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2001

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Articles 151 - 180 of 245

Full-Text Articles in Mathematics

Theism And Mathematical Realism, John Byl Jan 2001

Theism And Mathematical Realism, John Byl

ACMS Journal 2004

This paper examines connections between theism and mathematical realism. Mathematical realism, which offers the best account of mathematics, strongly supports theism. Theism, in turn, supports mathematical realism. Theism readily explains the intricate relations between mathematics, matter, and mind. The attributes of the biblical God provide a justification for classical mathematics.

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Mathematics As Worship, David J. Stucki Jan 2001

Mathematics As Worship, David J. Stucki

ACMS Journal 2004

This paper treats worship in a broad, inclusive sense as the primary and necessary response of human beings to their creator. It provides a brief overview of the relationship between mathematics and theology from the Pythagoreans to the present. It argues that all knowledge is contingent upon faith and thus that contemplation of mathematical insights can lead to worship of God.

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A Multigrid Method For Elliptic Grid Generation Using Compact Schemes, Balaji S. Iyangar Jan 2001

A Multigrid Method For Elliptic Grid Generation Using Compact Schemes, Balaji S. Iyangar

Doctoral Dissertations

Traditional iterative methods are stalling numerical processes, in which the error has relatively small changes from one iteration to the next. Multigrid methods overcome the limitations of iterative methods and are computationally efficient. Convergence of iterative methods for elliptic partial differential equations is extremely slow. In particular, the convergence of the non-linear elliptic Poisson grid generation equations used for elliptic grid generation is very slow. Multigrid methods are fast converging methods when applied to elliptic partial differential equations. In this dissertation, a non-linear multigrid algorithm is used to accelerate the convergence of the non-linear elliptic Poisson grid generation method. The …

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Extended Powers Of Manifolds And The Adams Spectral Sequence, Robert R. Bruner Jan 2001

Extended Powers Of Manifolds And The Adams Spectral Sequence, Robert R. Bruner

Mathematics Faculty Research Publications

The extended power construction can be used to create new framed manifolds out of old. We show here how to compute the effect of such operations in the Adams spectral sequence, extending partial results of Milgram and the author. This gives the simplest method of proving that Jones’ 30-manifold has Kervaire invariant one, and allows the construction of manifolds representing Mahowald’s classes η4 and η5, among others.

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Cubic Hamiltonian Graphs And Generalized Knight's Tours, Siew Hui Ong Jan 2001

Cubic Hamiltonian Graphs And Generalized Knight's Tours, Siew Hui Ong

Student Works (2000-2009)

This thesis is divided into two parts, both related to hamiltonian graphs. The first part deals with 3-connected cubic bipartite planar graphs. By assuming that all 3-connected cubic bipartite planar graphs are hamiltonian, lower bounds for the number of Hamilton cycles in cubic bipartite planar graphs with given cyclic connectivity are obtained in Chapter 2. In Chapter 3, we show that Barnette's Conjecture is equivalent to the conjecture which states that for any two edges x and y on the same face of a 3-connected cubic bipartite planar hamiltonian graph, there is a Hamilton cycle passing through x and y1 …

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Enumeration Of Equicolourable Trees, Nicholas Pippenger Jan 2001

Enumeration Of Equicolourable Trees, Nicholas Pippenger

All HMC Faculty Publications and Research

A tree, being a connected acyclic graph, can be bicolored in two ways, which differ from each other by exchange of the colors. We shall say that a tree is equicolorable if these bicolorings assign the two colors to equal numbers of vertices. Labelled equicolored trees have been enumerated several times in the literature, and from this result it is easy to enumerate labelled equicolorable trees. The result is that the probability that a randomly chosen n-vertex labelled tree is equicolorable is asymptotically just twice the probability that its vertices would be equicolored if they were assigned colors by …

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A Mathematical Tumor Model With Immune Resistance And Drug Therapy: An Optimal Control Approach, Lisette G. De Pillis, Ami E. Radunskaya Jan 2001

A Mathematical Tumor Model With Immune Resistance And Drug Therapy: An Optimal Control Approach, Lisette G. De Pillis, Ami E. Radunskaya

All HMC Faculty Publications and Research

We present a competition model of cancer tumor growth that includes both the immune system response and drug therapy. This is a four-population model that includes tumor cells, host cells, immune cells, and drug interaction. We analyze the stability of the drug-free equilibria with respect to the immune response in order to look for target basins of attraction. One of our goals was to simulate qualitatively the asynchronous tumor-drug interaction known as “Jeffs phenomenon.” The model we develop is successful in generating this asynchronous response behavior. Our other goal was to identify treatment protocols that could improve standard pulsed chemotherapy …

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Residual Properties And Almost Equicontinuity, Ethan Akin, Eli Glasner Jan 2001

Residual Properties And Almost Equicontinuity, Ethan Akin, Eli Glasner

Mathematics and Statistics Faculty Research & Creative Works

A property P of a compact dynamical system (X, f) is called a residual property if it is inherited by factors, almost one-to-one lifts and surjective inverse limits. Many transitivity properties are residual. Weak disjointness from all property P systems is a residual property provided P is a residual property stronger than transitivity. Here two systems are weakly disjoint when their product is transitive. Our main result says that for an almost equicontinuous system (X, f) with associated monothetic group Λ, (X, f) is weakly disjoint from all P systems if the only P systems upon which Λ acts are …

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A 4-Dimensional 1-Lcc Shrinking Theorem, Mladen Bestvina, Robert J. Daverman, Gerard A. Venema Jan 2001

A 4-Dimensional 1-Lcc Shrinking Theorem, Mladen Bestvina, Robert J. Daverman, Gerard A. Venema

University Faculty Publications and Creative Works

This paper contains several shrinking theorems for decompositions of 4-dimensional manifolds. Let f : M → X be a closed, cell-like mapping of a 4-manifold M onto a metric space X and let Y be a closed subset of X such that X - Y is a 4-manifold and Y is locally simply co-connected in X. The main result states that f can be approximated by homeomorphisms if Y is a 1-dimensional ANR. The techniques of the proof also show that f can be approximated by homeomorphisms in case Y is an arbitrary 0-dimensional closed subset. Combining the two results …

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Existence Criteria For Singular Initial Value Problems With Sign Changing Nonlinearities, Ravi P. Agarwal, Donal O'Regan, V. Lakshmikantham Jan 2001

Existence Criteria For Singular Initial Value Problems With Sign Changing Nonlinearities, Ravi P. Agarwal, Donal O'Regan, V. Lakshmikantham

Mathematics and System Engineering Faculty Publications

A general existence theory is presented for initial value problems where our nonlinearity may be singular in its dependent variable and may also change sign.

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Modal Rules Are Co-Implications, Alexander Kurz Jan 2001

Modal Rules Are Co-Implications, Alexander Kurz

Engineering Faculty Articles and Research

In [13], it was shown that modal logic for coalgebras dualises—concerning definability— equational logic for algebras. This paper establishes that, similarly, modal rules dualise implications:It is shown that a class of coalgebras is definable by modal rules iff it is closed under H (images) and Σ (disjoint unions). As a corollary the expressive power of rules of infinitary modal logic on Kripke frames is characterised.

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Some New Approaches To Formulate And Estimate Friction-Bernoulli Jump Diffusion And Friction-Garch, Chihwa Kao Jan 2001

Some New Approaches To Formulate And Estimate Friction-Bernoulli Jump Diffusion And Friction-Garch, Chihwa Kao

Center for Policy Research

In this paper we propose a friction model with a Beroulli jump diffusion and a friction with GARCH to examine the exchange rates movements in Taiwan. The proposed model resolves the estimation problem associated with the stepwise movements of observed exchange rates. The specification maintains the desirable economic properties associated with movements in exchange rate returns and is empirically tractable. The AIC apparently favors the model based on Friction-GARCH model.

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Constructing Regular Ramanujan Graphs Via Graph Extension, Sage Michelle Accardo Jan 2001

Constructing Regular Ramanujan Graphs Via Graph Extension, Sage Michelle Accardo

Honors Capstones

No abstract provided.

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Strictly Positive Definite Functions On A Compact Group, Mohamed Allali, Tomasz Przebinda Jan 2001

Strictly Positive Definite Functions On A Compact Group, Mohamed Allali, Tomasz Przebinda

Mathematics, Physics, and Computer Science Faculty Articles and Research

We recognize a result of Schreiner, concerning strictly positive definite functions on a sphere in an Euclidean space, as a generalization of Bochner's theorem for compact groups.

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Symplectic Maps To Projective Spaces And Symplectic Invariants, Denis Auroux Jan 2001

Symplectic Maps To Projective Spaces And Symplectic Invariants, Denis Auroux

Turkish Journal of Mathematics

After reviewing recent results on symplectic Lefschetz pencils and symplectic branched covers of \CP^2, we describe a new construction of maps from symplectic manifolds of any dimension to \CP^2 and the associated monodromy invariants. We also show that a dimensional induction process makes it possible to describe any compact symplectic manifold by a series of words in braid groups and a word in a symmetric group.

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The Topology Of Symplectic Manifolds, Robert E. Gompf Jan 2001

The Topology Of Symplectic Manifolds, Robert E. Gompf

Turkish Journal of Mathematics

A topological structure is introduced that seems likely to provide a complete topological characterization of compact symplectic manifolds. The article begins with a leisurely introduction to symplectic manifolds from a topological viewpoint. It then focuses on Thurston's construction of a symplectic structure on the total space of a fiber bundle. This is generalized to a technique for putting a symplectic structure on the domain of a J-holomorphic map. A topological structure called a hyperpencil on a compact 2n-manifold is then defined; this is motivated by the special case of a linear system of curves on an algebraic manifold, and it …

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Surface Bundles: Some Interesting Examples, Jim Bryan, Ron Donagi, Andras I. Stipsicz Jan 2001

Surface Bundles: Some Interesting Examples, Jim Bryan, Ron Donagi, Andras I. Stipsicz

Turkish Journal of Mathematics

We show two constructions of surface bundles over Riemann surfaces admitting nonvanishing signatures.

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Torus Fibrations On Symplectic Four-Manifolds, Ivan Smith Jan 2001

Torus Fibrations On Symplectic Four-Manifolds, Ivan Smith

Turkish Journal of Mathematics

This paper has two essentially unrelated halves. In the first we prove that a closed symplectic four-manifold admitting a fibration by connected, homologically essential Lagrangian tori with "tame" singularities, is fibre-preserving diffeomorphic to a K3 surface or to a torus bundle over a torus with first Betti number at least three. In the second, we prove that these torus bundles over tori admit Lefschetz pencils by genus three curves. It follows that the genus three mapping class group admits infinitely many inequivalent irreducible positive relations. Motivations for the questions are provided from mirror symmetry, integrable systems and Seiberg-Witten theory: in …

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Sections Of Lefschetz Fibrations And Stein Fillings, Andras I. Stipsicz Jan 2001

Sections Of Lefschetz Fibrations And Stein Fillings, Andras I. Stipsicz

Turkish Journal of Mathematics

Using Eliashberg's theorem about Stein fillings of S^3 we prove that a section of a Lefschetz fibration over S^2 has nonnegative square. This observation, in particular, implies that the identity element 1\in \Gamma _g ^1 in the mapping class group of a genus-g surface with one boundary component cannot be written as a product of positive Dehn twists.

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Floer Homology And Its Continuity For Non-Compact Lagrangian Submanifolds, Yong-Geum Oh Jan 2001

Floer Homology And Its Continuity For Non-Compact Lagrangian Submanifolds, Yong-Geum Oh

Turkish Journal of Mathematics

We give a construction of the Floer homology of the pair of vnon-compact Lagrangian submanifolds, which satisfies natural continuity property under the Hamiltonian isotopy that moves the infinity but leaves the intersection set of the pair compact. This construction uses the concept of Lagrangian cobordism and certain singular Lagrangian submanifolds. We apply this construction to conormal bundles (or varieties) in the cotangent bundle, and relate it to a conjecture made by MacPherson on the intersection theory of the characteristic Lagrangian cycles associated to the perverse sheaves constructible to a complex stratification on the complex algebraic manifold.

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The Canonical Class Of A Symplectic Four Manifold, Ronald Fintushel, Ronald Stern Jan 2001

The Canonical Class Of A Symplectic Four Manifold, Ronald Fintushel, Ronald Stern

Turkish Journal of Mathematics

In this article we present examples of simply connected symplectic 4-manifolds X whose canonical classes are represented by complicated disjoint unions of symplectic submanifolds of X: Theorem. Given finite collections {g_i}, {m_i}, i=1,...,n, of positive integers, there is a minimal symplectic simply connected 4-manifold X whose canonical class is represented by a disjoint union of embedded symplectic surfaces K ~ S_{g_1,1} « ... « S_{g_1,m_1} « ... « S_{g_n,1} «... « S{g_n,m_n} where S_{g_i,j} is a surface of genus g_i. Furthermore, c_1^2(X) = c_h(X) - (2+ b) where b= S{i=1}^n m_i is the total number of connected components of the …

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A Partial Order On The Group Of Contactomorphisms Of $\R^{2n+1}$ Via Generating Functions, Mohan Bhupal Jan 2001

A Partial Order On The Group Of Contactomorphisms Of $\R^{2n+1}$ Via Generating Functions, Mohan Bhupal

Turkish Journal of Mathematics

In this note we construct a nontrivial partial order on the identity component of the group of compactly supported contactomorphisms of \R^{2n+1} using the method of generating functions. Our construction is in the framework of the theory developed by Viterbo in the paper \cite{V} wherein, among other things, he showed how one could use generating functions to construct a partial order on the group of compactly supported Hamiltonian symplectomorphisms of \R^{2n}.

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Knotting Of Algebraic Curves In Complex Surfaces, Sergey Finashin Jan 2001

Knotting Of Algebraic Curves In Complex Surfaces, Sergey Finashin

Turkish Journal of Mathematics

For any d\ge 5, I constructed infinitely many pairwise smoothly non-equivalent surfaces F\subset\Cp{2} homeomorphic to a non-singular algebraic curve of degree d, realizing the same homology class as such a curve and having abelian fundamental group \pi_1(\Cp2\stmin F). It is a special case of a more general theorem, which concerns for instance those algebraic curves, A, in a simply connected algebraic surface, X, which admit irreducible degenerations to a curve A_0, with a unique singularity of the type X_9, and such that A\cite A>16.

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The Verlinde Algebra Is Twisted Equivariant K-Theory, Daniel S. Freed Jan 2001

The Verlinde Algebra Is Twisted Equivariant K-Theory, Daniel S. Freed

Turkish Journal of Mathematics

The Verlinde algebra, which mathematically appears in the theory of loop groups and is related to moduli spaces of bundles over curves, turns out to be describable in terms of K-theory. This is a joint discovery with M. Hopkins and C. Teleman. Here we explain in heuristic terms how this fits naturally into ideas about the Chern-Simons topological field theory.

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Topological Quantum Field Theory And Hyperkähler Geometry, Justin Sawon Jan 2001

Topological Quantum Field Theory And Hyperkähler Geometry, Justin Sawon

Turkish Journal of Mathematics

Rozansky and Witten proposed a 3-dimensional sigma-model whose target space is a hyperkähler manifold. They conjectured that this theory has an associated TQFT, with vector spaces given by certain cohomology groups of the hyperkähler manifold. On the other hand, there is a certain modified TQFT constructed by Murakami and Ohtsuki using the universal quantum invariant. We explain how the Rozansky-Witten TQFT can be obtained from the latter by applying a "hyperkähler weight system".

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G-Bundles On Abelian Surfaces, Hyperk\"Aler Manifolds, And Stringy Hodge Numbers, Jim Bryan, Ron Donagi, Naichung Conan Leung Jan 2001

G-Bundles On Abelian Surfaces, Hyperk\"Aler Manifolds, And Stringy Hodge Numbers, Jim Bryan, Ron Donagi, Naichung Conan Leung

Turkish Journal of Mathematics

We study the moduli space M_{G} (A) of flat G-bundles on an Abelian surface A, where G is a compact, simple, simply connected, connected Lie group. Equivalently, M_{G} (A) is the (coarse) moduli space of s-equivalence classes of holomorphic semi-stable G^{\cnums }-bundles with trivial Chern classes. M_{G} (A) has the structure of a hyperk\"ahler orbifold. We show that when G is Sp(n) or SU (n), M_{G} (A) has a natural hyperk\"ahler desingularization which we exhibit as a moduli space of G^{\cnums }-bundles with an altered stability condition. In this way, we obtain the two known families of hyperk\"ahler manifolds, the …

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On The Tautological Ring Of \Bar{\Mathcal{M}}_{G,N}, Tom Graber, Ravi Vakil Jan 2001

On The Tautological Ring Of \Bar{\Mathcal{M}}_{G,N}, Tom Graber, Ravi Vakil

Turkish Journal of Mathematics

We prove that the dimension 0 part of the tautological ring of the moduli space of stable pointed curves is one-dimensional. This provides the first genus-free evidence for a conjecture of Faber and Pandharipande that the tautological ring of the moduli space is Gorenstein, answering in the affirmative a question of Hain and Looijenga.

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Induced Cat^1-Groups, Murat Alp Jan 2001

Induced Cat^1-Groups, Murat Alp

Turkish Journal of Mathematics

In this paper we define the pullback cat^1-group and show that this Pullback has a right adjoint which is the induced cat^1-group. Later we show that this right adjoint is a pushout of category of cat^1-groups. We calculate the Peiffer subgroups to find a finite group of the source of induced cat^1-groups. The generating set of Peiffer subgroups are also given in this paper. All results are corrected by a GAP[13] program package in [4]. This paper also contains the some computational examples which are the calculation-induced cat^1-group and comparative times between the induced crossed modules and induced cat^1-groups.

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A Class Of Monoids Embeddable In A Group, Ebru Keyman Jan 2001

A Class Of Monoids Embeddable In A Group, Ebru Keyman

Turkish Journal of Mathematics

In this paper, we develop a new method to show that a monoid, given by a certain kind of presentation, embeds in a group. A mathematical device called the diamond condition was used in [5] to prove that the singular braid monoid SB_n embeds. Motivated by this, we consider monoid presentations which have the basic properties of the presentation of the singular braid monoid. In the same way as in [5], we prove that the monoid embeds. The proof of the diamond condition is completely geometric in [5], but here we prove it by using elementary algebraic properties.

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On The Semi-Markovian Random Walk Process With Reflecting And Delaying Barrriers, Selahatti̇n Maden Jan 2001

On The Semi-Markovian Random Walk Process With Reflecting And Delaying Barrriers, Selahatti̇n Maden

Turkish Journal of Mathematics

In this paper, a semi-Markovian random walk process X(t) with reflecting barrier on the zero-level and delaying barrier on the \beta(\beta>0 )-level and the first falling moment of the process into the delaying barrier, (\gamma), are considered. Some probability characteristics of \gamma , such as its distribution function, moment generating function and expected value are calculated.

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