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Articles 22411 - 22440 of 27436

Full-Text Articles in Physical Sciences and Mathematics

On The Development Of The Intersection Of A Plane With A Polytope, Joseph O'Rourke Jan 2003

On The Development Of The Intersection Of A Plane With A Polytope, Joseph O'Rourke

Computer Science: Faculty Publications

Define a “slice” curve as the intersection of a plane with the surface of a polytope, i.e., a convex polyhedron in three dimensions. We prove that a slice curve develops on a plane without self-intersection. The key tool used is a generalization of Cauchy's arm lemma to permit nonconvex “openings” of a planar convex chain.

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Asymptotic Solutions Of Diffusion Models For Risk Reserves, Sally S. L. Shao Jan 2003

Asymptotic Solutions Of Diffusion Models For Risk Reserves, Sally S. L. Shao

Mathematics and Statistics Faculty Publications

We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the stochastic differential equation to a special class of initial and boundary value problems defined by a linear diffusion equation. Armedwith asymptotic analysis and perturbation theory, we obtain the asymptotic solutions of the diffusion models (possibly degenerate) governing the conditional probability of ruin over a finite …

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Extracting Movement Patterns Using Fuzzy And Neuro-Fuzzy Approaches, Haci Mustafa Palancioglu Jan 2003

Extracting Movement Patterns Using Fuzzy And Neuro-Fuzzy Approaches, Haci Mustafa Palancioglu

Electronic Theses and Dissertations

Several applications generate large volumes of data on movements including vehicle navigation, fleet management, wildlife tracking and in the near future cell phone tracking. Such applications require support to manage the growing volumes of movement data. Understanding how an object moves in space and time is fundamental to the development of an appropriate movement model of the object. Many objects are dynamic and their positions change with time. The ability to reason about the changing positions of moving objects over time thus becomes crucial. Explanations on movements of an object require descriptions of the patterns they exhibit over space and …

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Hyperbolic Transformations On Cubics In H², Frank S. Marfai Jan 2003

Hyperbolic Transformations On Cubics In H², Frank S. Marfai

Theses Digitization Project

The purpose of this thesis is to study the effects of hyperbolic transformations on the cubic that is determined by locus of centroids of the equilateral triangles in H² whose base coincides with the line y=0, and whose common vertex is at the origin. The derivation of the formulas within this work are based on the Poincaré disk model of H², where H² is understood to mean the hyperbolic plane. The thesis explores the properties of both the untransformed cubic (the original locus of centroids) and the transformed cubic (the original cubic taken under a linear fractional transformation).

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Fiber Sums Of Genus 2 Lefschetz Fibrations, Denis Auroux Jan 2003

Fiber Sums Of Genus 2 Lefschetz Fibrations, Denis Auroux

Turkish Journal of Mathematics

Using the recent results of Siebert and Tian about the holomorphicity of genus 2 Lefschetz fibrations with irreducible singular fibers, we show that any genus 2 Lefschetz fibration becomes holomorphic after fiber sum with a holomorphic fibration.

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Galois Symmetry On Floer Cohomology, Kenji Fukaya Jan 2003

Galois Symmetry On Floer Cohomology, Kenji Fukaya

Turkish Journal of Mathematics

In this article, we define an action of \hat{\Bbb Z} on the A_{\infty} category whose objects are rational Lagrangian submanifolds together with some other data. The group \hat{\Bbb Z} is a Galois group of the (universal) Novikov ring (field) over Laurent polynomial field. By mirror symmetry it will corresponds to the algebraic fundamental group of a punctured disk which parametrize the maximal degenerate family of the mirror complex manifold.

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Adjunction Inequality And Coverings Of Stein Surfaces, Stefan Nemirovski Jan 2003

Adjunction Inequality And Coverings Of Stein Surfaces, Stefan Nemirovski

Turkish Journal of Mathematics

A stronger form of the adjunction inequality is proved for immersed real surfaces in non simply-connected Stein surfaces. The result is applied to the geometry of Stein domains and analytic continuation on complex surfaces.

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Polyhedral Approximations Of Riemannian Manifolds, Anton Petrunin Jan 2003

Polyhedral Approximations Of Riemannian Manifolds, Anton Petrunin

Turkish Journal of Mathematics

I'm trying to understand which Riemannian manifolds can be Lipschitz approximated by polyhedral spaces of the same dimension with curvature bounded below. The necessary conditions I found consist of some special inequality for curvature at each point (the geometric curvature bound). This inequality is also sufficient condition for local approximation. I conjecture that it is also a sufficient condition for global approximation, and I can prove it if the curvature bound is positive. In general I can prove it only with the additional assumption that tangent bundle of the manifold is stably trivial.

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Comparing Open Book And Heegaard Decompositions Of 3-Manifolds, J. Hyam Rubinstein Jan 2003

Comparing Open Book And Heegaard Decompositions Of 3-Manifolds, J. Hyam Rubinstein

Turkish Journal of Mathematics

We study the maximal value of the Euler characteristic of the pages of all open book decompositions of closed orientable 3-manifolds. In particular, we describe some examples where the minimal genus Heegaard splittings of such 3-manifolds give rise to open book decompositions and other examples where the simplest open book decomposition has larger maximal Euler characteristic of pages than the smallest genus Heegaard splittings. Also, special properties of the Heegaard splitting associated to an open book decomposition are given. Techniques of minimal surface theory and hyperbolic geometry are shown to be useful for such problems.

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Abelian Fibred Holomorphic Symplectic Manifolds, Justin Sawon Jan 2003

Abelian Fibred Holomorphic Symplectic Manifolds, Justin Sawon

Turkish Journal of Mathematics

We study holomorphic symplectic manifolds which are fibred by abelian varieties. This structure is a higher dimensional analogue of an elliptic fibration on a K3 surface. We investigate when a holomorphic symplectic manifold is fibred in this way, and are led to several natural conjectures. We then study the geometry of these fibrations. The expectation is that this point of view will prove useful in understanding holomorphic symplectic manifolds, and possibly lead to a classification.

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Symplectic Surgeries From Singularities, Ivan Smith, Richard Thomas Jan 2003

Symplectic Surgeries From Singularities, Ivan Smith, Richard Thomas

Turkish Journal of Mathematics

We describe a variety of symplectic surgeries (not a priori compatible with Kaehler structures) which are obtained by combining local Kaehler degenerations and resolutions of singularities. The effect of the surgeries is to replace configurations of Lagrangian spheres with symplectic submanifolds. We discuss several examples in detail, relating them to existence questions for symplectic manifolds with c_1 > 0, c_1 = 0, c_1 < 0 in four and six dimensions.

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Some Asymptotic Results For The Semi-Markovian Random Walk With A Special Barrier, Tahi̇r Khani̇yev Jan 2003

Some Asymptotic Results For The Semi-Markovian Random Walk With A Special Barrier, Tahi̇r Khani̇yev

Turkish Journal of Mathematics

In this study, the semi-Markovian random walk with a special barrier (X(t)) is considered and under some weak assumptions the ergodicity of this process is discussed. Moreover, the characteristic function of ergodic distribution of X(t) is given by using a joint distribution of random variables N and Y_{N} and some exact formulas for the first and second moments of ergodic distribution of the process X(t) are obtained. Based on these results, the asymptotic behaviours of expectation and variance of this process are investigated as S-s \to \infty . It is finally proved that the ergodic distribution of the process is …

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Boundary Points Of Self-Affine Sets In R, İbrahi̇m Kirat Jan 2003

Boundary Points Of Self-Affine Sets In R, İbrahi̇m Kirat

Turkish Journal of Mathematics

Let A be an n \times n expanding matrix with integer entries and D = \{0, d_1, ... , d_{N-1} \} \subseteq {\Bbb{Z}}^n be a set of N distinct vectors, called an N-digit set. The unique non-empty compact set T = T(A,D) satisfying AT = T + D is called a self-affine set. If T has positive Lebesgue measure, it is called a self-affine region. In general, it is not clear how to determine a point to be on the boundary of a self-affine region. In this note, we consider one-dimensional self-affine regions T and present a simple approach to …

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On Lightlike Hypersurfaces Of A Semi-Riemannian Space Form, Rifat Güneş, Bayram Şahi̇n, Erol Kiliç Jan 2003

On Lightlike Hypersurfaces Of A Semi-Riemannian Space Form, Rifat Güneş, Bayram Şahi̇n, Erol Kiliç

Turkish Journal of Mathematics

In this paper, we study a Lightlike hypersurface of a semi-Riemann manifold. We show that a lightlike hypersurface is totally geodesic if and only if it is locally symmetric. Also, we show that a lightlike Hypersurface of IR_{4q}^{4m}(m,q > 1) is totally geodesic under some restrictions. Finally, we give some results on Ricci curvature of a lightlike hypersurface to be symmetric.

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On Pseudohyperbolical Curves In Minkowski Space-Time, Çeti̇n Camci, Kazim İlarslan, Emilija Sucurovic Jan 2003

On Pseudohyperbolical Curves In Minkowski Space-Time, Çeti̇n Camci, Kazim İlarslan, Emilija Sucurovic

Turkish Journal of Mathematics

In this paper, we characterize all spacelike, timelike and null curves lying on the pseudohyperbolic space H_0^3 in the Minkowski space--time E_1^4. Moreover, we prove that there are no timelike and no null curves lying on the pseudohyperbolic space H_0^3 in Minkowski space--time E_1^4.

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On Prime Submodules Of Finitely Generated Free Modules, Di̇lek Pusat Yilmaz Jan 2003

On Prime Submodules Of Finitely Generated Free Modules, Di̇lek Pusat Yilmaz

Turkish Journal of Mathematics

The aim of this work is to investigate prime submodules of finitely generated free modules over commutative domains in some special cases.

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Groups Whose Proper Subgroups Are Hypercentral Of Length At Most \Leq \Omega, Selami̇ Ercan Jan 2003

Groups Whose Proper Subgroups Are Hypercentral Of Length At Most \Leq \Omega, Selami̇ Ercan

Turkish Journal of Mathematics

Groups, all proper subgroups of which are hypercentral of length at most \omega and every proper subgroup of which is a B_{n}-group for a natural number n depending on the subgroup, are studied in this article.

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Automorphism Groups Of (M-1)-Surfaces With The M-Property, Adnan Melekoğlu Jan 2003

Automorphism Groups Of (M-1)-Surfaces With The M-Property, Adnan Melekoğlu

Turkish Journal of Mathematics

A compact Riemann surface X of genus g is called an (M-1)-surface if it admits an anticonformal involution that fixes g simple closed curves, the second maximum number by Harnack's theorem. If X also admits an automorphism of order g which cyclically permutes these g curves, then we shall call X an (M-1)-surface with the M-property. In this paper we investigate the automorphism groups of (M-1)-surfaces with the M-property.

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Fuzzy Ideals In Gamma-Rings, Mehmet Ali̇ Öztürk, Mustafa Uçkun, Young Bae Jun Jan 2003

Fuzzy Ideals In Gamma-Rings, Mehmet Ali̇ Öztürk, Mustafa Uçkun, Young Bae Jun

Turkish Journal of Mathematics

The converse of [7, Theorem 3.3] is provided. For an Artinian \Gamma-ring, a few results are investigated.

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On The Weak-Integrity Of Trees, Alpay Kirlangiç Jan 2003

On The Weak-Integrity Of Trees, Alpay Kirlangiç

Turkish Journal of Mathematics

In this paper the concept of {\em weak-integrity} is introduced as a new measure of the stability of a graph \( G \) and it is defined as I_{w}(G)={\min_{S\subset V(G)}\{ S +m_{e}(G-S)\}}, where m_{e}(G-S) denotes the number of edges of a largest component of G-S. We investigate the weak-integrity of trees and compute the weak-integrity of a binomial tree and all the trees with at most 7 vertices. We also give some results about the weak-integrity of graphs obtained from binary operations.

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On Invariant Submanifolds Of Riemannian Warped Product Manifold, Mehmet Atçeken, Bayram Şahi̇n, Erol Kiliç Jan 2003

On Invariant Submanifolds Of Riemannian Warped Product Manifold, Mehmet Atçeken, Bayram Şahi̇n, Erol Kiliç

Turkish Journal of Mathematics

In this paper, we generalize the geometry of the invariant submanifolds of Riemannian product manifold to the geometry of the invariant submanifolds of Riemannian warped product manifold. We investigate some properties of an invariant submanifolds of a Riemannian warped product manifold. We show that every invariant submanifold of the Riemannian warped product manifold is a Riemannian warped product manifold. Also, we give a theorem on the pseudo-umbilical invariant submanifold. Further, we obtain that integral manifolds on an invariant submanifold are curvature-invariant submanifolds. Finally, we give a necessary condititon on a totally umbilical invariant submanifold to be totally geodesic.

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Uniqueness Of Primary Decompositions, Patrick F. Smith Jan 2003

Uniqueness Of Primary Decompositions, Patrick F. Smith

Turkish Journal of Mathematics

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

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On Intuitionistic Fuzzy Subhypernear-Rings Of Hypernear-Rings, Kyung Ho Kim Jan 2003

On Intuitionistic Fuzzy Subhypernear-Rings Of Hypernear-Rings, Kyung Ho Kim

Turkish Journal of Mathematics

In this paper, we introduce the concept of an intuitionistic fuzzy subhypernear-ring of a hypernear-ring and obtain some results in this connection.

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Professor Masatoshi Gündüz Ikeda: A Life Devoted To Mathematics, Cemal Koç Jan 2003

Professor Masatoshi Gündüz Ikeda: A Life Devoted To Mathematics, Cemal Koç

Turkish Journal of Mathematics

No abstract provided.

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On The Extended Hecke Groups \Overline{H}(\Lambda _Q), Ni̇hal Yilmaz Özgür, Recep Şahi̇n Jan 2003

On The Extended Hecke Groups \Overline{H}(\Lambda _Q), Ni̇hal Yilmaz Özgür, Recep Şahi̇n

Turkish Journal of Mathematics

Hecke groups H(\lambda _q) have been studied extensively for many aspects in the literature, [5], [8]. The Hecke group H(\lambda_3), the modular group PSL(2, \Bbb{Z} ) , has especially been of great interest in many fields of mathematics, for example number theory, automorphic function theory and group theory. In this paper we consider the extended Hecke groups \overline{H}(\lambda _q) which are defined analogously with the extended modular group. We find the conjugacy classes of torsion elements in \overline{H}(\lambda _q). Using this we give some results about the normal subgroups and Fuchsian subgroups of \overline{H}(\lambda _q).

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On Positive Solutions Of Boundary Value Problems For Nonlinear Second Order Difference Equations, Nüket Aykut, Gusein Sh. Guseinov Jan 2003

On Positive Solutions Of Boundary Value Problems For Nonlinear Second Order Difference Equations, Nüket Aykut, Gusein Sh. Guseinov

Turkish Journal of Mathematics

In this paper we study nonlinear second order difference equations subject to separated linear boundary conditions. Sign properties of the associated Green's functions are investigated and existence results for positive solutions of the nonlinear boundary value problem are established. Upper and lower bounds for these positive solutions also are given.

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On General Fibonacci Sequences In Groups, Engi̇n Özkan Jan 2003

On General Fibonacci Sequences In Groups, Engi̇n Özkan

Turkish Journal of Mathematics

In this paper, we have constituted 3-step general Fibonacci sequences in a nilpotent group with exponent p (p is a prime number) and nilpotency class 4 and given formulas to find the \alpha term of the sequence.

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Rough Oscillatory Singular Integral Operators-Ii, Ahmad Al-Salman, Ali A. Al-Jarrah Jan 2003

Rough Oscillatory Singular Integral Operators-Ii, Ahmad Al-Salman, Ali A. Al-Jarrah

Turkish Journal of Mathematics

In this paper, we study certain classes of oscillatory singular integral operators with kernels in Llog L(S^{n-1}) which is known to be the most desirable size condition for the L^{p} boundedness to hold. We prove that such operators are bounded on L^{p}. Our results extend and improve previously known results. Variations of our approach in this paper can be applied to handle more general oscillatory singular integral operators. This concludes by indicating a variety of results that can be obtained.

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Fourth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics Jan 2003

Fourth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics

Kenneth C. Schraut Memorial Lectures

No abstract provided.

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Ideals, Varieties, And Groebner Bases, Joyce Christine Ahlgren Jan 2003

Ideals, Varieties, And Groebner Bases, Joyce Christine Ahlgren

Theses Digitization Project

The topics explored in this project present and interesting picture of close connections between algebra and geometry. Given a specific system of polynomial equations we show how to construct a Groebner basis using Buchbergers Algorithm. Gröbner bases have very nice properties, e.g. they do give a unique remainder in the division algorithm. We use these bases to solve systems of polynomial quations in several variables and to determine whether a function lies in the ideal.

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