Physical Sciences and Mathematics Commons^™

Spectral Problems For Operator Pencils In Non-Separated Root Zones, Mahi̇r Hasanov

Turkish Journal of Mathematics

Variational principles for real eigenvalues of self-adjoint operator pencils in non-separated root zones are studied.

Distances Between Composition Operators, Valentin Matache

Mathematics Faculty Publications

Composition operators Cϕ induced by a selfmap ϕ of some set S are operators acting on a space consisting of functions on S by composition to the right with ϕ, that is Cϕf = f ◦ ϕ. In this paper, we consider the Hilbert Hardy space H2 on the open unit disk and find exact formulas for distances kCϕ − Cψk between composition operators. The selfmaps ϕ and ψ involved in those formulas are constant, inner, or analytic selfmaps of the unit disk fixing the origin.

Preservice Teachers’ Mapping Structures Acting On Representational Quantities, Gunhan Caglayan

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

In this article, I write about my research on five preservice secondary teachers’ (PST) understanding and sense making of representational quantities associated with magnetic color cubes and tiles. Data came from individual interviews during which I asked PST problems guided by five main tasks: prime and composite numbers, summation of counting numbers, odd numbers, even numbers, and polynomial expressions in x and y. My work drew upon an analysis framework (Behr et. al, 1994) supported by a unit coordination construct (Steffe, 1988) associated with linear and areal quantities inherent in the nature of figures produced by these PST. Linear quantities …

On Dimension Of Modules, S. Karimzadeh, Reza Nekooei

Turkish Journal of Mathematics

In this paper we prove the lying over and going down theorems for modules. Finally, we apply the above theorems and prove some results on the dimension of a module and its submodule.

Some Curvature Tensors On A Trans-Sasakian Manifold, C. S. Bagewadi, --- Venkatesha

Turkish Journal of Mathematics

The object of the present paper is to study the geometry of trans-Sasakian manifold when it is projectively semi-symmetric, Weyl semi-symmetric and concircularly semi-symmetric.

Lightlike Hypersurfaces Of Semi-Euclidean Spaces Satisfying Curvature Conditions Of Semisymmetry Type, Bayram Şahi̇n

Turkish Journal of Mathematics

In this paper, we investigate lightlike hypersurfaces which are semi-symmetric, Ricci semi-symmetric, parallel or semi-parallel in a semi-Euclidean space. We obtain that every screen conformal lightlike hypersurface of the Minkowski spacetime is semi-symmetric. For higher dimensions, we show that the semi-symmetry condition of a screen conformal lightlike hypersurface reduces to the semi-symmetry condition of a leaf of its screen distribution. We also obtain that semi-symmetric and Ricci semi-symmetric lightlike hypersurfaces are totally geodesic under certain conditions. Moreover, we show that there exist no non-totally geodesic parallel hypersurfaces in a Lorentzian space.

On P-Sasakian Manifolds Satisfying Certain Conditions On The Concircular Curvature Tensor, Ci̇han Özgür, Mukut Mani Tripathi

Turkish Journal of Mathematics

We classify P-Sasakian manifolds, which satisfy the conditions Z(\xi ,X) · Z = 0, Z(\xi ,X) · R = 0, R(\xi ,X) · Z = 0, Z(\xi ,X) · S = 0 and Z(\xi ,X) · C = 0.

Rayleigh Number In A Stability Problem For A Micropolar Fluid, Ioana Florica Dragomirescu

Turkish Journal of Mathematics

Approximate numerical evaluations of the Rayleigh number are obtained for a stability problem of thermal convection in a heat-conducting micropolar fluid layer between two rigid boundaries [7]. The influences of all the physical parameters on the values of the Rayleigh number are studied. Also, approximate neutral curves and neutral surfaces are represented in various parameters spaces.

Extreme Points Of Certain Subsets Of Hermitian Elements In Banach Algebras, Gerd Herzog, Christoph Schmoeger

Turkish Journal of Mathematics

We consider the real Banach spaces H(A) of all hermitian elements of a complex Banach algebra A. We prove that if an even power of a \in N(A) is hermitian, then a is an extreme point of the unit ball of H(A) if and only if a^2 = 1. Moreover, if an odd power of a \in H(A) is hermitian and a is an extreme point of the unit ball of H(A), then a^3 = a.

Higher Order Generalization Of Positive Linear Operators Defined By A Class Of Borel Measures, Oktay Duman

Turkish Journal of Mathematics

In the present paper, we introduce a sequence of linear operators, which is a higher order generalization of positive linear operators defined by a class of Borel measures studied in [2]. Then, using the concept of A-statistical convergence we obtain some approximation results which are stronger than the aspects of the classical approximation theory.

Closure Of Minimal Extensions, M. El Hajoui, A. Miri

Turkish Journal of Mathematics

Let R be a commutative ring with a unit and M an R-module. In this paper we give a comparison between the F-closure in M of an R-submodule having a minimal extension and the closure of this minimal extension for the same Gabriel topology defined on the ring R. If J(R) \in F we prove that both closures are the same. Moreover, if R is Artinian or semi-simple then the converse also holds.

The Generalized Hyers--Ulam--Rassias Stability Of A Cubic Functional Equation, Abbas Najati

Turkish Journal of Mathematics

In this paper, we obtain the general solution and the generalized Hyers--Ulam--Rassias stability for a cubic functional equation f(mx+y)+f(mx-y)=mf(x+y)+mf(x-y)+2(m^3-m)f(x) for a positive integer m \geq 1.

Locally Finite Simple Moufang Loops, J. I. Hall

Turkish Journal of Mathematics

A Moufang loop is a binary system that satisfies a particular weak form of the associative law. Doro and Glauberman observed that there is a direct connection between simple Moufang loops and simple groups with triality. Using this correspondence, Liebeck proved that nonassociative finite simple Moufang loops arise from split octonion algebras over finite fields. We extend Liebeck's theorem to the case of locally finite simple Moufang loops.

Lengths Of Subsets In Coxeter Groups, Sarah B. Hart, Peter J. Rowley

Turkish Journal of Mathematics

No abstract provided.

Barely Transitive Groups, Mahmut Kuzucuoğlu

Turkish Journal of Mathematics

This is a survey article on barely transitive groups. It also involves some recent results in the case of a non-locally finite barely transitive group.

A Non-Linear Locally Finite Simple Group With A P-Group As Centralizer, U. Meierfrankenfeld

Turkish Journal of Mathematics

We show that there exists a non-linear, locally finite, simple group such that the centralizer of every non-trivial element is (locally solvable)-by-finite.

Linear Automorphism Groups Of Relatively Free Groups, A. Yu. Olshanskii

Turkish Journal of Mathematics

Let G be a free group in a variety of groups, but G is not absolutely free. We prove that the group of automorphisms Aut(G) is linear if and only if G is a finitely generated virtually nilpotent group.

Finitary Actions And Invariant Ideals, D. S. Passman

Turkish Journal of Mathematics

Let K be a field and let G be a group. If G acts on an abelian group V, then it acts naturally on any group algebra K[V], and we are concerned with classifying the G-stable ideals of K[V]. In this paper, we consider a rather concrete situation. We take G to be an infinite locally finite simple group acting in a finitary manner on V. When G is a finitary version of a classical linear group, then we show that the augmentation ideal \omega K[G] is the unique proper G-stable ideal of K[V]. On the other hand, if G …

Quantization In Astrophysics, Brownian Motion, And Supersymmetry, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

The present book discusses, among other things, various quantization phenomena found in Astrophysics and some related issues including Brownian Motion. With recent discoveries of exoplanets in our galaxy and beyond, this Astrophysics quantization issue has attracted numerous discussions in the past few years. Most chapters in this book come from published papers in various peer-reviewed journals, and they cover different methods to describe quantization, including Weyl geometry, Supersymmetry, generalized Schrödinger, and Cartan torsion method. In some chapters Navier-Stokes equations are also discussed, because it is likely that this theory will remain relevant in Astrophysics and Cosmology While much of the …

Degradation Models And Implied Lifetime Distributions, Suk Joo Bae, Way Kuo, Paul H. Kvam

Department of Math & Statistics Faculty Publications

In experiments where failure times are sparse, degradation analysis is useful for the analysis of failure time distributions in reliability studies. This research investigates the link between a practitioner's selected degradation model and the resulting lifetime model. Simple additive and multiplicative models with single random effects are featured. Results show that seemingly innocuous assumptions of the degradation path create surprising restrictions on the lifetime distribution. These constraints are described in terms of failure rate and distribution classes.

A Note On Relations For Reliability Measures In Zero-Adjusted Models, Broderick O. Oluyede, Mavis Pararai

Department of Mathematical Sciences Faculty Publications

In this note we examine and study relations in zero-adjusted models. Relations for reliability measures in the adjusted and unadjusted models are established and appropriate comparisons including the relative error are presented. The relative error is shown to be a decreasing function of the counts. Some inequalities and comparisons for weighted zero-adjusted models are established.

On Strongly Asymptotic L(P) Spaces And Minimality, S J. Dilworth, V Ferenczi, Denka Kutzarova, E Odell

Faculty Publications

No abstract provided.

On Littlewood-Paley Functions, Leslie C. Cheng

Mathematics Faculty Research and Scholarship

We prove that, for a compactly supported L-q function Phi with vanishing integral on Rn, the corresponding square function operator SF is bounded on L-p for vertical bar 1/p - 1/2 vertical bar < min{(q-1)/2, 1/2}.

Neutrality And Many-Valued Logics, Florentin Smarandache, Andrew Schumann

Branch Mathematics and Statistics Faculty and Staff Publications

ThisbookwrittenbyA. Schumann &F. Smarandache isdevotedtoadvances of non-Archimedean multiple-validity idea and its applications to logical reasoning. Leibnitz was the first who proposed Archimedes’ axiom to be rejected. He postulated infinitesimals (infinitely small numbers) of the unit interval [0,1] which are larger than zero, but smaller than each positive real number. Robinson applied this idea into modern mathematics in [117] and developed so-called non-standard analysis. In the framework of non-standard analysis there were obtained many interesting results examined in [37], [38], [74], [117].

There exists also a different version of mathematical analysis in that Archimedes’ axiom is rejected, namely, p-adic analysis (e.g., …

Hadron Models And Related New Energy Issues, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The present book covers a wide-range of issues from alternative hadron models to their likely implications in New Energy research, including alternative interpretation of lowenergy reaction (coldfusion) phenomena. The authors explored some new approaches to describe novel phenomena in particle physics. M Pitkanen introduces his nuclear string hypothesis derived from his Topological Geometrodynamics theory, while E. Goldfain discusses a number of nonlinear dynamics methods, including bifurcation, pattern formation (complex GinzburgLandau equation) to describe elementary particle masses. Fu Yuhua discusses a plausible method for prediction of phenomena related to New Energy development. F. Smarandache discusses his unmatter hypothesis, and A. Yefremov …

Lipschitz Continuity And Gateaux Differentiability Of The Best Approximation Operator In Vector-Valued Chebyshev Approximation, Martin Bartelt, John Swetits

Mathematics & Statistics Faculty Publications

When G is a finite-dimensional Haar subspace of C ( X, R^k), the vector-valued functions (including complex-valued functions when k is 2) frorn a finite set X to Euclidean k-dimensional space, it is well-known that at any function f in C ( X, R^k) the best approximation operator satisfies the Strong Unicity condition of order 2 and a Lipschitz (Holder) condition of order 1/2. This note shows that in fact the best approximation operator satisfies the usual Lipschitz condition of order 1 and has a Gateaux derivative on a dense set of functions in C …

Optimising The Ratio Of Horseradish Peroxidase And Glucose Oxidase On A Bienzyme Electrode: Comparison Of A Theoretical And Experimental Approach, Dana Mackey, Anthony Killard, Adriano Ambrosi, Malcolm Smyth

Articles

This study compares the behaviour of an electrochemical enzyme biosensor with a theoretical analysis based on a mathematical model and numerical simulation. The biosensor is based on a bi-enzyme channelling configuration, employing the enzymes glucose oxidase and horseradish peroxidase, with direct electron transfer of horseradish peroxidase at a conducting polymer electrode. This was modelled by a system of partial differential equations and boundary conditions representing convective and diffusive transport of the substrates glucose and hydrogen peroxide, as well as reaction kinetics of the bienzyme electrode. The main parameter investigated was the ratio of the two immobilised enzymes, with the aim …

Using Technology To Design Teaching Modules In Mathematics And Science, Ollie I. Manley

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Technology is changing the way in which mathematics and science are taught, and this radical transformation in teaching is causing teachers to take a closer look at how lessons are designed. In an effort to demonstrate how to design instructional modules using technology, this paper will include the following: 1)A review of the National Educational Technology Standards for teachers to establish a framework for the development of the teaching modules; 2)instructional designs and techniques with special emphasis on multiple intelligence and critical thinking skills; 3) strategies and techniques for infusing technology into a standard based curriculum; and 4) an analysis …

Fourier Transform Of Bernstein–Bézier Polynomials, Tian-Xiao He, Charles Chui, Qingtang Jiang

Scholarship

Explicit formulae, in terms of Bernstein–Bézier coefficients, of the Fourier transform of bivariate polynomials on a triangle and univariate polynomials on an interval are derived in this paper. Examples are given and discussed to illustrate the general theory. Finally, this consideration is related to the study of refinement masks of spline function vectors.

Graded Sparse Graphs And Matroids, Audrey Lee, Ileana Streinu, Louis Theran

Computer Science: Faculty Publications

Sparse graphs and their associated matroids play an important role in rigidity theory, where they capture the combinatorics of some families of generic minimally rigid structures. We define a new family called graded sparse graphs, arising from generically pinned bar-and-joint frameworks, and prove that they also form matroids. We also address several algorithmic problems on graded sparse graphs: Decision, Spanning, Extraction, Components, Optimization, and Extension. We sketch variations on pebble game algorithms to solve them.