Mathematics Commons^™

A Novel Algorithm To Forecast Enrollment Based On Fuzzy Time Series, Haneen T. Jasim, Abdul G. Jasim Salim, Kais I. Ibraheem

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we propose a new method to forecast enrollments based on fuzzy time series. The proposed method belongs to the first order and time-variant methods. Historical enrollments of the University of Alabama from year 1948 to 2009 are used in this study to illustrate the forecasting process. By comparing the proposed method with other methods we will show that the proposed method has a higher accuracy rate for forecasting enrollments than the existing methods.

Computable Linear Orders And Turing Reductions, Whitney P. Turner

Master's Theses

This thesis explores computable linear orders through Turing Reductions and codes zero jump and zero double jump into linear orders using discrete, dense, and block linear relations.

From Velocities To Fluxions, Marco Panza

MPP Published Research

"Though the De Methodis results, for its essential structure and content, from a re-elaboration of a previous unfinished treatise composed in the Fall of 1666—now known, after Whiteside, as The October 1666 tract on fluxions ([22], I, pp. 400-448)—, the introduction of the term ‘fluxion’ goes together with an important conceptual change concerned with Newton’s understanding of his own achievements. I shall argue that this change marks a crucial step in the origins of analysis, conceived as an autonomous mathematical theory."

Prove It!, Kenny W. Moran

Journal of Humanistic Mathematics

A dialogue between a mathematics professor, Frank, and his daughter, Sarah, a mathematical savant with a powerful mathematical intuition. Sarah's intuition allows her to stumble into some famous theorems from number theory, but her lack of academic mathematical background makes it difficult for her to understand Frank's insistence on the value of proof and formality.

On The Logic Of Reverse Mathematics, Alaeddine Saadaoui

Theses, Dissertations and Capstones

The goal of reverse mathematics is to study the implication and non-implication relationships between theorems. These relationships have their own internal logic, allowing some implications and non-implications to be derived directly from others. The goal of this thesis is to characterize this logic in order to capture the relationships between specific mathematical works. The results of our study are a finite set of rules for this logic and the corresponding soundness and completeness theorems. We also compare our logic with modal logic and strict implication logic. In addition, we explain two applications of S-logic in topology and second order arithmetic.

Completeness For The Coalgebraic Cover Modality, Clemens Kupke, Alexander Kurz, Yde Venema

Engineering Faculty Articles and Research

We study the finitary version of the coalgebraic logic introduced by L. Moss. The syntax of this logic, which is introduced uniformly with respect to a coalgebraic type functor, required to preserve weak pullbacks, extends that of classical propositional logic with a so-called coalgebraic cover modality depending on the type functor. Its semantics is defined in terms of a categorically defined relation lifting operation.

As the main contributions of our paper we introduce a derivation system, and prove that it provides a sound and complete axiomatization for the collection of coalgebraically valid inequalities. Our soundness and completeness proof is algebraic, …

Strongly Complete Logics For Coalgebras, Alexander Kurz, Jiří Rosický

Engineering Faculty Articles and Research

Coalgebras for a functor model different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary logics for set-based coalgebras. In particular, a general construction of a logic from an arbitrary set-functor is given and proven to be strongly complete under additional assumptions. We proceed in three parts.

Part I argues that sifted colimit preserving functors are those functors that preserve universal algebraic structure. Our main theorem here states that a functor preserves sifted colimits if and only if it has a finitary presentation by operations and equations. Moreover, the presentation of the …

Coalgebraic Logics (Dagstuhl Seminar 12411), Ernst-Erich Doberkat, Alexander Kurz

Engineering Faculty Articles and Research

This report documents the program and the outcomes of Dagstuhl Seminar 12411 “Coalgebraic Logics”. The seminar deals with recent developments in the area of coalgebraic logic, a branch of logics which combines modal logics with coalgebraic semantics. Modal logic finds its uses when reasoning about behavioural and temporal properties of computation and communication, coalgebras have evolved into a general theory of systems. Consequently, it is natural to combine both areas for a mathematical description of system specification. Coalgebraic logics are closely related to the broader categories semantics/formal methods and verification/logic.

Neutrosophic Super Matrices And Quasi Super Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors study neutrosophic super matrices. The concept of neutrosophy or indeterminacy happens to be one the powerful tools used in applications like FCMs and NCMs where the expert seeks for a neutral solution. Thus this concept has lots of applications in fuzzy neutrosophic models like NRE, NAM etc. These concepts will also find applications in image processing where the expert seeks for a neutral solution. Here we introduce neutrosophic super matrices and show that the sum or product of two neutrosophic matrices is not in general a neutrosophic super matrix. Another interesting feature of this book is …

Semigroup As Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors study the zero divisor graph and unit graph of a semigroup. The zero divisor graphs of semigroups Zn under multiplication is studied and characterized.

Non Associative Algebraic Structures Using Finite Complex Numbers, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Authors in this book for the first time have constructed nonassociative structures like groupoids, quasi loops, non associative semirings and rings using finite complex modulo integers. The Smarandache analogue is also carried out. We see the nonassociative complex modulo integers groupoids satisfy several special identities like Moufang identity, Bol identity, right alternative and left alternative identities. P-complex modulo integer groupoids and idempotent complex modulo integer groupoids are introduced and characterized. This book has six chapters. The first one is introductory in nature. Second chapter introduces complex modulo integer groupoids and complex modulo integer loops.

Quasi Set Topological Vector Subspaces, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors introduce four types of topological vector subspaces. All topological vector subspaces are defined depending on a set. We define a quasi set topological vector subspace of a vector space depending on the subset S contained in the field F over which the vector space V is defined. These quasi set topological vector subspaces defined over a subset can be of finite or infinite dimension. An interesting feature about these spaces is that there can be several quasi set topological vector subspaces of a given vector space. This property helps one to construct several spaces with …

The Geometry Of Homological Triangles, Florentin Smarandache, Ion Patrascu

Branch Mathematics and Statistics Faculty and Staff Publications

This book is addressed to students, professors and researchers of geometry, who will find herein many interesting and original results. The originality of the book The Geometry of Homological Triangles consists in using the homology of triangles as a “filter” through which remarkable notions and theorems from the geometry of the triangle are unitarily passed. Our research is structured in seven chapters, the first four are dedicated to the homology of the triangles while the last ones to their applications. In the first chapter one proves the theorem of homological triangles (Desargues, 1636), one survey the remarkable pairs of homological …

Applications Of Extenics To 2d-Space And 3d-Space, Florentin Smarandache, Victor Vladareanu

Branch Mathematics and Statistics Faculty and Staff Publications

In this article one proposes several numerical examples for applying the extension set to 2D- and 3D-spaces. While rectangular and prism geometrical figures can easily be decomposed from 2D and 3D into 1D linear problems, similarly for the circle and the sphere, it is not possible in general to do the same for other geometrical figures.

Cardinal Functions And Integral Functions, Florentin Smarandache, Mircea Selariu, Marian Nitu

Branch Mathematics and Statistics Faculty and Staff Publications

This paper presents the correspondences of the eccentric mathematics of cardinal and integral functions and centric mathematics, or ordinary mathematics. Centric functions will also be presented in the introductory section, because they are, although widely used in undulatory physics, little known. In centric mathematics, cardinal sine and cosine are dened as well as the integrals. Both circular and hyperbolic ones. In eccentric mathematics, all these central functions multiplies from one to innity, due to the innity of possible choices where to place a point. This point is called eccenter S(s;") which lies in the plane of unit circle UC(O;R = …

Neutrosophic Masses & Indeterminate Models Applications To Information Fusion, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we introduce the indeterminate models in information fusion, which are due either to the existence of some indeterminate elements in the fusion space or to some indeterminate masses. The best approach for dealing with such models is the neutrosophic logic.

Special Dual Like Numbers And Lattices, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors introduce a new type of dual numbers called special dual like numbers. These numbers are constructed using idempotents in the place of nilpotents of order two as new element. That is x = a + bg is a special dual like number where a and b are reals and g is a new element such that g2 =g. The collection of special dual like numbers forms a ring. Further lattices are the rich structures which contributes to special dual like numbers. These special dual like numbers x = a + bg; when a and b …

Fuzzy Linguistic Topological Spaces, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Amal

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Set Ideal Topological Spaces, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors for the first time introduce a new type of topological spaces called the set ideal topological spaces using rings or semigroups, or used in the mutually exclusive sense. This type of topological spaces use the class of set ideals of a ring (semigroups). The rings or semigroups can be finite or infinite order. By this method we get complex modulo finite integer set ideal topological spaces using finite complex modulo integer rings or finite complex modulo integer semigroups. Also authors construct neutrosophic set ideal toplogical spaces of both finite and infinite order as well as …

Verifying Harder's Conjecture For Classical And Siegel Modular Forms, Davia Sulon

Honors Theses

A conjecture by Harder shows a surprising congruence between the coefficients of “classical” modular forms and the Hecke eigenvalues of corresponding Siegel modular forms, contigent upon “large primes” dividing the critical values of the given classical modular form.

Harder’s Conjecture has already been verified for one-dimensional spaces of classical and Siegel modular forms (along with some two-dimensional cases), and for primes p 37. We verify the conjecture for higher-dimensional spaces, and up to a comparable prime p.

Lagrange's Theory Of Analytical Functions And His Ideal Of Purity Of Method, Giovanni Ferraro, Marco Panza

MPP Published Research

We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, for Lagrange, concern the solidity of its ultimate bases, but rather purity of method—the generality and internal organization of …

A New Algorithm For Solving Shortest Path Problem On A Network With Imprecise Edge Weight, Amit Kumar, Manjot Kumar

Applications and Applied Mathematics: An International Journal (AAM)

Nayeem and Pal (Shortest path problem on a network with imprecise edge weight, Fuzzy Optimization and Decision Making 4, 293-312, 2005) proposed a new algorithm for solving shortest path problem on a network with imprecise edge weight. In this paper the shortcomings of the existing algorithm, (Nayeem and Pal, 2005) are pointed out and to overcome these shortcomings a new algorithm is proposed. To show the advantages of the proposed algorithm over existing algorithm the numerical examples presented in (Nayeem and Pal, 2005) are solved using the proposed algorithm and obtained results are discussed.

Reliability Analysis Of A Series And Parallel Network Using Triangular Intuitionistic Fuzzy Sets, D. Pandey, S. K. Tyagi, Vinesh Kumar

Applications and Applied Mathematics: An International Journal (AAM)

This paper describes a novel approach, based on intuitionistic fuzzy set theory for reliability analysis of series and parallel network. The triangular intuitionistic fuzzy sets are used to represent the failure possibility of each basic (terminal) event to get more comprehensive results for the failure possibility of the top event. The proposed technique is demonstrated on a web server LOG data used to illustrate HTTP (Hyper Text Transfer Protocol) failure

Exact Optimal Solution Of Fuzzy Critical Path Problems, Amit Kumar, Parmpreet Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a fuzzy critical path problem is chosen to show that the results, obtained by using the existing method [Liu, S.T.: Fuzzy activity times in critical path and project crashing problems. Cybernetics and Systems 34 (2), 161-172 (2003)], could be improved to reflect, more appropriate real life situations. To obtain more accurate results of fuzzy critical path problems, a new method that modifies the existing one is proposed here. To demonstrate the advantages of the proposed method it is used to solve a specific fuzzy critical path problem.

Relocatable Field Programmable Gate Array Bitstreams For Fault Tolerance, David P. Montminy, Rusty O. Baldwin, Paul D. Williams

AFIT Patents

A Field Programmable Gate Array (FPGA) circuit capable of operating through at least one fault. The FPGA circuit includes a configuration memory and an embedded microprocessor. The embedded microprocessor having access to the configuration memory, static modules, at least one relocatable module, and at least one spare module. The relocatable module being relocatable from a first target area to a second target area. The relocatable module being relocatable by manipulating a partial bitstream with the embedded microprocessor. The microprocessor calculating a plurality of bitstream changes, to relocate the at least one relocatable module using at least triple modular redundancy (TMR).

Modal Logic And Its Applications, Explained Using Puzzles And Examples, Marek Perkowski

Systems Science Friday Noon Seminar Series

The talk introduces Modal Logic as an extension of classical propositional and First Order Logics. We discuss motivations of Lewis to create modal logic system, axioms and rules of proof. Several examples illustrate deriving theorems from axioms. "Muddy Children" puzzle is used to explain the principles of dealing with uncertainty problems where a temporal lack of response is used as additional information. Other examples include "Narrow Bridge" problem/game which relates to the problem of necessary evil in the world, robot planning and law and robot morality problems, especially related to military robots and use of force by police. Kripke semantics …

Statistical Properties Of A Convoluted Beta-Weibull Distribution, Jianan Sun

Theses, Dissertations and Capstones

A new class of distributions recently developed involves the logit of the beta distribution. Among this class of distributions are the beta-normal (Eugene et.al. (2002)); beta-Gumbel (Nadarajah and Kotz (2004)); beta-exponential (Nadarajah and Kotz (2006)); beta-Weibull (Famoye et al. (2005)); beta-Rayleigh (Akinsete and Lowe (2008)); beta-Laplace (Kozubowski and Nadarajah (2008)); and beta-Pareto (Akinsete et al. (2008)), among a few others. Many useful statistical properties arising from these distributions and their applications to real life data have been discussed in the literature. One approach by which a new statistical distribution is generated is by the transformation of random variables having known …

Relation Liftings On Preorders And Posets, Marta Bílková, Alexander Kurz, Daniela Petrişan, Jiří Velebil

Engineering Faculty Articles and Research

The category Rel(Set) of sets and relations can be described as a category of spans and as the Kleisli category for the powerset monad. A set-functor can be lifted to a functor on Rel(Set) iff it preserves weak pullbacks. We show that these results extend to the enriched setting, if we replace sets by posets or preorders. Preservation of weak pullbacks becomes preservation of exact lax squares. As an application we present Moss’s coalgebraic over posets.

Generic Trace Logics, Christian Kissig, Alexander Kurz

Engineering Faculty Articles and Research

We combine previous work on coalgebraic logic with the coalgebraic traces semantics of Hasuo, Jacobs, and Sokolova.

Towards Nominal Formal Languages, Alexander Kurz, Tomoyuki Suzuki, Emilio Tuosto

Engineering Faculty Articles and Research

We introduce formal languages over infinite alphabets where words may contain binders.We define the notions of nominal language, nominal monoid, and nominal regular expressions. Moreover, we extend history-dependent automata (HD-automata) by adding stack, and study the recognisability of nominal languages.