Mathematics Commons^™

Procedural Support For Cooperative Negotiations: Theoretical Design And Practical Implementation, Matthias G. Raith, Francis Su

All HMC Faculty Publications and Research

We discuss the theoretical design of algorithms for solving distributional conflicts within groups. We consider an algorithm to be procedural if the implementation of the outcome requires the participation of the players, or if it can even be conducted by the players themselves without computational assistance. We compare two procedures for multilateral problems of fair division; both establish envy-freeness, given the possibility of monetary compensations between players.

A Simple Vaccination Model With Multiple Endemic States, Christopher Kribs, Jorge X. Velasco-Hernandez

Mathematics Faculty Publications - Archive

A simple two-dimensional SIS model with vaccination exhibits a backward bifurcation for some parameter values. A two-population version of the model leads to the consideration of vaccination policies in paired border towns. The results of our mathematical analysis indicate that a vaccination campaign φ meant to reduce a disease's reproduction number R(φ) below one may fail to control the disease. If the aim is to prevent an epidemic outbreak, a large initial number of infective persons can cause a high endemicity level to arise rather suddenly even if the vaccine-reduced reproduction number is below threshold. If the aim is to …

Two (Multi) Point Nonlinear Lyapunov Systems Associated With An Nth Order Nonlinear System Of Differential Equations - Existence And Uniqueness, Kanuri N. Murty, Gary W. Howell, G. V.R.L. Sarma

Mathematics and System Engineering Faculty Publications

This paper presents a criterion for the existence and uniqueness of solutions to two and multipoint boundary value problems associated with an nth order nonlinear Lyapunov system. A variation of parameters formula is developed and used as a tool to obtain existence and uniqueness. We discuss solution of the second order problem by the ADI method and develop a fixed point method to find the general solution of the nth order Lyapunov system. The results of Barnett (SIAM J. Appl. Anal. 24(1), 1973) are a particular case.

Notes On Coalgebras, Cofibrations And Concurrency, Alexander Kurz, Dirk Pattinson

Engineering Faculty Articles and Research

We consider categories of coalgebras as (co)-fibred over a base category of parameters and analyse categorical constructions in the total category of deterministic and non-deterministic coalgebras.

Rotary Honing: A Variant Of The Taylor Paint-Scraper Problem, Christopher Hills, H. Moffatt

Articles

The three-dimensional Row in a corner of fixed angle α induced by the rotation in its plane of one of the boundaries is considered. A local similarity solution valid in a neighbourhood of the centre of rotation is obtained and the streamlines are shown to be closed curves. The effects of inertia are considered and are shown to be significant in a small neighbourhood of the plane of symmetry of the flow. A simple experiment confirms that the streamlines are indeed nearly closed; their projections on planes normal to the line of intersection of the boundaries are precisely the 'Taylor' …

Bounds For The Points Of Spectral Concentration Of Sturm-Liouville Problems, Daphne Gilbert, B.J. Harris

Articles

§1. Introduction. We consider the spectral function ρα(λ) associated with the Sturm–Liouville equation

with the boundary condition

A Special Quasi-Linear Mapping And Its Degree, Aki̇f Abbasov

Turkish Journal of Mathematics

In this article, for the purpose of expanding to the mappings between Banach manifolds, a degree is determined in for the mappings between Banach spaces, which are from the obvious class.

On The Asymptotics Of Fourier Coefficients For The Potential In Hill's Equation, Haskiz Coşkun

Turkish Journal of Mathematics

We consider Hill's equation $y'' +(\lambda -q)y=0$ where $q\in L^{1}[0,\pi ].$ We show that if $l_{n}-$the length of the $n-th$ instability interval$-$ is of order $O(n^{-k})$ then the real Fourier coefficients $a_{n},b_{n}$ of $q$ are of the same order for$(k=1,2,3)$, which in turn implies that $q^{(k-2)}$, the $(k-2)th$ derivative of $q$, is absolutely continuous almost everywhere for $k=2,3.$

On The Metabelian Local Artin Map I: Galois Conjugation Law, Kazim İlhan İkeda

Turkish Journal of Mathematics

It is proved that, for a (henselian) local field $K$ and for a fixed Lubin-Tate splitting $\phi$ over $K$, the metabelian local Artin map (?, $K)_{\phi}: B(K, \phi) \tilde{\rightarrow} Gal (K^{(ab)^2} / K)$ satisfies the Galois conjugation law $$(\tilde{\sigma}^+(\alpha), \sigma (K))_{\tilde{\sigma}\phi\tilde{\sigma}^{-1}} = \tilde{\sigma} _{K^{(ab)^2}} (\alpha, K)_{\phi}\tilde{\sigma}^{-1} _{\tilde{\sigma}(K^{(ab)^2})}$$ for any $\alpha \in B(K, \phi)$, and for any embedding $\sigma : K \hookrightarrow K^{sep}$, where $\tilde{\sigma} \in$ Aut $(K^{sep}$) is a fixed extension to $K^{sep}$ of the embedding $\sigma : K \hookrightarrow K^{sep}$.

Representing Systems Of Exponentials And Projection On Initial Data In The Cauchy Problem, Yu. F. Korobeinik

Turkish Journal of Mathematics

The Cauchy problem for the equation \begin{equation} Mw\equiv \sum_{j=0}^m\sum_{s=0}^{l_j}a_{s,j}\frac{\partial^{s+j}w(z_1,z_2)}{\partial z_1^s\partial z_2^j}=0 \end{equation} \begin{equation} \frac{\partial^nw(z_1,z_2)}{\partial z_2^n}\mid_{z_{2}=0}=\varphi_n(z_1), n=0,1,\ldots , m-1 \end{equation} is investigated under the condition $l_j\leq l_m, j=0,1,\ldots,m-1$. It is shown that the operator of projection of solution of (1) on its initial data (2) in a definite situation has a linear continuous right inverse which can be determined effectively with the help of representing systems of exponentials in the space of initial data.

Asymptotic Behavior Of The Zero Solutions To Generalized Pipe And Rotating Shaft Equations, Ayfer Kurt

Turkish Journal of Mathematics

A non-autonomous partial differential equation describing the dynamics of a uniform pipe and a system describing the dynamics of a rotating shaft are considered.Sufficient conditions for the global asymptotic stability of the zero solution of the boundary value problem for the differential equation and the system under consideration are established by using the Lyapunov function technique.

Zeros Of \Zeta^{''}(S) & \Zeta^{'''}(S) In \Sigma< 1/2, Cem Yalçin Yildirim

Turkish Journal of Mathematics

There is only one pair of non-real zeros of $\zeta^{''}(s)$, and of $\zeta^{'''}(s)$, in the left half-plane. The Riemann Hypothesis implies that $\zeta''(s)$ and $\zeta'''(s)$ have no zeros in the strip $0 \leq \Re\,s < {1\over 2} $.

A Local Zero-Two Law And Some Applications, Radu Zaharopol

Turkish Journal of Mathematics

In the paper we obtain a local zero-two law for positive contractions of $L^1$-spaces, which we use in order to offer new proofs of a theorem of Orey concerning Markov chains, and of the strong asymptotic stability of certain Markov operators that have appeared in the study of the Tjon-Wu equation and in connection with the Hannsgen and Tyson model of the cell cycle.

On The Efficiency Of Finite Simple Semigroups, H. Ayik, C. M. Campbell, J. J. O'Connor, N. Ruskuc

Turkish Journal of Mathematics

Let $S$ be a finite simple semigroup, given as a Rees matrix semigroup $\mathcal{M}[G;I,\Lambda ;P]$ over a group $G$. We prove that the second homology of $S$ is $H_{2}(S)=H_{2}(G)\times {\mathbb Z}^{( I -1)( \Lambda -1)}$. It is known that for any finite presentation $\langle \: A\: \: R\: \rangle$ of $S$ we have $ R - A \geq \mbox{rank}(H_{2}(S))$; we say that $S$ is efficient if equality is attained for some presentation. Given a presentation $\langle \: A_{1}\: \: R_{1}\: \rangle$ for $G$, we find a presentation $\langle \: A\: \: R\: \rangle$ for $S$ such that $ R - …

A Generalized Trapezoid Inequality For Functions Of Bounded Variation, P. Cerone, S. S. Dragomir, C. E. M. Pearce

Turkish Journal of Mathematics

We establish a generalization of a recent trapezoid inequality for functions of bounded variation. A number of special cases are considered. Applications are made to quadrature formulae, probability theory, special means and the estimation of the beta function.

Some Commutativity Results For S -Unital Rings, Moharram A. Khan

Turkish Journal of Mathematics

In the present paper, it is shown that if $R$ is a left ( resp. right) $s$-unital ring satisfying $[f(y^mx^ry^s) \pm x^ty, x] = 0$ (resp. $[f(y^mx^ry^s) \pm yx^t, x] = 0),$ where $m, r, s, t$ are fixed non-negative integers and $f(\lambda)$ is a polynomial in ${\lambda}^2{\bf Z}[\lambda],$ then $R$ is commutative. Commutativity of $R$ has also been investigated under different sets of constraints on integral exponents.

Applications Of The Tachibana Operator On Problems Of Lifts, Abdullah Mağden, Ekrem Kadioğlu, Ari̇f A. Salimov

Turkish Journal of Mathematics

The purpose of the present paper is to study, using the Tachibana operator, the complete lifts of affinor structures along a pure cross-section of the tensor bundle and to investigate their transfers. The results obtained are to some extent similar to results previously established for tangent (cotangent) bundles \lbrack 1\rbrack. However there are various important differences and it appears that the problem of lifting affinor structures to the tensor bundle on the pure cross-section presents difficulties which are not encountered in the case of the tangent (cotangent) bundle.

Oscillation Criteria For Second Order Nonlinear Differential Equations With Damping, Aydin Ti̇ryaki̇, Ağacik Zafer

Turkish Journal of Mathematics

Oscillation criteria are given for second order nonlinear differential equations with damping of the form $$(a(t) \psi (x ) \dot x)\dot{}+ p(t) \dot x + q (t) f (x ) = 0,\quad t\geq t_0,$$ where $p$ and $q$ are allowed to change signs on $[t_0,\infty)$. We employ the averaging technique to obtain sufficient conditions for oscillation of solutions of the above equation. Our results generalize and extend some known oscillation criteria in the literature.

Some Graph Type Hypersurfaces In A Semi-Euclidean Space, Ikawa Toshihiko, Honda Kyoko

Turkish Journal of Mathematics

We consider some graph type hypersurfaces in a semi-Euclidean space $\Bbb R^{n+1}_{q}$ and give conditions of the dimension $n+1$ and the index $q$ when a hypersurface is lightlike, totally geodesic and minimal.

Conjugacy Classes Of Elliptic Elements In The Picard Group, Ni̇hal Yilmaz, İsmai̇l Naci̇ Cangül

Turkish Journal of Mathematics

The Picard group $\mathbf{P}$ is a discrete subgroup of $PSL(2,\Bbb{C})$ with Gaussian integer coefficients. Here it is shown that the total number of conjugacy classes of elliptic elements of order 2 and 3 in $\mathbf{P}$, which is given as seven by B. Fine $\left[ 3\right] $, can actually be reduced to four and using this, the conditions for the maximal Fuchsian subgroups of $\mathbf{P}$ to have elliptic elements of orders 2 and 3 are found.

The K-Derivation Of A Gamma-Ring, Hati̇ce Kandamar

Turkish Journal of Mathematics

In this paper, the $k$-derivation is defined on a $\Gamma$-ring $M$ (that is, if $M$ is a $\Gamma$-ring, $d:M\to M$ and $k:\Gamma\to \Gamma$ are to additive maps such that $d(a\beta b )= d(a)\beta b + ak(\beta)b + a\beta d(b) $ for all $a,b\in M, \quad \beta \in \Gamma$, then $d$ is called a $k$-derivation of $M$) and the following results are proved. (1) Let $R$ be a ring of characteristic not equal to 2 such that if $xry=0$ for all $x, y\in R$ then $r=0$. If $d$ is a $k$-derivation of the $(R=)\Gamma$-ring $R$ with $k=d$, then $d$ is the …

Qr-Submanifolds And Almost Contact 3-Structure, Rifat Güneş, Bayram Şahi̇n, Sadik Keleş

Turkish Journal of Mathematics

In this paper,QR-submanifolds of quaternion Kaehlerian manifolds with $\dim \nu ^{\perp }=1$ has been considered. It is shown that each QR-submanifold of quaternion Kaehlerian manifold with $\dim \nu ^{\perp }=1$ is a manifold with an almost contact 3-structure. We apply geometric theory of almost contact 3-structure to the classification of QR-submanifolds (resp.Real hypersurfaces) of quaternion Kaehler manifolds (resp.$IR^{4m}$, $m>1$). Some results on integrability of an invariant distribution of a QR-submanifold and on the immersions of its leaves are also obtained.

Lifts Of Derivations To The Semitangent Bundle, Ari̇f A. Salimov, Ekrem Kadioğlu

Turkish Journal of Mathematics

The main purpose of this paper is to investigate the complete lifts of derivations for semitangent bundle and to discuss relations between these and lifts already known.

On Characterization Of Metric Completeness, Guo-Jing Jiang

Turkish Journal of Mathematics

We give seven necessary and sufficient conditions for a metric space to be complete.

On Torsion-Free Barely Transitive Groups, Mahmut Kuzucuoğlu

Turkish Journal of Mathematics

B. Hartley asked the following question: Does there exist a torsion free barely transitive group? Existence of torsion free simple barely transitive group is also unknown. We answer the latter question negatively in a special case. Moreover we proved the following: Let $G$ be a simple barely transitive group, and $H$ be a stabilizer of a point. If for a non-identity element $x \in G$, $C_G (x)$ is infinite then, $C_G (x)$ cannot contain $H$.

Intrinsic Equations For A Relaxed Elastic Line On An Oriented Hypersurface In The Minkowski Space R^N_1, Nevi̇n Gürbüz, Ali̇ Görgülü

Turkish Journal of Mathematics

We gived the intrinsic equations for a relaxed elastic line on an oriented surface in ${\Bbb {R}}_1^3$ ([1],[2]). In this paper, we derived the intrinsic equations for a relaxed elastic line on an oriented time-like hypersurface and space-like hypersurface in the Minkowski space ${\Bbb {R}}_1^n$ and gived additional results about relaxed elastic lines on various timelike and spacelike hypersurface in the Minkowski space ${\Bbb {R}}_1^n$.

On Generalized Higher Derivations, Atsushi Nakajima

Turkish Journal of Mathematics

We define the notion of generalized higher derivations and give some elementary relations between generalized higher derivations and higher derivations in the usual sense. We extend the result of an exact sequence of the set of all derivations $\text{Der}(A, M)$ and the set of all generalized derivations $g\text{Der}(A, M)$ given in [N1, Theorem 2.4]. Moreover, we discuss generalized higher Jordan derivations and Lie derivations.

Conjugacy Structure Type And Degree Structure Type In Finite P-Groups, Yadalah Marefat

Turkish Journal of Mathematics

Let $G$ be a finite $p-$group, and denote by $k(G)$ number of conjugacy classes in $G$. The aim of this paper is to introduce the conjugacy structure type and degree structure type for $p-$groups, and determine these parameters for $p-$groups of order $p^5$, and calculate $k(G)$ for them.

The Pitch And The Angle Of Pitch Of A Closed Nonnull Ruled Hypersurface Whose Generator Is Spacelike In R^{K+2}_1, Ayşe Altin, Aysel Turgut Vanli

Turkish Journal of Mathematics

In this paper, the pitch and the angle of pitch of a closed nonnull ruled hypersurface whose generators are spacelike are calculated in $R^{k+2}_1 $.

New And Old Types Of Homogeneity, Ali̇ Ahmad Fora

Turkish Journal of Mathematics

We introduce new types of homogeneity ; namely : locally homogeneity and closed homogeneity .Several results are included discussing some relations between these types and the old ones. Some characterization and decomposition theorems are obtained. Relevant examples and counterexamples are discussed throughout this paper.