Mathematics Commons^™

On The Convergence Of The Summation Formulas Constructed By Using A Symbolic Operator Approach, Tian-Xiao He, Leetsch Hsu, Peter Shiue

Scholarship

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This paper deals with the convergence of the summation of power series of the form Σ_{a ≤ k ≤ b}f(k)x^k, where 0 ≤ a ≤ b < ∞, and {f(k)} is a given sequence of numbers with k ∈ [a, b) or f(t) a differentiable function defined on [a, b). Here, the summation is found by using the symbolic operator approach shown in [1]. We will give a different type of the remainder of the summation formulas. The convergence of the corresponding power series will be determined consequently. Several examples such as the generalized Euler's transformation series will also be given. In addition, we will compare the convergence of the given series transforms.

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Construction Of Rational Points On Elliptic Curves Over Finite Fields, Andrew Shallue, Christiaan Van De Woestijne

Scholarship

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We give a deterministic polynomial-time algorithm that computes a nontrivial rational point on an elliptic curve over a finite field, given a Weierstrass equation for the curve. For this, we reduce the problem to the task of finding a rational point on a curve of genus zero.

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Some General Notions Of Stochastic Orderings For Weighted Reliability And Uncertainty Measures With Applications, Broderick O. Oluyede

Mathematical Sciences: Faculty Publications

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In this note, stochastic comparisons of reliability measures and related functions are presented. Inequalities for uncertainty of a residual life distribution and certain modified cross-entropy or discrimination information measures under weighted models are established. Comparisons of the expected uncertainty about the remaining lifetime of a component for weighted conditional distributions and unweighted conditional distributions are presented.

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Counting Coffee Combinations: An Example Of The Fundamental Principle Of Counting, David R. Duncan, Bonnie H. Litwiller

Faculty Work

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Teachers in courses which involve probability and statistics are always looking for situations in which the Fundamental Principle of Counting (FPC) can be exemplified. We shall present an example involving a coffee vending machine at a highway rest stop.

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[Introduction To] The Cauchy Transform, William T. Ross, Joseph A. Cima, Alec L. Matheson

Bookshelf

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The Cauchy transform of a measure on the circle is a subject of both classical and current interest with a sizable literature. This book is a thorough, well-documented, and readable survey of this literature and includes full proofs of the main results of the subject. This book also covers more recent perturbation theory as covered by Clark, Poltoratski, and Aleksandrov and contains an in-depth treatment of Clark measures.

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Eigenvalue Comparisons For Boundary Value Problems Of The Discrete Beam Equation, Jun Ji, Bo Yang

Faculty Articles

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We study the behavior of all eigenvalues for boundary value problems of fourth-order difference equations Delta(4)yi = lambda a(i+2)y(i+2), - 1= b(j), 1

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The Formal Laplace-Borel Transform Of Fliess Operators And The Composition Product, Yaqin Li, W. Steven Gray

Electrical & Computer Engineering Faculty Publications

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The formal Laplace-Borel transform of an analytic integral operator, known as a Fliess operator, is defined and developed. Then, in conjunction with the composition product over formal power series, the formal Laplace-Borel transform is shown to provide an isomorphism between the semigroup of all Fliess operators under operator composition and the semigroup of all locally convergent formal power series under the composition product. Finally, the formal Laplace-Borel transform is applied in a systems theory setting to explicitly derive the relationship between the formal Laplace transform of the input and output functions of a Fliess operator. This gives a compact interpretation …

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Disintegration-Of-Measure Techniques For Commuting Multivariable Weighted Shifts, Raúl E. Curto, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

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We employ techniques from the theory of disintegration of measures to study the Lifting Problem for commuting $n$-tuples of subnormal weighted shifts. We obtain a new necessary condition for the existence of a lifting, and generate new pathology associated with bringing together the Berger measures associated to each individual weighted shift. For subnormal $2$-variable weighted shifts, we then find the precise relation between the Berger measure of the pair and the Berger measures of the shifts associated to horizontal rows and vertical columns of weights.

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The Range Of Angles In The Euler-Gergonne-Soddy Triangle, David J. Gisch

Dissertations and Theses @ UNI

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For any triangle one can construct its Euler-Gergonne-Soddy triangle (EGST). In 1996 it was shown that the EGST is always a right triangle. In this work we compute the range of the other angles of the EGST by calculating the maximum angle of the EGST at the de Longchamps point.

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Injective Modules And Prime Ideals Of Universal Enveloping Algebras, Jorg Feldvoss

University Faculty and Staff Publications

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In this paper we study injective modules over universal enveloping algebras of finite-dimensional Lie algebras over fields of arbitrary characteristic. Most of our results are dealing with fields of prime characteristic but we also elaborate on some of their analogues for solvable Lie algebras over fields of characteristic zero. It turns out that analogous results in both cases are often quite similar and resemble those familiar from commutative ring theory.

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On Doubly Periodic Solutions Of Quasilinear Hyperbolic Equations Of The Fourth Order, T. Kiguradze, T. Smith

Publications

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The problem on doubly periodic solutions is considered for a class of quasilinear hyperbolic equations. Effective sufficient conditions of solvability and unique solvability of this problem are established.

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The Ground Axiom, Jonas Reitz

Dissertations, Theses, and Capstone Projects

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A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set-forcing extension of any inner model. The Ground Axiom is first-order expressible, and any model of ZFC has a class-forcing extension which satisfies it. The Ground Axiom is independent of many well-known set-theoretic assertions including the Generalized Continuum Hypothesis, the assertion V=HOD that every set is ordinal definable, and the existence of measurable and supercompact cardinals. The related Bedrock Axiom, asserting that the universe is a set-forcing extension of a model satisfying the Ground Axiom, is also first-order expressible, and its negation is consistent. …

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Advances And Applications Of Dezert-Smarandache Theory (Dsmt) For Information Fusion (Collected Works), Vol. 2, Florentin Smarandache, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

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This second volume dedicated to Dezert-Smarandache Theory (DSmT) in Information Fusion brings in new fusion quantitative rules (such as the PCR1-6, where PCR5 for two sources does the most mathematically exact redistribution of conflicting masses to the non-empty sets in the fusion literature), qualitative fusion rules, and the Belief Conditioning Rule (BCR) which is different from the classical conditioning rule used by the fusion community working with the Mathematical Theory of Evidence.

Other fusion rules are constructed based on T-norm and T-conorm (hence using fuzzy logic and fuzzy set in information fusion), or more general fusion rules based on N-norm …

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Unfolding The Labyrinth: Open Problems In Physics, Mathematics, Astrophysics, And Other Areas Of Science, Florentin Smarandache, Victor Christianto, Fu Yuhua, Radi Khrapko, John Hutchison

Branch Mathematics and Statistics Faculty and Staff Publications

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The reader will find herein a collection of unsolved problems in mathematics and the physical sciences. Theoretical and experimental domains have each been given consideration. The authors have taken a liberal approach in their selection of problems and questions, and have not shied away from what might otherwise be called speculative, in order to enhance the opportunities for scientific discovery. Progress and development in our knowledge of the structure, form and function of the Universe, in the true sense of the word, its beauty and power, and its timeless presence and mystery, before which even the greatest intellect is awed …

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Neutrosophic Rings, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

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In this book we define the new notion of neutrosophic rings. The motivation for this study is two-fold. Firstly, the classes of neutrosophic rings defined in this book are generalization of the two well-known classes of rings: group rings and semigroup rings. The study of these generalized neutrosophic rings will give more results for researchers interested in group rings and semigroup rings. Secondly, the notion of neutrosophic polynomial rings will cause a paradigm shift in the general polynomial rings. This study has to make several changes in case of neutrosophic polynomial rings. This would give solutions to polynomial equations for …

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Fuzzy Interval Matrices, Neutrosophic Interval Matrices And Their Applications, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

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The new concept of fuzzy interval matrices has been introduced in this book for the first time. The authors have not only introduced the notion of fuzzy interval matrices, interval neutrosophic matrices and fuzzy neutrosophic interval matrices but have also demonstrated some of its applications when the data under study is an unsupervised one and when several experts analyze the problem. Further, the authors have introduced in this book multiexpert models using these three new types of interval matrices. The new multi expert models dealt in this book are FCIMs, FRIMs, FCInMs, FRInMs, IBAMs, IBBAMs, nIBAMs, FAIMs, FAnIMS, etc. Illustrative …

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Some Neutrosophic Algebraic Structures And Neutrosophic N-Algebraic Structures, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

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In this book, for the first time we introduce the notion of neutrosophic algebraic structures for groups, loops, semigroups and groupoids and also their neutrosophic N-algebraic structures. One is fully aware of the fact that many classical theorems like Lagrange, Sylow and Cauchy have been studied only in the context of finite groups. Here we try to shift the paradigm by studying and introducing these theorems to neutrosophic semigroups, neutrosophic groupoids, and neutrosophic loops. We have intentionally not given several theorems for semigroups and groupoid but have given several results with proof mainly in the case of neutrosophic loops, biloops …

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Introduction To N-Adaptive Fuzzy Models To Analyze Public Opinion On Aids, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

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“AIDS is not simply a physical malady, it is also an artifact of social and sexual transgression, violated taboo, fractured identity—political and personal projections. Its key words are primarily the property of the powerful. AIDS: Keywords – is my attempt to identify and contest some of the assumptions underlying our current ‘knowledge’. In this effort I am joined by many AIDS activists including people living with AIDS— Acquired Immuno Deficiency Syndrome. “A syndrome is a pattern of symptoms pointing to a “morbid state” which may or may not be caused by infectious agents; a disease, on the other hand is, …

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Computational Modeling In Applied Problems: Collected Papers On Econometrics, Operations Research, Game Theory And Simulation, Florentin Smarandache, Sukanto Bhattacharya, Mohammad Khoshnevisan

Branch Mathematics and Statistics Faculty and Staff Publications

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Computational models pervade all branches of the exact sciences and have in recent times also started to prove to be of immense utility in some of the traditionally 'soft' sciences like ecology, sociology and politics. This volume is a collection of a few cuttingedge research papers on the application of variety of computational models and tools in the analysis, interpretation and solution of vexing real-world problems and issues in economics, management, ecology and global politics by some prolific researchers in the field.

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Sequences Of Numbers Involved In Unsolved Problems, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

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Here it is a long list of sequences, functions, unsolved problems, conjectures, theorems, relationships, operations, etc. Some of them are inter-connected. 1) Consecutive Sequence: 1,12,123,1234,12345,123456,1234567,12345678,123456789,12345678910, 1234567891011,123456789101112,12345678910111213,... How many primes are there among these numbers? In a general form, the Consecutive Sequence is considered in an arbitrary numeration base B.

References:

Student Conference, University of Craiova, Department of Mathematics, April 1979, "Some problems in number theory" by Florentin Smarandache.

Arizona State University, Hayden Library, "The Florentin Smarandache papers" special collection, Tempe, AZ 85287-1006, USA.

The Encyclopedia of Integer Sequences", by N. J. A. Sloane and S. Plouffe, Academic Press, San Diego, …

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The Kronecker Product, Bobbi Jo Broxson

UNF Graduate Theses and Dissertations

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This paper presents a detailed discussion of the Kronecker product of matrices. It begins with the definition and some basic properties of the Kronecker product. Statements will be proven that reveal information concerning the eigenvalues, singular values, rank, trace, and determinant of the Kronecker product of two matrices. The Kronecker product will then be employed to solve linear matrix equations. An investigation of the commutativity of the Kronecker product will be carried out using permutation matrices. The Jordan - Canonical form of a Kronecker product will be examined. Variations such as the Kronecker sum and generalized Kronecker product will be …

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Interdependency Of Pharmacokinetic Parameters: A Chicken-And-Egg Problem? Not!, Reza Mehvar

Pharmacy Faculty Articles and Research

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Pharmacokinetic (PK) software packages are widely used by scientists in different disciplines to estimate PK parameters. However, their use without a clear understanding of physiological parameters affecting the PK parameters and how different PK parameters are related to each other may result in erroneous interpretation of data. Often, mathematical relationships used for the estimation of PK parameters obscure the true physiological relationships among these parameters, prompting a discussion of which parameter came first and giving the appearance of the-chicken-and-the-egg dilemma. In this article, the author attempts to show how different PK parameters are related to physiological parameters and each other …

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Mathematically Modeling The Effects Of Counting Factor (Cf) In Dictyostelium Discoideum, J. C. Dallon, W. Jang, R. H. Gomer

Faculty Publications

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Size regulation is a crucial feature in many biological systems, with misregulation leading to dysplasia or hyperplasia. The recent discovery of counting factor (CF) in Dictyostelium discoideum will lead to a greater understanding of how the system regulates the size of a group of cells. In this paper we mathematically model the known effects of CF using two different models: a cellular automata model and a discrete continuum hybrid model. With the use of these models we are able to understand how modulation of adhesion and motile forces by CF can facilitate stream breakup. In addition, the modelling suggests a …

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