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2002

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Articles 121 - 150 of 240

Full-Text Articles in Mathematics

Accuracy, Resolution And Stability Properties Of A Modified Chebyshev Method, Jodi Mead, Rosemary A. Renaut Jan 2002

Accuracy, Resolution And Stability Properties Of A Modified Chebyshev Method, Jodi Mead, Rosemary A. Renaut

Mathematics Faculty Publications and Presentations

While the Chebyshev pseudospectral method provides a spectrally accurate method, integration of partial differential equations with spatial derivatives of order M requires time steps of approximately O(N−2M) for stable explicit solvers. Theoretically, time steps may be increased to O(N−M) with the use of a parameter, α-dependent mapped method introduced by Kosloff and Tal-Ezer [ J. Comput. Phys., 104 (1993), pp. 457–469]. Our analysis focuses on the utilization of this method for reasonable practical choices for N, namely N ≲ 30, as may be needed for two- or three dimensional modeling. Results presented …

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Left Adjoint Of Pullback Cat^1- Profinite Groups, Murat Alp Jan 2002

Left Adjoint Of Pullback Cat^1- Profinite Groups, Murat Alp

Turkish Journal of Mathematics

In this paper, we present a brief review crossed modules \cite{whitehead}, cat^1-groups \cite{loday}, profinite crossed modules \cite{kortim}, cat^1-profinite groups \cite{kortim}, pullback profinite crossed modules \cite{kortim} and also the pullback cat^1- profinite groups \cite{hind}. We prove that the pulback cat^1-profinite group has a left adjoint which is the induced cat^1-group.

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New Tensor Norms And Operator Ideals Associated To Interpolation Spaces Between Sequence Spaces, G. Castaneda, J. A. Lopez Molina, M. J. Rivera Jan 2002

New Tensor Norms And Operator Ideals Associated To Interpolation Spaces Between Sequence Spaces, G. Castaneda, J. A. Lopez Molina, M. J. Rivera

Turkish Journal of Mathematics

We introduce a wide class of tensor norms g_{\lambda,\rho} which are defined with the help of interpolation spaces between perfect sequence spaces defined by a general parameter real interpolation method. We also characterize the associated \lambda_{\rho}-nuclear and \lambda_{\rho}-integral operators.

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Characterizations Of Artinian And Noetherian Gamma-Rings In Terms Of Fuzzy Ideals, Mehmet Ali̇ Öztürk, Mustafa Uçkun, Young Bae Jun Jan 2002

Characterizations Of Artinian And Noetherian Gamma-Rings In Terms Of Fuzzy Ideals, Mehmet Ali̇ Öztürk, Mustafa Uçkun, Young Bae Jun

Turkish Journal of Mathematics

Using fuzzy ideals, characterizations of Noetherian \Gamma-rings are given, and a condition for a \Gamma-ring to be Artinian is also given.

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On Non-Existence Of Korovkin's Theorem In The Space Of L_{P}-Locally Integrable Functions, A. D. Gadjiev, Ertan İbi̇kli̇ Jan 2002

On Non-Existence Of Korovkin's Theorem In The Space Of L_{P}-Locally Integrable Functions, A. D. Gadjiev, Ertan İbi̇kli̇

Turkish Journal of Mathematics

It is shown that a Korovkin-type theorem does not hold in the weighted space of L_{p}-locally integrable functions on the whole real axis.

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Deformation Inequivalent Complex Conjugated Complex Structures And Applications, Viatcheslav Kharlamov, Viktor Kulikov Jan 2002

Deformation Inequivalent Complex Conjugated Complex Structures And Applications, Viatcheslav Kharlamov, Viktor Kulikov

Turkish Journal of Mathematics

We start from a short summary of our principal result from [KK]: an example of a complex algebraic surface which is not deformation equivalent to its complex conjugate and which, moreover, has no homeomorphisms reversing the canonical class. Then, we generalize this result to higher dimensions and construct several series of higher dimensional compact complex manifolds having no homeomorphisms reversing the canonical class. After that, we resume and broaden the applications given in [KK] and [KK2], in particular, as a new application, we propose examples of (deformation) non equivalent symplectic structures with opposite canonical classes.

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Combinatorial Patchworking Of Real Pseudo-Holomorphic Curves, Ilia Itenberg, Eugenii Shustin Jan 2002

Combinatorial Patchworking Of Real Pseudo-Holomorphic Curves, Ilia Itenberg, Eugenii Shustin

Turkish Journal of Mathematics

The Viro method of construction of real algebraic varieties with prescribed topology uses convex subdivisions of Newton polyhedra. We show that in the case of arbitrary (not necessarily convex) subdivisions of polygons corresponding to C P^2 and rational ruled surfaces \Sigma_a, a \geq 0 the Viro method produces pseudo-holomorphic curves. The version of the Viro method discussed in the paper also gives a possibility to construct singular pseudo-holomorphic curves by gluing singular algebraic curves whose collections of singularities do not permit to glue these curves in the framework of the standard Viro method. As an application, we construct a series …

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On 1-Point Gromov-Witten Invariants Of The Hilbert Schemes Of Points On Surfaces, Wei-Ping Li, Zhenbo Qin Jan 2002

On 1-Point Gromov-Witten Invariants Of The Hilbert Schemes Of Points On Surfaces, Wei-Ping Li, Zhenbo Qin

Turkish Journal of Mathematics

We compute certain 1-point genus-0 Gromov-Witten invariants of the Hilbert scheme of points on a simply-connected smooth projective surface.

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Evidence For A Conjecture Of Pandharipande, Jim Bryan Jan 2002

Evidence For A Conjecture Of Pandharipande, Jim Bryan

Turkish Journal of Mathematics

In his paper ``Hodge integrals and degenerate contributions'', Pandharipande studied the relationship between the enumerative geometry of certain 3-folds and the Gromov-Witten invariants. In some good cases, enumerative invariants (which are manifestly integers) can be expressed as a rational combination of Gromov-Witten invariants. Pandharipande speculated that the same combination of invariants should yield integers even when they do not have any enumerative significance on the 3-fold. In the case when the 3-fold is the product of a complex surface and an elliptic curve, Pandharipande has computed this combination of invariants on the 3-fold in terms of the Gromov-Witten invariants of …

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Variations On Fintushel-Stern Knot Surgery On 4-Manifolds, Selman Akbulut Jan 2002

Variations On Fintushel-Stern Knot Surgery On 4-Manifolds, Selman Akbulut

Turkish Journal of Mathematics

We discuss some consequences Fintushel-Stern `knot surgery' operation coming from its handlebody description. We give some generalizations of this operation and give a counterexample to their conjecture.

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Braids And Symplectic Four-Manifolds With Abelian Fundamental Group, Paul Seidel Jan 2002

Braids And Symplectic Four-Manifolds With Abelian Fundamental Group, Paul Seidel

Turkish Journal of Mathematics

We explain how a version of Floer homology can be used as an invariant of symplectic manifolds with b_1>0. As a concrete example, we look at four-manifolds produced from braids by a surgery construction. The outcome shows that the invariant is nontrivial; however, it is an open question whether it is stronger than the known ones.

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Low-Dimensional Homology Groups Of Mapping Class Groups: A Survey, Mustafa Korkmaz Jan 2002

Low-Dimensional Homology Groups Of Mapping Class Groups: A Survey, Mustafa Korkmaz

Turkish Journal of Mathematics

In this survey paper, we give a complete list of known results on the first and the second homology groups of surface mapping class groups. Some known results on higher (co) homology are also mentioned.

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Gauge Theory And Stein Fillings Of Certain 3-Manifolds, Andras I. Stipsicz Jan 2002

Gauge Theory And Stein Fillings Of Certain 3-Manifolds, Andras I. Stipsicz

Turkish Journal of Mathematics

In the following we show that a Stein filling S of the 3-torus T^3 is homeomorphic to D^2 \times T^2. In the proof we also show that if S is Stein and \partial S is diffeomorphic to the Seifert fibered 3-manifold -\Sigma (2,3,11) then b_1(S)=0 and Q_S=H. Similar results are obtained for the Poincaré homology sphere \pm \Sigma (2,3,5); in studying these fillings we apply recent gauge theoretic results, and prove our theorems by determining certain Seiberg-Witten invariants.

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On Summand Sum And Summand Intersection Property Of Modules, Mustafa Alkan, Abdullah Harmanci Jan 2002

On Summand Sum And Summand Intersection Property Of Modules, Mustafa Alkan, Abdullah Harmanci

Turkish Journal of Mathematics

R will be an associative ring with identity and modules M will be unital left R- modules. In this work, extending modules and lifting modules with the SSP (or SIP) are studied. A necessary and sufficient condition for a module M to have the SSP is that for every decomposition M = A\oplus B and f\in Hom(A,B), Im(f) is a direct summand of B. Among others it is shown also that a (C_3) module with the SIP has the SSP, and a (D_3) module with SSP has the SIP.

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Asymptotic Formulas For The Eigenvalues Of The Schrodinger Operator, Şi̇ri̇n Atilgan, Sedef Karakiliç, Oktay A. Veliev Jan 2002

Asymptotic Formulas For The Eigenvalues Of The Schrodinger Operator, Şi̇ri̇n Atilgan, Sedef Karakiliç, Oktay A. Veliev

Turkish Journal of Mathematics

In this paper, we obtain asymptotic formulas for the eigenvalues of the d-dimensional Schrodinger operator L=-\Delta +q(x) in d-dimensional parallelepiped F with Dirichlet and Neumann boundary conditions.

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Remarks On Bounded Operators In Köthe Spaces, P. B. Djakov, T. Terzi̇oğlu, M. Yurdakul, V. P. Zahariuta Jan 2002

Remarks On Bounded Operators In Köthe Spaces, P. B. Djakov, T. Terzi̇oğlu, M. Yurdakul, V. P. Zahariuta

Turkish Journal of Mathematics

We prove that if \lambda(A),\lambda(B) and \lambda(C) are Köthe spaces such that L(\lambda(A),\lambda(B)) and L(\lambda(C),\lambda(A)) consist of bounded operators then each operator acting on \lambda(A) that factors over \lambda(B)\widehat\otimes_{\pi} \lambda(C) is bounded.

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On The Existence Of Nontrivial Solutions To Some Elliptic Variational Inequalities, Vy Khoi Le, Klaus Schmitt Jan 2002

On The Existence Of Nontrivial Solutions To Some Elliptic Variational Inequalities, Vy Khoi Le, Klaus Schmitt

Mathematics and Statistics Faculty Research & Creative Works

The paper is concerned with the existence of nontrivial solutions of the obstacle problem: u ε K: ∫Ω ▽u▽ (v - u) dx - λ ∫ Ω u (v - u) dx ≥ ∫ Ω p (x, u) (v - u) dx ∀x ε K, where K = {v ε Ho1(Ω): v ≤ Ψ a.e. on Ω}. By using a generalized mountain pass theorem for inequalities, we prove, subject to some restrictions on the obstacle Ψ, the existence of nontrivial solutions of the above inequality.

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N-Commutator Groups, A. A. Mehrvarz, K. Azizi Jan 2002

N-Commutator Groups, A. A. Mehrvarz, K. Azizi

Turkish Journal of Mathematics

A sufficient condition such that any element of G' (the commutator subgroup of G) can be represented as a product of n commutators, was studied in \cite{GAL62}. In this article we study a necessary and sufficient condition such that any element of G' can be represented as a product of n commutators, Let n be the smallest nature number such that any element of finite group G can be represented as a product of n commutators. A group G with this property will be called an n -commutator group, and n will be denoted by c(G) . Then \frac{\ln( G' …

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Intrinsic Knotting And Linking Of Complete Graphs, Erica Flapan Jan 2002

Intrinsic Knotting And Linking Of Complete Graphs, Erica Flapan

Pomona Faculty Publications and Research

We show that for every m∈N, there exists an n∈N such that every embedding of the complete graph Kn in R3 contains a link of two components whose linking number is at least m. Furthermore, there exists an r∈N such that every embedding of Kr in R3 contains a knot Q with |a2(Q)| ≥ m, where a2(Q) denotes the second coefficient of the Conway polynomial of Q.

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1p Spaces, Anh Tuyet Tran Jan 2002

1p Spaces, Anh Tuyet Tran

Theses Digitization Project

In this paper we will study the 1p spaces. We will begin with definitions and different examples of 1p spaces. In particular, we will prove Holder's and Minkowski's inequalities for 1p sequence.

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Decomposition Of Pascal’S Kernels Mod PS, Richard P. Kubelka Jan 2002

Decomposition Of Pascal’S Kernels Mod PS, Richard P. Kubelka

Faculty Publications

For a prime p we define Pascal's Kernel K(p,s) = [k(p,s)ij]∞i,j=0 as the infinite matrix satisfying k(p,s)ij = 1/px(i+jj) mod p if (i+jj) is divisible by ps and k(p,s)ij = 0 otherwise. While the individual entries of Pascal's Kernel can be computed using a formula of Kazandzidis that has been known for some time, our purpose here will be to use that formula …

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Renewal Theory For Uniform Random Variables, Steven Robert Spencer Jan 2002

Renewal Theory For Uniform Random Variables, Steven Robert Spencer

Theses Digitization Project

This project will focus on finding formulas for E[N(t)] using one of the classical problems in the discipline first, and then extending the scope of the problem to include overall times greater than the time t in the original problem. The expected values in these cases will be found using the uniform and exponential distributions of random variables.

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The Cyclic Cutwidth Of Mesh Cubes, Dwayne William Clarke Jan 2002

The Cyclic Cutwidth Of Mesh Cubes, Dwayne William Clarke

Theses Digitization Project

This project's purpose was to understand the workings of a new theorem introduced in a professional paper on the cutwidth of meshes and then use this knowledge to apply it to the search for the cyclic cutwidth of the n-cube.

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Sheaf Cohomology Of Conscious Entity, Goro Kato Jan 2002

Sheaf Cohomology Of Conscious Entity, Goro Kato

Mathematics

Awareness of a conscious entity can exist without elements; therefore, the general notion of an object of a category is employed. One of the characterization of understanding is: for a given local infonnation (awareness) there exists a global information whose restriction is the given information. For such mental activities, category and sheaf theories are employed to formulate consciousness. We will show that the cohomology (more general precohomology) object, a subquotient object, better represents the essence of a conscious entity than an object itself. We will also give a definition of an observation to fonnulate the collapse of the wave and …

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Fundamental Theorem Of Algebra, Paul Shibalovich Jan 2002

Fundamental Theorem Of Algebra, Paul Shibalovich

Theses Digitization Project

The fundamental theorem of algebra (FTA) is an important theorem in algebra. This theorem asserts that the complex field is algebracially closed. This thesis will include historical research of proofs of the fundamental theorem of algebra and provide information about the first proof given by Gauss of the theorem and the time when it was proved.

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Egyptian Fractions, Jodi Ann Hanley Jan 2002

Egyptian Fractions, Jodi Ann Hanley

Theses Digitization Project

Egyptian fractions are what we know as unit fractions that are of the form 1/n - with the exception, by the Egyptians, of 2/3. Egyptian fractions have actually played an important part in mathematics history with its primary roots in number theory. This paper will trace the history of Egyptian fractions by starting at the time of the Egyptians, working our way to Fibonacci, a geologist named Farey, continued fractions, Diophantine equations, and unsolved problems in number theory.

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\Theta-Euclidean L-Fuzzy Ideals Of Rings, Ayten Koç, Erol Balkanay Jan 2002

\Theta-Euclidean L-Fuzzy Ideals Of Rings, Ayten Koç, Erol Balkanay

Turkish Journal of Mathematics

The concept of fuzzy ideals is extended by introducing \theta -Euclidean L-fuzzy ideals in rings. In particular, some structural theorems for a \theta -Euclidean L-fuzzy ideal of R are proved.

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Category Theory And Consciousness, Goro Kato, Daniele C. Struppa Jan 2002

Category Theory And Consciousness, Goro Kato, Daniele C. Struppa

Mathematics

No abstract provided.

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Orbifold Homeomorphism And Diffeomorphism Groups, Joseph E. Borzellino, Victor Brunsden Jan 2002

Orbifold Homeomorphism And Diffeomorphism Groups, Joseph E. Borzellino, Victor Brunsden

Mathematics

In this paper we outline results on orbifold diffeomorphism groups that were presented at the International Conference on Infinite Dimensional Lie Groups in Geometry and Representation Theory at Howard University, Washington DC on August 17-21, 2000. Specifically, we define the notion of reduced and unreduced orbifold diffeomorphism groups. For the reduced orbifold diffeomorphism group we state and sketch the proof of the following recognition result: Let O1 and O2 be two compact, locally smooth orbifolds. Fix r ≥ 0. Suppose that Φ : Diffr (O1) → Diffr (O2) is a group isomorphism. Then Φ is induced by redred a (topological) …

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Enumeration Of Matchings In The Incidence Graphs Of Complete And Complete Bipartite Graphs, Nicholas Pippenger Jan 2002

Enumeration Of Matchings In The Incidence Graphs Of Complete And Complete Bipartite Graphs, Nicholas Pippenger

All HMC Faculty Publications and Research

If G = (V, E) is a graph, the incidence graphI(G) is the graph with vertices I ∪ E and an edge joining v ∈ V and e ∈ E when and only when v is incident with e in G. For G equal to Kn (the complete graph on n vertices) or Kn,n (the complete bipartite graph on n + n vertices), we enumerate the matchings (sets of edges, no two having a vertex in common) in I(G), both exactly (in terms of generating …

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