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2011

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Articles 631 - 660 of 882

Full-Text Articles in Mathematics

Non-Contiguous Pattern Avoidance In Binary Trees, Michael Dairyko, Samantha Tyner, Casey Wynn Jan 2011

Non-Contiguous Pattern Avoidance In Binary Trees, Michael Dairyko, Samantha Tyner, Casey Wynn

Symposium on Research and Creative Expression (SORCE)

We consider the enumeration of binary trees avoiding non-contiguous binary tree patterns. We begin by modifying a known algorithm that counts binary trees avoiding a single contiguous tree pattern. Next, we use this algorithm to prove several theorems about the generating function whose nth coefficient gives the number of n-leaf trees avoiding a pattern. In addition, we investigate and structurally explain the recurrences that arise from these generating functions. Finally, we examine the enumeration of binary trees avoiding multiple tree patterns.

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Modeling Infectious Diseases : Two Strain Diseases In Metapopulations, Daniel Rossi, Sydney Philipps, Rachel Vonarb Jan 2011

Modeling Infectious Diseases : Two Strain Diseases In Metapopulations, Daniel Rossi, Sydney Philipps, Rachel Vonarb

Symposium on Research and Creative Expression (SORCE)

Infectious diseases often mutate and are carried between regions. We consider a mathematical model which begins to account for these factors. We assume two disjoint populations that only occasionally comingle, and two strains of a disease present in these populations. Of interest are the equations describing the dynamics of this system, the conditions under which epidemics will occur, and the long term behavior of the system under various initial conditions. We find that in many ways this system is similar to a simpler one-population model. However, we find evidence that there may be conditions under which both disease strains can …

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Properties Of Rd-Projective And Rd-Injective Modules, Lixin Mao Jan 2011

Properties Of Rd-Projective And Rd-Injective Modules, Lixin Mao

Turkish Journal of Mathematics

In this paper, we first study RD-projective and RD-injective modules using, among other things, covers and envelopes. Some new characterizations for them are obtained. Then we introduce the RD-projective and RD-injective dimensions for modules and rings. The relations between the RD-homological dimensions and other homological dimensions are also investigated.

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Krull Dimension Of Types In A Class Of First-Order Theories, Domenico Zambella Jan 2011

Krull Dimension Of Types In A Class Of First-Order Theories, Domenico Zambella

Turkish Journal of Mathematics

We study a class of first-order theories whose complete quantifier-free types with one free variable either have a trivial positive part or are isolated by a positive quantifier-free formula---plus a few other technical requirements. The theory of vector spaces and the theory fields are examples. We prove the amalgamation property and the existence of a model-companion. We show that the model-companion is strongly minimal. We also prove that the length of any increasing sequence of prime types is bounded, so every formula has finite Krull dimension.

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Some Properties Of Associate And Presimplifiable Rings, Manal Ghanem Jan 2011

Some Properties Of Associate And Presimplifiable Rings, Manal Ghanem

Turkish Journal of Mathematics

In this paper we study some properties of associate and presimplifiable rings. We give a characterization of the associate (resp., domainlike) pullback P of R_1 \rightarrow{R_3} \leftarrow{R_2}, where R_1 and R_2 are two presimplifiable (resp., domainlike) rings. We prove that R is presimplifiable ring if and only if the factor ring R/{nil(R)} is presimplifiable and the ideal nil(R) is presimplifiable. Then we investigate the associate and presimplifiable property of the dual rings {R[x]/\langle{x^2}\rangle} and its modules through the base ring R and its modules.

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Module Classes And The Lifting Property, Muhammet Tamer Koşan Jan 2011

Module Classes And The Lifting Property, Muhammet Tamer Koşan

Turkish Journal of Mathematics

Let R be a ring. A collection of R-modules containing the zero module and closed under isomorphisms will be denoted by X. An R-module M is said to be X-lifting if for every X-submodule N of M there exists A \leq N such that M=A \oplus B and N \cap B is small in B [11]. In the present paper, we consider the question: Can we characterize X-lifting modules via objects of the class X?

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Universal Inequalities And Bounds For Weighted Eigenvalues Of The Schrödinger Operator On The Heisenberg Group, Hejun Sun Jan 2011

Universal Inequalities And Bounds For Weighted Eigenvalues Of The Schrödinger Operator On The Heisenberg Group, Hejun Sun

Turkish Journal of Mathematics

For a bounded domain \Omega in the Heisenberg group H^n, we investigate the Dirichlet weighted eigenvalue problem of the Schrödinger operator - \Delta_{H^n} +V, where \Delta_{H^n} is the Kohn Laplacian and V is a nonnegative potential. We establish a Yang-type inequality for eigenvalues of this problem. It contains the sharpest result for \Delta_{H^n} in [17] of Soufi, Harrel II and Ilias. Some estimates for upper bounds of higher order eigenvalues and the gaps of any two consecutive eigenvalues are also derived. Our results are related to some previous results for the Laplacian \Delta and the Schrödinger operator -\Delta+V on a …

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Hypersurfaces With Constant Mean Curvature In A Real Space Form, Shichang Shu, Sanyang Liu Jan 2011

Hypersurfaces With Constant Mean Curvature In A Real Space Form, Shichang Shu, Sanyang Liu

Turkish Journal of Mathematics

Let M^n be an n\(n \geq 3)-dimensional complete connected and oriented hypersurface in M^{n+1}(c)(c \geq 0) with constant mean curvature H and with two distinct principal curvatures, one of which is simple. We show that (1) if c=1 and the squared norm of the second fundamental form of M^n satisfies a rigidity condition (1.3), then M^n is isometric to the Riemannian product S^1(\sqrt{1-a^2}) \times S^{n-1}(a); (2) if c=0, H \neq 0 and the squared norm of the second fundamental form of M^n satisfies S \geq n^2H^2/(n-1), then M^n is isometric to the Riemannian product S^{n-1}(a)\times R or S^1(a) \times R^{n-1}

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On Generalized Witt Algebras In One Variable, Ki Bong Nam, Jonathan Pakianathan Jan 2011

On Generalized Witt Algebras In One Variable, Ki Bong Nam, Jonathan Pakianathan

Turkish Journal of Mathematics

We study a class of infinite dimensional Lie algebras called generalized Witt algebras (in one variable). These include the classical Witt algebra and the centerless Virasoro algebra as important examples. We show that any such generalized Witt algebra is a semisimple, indecomposable Lie algebra which does not contain any abelian Lie subalgebras of dimension greater than one. We develop an invariant of these generalized Witt algebras called the spectrum, and use it to show that there exist infinite families of nonisomorphic, simple, generalized Witt algebras and infinite families of nonisomorphic, nonsimple, generalized Witt algebras. We develop a machinery that can …

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On The Uniqueness Of Strongly Flat Covers Of Cyclic Acts, Majid Ershad, Roghaieh Khosravi Jan 2011

On The Uniqueness Of Strongly Flat Covers Of Cyclic Acts, Majid Ershad, Roghaieh Khosravi

Turkish Journal of Mathematics

In [1], strongly flat covers of cyclic acts are discussed and it is asked if strongly flat covers are unique. From this point of view, in this paper we give numerous classes of monoids over which strongly flat covers of cyclic acts are unique.

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Weingarten Quadric Surfaces In A Euclidean 3-Space, Min Hee Kim, Dae Won Yoon Jan 2011

Weingarten Quadric Surfaces In A Euclidean 3-Space, Min Hee Kim, Dae Won Yoon

Turkish Journal of Mathematics

In this paper, we study quadric surfaces in a Euclidean 3-space. Furthermore, we classify quadric surfaces in a Euclidean 3-space in terms of the Gaussian curvature and the mean curvature.

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Covers And Envelopes With Respect To A Semidualizing Module, Xiaoguang Yan, Xiaosheng Zhu Jan 2011

Covers And Envelopes With Respect To A Semidualizing Module, Xiaoguang Yan, Xiaosheng Zhu

Turkish Journal of Mathematics

Let R be a commutative ring and C be a semidualizing R-module. For a given class of R-modules Q, we define a class Q_C by M \in Q_C \Leftrightarrow Hom_R(C,M) \in Q. We prove that if Q \subseteq (R) is a Kaplansky class and closed under direct sums, then Q_C^{\bot} is special preenveloping. As corollaries, we can show that p_C^{n \bot} and f_C^{n \bot} are both special preenveloping. Finally, we show that I_C^n is covering, I_C^{n \bot} is enveloping and special preenveloping provided R is Noetherian.

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Some Results On G-Frames In Hilbert Spaces, Abdolaziz Abdollahi, Elham Rahimi Jan 2011

Some Results On G-Frames In Hilbert Spaces, Abdolaziz Abdollahi, Elham Rahimi

Turkish Journal of Mathematics

In this paper we show that every g-frame for a Hilbert space H can be represented as a linear combination of two g-orthonormal bases if and only if it is a g-Riesz basis. We also show that every g-frame can be written as a sum of two tight g-frames with g-frame bounds one or a sum of a g-orthonormal basis and a g-Riesz basis for H. We further give necessary and sufficient conditions on g-Bessel sequences {\Lambda_i \in L (H,H_i) : i \in J} and {\Gamma_i \in L(H,H_i): i \in J} and operators L_1, L_2 on H so that {\Lambda_iL_1+\Gamma_iL_2: …

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Conjugate Convolution And Characterizations Of Inner Amenable Locally Compact Groups, Bahram Mohammadzadeh Jan 2011

Conjugate Convolution And Characterizations Of Inner Amenable Locally Compact Groups, Bahram Mohammadzadeh

Turkish Journal of Mathematics

For locally compact group G, we give some characterizations of inner amenability of G by conjugate convolution operations. Moreover, we study multiples of positive elements in group algebra L^1(G), whenever G is inner amenable.

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An Exploration Of Modeling Techniques For The Study Of The Dynamics Of E-Mail Viruses, Karin Weule Jan 2011

An Exploration Of Modeling Techniques For The Study Of The Dynamics Of E-Mail Viruses, Karin Weule

Theses, Dissertations and Culminating Projects

We analyze real data sets from two e-mail viruses, the Magistr.b and the Sircam.a to explore how we can use mathematical models to predict the behavior described by the data. Analysis of the data is conducted primarily with computer programming in MatLab. We focus mainly on the use of two continuous models commonly used in the study of biological diseases, the SIS and the SIR models. A discrete modeling approach using agent-based simulations is also explored and revealed to be potentially useful in developing a compartmentalized model that incorporates both SIS and SIR model behavior. The theory behind the continuous …

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On Lower Bounds Of The Chung-Diaconis-Graham Random Process, Richard Eugene Neville Jan 2011

On Lower Bounds Of The Chung-Diaconis-Graham Random Process, Richard Eugene Neville

Legacy Theses & Dissertations (2009 - 2024)

Chung, Diaconis, and Graham considered random processes of the form X_(n+1)=(a_n)X_n+b_n (mod p) where p is odd, X_0=0, b_n are i.i.d. for n=0,1,2,... with P(b_n=0)=P(b_n=1)=P(b_n=-1)=1/3, and a_n=2 always. Later, Hildebrand was able to establish a lower bound for this process as p approaches infinity. This paper will prove the following conclusions on lower bounds of the Chung-Diaconis-Graham random process:

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A Fredholm Alternative-Like Result On Power Bounded Operators, Ali̇ Ülger, Onur Yavuz Jan 2011

A Fredholm Alternative-Like Result On Power Bounded Operators, Ali̇ Ülger, Onur Yavuz

Turkish Journal of Mathematics

Let X be a complex Banach space and T:X\rightarrow X be a power bounded operator, i.e., \sup_{n \geq 0}\ T^n\

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Analysis Of A Differential Equation Model Of Hiv Infection Of Cd4^+ T-Cells With Saturated Reverse Function, Xiangyun Shi, Gang Li, Xueyong Zhou, Xinyu Song Jan 2011

Analysis Of A Differential Equation Model Of Hiv Infection Of Cd4^+ T-Cells With Saturated Reverse Function, Xiangyun Shi, Gang Li, Xueyong Zhou, Xinyu Song

Turkish Journal of Mathematics

In this paper, an ordinary differential equation model of HIV infection of CD4^+ T-cells with saturated reverse function is studied. We prove that if the basic reproduction number R_0

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A Beurling-Type Theorem In Bergman Spaces, Ali Abkar Jan 2011

A Beurling-Type Theorem In Bergman Spaces, Ali Abkar

Turkish Journal of Mathematics

It is known that Beurling's theorem concerning invariant subspaces is not true in the Bergman space (in contrast to the Hardy space case). However, Aleman, Richter, and Sundberg proved that every cyclic invariant subspace in the Bergman space \lpad, 0

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Central Simple Superalgebras With Superantiautomorphism Of Order Two Of The Second Kind, Ameer Jaber Jan 2011

Central Simple Superalgebras With Superantiautomorphism Of Order Two Of The Second Kind, Ameer Jaber

Turkish Journal of Mathematics

Our main purpose is to develop the theory of existence of superantiautomorphisms of order two of the second kind (which are caled superinvolutions of the second kind) on finite dimensional central simple superalgebras A=M_n(D), where D is a finite dimensional division superalgebra with nontrivial grading over K, where K is a field of any characteristic. We determine which finite dimensional central simple superalgebras posses a superinvolution of the second kind and put these results in the context of the Albert-Reihm Theorem on the existence of involutions of the second kind.

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On The Stability Of Basisness In L_P(1 < P < +\Infty) Of Cosines And Sines, Ali Huseynli Jan 2011

On The Stability Of Basisness In L_P(1 < P < +\Infty) Of Cosines And Sines, Ali Huseynli

Turkish Journal of Mathematics

We study the basis properties in L_p(0, \pi) (1 < p < \infty) of the solution system of Sturm--Liouville equations with different types of initial conditions. We first establish some results on the stability of the basis property of cosines and sines in L_p(0, \pi) (1 < p < \infty) and then show that the solution system above forms a basis in L_p(0, \pi) if and only if certain cosine system (or sine system, depending on type of initial conditions) forms a basis in L_p(0, \pi).

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Existence Of Three Solutions To A Non-Homogeneous Multi-Point Bvp Of Second Order Differential Equations, Yuji Liu Jan 2011

Existence Of Three Solutions To A Non-Homogeneous Multi-Point Bvp Of Second Order Differential Equations, Yuji Liu

Turkish Journal of Mathematics

This paper is concerned with a non-homogeneous multi-point boundary value problem of second order differential equation with one-dimensional p-Laplacian. Using multiple fixed point theorems, sufficient conditions to guarantee the existence of at least three solutions of this kind of BVP are established. Two examples are presented to illustrate the main results.

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Blow-Up Time For A Semilinear Parabolic Equation With Variable Reaction, Theodore Kouassi Boni, Remi Kouadio Kouakou Jan 2011

Blow-Up Time For A Semilinear Parabolic Equation With Variable Reaction, Theodore Kouassi Boni, Remi Kouadio Kouakou

Turkish Journal of Mathematics

In this paper, we address the solution of a semilinear heat equation with variable reaction subject to Dirichlet boundary conditions and nonnegative initial datum. Under some assumptions, we show that the solution of the above problem blows up in a finite time, and its blow-up time goes to that of the solution of a certain differential equation. Finally, we give some numerical results to illustrate our analysis.

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Order Continuous Operators On Cd_0(K,E) And Cd_W(K,E)-Spaces, Faruk Polat Jan 2011

Order Continuous Operators On Cd_0(K,E) And Cd_W(K,E)-Spaces, Faruk Polat

Turkish Journal of Mathematics

In [2], Alpay and Ercan characterized order continuous duals of spaces CD_0(K, E) and CD_w(K, E) where K is a compact Hausdorff space without isolated points and E is a Banach lattice. In this note, we generalize their results to an arbitrary Dedekind complete Banach lattice F, that is to say, we characterize order continuous operators on these spaces taking values in an arbitrary Dedekind complete Banach lattice F.

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Null Mannheim Curves In The Minkowski 3-Space E_1^3, Handan Özteki̇n, Mahmut Ergüt Jan 2011

Null Mannheim Curves In The Minkowski 3-Space E_1^3, Handan Özteki̇n, Mahmut Ergüt

Turkish Journal of Mathematics

In this study, we give the definition of null Mannheim curve with timelike or spacelike Mannheim partner curve in the Minkowski 3-space E _1^3. We get the necessary and sufficient conditions for the null Mannheim curves. Then we investigate the null and timelike or spacelike generalized helix as the null Mannheim curve and timelike or spacelike Mannheim partner curve, respectively.

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Slant Lightlike Submanifolds Of Indefinite Kenmotsu Manifolds, Ram Gupta, Sharfuddin Ahamad Jan 2011

Slant Lightlike Submanifolds Of Indefinite Kenmotsu Manifolds, Ram Gupta, Sharfuddin Ahamad

Turkish Journal of Mathematics

In this paper, we introduce the notion of a slant lightlike submanifold of an indefinite Kenmotsu manifold. We provide a non-trivial example and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold. Also, we give an example of a minimal slant lightlike submanifold of R_2^{9} and prove some characterization theorems.

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Relative Nullity Foliations And Lightlike Hypersurfaces In Indefinite Kenmotsu Manifolds, Fortune Massamba Jan 2011

Relative Nullity Foliations And Lightlike Hypersurfaces In Indefinite Kenmotsu Manifolds, Fortune Massamba

Turkish Journal of Mathematics

This paper deals with the relative nullity distributions of lightlike hypersurfaces of indefinite Kenmotsu space forms, tangent to the structure vector field. Theorems on parallel vector fields are obtained. We give characterization theorems for the relative nullity distributions as well as for Einstein, totally contact umbilical and flat lightlike hypersurfaces. We show that, under a certain condition, Einstein lightlike hypersurfaces in indefinite Kenmotsu space forms have parallel screen distributions. We prove that on a parallel (or totally umbilical) lightlike hypersurface, the relative nullity space coincides with the tangent vector space.

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Jackknife And Bootstrap With Cycling Blocks For The Estimation Of Fractional Parameter In Arfima Model, Lorenc Ekonomi, Argjir Butka Jan 2011

Jackknife And Bootstrap With Cycling Blocks For The Estimation Of Fractional Parameter In Arfima Model, Lorenc Ekonomi, Argjir Butka

Turkish Journal of Mathematics

One of most important problems concerning the ARFIMA time series model is the estimation of fractional parameter d. Various methods have been used to solve this problem, such as the log-periodogram regression of a process. In this article we propose two jackknife and bootstrap methods, which aid in the estimation of fractional parameter d. These methods involve non-overlapping blocks and moving blocks with random starting point and length. We have conducted several simulations and the results show that the estimations obtained are very close to the real parameter value.

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Invariant Subspace Problem For Positive L-Weakly And M-Weakly Compact Operators, Cevri̇ye Tonyali, Erdal Bayram Jan 2011

Invariant Subspace Problem For Positive L-Weakly And M-Weakly Compact Operators, Cevri̇ye Tonyali, Erdal Bayram

Turkish Journal of Mathematics

In this paper, we show that positive L-weakly and M-weakly compact operators on some real Banach lattices have a non-trivial closed invariant subspace. Also, we prove that any positive L-weakly (or M-weakly) compact operator T:E \rightarrow E\ has a non-trivial closed invariant subspace if there exists a Dunford-Pettis operator S:E \rightarrow E satisfying 0 \leq T \leq S, where E is Banach lattice.

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Numerical Solutions For A Model Of Tissue Invasion And Migration Of Tumour Cells, Mikhail Kolev, Barbara Zubik-Kowal Jan 2011

Numerical Solutions For A Model Of Tissue Invasion And Migration Of Tumour Cells, Mikhail Kolev, Barbara Zubik-Kowal

Mathematics Faculty Publications and Presentations

The goal of this paper is to construct a new algorithm for the numerical simulations of the evolution of tumour invasion and metastasis. By means of mathematical model equations and their numerical solutions we investigate how cancer cells can produce and secrete matrix degradative enzymes, degrade extracellular matrix, and invade due to diffusion and haptotactic migration. For the numerical simulations of the interactions between the tumour cells and the surrounding tissue, we apply numerical approximations, which are spectrally accurate and based on small amounts of grid-points. Our numerical experiments illustrate the metastatic ability of tumour cells.

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