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Articles 1 - 11 of 11
Full-Text Articles in Number Theory
The Evolution Of Cryptology, Gwendolyn Rae Souza
The Evolution Of Cryptology, Gwendolyn Rae Souza
Electronic Theses, Projects, and Dissertations
We live in an age when our most private information is becoming exceedingly difficult to keep private. Cryptology allows for the creation of encryptive barriers that protect this information. Though the information is protected, it is not entirely inaccessible. A recipient may be able to access the information by decoding the message. This possible threat has encouraged cryptologists to evolve and complicate their encrypting methods so that future information can remain safe and become more difficult to decode. There are various methods of encryption that demonstrate how cryptology continues to evolve through time. These methods revolve around different areas of …
Drawing Numbers And Listening To Patterns, Loren Zo Haynes
Drawing Numbers And Listening To Patterns, Loren Zo Haynes
Honors College Theses
The triangular numbers is a series of number that add the natural numbers. Parabolic shapes emerge when this series is placed on a lattice, or imposed with a limited number of columns that causes the sequence to continue on the next row when it has reached the kth column. We examine these patterns and construct proofs that explain their behavior. We build off of this to see what happens to the patterns when there is not a limited number of columns, and we formulate the graphs as musical patterns on a staff, using each column as a line or space …
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 …
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 …
Luhn Primes Of Order Ω, Florentin Smarandache, Octavian Cira
Luhn Primes Of Order Ω, Florentin Smarandache, Octavian Cira
Branch Mathematics and Statistics Faculty and Staff Publications
A prime p, that added to its reverse results in a new prime is called a Luhn prime . The number 229 is a Luhn prime because 229 + 922 = 1151 and 1151 is also a prime . We extend the definition of Luhn primes, present some of the of their properties and ways to determine them .
Interval-Valued Neutrosophic Oversets, Neutrosophic Undersets, And Neutrosophic Offsets, Florentin Smarandache
Interval-Valued Neutrosophic Oversets, Neutrosophic Undersets, And Neutrosophic Offsets, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
We have proposed since 1995 the existence of degrees of membership of an element with respect to a neutrosophic set to also be partially or totally above 1 (over-membership), and partially or totally below 0 (under-membership) in order to better describe our world problems [published in 2007].
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 …
Applying Dijkstra Algorithm For Solving Neutrosophic Shortest Path Problem, Florentin Smarandache, Luige Vladareanu, Said Broumi, Assia Bakali, Muhammad Akram
Applying Dijkstra Algorithm For Solving Neutrosophic Shortest Path Problem, Florentin Smarandache, Luige Vladareanu, Said Broumi, Assia Bakali, Muhammad Akram
Branch Mathematics and Statistics Faculty and Staff Publications
The selection of shortest path problem is one the classic problems in graph theory. In literature, many algorithms have been developed to provide a solution for shortest path problem in a network. One of common algorithms in solving shortest path problem is Dijkstra’s algorithm. In this paper, Dijkstra’s algorithm has been redesigned to handle the case in which most of parameters of a network are uncertain and given in terms of neutrosophic numbers. Finally, a numerical example is given to explain the proposed algorithm.
Single Valued Neutrosophic Graphs: Degree, Order And Size, Florentin Smarandache, Said Broumi, Mohamed Talea, Assia Bakali
Single Valued Neutrosophic Graphs: Degree, Order And Size, Florentin Smarandache, Said Broumi, Mohamed Talea, Assia Bakali
Branch Mathematics and Statistics Faculty and Staff Publications
The single valued neutrosophic graph is a new version of graph theory presented recently as a generalization of fuzzy graph and intuitionistic fuzzy graph. The single valued neutrosophic graph (SVN-graph) is used when the relation between nodes (or vertices) in problems are indeterminate. In this paper, we examine the properties of various types of degrees, order and size of single valued neutrosophic graphs and a new definition for regular single valued neutrosophic graph is given.