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2007

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Articles 301 - 330 of 541

Full-Text Articles in Mathematics

Relationships Between Braid Length And The Number Of Braid Strands, Cornelia A. Van Cott Jan 2007

Relationships Between Braid Length And The Number Of Braid Strands, Cornelia A. Van Cott

Mathematics

For a knot K, let ℓ(K,n) be the minimum length of an n–stranded braid representative of K. Fixing a knot K, ℓ(K,n) can be viewed as a function of n, which we denote by ℓK(n). Examples of knots exist for which ℓK(n) is a nonincreasing function. We investigate the behavior of ℓK(n), developing bounds on the function in terms of the genus of K. The bounds lead to the conclusion that for any knot K the function ℓK(n) is eventually stable. We study the stable behavior of ℓK(n), with stronger results for homogeneous knots. For knots of nine or fewer …

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Π01 Classes And Strong Degree Spectra Of Relations, John Chisholm, Jennifer Chubb, Valentina S. Harizanov, Denise R. Hirschfeldt, Carl G. Jockusch, Timothy H. Mcnicholl, Sarah Pingrey Jan 2007

Π01 Classes And Strong Degree Spectra Of Relations, John Chisholm, Jennifer Chubb, Valentina S. Harizanov, Denise R. Hirschfeldt, Carl G. Jockusch, Timothy H. Mcnicholl, Sarah Pingrey

Mathematics

We study the weak truth-table and truth-table degrees of the images of subsets of computable structures under isomorphisms between computable structures. In particular, we show that there is a low c.e. set that is not weak truth-table reducible to any initial segment of any scattered computable linear order. Countable Π01 subsets of 2w and Kolmogorov complexity play a major role in the proof.

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Sonia Kovalevsky Math For Girls Day General Information, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings Jan 2007

Sonia Kovalevsky Math For Girls Day General Information, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings

Math for Girls Day Documents

PowerPoint presentation about Lincoln University Sonia Kovalevsky (LUSK) Math for Girls Day.

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The Convolution On Time Scales, Gusein Sh. Guseinov, Martin Bohner Jan 2007

The Convolution On Time Scales, Gusein Sh. Guseinov, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

The main theme in this paper is an initial value problem containing a dynamic version of the transport equation. via this problem, the delay (or shift) of a function defined on a time scale is introduced, and the delay in turn is used to introduce the convolution of two functions defined on the time scale. In this paper, we give some elementary properties of the delay and of the convolution and we also prove the convolution theorem. Our investigation contains a study of the initial value problem under consideration as well as some results about power series on time scales. …

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Trench's Perturbation Theorem For Dynamic Equations, Stevo Stevic, Martin Bohner Jan 2007

Trench's Perturbation Theorem For Dynamic Equations, Stevo Stevic, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We consider a nonoscillatory second-order linear dynamic equation on a time scale together with a linear perturbation of this equation and give conditions on the perturbation that guarantee that the perturbed equation is also nonoscillatory and has solutions that behave asymptotically like a recessive and dominant solutions of the unperturbed equation. As the theory of time scales unifies continuous and discrete analysis, our results contain as special cases results for corresponding differential and difference equations by William F. Trench.

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Oscillation And Nonoscillation Of Forced Second Order Dynamic Equations, Christopher C. Tisdell, Martin Bohner Jan 2007

Oscillation And Nonoscillation Of Forced Second Order Dynamic Equations, Christopher C. Tisdell, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

Oscillation and nonoscillation properties of second order Sturm-Liouville dynamic equations on time scales — for example, second order self-adjoint differential equations and second order Sturm-Liouville difference equations — have attracted much interest. Here we consider a given homogeneous equation and a corresponding equation with forcing term. We give new conditions implying that the latter equation inherits the oscillatory behavior of the homogeneous equation. We also give new conditions that introduce oscillation of the inhomogeneous equation while the homogeneous equation is nonoscillatory. Finally, we explain a gap in a result given in the literature for the continuous and the discrete case. …

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The Dynamics And Interaction Of Quantized Vortices In The Ginzburg-Landau-Schrödinger Equation, Yanzhi Zhang, Weizhu Bao, Qiang Du Jan 2007

The Dynamics And Interaction Of Quantized Vortices In The Ginzburg-Landau-Schrödinger Equation, Yanzhi Zhang, Weizhu Bao, Qiang Du

Mathematics and Statistics Faculty Research & Creative Works

The dynamic laws of quantized vortex interactions in the Ginzburg-Landau-Schrödinger equation (GLSE) are analytically and numerically studied. A review of the reduced dynamic laws governing the motion of vortex centers in the GLSE is provided. The reduced dynamic laws are solved analytically for some special initial data. By directly simulating the GLSE with an efficient and accurate numerical method proposed recently in [Y. Zhang, W. Bao, and Q. Du, Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation, European J. Appl. Math., to appear], we can qualitatively and quantitatively compare quantized vortex interaction patterns of the GLSE with those from the …

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On A Sub-Supersolution Method For The Prescribed Mean Curvature Problem, Vy Khoi Le Jan 2007

On A Sub-Supersolution Method For The Prescribed Mean Curvature Problem, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

The paper is about a sub-supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational inequality and propose appropriate concepts of sub- and supersolutions for such inequality. Existence and enclosure results for solutions and extremal solutions between sub- and supersolutions are established.

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Discrete Approximations, Relaxation, And Optimization Of One-Sided Lipschitzian Differential Inclusions In Hilbert Spaces, Tzanko Donchev, Elza Farkhi, Boris S. Mordukhovich Jan 2007

Discrete Approximations, Relaxation, And Optimization Of One-Sided Lipschitzian Differential Inclusions In Hilbert Spaces, Tzanko Donchev, Elza Farkhi, Boris S. Mordukhovich

Mathematics Research Reports

We study discrete approximations of nonconvex differential inclusions in Hilbert spaces and dynamic optimization/optimal control problems involving such differential inclusions and their discrete approximations. The underlying feature of the problems under consideration is a modi- fied one-sided Lipschitz condition imposed on the right-hand side (i.e., on the velocity sets) of the differential inclusion, which is a significant improvement of the conventional Lipschitz continuity. Our main attention is paid to establishing efficient conditions that ensure the strong approximation (in the W^1,p-norm as p greater than or equal to 1) of feasible trajectories for the one-sided Lipschitzian differential inclusions under. consideration by …

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Inversion For Non-Smooth Models With Physical Bounds, Partha S. Routh, Leming Qu, Mrinal K. Sen, Phil D. Anno Jan 2007

Inversion For Non-Smooth Models With Physical Bounds, Partha S. Routh, Leming Qu, Mrinal K. Sen, Phil D. Anno

Mathematics Faculty Publications and Presentations

Geological processes produce structures at multiple scales. A discontinuity in the subsurface can occur due to layering, tectonic activities such as faulting, folding and fractures. Traditional approaches to invert geophysical data employ smoothness constraints. Such methods produce smooth models and thefore sharp contrasts in the medium such as lithological boundaries are not easily discernible. The methods that are able to produce non-smooth models, can help interpret the geological discontinuity. In this paper we examine various approaches to obtain non-smooth models from a finite set of noisy data. Broadly they can be categorized into approaches: (1) imposing non-smooth regularization in the …

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Ergodicity Conditions In A Simple Best Effort Queueing Networks, Abdeldjebbar Kandouci, Abdelmadjid Ezzine, Toufik Guendouzi Jan 2007

Ergodicity Conditions In A Simple Best Effort Queueing Networks, Abdeldjebbar Kandouci, Abdelmadjid Ezzine, Toufik Guendouzi

Turkish Journal of Mathematics

No abstract provided.

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Semi-Slant Submanifolds Of A Nearly Kaehler Manifold, Viqar Azam Khan, Meraj Ali Khan Jan 2007

Semi-Slant Submanifolds Of A Nearly Kaehler Manifold, Viqar Azam Khan, Meraj Ali Khan

Turkish Journal of Mathematics

The aim in the present paper is to study some basic geometric properties of semi-slant submanifolds of a nearly Kaehler manifold.

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On Cartan Spaces With (\Alpha, \Beta)-Metric, H. G. Nagaraja Jan 2007

On Cartan Spaces With (\Alpha, \Beta)-Metric, H. G. Nagaraja

Turkish Journal of Mathematics

É. Cartan [2] has originally introduced a Cartan space, which is considered as dual of Finsler space. H. Rund [10], F. Brickell [1] and others studied the relation between these two spaces. The theory of Hamilton spaces was introduced and studied by R. Miron ([8 , [9]). He proved that Cartan space is a particular case of Hamilton space. T. Igrashi ([5], [6]) introduced the notion of the (\alpha, \beta)-metric in Cartan spaces and obtained the metric tensor and the invariants \rho and r which characterize the special classes of Cartan spaces with (\alpha, \beta)-metric. This paper presents a study …

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The Compact Metric Space Of The Lattice Of Varieties And ^{*}-Varieties Of C^{*}-Algebras, G. Khalilzadeh, Mohammad Hasan Faroughi Jan 2007

The Compact Metric Space Of The Lattice Of Varieties And ^{*}-Varieties Of C^{*}-Algebras, G. Khalilzadeh, Mohammad Hasan Faroughi

Turkish Journal of Mathematics

Variety of Banach algebras is a non-empty class of Banach algebras in which there exist a family of laws such that all of its members satisfy all of the laws. In this paper, we have used merely mathematical items such as Banach algebras and varieties including Banach algebras in order to change the space of all varieties of Banach algebras into a compact metric space. We prove some theorems in the metric space of zero at infinity varieties, define the ^*-varieties of ^{*}-algebra and prove many theorems about ^*-varieties of C^*-algebras.

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Equilibria In A Dipersal Model For Structured Populations, Maref Y. M. Alzoubi Jan 2007

Equilibria In A Dipersal Model For Structured Populations, Maref Y. M. Alzoubi

Turkish Journal of Mathematics

We derive a model for structured population with a two-phase life cycle. Growth and reproduction occur during the first phase. The first phase is followed by a dispersal phase in which individuals are allowed to move throughout a habitat. Also, we prove the existence of a branch of positive equilibria using bifurcation results of Rabinowitz.

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On Nuclearity Of Köthe Spaces, Erdal Karapinar, V. Zakharyuta Jan 2007

On Nuclearity Of Köthe Spaces, Erdal Karapinar, V. Zakharyuta

Turkish Journal of Mathematics

In this study we observe that the Köthe space K^{l_p}(A) is nuclear if it is isomorphic to a complemented subspace of K^{l_q}(B) for 1\leq p < q < \infty and p < 2.

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Induced Mappings On Boolean Algebras Of Clopen Sets And On Projections Of The C^*-Algebra C(X), Ahmed Al-Rawashdeh, Wasfi Shatanawi Jan 2007

Induced Mappings On Boolean Algebras Of Clopen Sets And On Projections Of The C^*-Algebra C(X), Ahmed Al-Rawashdeh, Wasfi Shatanawi

Turkish Journal of Mathematics

For a compact space X, any group automorphism \varphi of C(X,S^1) induces a mapping \Theta on the Boolean algebra of the clopen subsets of X. We prove that the disjointness of \Theta equivalent to \theta_{\varphi} is an orthoisomorphism on the sets of projections of the C^*-algebra C(X), when \varphi(-1)=-1. Indeed, \Theta is a Boolean isomorphism iff \theta_{\varphi} preserves the product of projections. If X is equipped with a probability measure \mu, on a certain \sigma-algebra of X, we show (under some condition) that \Theta preserves the disjoint of clopen subsets, up to sets of measure zero, or equivalently, the mapping …

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Some Remarks On The L^P - L^Q Boundedness Of Uc_{\Varphi}, M. R. Jabbarzadeh Jan 2007

Some Remarks On The L^P - L^Q Boundedness Of Uc_{\Varphi}, M. R. Jabbarzadeh

Turkish Journal of Mathematics

In this paper we will consider the weighted composition operators between two different L^p-spaces and then we characterize the functions u and transformations \varphi that induce weighted composition operator uC_{\varphi} between L^p(X, \Sigma, \mu)-spaces by using some properties of conditional expectation operator, pair (u, \varphi) and the measure space (X, \Sigma, \mu).

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Braiding For Categorical And Crossed Lie Algebras And Simplicial Lie Algebras, Erdal Ulualan Jan 2007

Braiding For Categorical And Crossed Lie Algebras And Simplicial Lie Algebras, Erdal Ulualan

Turkish Journal of Mathematics

In this work, we give the notion of braiding for categorical Lie algebras and crossed modules of Lie algebras and we give an equivalence between them.

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On The Unique Continuation Property For The Higher Order Nonlinear Schrödinger Equation With Constant Coefficients, Vanilde Bisognin, Octavio Paulo Vera Villagran Jan 2007

On The Unique Continuation Property For The Higher Order Nonlinear Schrödinger Equation With Constant Coefficients, Vanilde Bisognin, Octavio Paulo Vera Villagran

Turkish Journal of Mathematics

We solve the unique continuation property: If u is a solution of the higher order nonlinear Schrödinger equation with constant coefficients with t_1 < t_2 which is sufficiently smooth and such that supp u( . , t_j) \subset (a, b), -\infty < a < b < \infty, j = 1, 2, then u \equiv 0.

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Steepness In Natural Exponential Families, Afif Masmoudi Jan 2007

Steepness In Natural Exponential Families, Afif Masmoudi

Turkish Journal of Mathematics

The present paper studies and develops the notion of steepness in multivariate natural exponential families. Let F = \{P(m,F); m \in M_F\} be a multidimensional natural exponential family parameterized by its domain of the means M_F and let \overline{m} be an element of \partial M_F the means domain boundary. A necessary and sufficient condition for the variance function V_F is established so that the family F be steep at \overline{m} \in \partial M_F. Some characteristic properties of a steep family are given. Also, we investigate the asymptotic behaviour of a steep family F at \overline{m}.

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Multipliers And The Relative Completion In L_W^P(G), Cenap Duyar, A. Turan Gürkanli Jan 2007

Multipliers And The Relative Completion In L_W^P(G), Cenap Duyar, A. Turan Gürkanli

Turkish Journal of Mathematics

Quek and Yap defined a relative completion à for a linear subspace A of L^p(G), 1 \leq p < \infty ; and proved that there is an isometric isomorphism, between Hom_{L^1(G)}(L^1(G), A) and Ã, where Hom_{L^1(G)}(L^1(G),A) is the space of the module homomorphisms (or multipliers) from L^1(G) to A. In the present, we defined a relative completion à for a linear subspace A of L_w^p(G) ,where w is a Beurling's weighted function and L_w^p(G) is the weighted L^p(G) space, ([14]). Also, we proved that there is an algeabric isomorphism and homeomorphism, between Hom_{L_w^1(G)} (L_w^1(G),A) and Ã. At the end of this work we gave some applications and examples.

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The Construction Of Maximum Independent Set Of Matrices Via Clifford Algebras, Nedi̇m Deği̇rmenci̇, Nüli̇fer Özdemi̇r Jan 2007

The Construction Of Maximum Independent Set Of Matrices Via Clifford Algebras, Nedi̇m Deği̇rmenci̇, Nüli̇fer Özdemi̇r

Turkish Journal of Mathematics

In [1], [2] and [6] the maximum number of some special type n x n matrices with elements in F whose nontrivial linear combinations with real coefficients are nonsingular is studied where F is the real field R, the complex field C or the skew field H of quaternions. In this work we construct such matrices explicitly by using representations of Clifford algebras. At the end we give some analogues of the celebrated theorem of Radon-Hurwitz.

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On The Normalizer Of The Congruence Subgroup H_0^5(I) Of The Hecke Group H^5, Süleyman Uzun Jan 2007

On The Normalizer Of The Congruence Subgroup H_0^5(I) Of The Hecke Group H^5, Süleyman Uzun

Turkish Journal of Mathematics

Let l = 2 cos \frac{\pi}{5} and let H^5 be the Hecke group associated to l. In this paper, the normalizers of the congruence subgroups H_0^5(I) in PSL(2Z[\lambda]) are studied in the case where I = (2)^aI ', (2, I') = 1 and I' is a prime ideal.

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An Investigation On A Subclass Of P-Valently Starlike Functions In The Unit Disc, Yaşar Polatoğlu, Meti̇n Bolcal, Arzu Şen, Emel Yavuz Duman Jan 2007

An Investigation On A Subclass Of P-Valently Starlike Functions In The Unit Disc, Yaşar Polatoğlu, Meti̇n Bolcal, Arzu Şen, Emel Yavuz Duman

Turkish Journal of Mathematics

Let A_p denote the class of functions of the form f(z) = z^p+a_{p+1}z^{p+1}+a_{p+2}z^{p+2}+ ··· which are regular and p-valent in the open unit disc D = {z : z < 1}. Let M_p(\alpha) be the subclass of A_p consisting of functions f(z) which satisfy Re ( z \frac{f'(z)}{f(z)}) < \alpha, (z \in D) for some real \alpha (\alpha > 1). The aim of this paper is to give a representation theorem, a distortion theorem and a coefficient inequality for the class M_p(\alpha).

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Estimates For Fourier Transform Of Measures Supported On Singular Hypersurfaces, Isroil A. Ikromov Jan 2007

Estimates For Fourier Transform Of Measures Supported On Singular Hypersurfaces, Isroil A. Ikromov

Turkish Journal of Mathematics

We consider hypersurfaces S \subset \RR^3 with zero Gaussian curvature at every ordinary point with surface measure dS and define the surface measure d\mu = \psi(x)dS(x) for smooth function \psi with compact support. We obtain uniform estimates for the Fourier transform of measures concentrated on such hypersurfaces. We show that due to the damping effect of the surface measure the Fourier transform decays faster than O( \xi ^{-1/h}), where h is the height of the phase function. In particular, Fourier transform of measures supported on the exceptional surfaces decays in the order O( \xi ^{-1/2}) (as \xi \to +\infty).

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Uniqueness Of Coprimary Decompositions, M. Maani-Shirazi, P. F. Smith Jan 2007

Uniqueness Of Coprimary Decompositions, M. Maani-Shirazi, P. F. Smith

Turkish Journal of Mathematics

Uniqueness properties of coprimary decompositions of modules over non-commutative rings are presented.

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Slant Submanifolds Of Kaehler Product Manifolds, Bayram Şahi̇n, Sadik Keleş Jan 2007

Slant Submanifolds Of Kaehler Product Manifolds, Bayram Şahi̇n, Sadik Keleş

Turkish Journal of Mathematics

In this paper, we study slant submanifolds of a Kaehler product manifold. We show that an F-invariant slant submanifold of Kaehler product manifold is a product manifold. We also obtain some curvature inequalities in terms of scalar curvature and Ricci tensor.

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Traces Of Maximal Ideals Of Topological Algebras In Their Subalgebras, Mart Abel, Mati Abel Jan 2007

Traces Of Maximal Ideals Of Topological Algebras In Their Subalgebras, Mart Abel, Mati Abel

Turkish Journal of Mathematics

Let K be one of the fields R or C, A a topological associative algebra over K with separately continuous multiplication, B a subalgebra of A and M a closed maximal regular left (right or two-sided) ideal of A such that the trace M \cap B of M is a proper subset of B. In cases, when B is a Gelfand-Mazur subalgebra of A or a subalgebra of the centre Z(A) of A, such classes of topological algebras in which M \cap B (in the subset topology) is a closed maximal regular left (respectively, right or two-sided) ideal of B, …

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Quasi-Permutation Representations Of Groups Of Order 64, Houshang Behravesh, Ghodrat Ghaffarzadeh Jan 2007

Quasi-Permutation Representations Of Groups Of Order 64, Houshang Behravesh, Ghodrat Ghaffarzadeh

Turkish Journal of Mathematics

In [1], we gave algorithms to calculate c(G), q(G) and p(G) for a finite group G. In this paper, we will calculate c(G), q(G), p(G) for non-abelian groups G, where G =64.

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