Physical Sciences and Mathematics Commons^™

Intersecting Circles And Their Inner Tangent Circle, Max Tran

Publications and Research

We derive the general equation for the radius of the inner tangent circle that is associated with three pairwise intersecting circles. We then look at three special cases of the equation.

Fade Statistics For A Lasercom System And The Joint Pdf Of A Gamma-Gamma Distributed Irradiance And Its Time Derivative, Frida Stromqvist Vetelino

Electronic Theses and Dissertations

The performance of lasercom systems operating in the atmosphere is reduced by optical turbulence, which causes irradiance fluctuations in the received signal. The result is a randomly fading signal. Fade statistics for lasercom systems are determined from the probability density function (PDF) of the irradiance fluctuations. The expected number of fades per second and their mean fade time require the joint PDF of the fluctuating irradiance and its time derivative. Theoretical integral expressions, as well as closed form, analytical approximations, were developed for the joint PDF of a gamma-gamma distributed irradiance and its time derivative, and the corresponding expression for …

Quasi Separation Axioms, Mohammad S. Sarsak

Turkish Journal of Mathematics

In [5], Maheshwari et al. introduced and studied some new separation axioms, namely, quasi semi T_i axioms where i \in {0, 1, 2}, the quasi semi T_{1/2} axiom was then introduced and investigated by Gyu-Ihn et al. in [2]. In the present paper we introduce and study quasi T_i axioms, i \in {0, 1 / 2, 1, 2} as a special variety of quasi semi T_i axioms, the class of quasi T_{1/2} (respectively, quasi T_1) bitopological spaces is placed between quasi T_0 (respectively, quasi T_{1/2}) bitopological spaces and quasi T_1 (respectively, quasi T_2) bitopological spaces. Among several counter examples we …

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

Bookshelf

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.

Decompositions Of Continuity, Talal Al-Hawary, Ahmad Al-Omari

Turkish Journal of Mathematics

In 2004, Al-Hawary and Al-Omari introduced and explored the class of \omega^o-open sets which is strictly stronger than the class of \omega-open sets and weaker than that of open sets. In this paper, we introduce what we call \omega^o-continuity and \omega_X^o-continuity and we give several characterizations and two decompositions of \omega ^o-continuity. Finally, new decompositions of continuity are provided.

Spanning Trails Containing Given Edges, Weiqi Luo, Zhi-Hong Chen, Wei-Guo Chen

Scholarship and Professional Work - LAS

A graph G is Eulerian-connected if for any u and v in V ( G ) , G has a spanning ( u , v ) -trail. A graph G is edge-Eulerian-connected if for any e ′ and e ″ in E ( G ) , G has a spanning ( e ′ , e ″ ) -trail. For an integer r ⩾ 0 , a graph is called r -Eulerian-connected if for any X ⊆ E ( G ) with | X | ⩽ r , and for any u , v ∈ V ( G ) , G …

Applications Of Computational Homology, Christopher Aaron Johnson

Theses, Dissertations and Capstones

Homology is a field of topology that classifies objects based on the number of n- dimensional holes (cuts, tunnels, voids, etc.) they possess. The number of its real life ap- plications is quickly growing, which requires development of modern computational meth- ods. In my thesis, I will present methods of calculation, algorithms, and implementations of simplicial homology, alpha shapes, and persistent homology.

The Alpha Shapes method represents a point cloud as the union of balls centered at each point, and based on these balls, a complex can be built and homology computed. If the balls are allowed to grow, one …

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

Scholarship

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.

History Of The Department Of Mathematical Sciences At The University Of Montana: A Collection Of Interviews, Varoujan Bedros, Daniel F. Finch, Charles Myers, Merry Rampy, Johnny W. Lott (Editor)

History of the Department of Mathematical Sciences at UM: A Collection of Interviews

A collection of transcribed oral history interviews conducted in 1999 with current and recently retired faculty members of the Department of Mathematics.

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

Publications

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.

Temporal Processing In The Exponential Integrate-And-Fire Model Is Nonlinear, Joanna R. Wares, Todd W. Troyer

Department of Math & Statistics Faculty Publications

The exponential integrate-and-fire (EIF) model was introduced by Fourcaud-Trocme et al. (2003) as an extension of the standard leaky integrate-and-fire model (LIF). Here, the nonlinearity in the EIF model’s temporal response to square-wave inputs is investigated. Comparing the time course of onset and offset responses revealed that offset responses have a steeper initial slope, but a slower approach to equilibrium. A linear systems analysis performed for these square-wave inputs indicates that at frequencies above ~40 Hz, gain was slightly smaller for square-wave inputs, but phase did not change significantly relative to simulations in which the corresponding sinusoids were presented in …

Computing The Arithmetic Genus Of Hilbert Modular Fourfolds, Helen G. Grundman, L. E. Lippincott

Mathematics Faculty Research and Scholarship

The Hilbert modular fourfold determined by the totally real quartic number field k is a desingularization of a natural compactification of the quotient space Gamma(k)\H-4, where Gamma(k) = PSL2(O-k) acts on H-4 by fractional linear transformations via the four embeddings of k into R. The arithmetic genus, equal to one plus the dimension of the space of Hilbert modular cusp forms of weight (2, 2, 2, 2), is a birational invariant useful in the classification of these varieties. In this work, we describe an algorithm allowing for the automated computation of the arithmetic genus and give sample results.

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

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 …

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

Branch Mathematics and Statistics Faculty and Staff Publications

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 …

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

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.

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

Branch Mathematics and Statistics Faculty and Staff Publications

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 …

Poisson Structure And Action-Angle Variables For The Camassa-Holm Equation, Adrian Constantin, Rossen Ivanov

Articles

The Poisson brackets for the scattering data of the Camassa-Holm equation are computed. Consequently, the action-angle variables are expressed in terms of the scattering data.

The Asymptotics Of Neutral Curve Crossing In Taylor–Dean Flow, C. P. Hills, A. P. Bassom

Articles

The fluid flow between a pair of coaxial circular cylinders generated by the uniform rotation of the inner cylinder and an azimuthal pressure gradient is susceptible to both Taylor and Dean type instabilities. The flow can be characterised by two parameters: a measure of the relative magnitude of the rotation and pressure effects and a non-dimensional Taylor number. This work considers the small gap, large wavenumber limit for linear perturbations when the onset of the Taylor and Dean instabilities is concurrent. A consistent, matched asymptotic solution is found across the whole annular domain and identifies five regions of interest: two …

The Pitch And The Pseudo Angle Of Pitch Of A Closed Piece Of (K+1)-Dimensional Ruled Surface In R_\Nu^N, Ayşe Altin

Turkish Journal of Mathematics

In this paper, we define the closed piece of ruled surface, the pitch and the pseudo angle of pitch of a closed piece of ruled surface and calculate these values in Minkowski space R_\nu^n= (R ^n,-\sum^{\nu}_{i=1}dx_i+\sum^n_{i=\nu+1}dx_i).

Second-Order Nonlinear Three Point Boundary-Value Problems On Time Scales, S. Gülşan Topal

Turkish Journal of Mathematics

We consider a second order three point boundary value problem for dynamic equations on time scales and establish criteria for the existence of at least two positive solutions of an eigenvalue problem by an application of a fixed point theorem in cones. Existence result for non-eigenvalue problem is also given by the monotone method.

P-Elastica In The 3-Dimensional Lorentzian Space Forms, Nevi̇n Gürbüz

Turkish Journal of Mathematics

R Huang worked the p-elastic in a Riemannian manifold with constant sectional curvature [1]. In this work, we solve the Euler-Lagrange equation by quadrature and study the Frenet equation of the p-elastica by using the Killing field in the three dimensional Lorentzian space forms

Existence Of Periodic Solutions For Second Order Rayleigh Equations With Piecewise Constant Argument, Gen-Qiang Wang, Sui Sun Cheng

Turkish Journal of Mathematics

Based on a continuation theorem of Mawhin, periodic solutions are found for the second-order Rayleigh equation with piecewise constant argument.

On Irregular Semi Strong P-Adic U Numbers, Hülya Duru

Turkish Journal of Mathematics

The concept of the ``relation of comparability'' was introduced by Maillet in [7], who showed that if \alpha,\beta are comparable Liouville numbers then each of the numbers \alpha +\beta, \alpha -\beta, \alpha \beta and \alpha /\beta is either a rational or Lioville number. Moreover those which are Liouville numbers are comparable aamong theem and to \alpha and \beta. Maillet's proof uses in an essential way the transitivity of the comparability relation. Unfortunately, as the comparability relation is not transitive, his proof is defective. In this paper, without using the comparability relation, we obtain some uncountable subfields of p-adic numbers field, …

On Cauchy's Bound For Zeros Of A Polynomial, V. K. Jain

Turkish Journal of Mathematics

In this note, we improve upon Cauchy's classical bound, and upon some recent bounds for the moduli of the zeros of a polynomial.

On Finitary Permutation Groups, Ali̇ Osman Asar

Turkish Journal of Mathematics

In this work we give some sufficient conditions under which the structure of a transitive group of finitary permutations on an infinite set can be determined from the structure of a point stabilizer. Also, we give some sufficient conditions for the existence of a proper subgroup having an infinite orbit in a totally imprimitive p-group of finitary permutations. These results, with the help of some known results, give sufficient conditions for the nonexistence of a perfect locally finite minimal non FC - (p-group).

On Certain Modified Meyer-König And Zeller Operators, Lucyna Rempulska, Karolina Tomczak

Turkish Journal of Mathematics

We introduce certain modified Meyer-König and Zeller operators and we study their approximation properties. The similar results for modified Bernstein polynomials were given in [6].

The Homological Theory Of Degree Of Fql-Mappings, Aki̇f Abbasov

Turkish Journal of Mathematics

In this article the homological theory is specially worked out, ìadaptedî for definition of the degree of mapping from one of the classes of infinite-dimensional mappings, exactly FQL-mappings, introduced in [7].

Finite Groups All Of Whose Abelian Subgroups Of Equal Order Are Conjugate, Sezgi̇n Sezer, Robert W. Van Der Waall

Turkish Journal of Mathematics

In this paper we classify the finite groups whose abelian subgroups of equal order (B^*-groups) are conjugate. The classification has been achieved by means of a lot of general structure properties of B^*-groups, provided in the course of the paper.

Quasi-Dual Modules, M. Tamer Koşan

Turkish Journal of Mathematics

Let R be a ring, M be a right R-module and S = End_R(M). M is called a quasi-dual module if, for every R-submodule N of M, N is a direct summand of r_M(X) where X \subseteq S. In this article, we study and provide several characterizations of this module classes. We show that if M is quasi-dual module, then, for all m \in M, r_M \ell_S(m) = mR \oplus K for some submodule K of M. We also show that every quasi-dual module is a Kasch module and Z(_SM) \subseteq Rad (M_R).

On Lifts Of Paracomplex Structures, Mehmet Tekkoyun

Turkish Journal of Mathematics

In this paper, we obtain vertical, complete and horizontal lifts of paracomplex geometric structures on paracomplex manifolds to its tangent bundle. Also, we obtain integrability on paracomplex tangent bundle.