions varying over families can detect geometric phenomena: crossing components of a certain intersection multiplicity and ramification over the weight space. Our methods involve proving a converse to a result of Vatsal relating congruences between eigenforms to their algebraic special $L$-values and then $p$-adically interpolating congruences using …
Mckay Graphs And Modular Representation Theory, Polina Aleksandrovna Vulakh
Mckay Graphs And Modular Representation Theory, Polina Aleksandrovna Vulakh
Senior Projects Spring 2016
Ordinary representation theory has been widely researched to the extent that there is a well-understood method for constructing the ordinary irreducible characters of a finite group. In parallel, John McKay showed how to associate to a finite group a graph constructed from the group's irreducible representations. In this project, we prove a structure theorem for the McKay graphs of products of groups as well as develop formulas for the graphs of two infinite families of groups. We then study the modular representations of these families and give conjectures for a modular version of the McKay graphs.
Kronecker's Theory Of Binary Bilinear Forms With Applications To Representations Of Integers As Sums Of Three Squares, Jonathan A. Constable
Kronecker's Theory Of Binary Bilinear Forms With Applications To Representations Of Integers As Sums Of Three Squares, Jonathan A. Constable
Theses and Dissertations--Mathematics
In 1883 Leopold Kronecker published a paper containing “a few explanatory remarks” to an earlier paper of his from 1866. His work loosely connected the theory of integral binary bilinear forms to the theory of integral binary quadratic forms. In this dissertation we discover the statements within Kronecker's paper and offer detailed arithmetic proofs. We begin by developing the theory of binary bilinear forms and their automorphs, providing a classification of integral binary bilinear forms up to equivalence, proper equivalence and complete equivalence.
In the second chapter we introduce the class number, proper class number and complete class number as …
Special Type Of Fixed Point Pairs Using Mod Rectangular Matrix Operators, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Special Type Of Fixed Point Pairs Using Mod Rectangular Matrix Operators, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time define a special type of fixed points using MOD rectangular matrices as operators. In this case the special fixed points or limit cycles are pairs which is arrived after a finite number of iterations. Such study is both new and innovative for it can find lots of applications in mathematical modeling. Since all these Zn or I nZ or 〈Zn ∪ g〉 or 〈Zn ∪ g〉I or C(Zn) or CI(Zn) are all of finite order we are sure to arrive at a MOD fixed point pair or a MOD limit cycle pair …
Problems On Mod Structures, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Problems On Mod Structures, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time give several types of problems on MOD structures happens to be an interesting field of study as it makes the whole 4 quadrant plane into a single quadrant plane and the infinite line into a half closed open interval. So study in this direction will certainly yield several interesting results. The law of distributivity is not true. Further the MOD function in general do not obey all the laws of integration or differentiation. Likewise MOD polynomials in general do not satisfy the basic properties of polynomials like its roots etc. Thus over …
Nidus Idearum. Scilogs, I: De Neutrosophia, Florentin Smarandache
Nidus Idearum. Scilogs, I: De 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 first books of scilogs collected from my nest of ideas, one may find new and old questions and solutions, some of them already put at work, others …
Nidus Idearum. Scilogs, Ii: De Rerum Consectatione, Florentin Smarandache
Nidus Idearum. Scilogs, Ii: De Rerum Consectatione, 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 second book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, some of them already put at work, others …
Mathematics. Possible Subjects For The High School Entrance Examination And The Capacity Examination In Romania, Florentin Smarandache, Constantin Coanda, Ionuț Ivanescu
Mathematics. Possible Subjects For The High School Entrance Examination And The Capacity Examination In Romania, Florentin Smarandache, Constantin Coanda, Ionuț Ivanescu
Branch Mathematics and Statistics Faculty and Staff Publications
The present book tries to offer students and teachers knowledge evaluation tools for all the chapters from the current Romanian mathematics syllabus. In the evolution of teenagers, the phase of admission in high schools mobilizes particular efforts and emotions. The present workbook aims to be a permanent advisor in the agitated period starting with the capacity examination and leading to the admittance to high school. The tests included in this workbook have a complementary character as opposed to the many materials written with the purpose to support all those who prepare for such examinations and they refer to the entire …
Various Arithmetic Functions And Their Applications, Florentin Smarandache, Octavian Cira
Various Arithmetic Functions And Their Applications, Florentin Smarandache, Octavian Cira
Branch Mathematics and Statistics Faculty and Staff Publications
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc. on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes squares cubes factorials, almost primes, mobile periodicals, functions, tables, prime square factorial bases, generalized factorials, generalized palindromes, so on, have been extracted from the Archives of American Mathematics (University of Texas at Austin) and Arizona State University (Tempe): "The Florentin Smarandache papers" special collections, University of Craiova Library, and Arhivele Statului (Filiala Vâlcea & Filiala Dolj, România). The book is based on …
Galois 2-Extensions, Masoud Ataei Jaliseh
Galois 2-Extensions, Masoud Ataei Jaliseh
Electronic Thesis and Dissertation Repository
The inverse Galois problem is a major question in mathematics. For a given base field and a given finite group $G$, one would like to list all Galois extensions $L/F$ such that the Galois group of $L/F$ is $G$.
In this work we shall solve this problem for all fields $F$, and for group $G$ of unipotent $4 \times 4$ matrices over $\mathbb{F}_2$. We also list all $16$ $U_4 (\mathbb{F}_2)$-extensions of $\mathbb{Q}_2$. The importance of these results is that they answer the inverse Galois problem in some specific cases.
This is joint work with J\'an Min\'a\v{c} and Nguyen Duy T\^an.
Generalizations And Algebraic Structures Of The Grøstl-Based Primitives, Dmitriy Khripkov, Nicholas Lacasse, Bai Lin, Michelle Mastrianni, Liljana Babinkostova (Mentor)
Generalizations And Algebraic Structures Of The Grøstl-Based Primitives, Dmitriy Khripkov, Nicholas Lacasse, Bai Lin, Michelle Mastrianni, Liljana Babinkostova (Mentor)
Idaho Conference on Undergraduate Research
With the large scale proliferation of networked devices ranging from medical implants like pacemakers and insulin pumps, to corporate information assets, secure authentication, data integrity and confidentiality have become some of the central goals for cybersecurity. Cryptographic hash functions have many applications in information security and are commonly used to verify data authenticity. Our research focuses on the study of the properties that dictate the security of a cryptographic hash functions that use Even-Mansour type of ciphers in their underlying structure. In particular, we investigate the algebraic design requirements of the Grøstl hash function and its generalizations. Grøstl is an …
Unique Prime Factorization Of Ideals In The Ring Of Algebraic Integers Of An Imaginary Quadratic Number Field, Nolberto Rezola
Unique Prime Factorization Of Ideals In The Ring Of Algebraic Integers Of An Imaginary Quadratic Number Field, Nolberto Rezola
Electronic Theses, Projects, and Dissertations
The ring of integers is a very interesting ring, it has the amazing property that each of its elements may be expressed uniquely, up to order, as a product of prime elements. Unfortunately, not every ring possesses this property for its elements. The work of mathematicians like Kummer and Dedekind lead to the study of a special type of ring, which we now call a Dedekind domain, where even though unique prime factorization of elements may fail, the ideals of a Dedekind domain still enjoy the property of unique prime factorization into a product of prime ideals, up to order …
Commutative N-Ary Arithmetic, Aram Bingham
Commutative N-Ary Arithmetic, Aram Bingham
University of New Orleans Theses and Dissertations
Motivated by primality and integer factorization, this thesis introduces generalizations of standard binary multiplication to commutative n-ary operations based upon geometric construction and representation. This class of operations are constructed to preserve commutativity and identity so that binary multiplication is included as a special case, in order to preserve relationships with ordinary multiplicative number theory. This leads to a study of their expression in terms of elementary symmetric polynomials, and connections are made to results from the theory of polyadic (n-ary) groups. Higher order operations yield wider factorization and representation possibilities which correspond to reductions in the set of primes …
A Fundamental Unit Of O_K, Susana L. Munoz
A Fundamental Unit Of O_K, Susana L. Munoz
Electronic Theses, Projects, and Dissertations
In the classical case we make use of Pells equation to compute units in the ring OF. Consider the parallel to the classical case and the quadratic field extension that creates the ring OK. We use the generalized Pell's equation to find the units in this ring since they are solutions. Through the use of continued fractions we may further characterize this ring and compute its units.
Polynomials Occuring In Generating Function Identities For B-Ary Partitions, David Dakota Blair
Polynomials Occuring In Generating Function Identities For B-Ary Partitions, David Dakota Blair
Graduate Student Publications and Research
Let p_b(n) be the number of integer partitions of n whose parts are powers of b. For each m there is a generating function identity:
f_m(b,q)\sum_{n} p_b(n) q^n = (1-q)^m \sum_{n} p_b(b^m n q)q^n
where n ranges over all integer values. The proof of this identity appears in the doctoral thesis of the author. For more information see http://dakota.tensen.net/2015/rp/.
This dataset is a JSON object with keys m from 1 to 23 whose values are f_m(b,q).
Mod Planes: A New Dimension To Modulo Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Mod Planes: A New Dimension To Modulo Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book for the first time authors study mod planes using modulo intervals [0, m); 2 ≤ m ≤ ∞. These planes unlike the real plane have only one quadrant so the study is carried out in a compact space but infinite in dimension. We have given seven mod planes viz real mod planes (mod real plane) finite complex mod plane, neutrosophic mod plane, fuzzy mod plane, (or mod fuzzy plane), mod dual number plane, mod special dual like number plane and mod special quasi dual number plane. These mod planes unlike real plane or complex plane or neutrosophic …
Basis Criteria For N-Cycle Integer Splines, Ester Gjoni
Basis Criteria For N-Cycle Integer Splines, Ester Gjoni
Senior Projects Spring 2015
In this project we work with integer splines on graphs with positive integer edge labels. We focus on graphs that are n-cycles for some natural number n. We find an explicit condition for when a set of splines can form a module basis for n-cycle splines. In general, a set of splines forms a Z-module basis if and only if their determinant is equal to the product of the edge labels divided by the greatest common divisor of those edge labels.
Mod Functions: A New Approach To Function Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Mod Functions: A New Approach To Function Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book the notion of MOD functions are defined on MOD planes. This new concept of MOD functions behaves in a very different way. Even very simple functions like y = nx has several zeros in MOD planes where as they are nice single line graphs with only (0, 0) as the only zero. Further polynomials in MOD planes do not in general follows the usual or classical laws of differentiation or integration. Even finding roots of MOD polynomials happens to be very difficult as they do not follow the fundamental theorem of algebra, viz a nth degree polynomial …
Infinite Quaternion Pseudo Rings Using [0, N), Florentin Smarandache, W.B. Vasantha Kandasamy
Infinite Quaternion Pseudo Rings Using [0, N), Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors study the properties of finite real quaternion ring which was introduced in [2000]. Here a complete study of these finite quaternion rings are made. Also polynomial quaternion rings are defined, they happen to behave in a very different way. In the first place the fundamental theorem of algebra, “a nth degree polynomial has n and only n roots”, n is untrue in case of polynomial in polynomial quaternion rings in general. Further the very concept of derivative and integrals of these polynomials are untrue. Finally interval pseudo quaternion rings also behave in an erratic way. Not …
Natural Neutrosophic Numbers And Mod Neutrosophic Numbers, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Natural Neutrosophic Numbers And Mod Neutrosophic Numbers, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors answer the question proposed by Florentin Smarandache “Does there exist neutrosophic numbers which are such that they take values differently and behave differently from I; the indeterminate?”. We have constructed a class of natural neutrosophic numbers m 0I , m xI , m yI , m zI where m 0I × m 0I = m 0I , m xI × m xI = m xI and m yI × m yI = m yI and m yI × m xI = m 0I and m zI × m zI = m 0I . Here take m …