Mathematics Commons^™

Interval Semirings, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the notion of interval semirings are introduced. The authors study and analyse semirings algebraically. Methods are given for the construction of non-associative semirings using loops and interval semirings or interval loops and semirings. Another type of non-associative semirings are introduced using groupoids and interval semirings or interval groupoids and semirings. Examples using integers and modulo integers are given. Also infinite semirings which are semifields are given using interval semigroups and semirings or semigroups and interval semirings or using groups and interval semirings. Interval groups are introduced to construct interval group interval semirings, and properties related with them …

Interval Semigroups, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book we introduce the notion of interval semigroups using intervals of the form [0, a], a is real. Several types of interval semigroups like fuzzy interval semigroups, interval symmetric semigroups, special symmetric interval semigroups, interval matrix semigroups and interval polynomial semigroups are defined and discussed. This book has eight chapters. The main feature of this book is that we suggest 241 problems in the eighth chapter. In this book the authors have defined 29 new concepts and illustrates them with 231 examples. Certainly this will find several applications. The authors deeply acknowledge Dr. Kandasamy for the proof reading …

Dsm Super Vector Space Of Refined Labels, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of supermatrices of refined labels. Authors prove super row matrix of refined labels form a group under addition. However super row matrix of refined labels do not form a group under product; it only forms a semigroup under multiplication. In this book super column matrix of refined labels and m × n matrix of refined labels are introduced and studied. We mainly study this to introduce to super vector space of refined labels using matrices. We in this book introduce the notion of semifield of refined labels using which …

Problems With And Without … Problems!, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This book is addressed to College honor students, researchers, and professors. It contains 136 original problems published by the author in various scientific journals around the world. The problems could be used to preparing for courses, exams, and Olympiads in mathematics. Many of these have a generalized form. For each problem we provide a detailed solution.

I was a professeur coopérant between 1982-1984, teaching mathematics in French language at Lycée Sidi EL Hassan Lyoussi in Sefrou, Province de Fès, Morocco. I used many of these problems for selecting and training, together with other Moroccan professors, in Rabat city, of the …

Modeling Hourly Electricity Prices: A Structural Time Series Approach Incorporating Modified Garch Innovations, Edirisinghe Mudiyanselage Asitha Edirisinghe

Doctoral Dissertations

"The main objective of this research is to develop time series based procedures for modeling day-ahead and real-time hourly electricity prices. Such empirical processes exhibit features that make the direct application of standard time series models infeasible. Four years of hourly day-ahead and real-time electricity price data from the region supplied by the American Electric Power (AEP) company through the PJM Regional Transmission Organization (RTO) and one half years of real-time electricity prices from the MISO RTO are utilized as an empirical basis for developing such procedures. The price data show several features, such as irregular seasonal behavior, weekly and …

The Weil Pairing On Elliptic Curves And Its Cryptographic Applications, Alex Edward Aftuck

UNF Graduate Theses and Dissertations

This thesis presents the Weil pairing on elliptic curves as a tool to implement a tripartite Diffie-Helman key exchange. Elliptic curves are introduced, as well as the addition operation that creates a group structure on its points. In leading to the definition of the Weil pairing, divisors of rational functions are studied, as well as the Weierstrass }-function, which shows the complex lattice as isomorphic to elliptic curves. Several important qualities of the Weil pairing are proved, and Miller's algorithm for quick calculation is shown. Next, the bipartite Diffie-Helman key exchange is discussed over finite fields and elliptic curves. Finally …

Understanding Streaming In Dictyostelium Discoideum: Theory Versus Experiments, J. C. Dallon, Brittany Dalton, Chelsea Malani

Faculty Publications

Recent experimental work involving Dictyostelium discoideum seems to contradict several theoretical models. Experiments suggest that localization of the release of the chemoattractant cyclic adenosine monophosphate to the uropod of the cell is important for stream formation during aggregation. Yet several mathematical models are able to reproduce streaming as the cells aggregate without taking into account localization of the chemoattractant. A careful analysis of the experiments and the theory suggests the two major features of the system which are important to stream formation are random cell motion and chemotaxis to regions of higher cell density. Random cell motion acts to reduce …

Quaternionic Hermitian Spinor Systems And Compatibility Conditions, Alberto Damiano, David Eelbode, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we show that the systems introduced in [12] and [22] are equivalent, both giving the notion of quaternionic Hermitian monogenic functions. This makes it possible to prove that the free resolution associated to the system is linear in any dimension, and that the first cohomology module is nontrivial, thus generalizing the results in [22]. Furthermore, exploiting the decomposition of the spinor space into sp(m)-irreducibles, we find a certain number of "algebraic" compatibility conditions for the system, suggesting that the usual spinor reduction is not applicable.

A Class Of Gaussian Processes With Fractional Spectral Measures, Daniel Alpay, Palle Jorgensen, David Levanony

Mathematics, Physics, and Computer Science Faculty Articles and Research

We study a family of stationary increment Gaussian processes, indexed by time. These processes are determined by certain measures σ (generalized spectral measures), and our focus here is on the case when the measure σ is a singular measure. We characterize the processes arising from when σ is in one of the classes of affine self-similar measures. Our analysis makes use of Kondratiev-white noise spaces. With the use of a priori estimates and the Wick calculus, we extend and sharpen (see Theorem 7.1) earlier computations of Ito stochastic integration developed for the special case of stationary increment processes having absolutely …

The Positive Real Lemma And Construction Of All Realizations Of Generalized Positive Rational Functions, Daniel Alpay, Izchak Lewkowicz

Mathematics, Physics, and Computer Science Faculty Articles and Research

We here extend the well known Positive Real Lemma (also known as the Kalman-Yakubovich-Popov Lemma) to complex matrix-valued generalized positive rational function, when non-minimal realizations are considered. All state space realizations are partitioned into subsets, each is identified with a set of matrices satisfying the same Lyapunov inclusion. Thus, each subset forms a convex invertible cone, cic in short, and is in fact is replica of all realizations of positive functions of the same dimensions. We then exploit this result to provide an easy construction procedure of all (not necessarily minimal) state space realizations of generalized positive functions. As a …

Study On Algebras With Retractions And Planes Over A Dvr., Prosenjit Das Dr.

Doctoral Theses

Aim:The main aim of this thesis is to study the following problems:1. For a Noetherian ring R, to find a set of minimal sufficient fibre conditions for an R-algebra with a retraction to R to be an A1-fibration over R.2. To investigate sufficient conditions for a factorial A1-form, with a retraction to the base ring, to be A1.3. To investigate whether planes of the form b(X, Y)Zn – a(X, Y) are co- ordinate planes in the polynomial ring in three variables X, Y and Z over a discrete valuation ring.The 1st problem will be discussed in Chapter 3 entitled Codimension- …

A Note On Solid Coloring Of Pure Simplicial Complexes, Joseph O'Rourke

Computer Science: Faculty Publications

We establish a simple generalization of a known result in the plane. The simplices in any pure simplicial complex in R^d may be colored with d+1 colors so that no two simplices that share a (d-1)-facet have the same color. In R² this says that any planar map all of whose faces are triangles may be 3-colored, and in R³ it says that tetrahedra in a collection may be "solid 4-colored" so that no two glued face-to-face receive the same color.

Warped Product Einstein Metrics Over Spaces With Constant Scalar Curvature, Chenxu He, Peter Petersen, William Wylie

Mathematics - All Scholarship

In this paper we study warped product Einstein metrics over spaces with constant scalar curvature. We call such a manifold rigid if the universal cover of the base is Einstein or is isometric to a product of Einstein manifolds. When the base is three dimensional and the dimension of the fiber is greater than one we show that the space is always rigid. We also exhibit examples of solvable four dimensional Lie groups that can be used as the base space of non-rigid warped product Einstein metrics showing that the result is not true in dimension greater than three. We …

On A Generalized Time-Varying Seir Epidemic Model With Mixed Point And Distributed Time-Varying Delays And Combined Regular And Impulsive Vaccination Controls, Ravi P. Agarwal, Manuel De La Sen, Asier Ibeas, Santiago Alonso-Quesada

Mathematics and System Engineering Faculty Publications

This paper discusses a generalized time-varying SEIR propagation disease model subject to delays which potentially involves mixed regular and impulsive vaccination rules. The model takes also into account the natural population growing and the mortality associated to the disease, and the potential presence of disease endemic thresholds for both the infected and infectious population dynamics as well as the lost of immunity of newborns. The presence of outsider infectious is also considered. It is assumed that there is a finite number of time-varying distributed delays in the susceptible-infected coupling dynamics influencing the susceptible and infected differential equations. It is also …

Classification Of Generalized Hadamard Matrices H(6,3) And Quaternary Hermitian Self-Dual Codes Of Length 18, Masaaki Harada, Clement Lam, Akihiro Munemasa, Vladimir Tonchev

Department of Mathematical Sciences Publications

All generalized Hadamard matrices of order 18 over a group of order 3, H(6,3),are enumerated in two different ways: once, as class regular symmetric (6,3)-nets,or symmetric transversal designs on 54 points and 54 blocks with a group of order 3 acting semi-regularly on points and blocks, and secondly,as collections of fullweight vectors in quaternary Hermitian self-dual codes of length 18. The second enumeration is based on the classification of Hermitian self-dual [18,9] codes over GF(4), completed in this paper. It is shown that up to monomial equivalence, there are 85 generalized Hadamard matrices H(6,3), and 245 inequivalent Hermitian self-dual codes …

Graphs Of Bounded Degree And The P-Harmonic Boundary, Michael J. Puls

Publications and Research

Let p be a real number greater than one and let G be a connected graph of bounded degree. We introduce the p-harmonic boundary of G and use it to characterize the graphs G for which the constant functions are the only p-harmonic functions on G. We show that any continuous function on the p-harmonic boundary of G can be extended to a function that is p-harmonic on G. We also give some properties of this boundary that are preserved under rough-isometries. Now let Gamma be a finitely generated group. As an application of our results, we characterize the vanishing …

Global Dimension Of Ci: Compete Or Collaborate, Arden L. Bement Jr.

PPRI Digital Library

No abstract provided.

Information-Preserving Structures: A General Framework For Quantum Zero-Error Information, Robin Blume-Kohout, Hui Khoon Ng, David Poulin, Lorenza Viola

Dartmouth Scholarship

Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system’s ability to carry information is constrained and defined by the noise in its dynamics. This paper introduces an operational framework, using information-preserving structures, to classify all the kinds of information that can be perfectly (i.e., with zero error) preserved by quantum dynamics. We prove that every perfectly preserved code has the same structure as a matrix algebra, and that preserved information can always be corrected. We …

Some Results For Integral Inclusions Of Volterra Type In Banach Spaces, Ravi P. Agarwal, Mouffak Benchohra, Juan Jose Nieto, Abdelghani Ouahab

Mathematics and System Engineering Faculty Publications

We first present several existence results and compactness of solutions set for the following Volterra type integral inclusions of the form: y(t) ∈ ∫0 t a(t-s)[Ay(s)+F(s,y(s)) ]ds,a.e.t ∈ J, where J=[ 0,b ], A is the infinitesimal generator of an integral resolvent family on a separable Banach space E, and F is a set-valued map. Then the Filippov's theorem and a Filippov-Waewski result are proved.

Quantitative Stability And Optimality Conditions In Convex Semi-Infinite And Infinite Programming, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra

Mathematics Research Reports

This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensional) spaces and that are indexed by an arbitrary fixed set T. Parameter perturbations on the right-hand side of the inequalities are measurable and bounded, and thus the natural parameter space is loo(T). Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map, which involves only the system data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. On one hand, in this …