Foliations And Global Inversion, 2010 Trinity University

#### Foliations And Global Inversion, Eduardo C. Balreira

*Mathematics Faculty Research*

We consider topological conditions under which a locally invertible map admits a global inverse. Our main theorem states that a local diffeomorphism f : M → Rn is bijective if and only if Hn−1(M) = 0 and the pre-image of every affine hyperplane is non-empty and acyclic. The proof is based on some geometric constructions involving foliations and tools from intersection theory. This topological result generalizes in finite dimensions the classical analytic theorem of Hadamard-Plastock, including its recent improvement by Nollet-Xavier. The main theorem also relates to a conjecture of the aforementioned authors, involving the well known Jacobian Conjecture in algebraic ...

Some Implications Of Chu's 10Ψ10 Generalization Of Bailey's 6Ψ6 Summation Formula, 2010 West Chester University of Pennsylvania

#### Some Implications Of Chu's 10Ψ10 Generalization Of Bailey's 6Ψ6 Summation Formula, James Mclaughlin, Andrew Sills

*Mathematics*

Lucy Slater used Bailey's 6*Ã*6 summation formula to derive the Bailey pairs she used to construct her famous list of 130 identities of the Rogers-Ramanujan type.

In the present paper we apply the same techniques to Chu's 10*Ã*10 generalization of Bailey's formula to produce quite general Bailey pairs. Slater's Bailey pairs are then recovered as special limiting cases of these more general pairs.

In re-examining Slater's work, we find that her Bailey pairs are, for the most part, special cases of more general Bailey pairs containing one or more free parameters ...

On Hyperplanes And Semispaces In Max-Min Convex Geometry, 2010 West Chester University of Pennsylvania

#### On Hyperplanes And Semispaces In Max-Min Convex Geometry, Viorel Nitica, Sergeĭ Sergeev

*Mathematics*

No abstract provided.

Methods Of Competing Risks Analysis Of End-Stage Renal Disease And Mortality Among People With Diabetes, 2010 University of Saskatchewan College of Medicine

#### Methods Of Competing Risks Analysis Of End-Stage Renal Disease And Mortality Among People With Diabetes, Hyun J. Lim, Xu Zhang, Roland Dyck, Nathaniel Osgood

*Mathematics and Statistics Faculty Publications*

Background: When a patient experiences an event other than the one of interest in the study, usually the probability of experiencing the event of interest is altered. By contrast, disease-free survival time analysis by standard methods, such as the Kaplan-Meier method and the standard Cox model, does not distinguish different causes in the presence of competing risks. Alternative approaches use the cumulative incidence estimator by the Cox models on cause-specific and on subdistribution hazards models. We applied cause-specific and subdistribution hazards models to a diabetes dataset with two competing risks (end-stage renal disease (ESRD) or death without ESRD) to measure ...

A Categorical Semantics For Fuzzy Predicate Logic, 2010 Illinois Wesleyan University

#### A Categorical Semantics For Fuzzy Predicate Logic, Lawrence Stout

*Scholarship*

The object of this study is to look at categorical approaches to many valued logic, both propositional and predicate, to see how different logical properties result from different parts of the situation. In particular, the relationship between the categorical fabric I introduced at Linz in 2004 and the Fuzzy Logics studied by Hajek (2003) [5], Esteva et al. (2003) [1], and Hajek (1998) [4], comes from restricting the kind of structures used for truth values. We see how the structure of the various kinds of algebras shows up in the categorical logic, giving a variant on natural deduction for these ...

Categorical Approaches To Non-Commutative Fuzzy Logic, 2010 Illinois Wesleyan University

#### Categorical Approaches To Non-Commutative Fuzzy Logic, Lawrence Stout

*Scholarship*

In this paper we consider what it means for a logic to be non-commutative, how to generate examples of structures with a non-commutative operation * which have enough nice properties to serve as the truth values for a logic. Inference in the propositional logic is gotten from the categorical properties (products, coproducts, monoidal and closed structures, adjoint functors) of the categories of truth values. We then show how to extend this view of propositional logic to a predicate logic using categories of propositions about a type A with functors giving change of type and adjoints giving quantifiers. In the case where ...

When Does A Category Built On A Lattice With A Monoidal Structure Have A Monoidal Structure?, 2010 Illinois Wesleyan University

#### When Does A Category Built On A Lattice With A Monoidal Structure Have A Monoidal Structure?, Lawrence Stout

*Scholarship*

In a word, sometimes. And it gets harder if the structure on L is not commutative. In this paper we consider the question of what properties are needed on the lattice L equipped with an operation * for several different kinds of categories built using Sets and L to have monoidal and monoidal closed structures. This works best for the Goguen category Set(L) in which membership, but not equality, is made fuzzy and maps respect membership. Commutativity becomes critical if we make the equality fuzzy as well. This can be done several ways, so a progression of categories is considered ...

Hydraulic Geometry Relationships And Regional Curves For The Inner And Outer Bluegrass Regions Of Kentucky, 2010 University of Kentucky

#### Hydraulic Geometry Relationships And Regional Curves For The Inner And Outer Bluegrass Regions Of Kentucky, Ruth Roseann Brockman

*University of Kentucky Master's Theses*

Hydraulic geometry relationships and regional curves are used in natural channel design to assist engineers, biologists, and fluvial geomorphologists in the efforts undertaken to ameliorate previous activities that have diminished, impaired or destroyed the structure and function of stream systems. Bankfull channel characteristics were assessed for 14 United States Geological Survey (USGS) gaged sites in the Inner Bluegrass and 15 USGS gaged sites in the Outer Bluegrass Regions of Kentucky. Hydraulic geometry relationships and regional curves were developed for the aforementioned regions.

Analysis of the regression relationships showed that bankfull discharge is a good explanatory variable for bankfull parameters such ...

Chi-Square Lower Bounds, 2010 University of Pennsylvania

#### Chi-Square Lower Bounds, Mark G. Low

*Statistics Papers*

The information inequality has been shown to be an effective tool for providing lower bounds for the minimax risk. Bounds based on the chi-square distance can sometimes offer a considerable improvement especially when applied iteratively. This paper compares these two methods in four examples including the bounded normal mean problem as well as obervations from a Poisson distribution.

Nonparametric Regression In Natural Exponential Families, 2010 University of Pennsylvania

#### Nonparametric Regression In Natural Exponential Families, T. Tony Cai, Harrison H. Zhou

*Statistics Papers*

Theory and methodology for nonparametric regression have been particularly well developed in the case of additive homoscedastic Gaussian noise. Inspired by asymptotic equivalence theory, there have been ongoing efforts in recent years to construct explicit procedures that turn other function estimation problems into a standard nonparametric regression with Gaussian noise. Then in principle any good Gaussian nonparametric regression method can be used to solve those more complicated nonparametric models. In particular, Brown, Cai and Zhou [3] considered nonparametric regression in natural exponential families with a quadratic variance function.

In this paper we extend the scope of Brown, Cai and Zhou ...

Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, 2010 Wright State University - Main Campus

#### Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, Joaquin Riviera, Yi Li

*Mathematics and Statistics Faculty Publications*

In this paper we discuss the existence of traveling wave solutions for a nonlocal reaction-diffusion model of Influenza A proposed in Lin et. al. (2003). The proof for the existence of the traveling wave takes advantage of the different time scales between the evolution of the disease and the progress of the disease in the population. Under this framework we are able to use the techniques from geometric singular perturbation theory to prove the existence of the traveling wave.

Optimal Control And Feedback Design Of State-Constrained Parabolic Systems In Uncertainty Conditions, 2010 Wayne State University

#### Optimal Control And Feedback Design Of State-Constrained Parabolic Systems In Uncertainty Conditions, Boris S. Mordukhovich

*Mathematics Research Reports*

The paper concerns minimax control problems for linear multidimensional parabolic systems with distributed uncertain perturbations and control functions acting in the Dirichlet boundary conditions. The underlying parabolic control system is functioning under hard/pointwise constraints on control and state variables. The main goal is to design a feedback control regulator that ensures the required state performance and robust stability under any feasible perturbations and minimize an energy-type functional under the worst perturbations from the given area. We develop a constructive approach to the minimax control design of constrained parabolic systems that is based on certain characteristic features of the parabolic ...

The Probabilistic Zeta Function, 2010 College of Saint Benedict/Saint John's University

#### The Probabilistic Zeta Function, Bret Benesh

*Mathematics Faculty Publications*

This paper is a summary of results on the *P _{G}*(

*s*) function, which is the reciprocal of the probabilistic zeta function for finite groups. This function gives the probability that

*s*randomly chosen elements generate a group

*G*, and information about the structure of the group

*G*is embedded in it.

The Topology Of Incidence Pseudographs, 2010 Otterbein University

#### The Topology Of Incidence Pseudographs, Thomas R. James, Reinhard Klette

*Mathematics Faculty Scholarship*

Incidence pseudographs model a (re°exive and symmetric) inci- dence relation between sets of various dimensions, contained in a count- able family. Work by Klaus Voss in 1993 suggested that this general discrete model allows to introduce a topology, and some authors have done some studies into this direction in the past (also using alternative discrete models such as, for example, abstract complexes or orders on sets of cells). This paper provides a comprehensive overview about the topology of incidence pseudographs. This topology has various appli- cations, such as in modeling basic data in 2D or 3D digital picture analysis ...

Using Correlation Coefficients To Estimate Slopes In Multiple Linear Regression, 2010 University of Montana, Missoula

#### Using Correlation Coefficients To Estimate Slopes In Multiple Linear Regression, Rudy Gideon

*Mathematical Sciences Faculty Publications*

This short note takes correlation coefficients as the starting point to obtain inferential results in linear regression. Under certain conditions, the population correlation coefficient and the sampling correlation coefficient can be related via a Taylor series expansion to allow inference on the coefficients in simple and multiple regression. This general method includes nonparametric correlation coefficients and so gives a universal way to develop regression methods. This work is part of a correlation estimation system that uses correlation coefficients to perform estimation in many settings, for example, time series, nonlinear and generalized linear models, and individual distributions.

The Evolution And Discovery Of The Species Of Equality In Euclid’S Elements, 2010 The University of Tennessee College of Law

#### The Evolution And Discovery Of The Species Of Equality In Euclid’S Elements, Lee T. Nutini

*Lee T Nutini*

A look at the evidence for an additional and novel type of equality found in Euclid's Elements.

Sketch Of A Typology Of Abstract Memristic Machines, 2010 ThinkArt Lab Glasgow

#### Sketch Of A Typology Of Abstract Memristic Machines, Rudolf Kaehr

*Rudolf Kaehr*

A typology of memristic machines is sketched. This sketch gives an overview and orientation to the paper “Towards Abstract Memristic Machines”. It also intents to propose a concise systematization of the newly introduced terms and strategies to memristics and morphogrammatics. This sketch is introducing four types of sign-use for four types of machines of fundamentally different paradigms: 1. semiotic, 2. monomorphic, 3. polymorphic and 4. bisimilar abstract machines. Further definitions of abstract machines have to be based on those graphematic notational systems. A realization of such constructions of abstract machines, in contrast to existing abstract machines of the theory of ...

Towards Abstract Memristic Machines, 2010 ThinkArt Lab Glasgow

From Universe To Polyverses, 2010 ThinkArt Lab Glasgow

#### From Universe To Polyverses, Rudolf Kaehr

*Rudolf Kaehr*

Some thoughts about the power of speculation behind important discoveries in mathematics, physics and computer science. The exercise shows that there is no need for a compulsory ultimate unifying universe. It is speculated that just this paradigm of a single ultimate universe is unmasking itself today as the main obstacle for further development in Western science and technology.

Morphogrammatics For Dummies: The Domino Approach, 2010 ThinkArt Lab Glasgow

#### Morphogrammatics For Dummies: The Domino Approach, Rudolf Kaehr

*Rudolf Kaehr*

Dominoes, morphograms, cellular automata, memristics. Topics: possible continuation, coalitions, cooperations, substitution, morphic bisimilarity.