Recursion, Infinity, And Modeling, 2009 Illinois Wesleyan University

#### Recursion, Infinity, And Modeling, Lawrence Stout, Hans-Jorg Tiede

*Lawrence N. Stout*

Hauser, Chomsky, and Fitch (2002) claim that a core property of the human language faculty is recursion and that this property "yields discrete infinity" (2002: 1571) of natural languages. On the other hand, recursion is often motivated by the observation that there are infinitely many sentences that should be generated by a finite number of rules. It should be obvious that one cannot pursue both arguments simultaneously, on pain of circularity. The main aim of this paper is to clarify both conceptually and methodologically the relationship between recursion and infinity in language. We want to argue that discrete infinity is ...

Counting Interesting Elections, 2009 Valparaiso University

#### Counting Interesting Elections, Lara Pudwell, Eric Rowland

*Lara K. Pudwell*

No abstract provided.

List Coloring And N-Monophilic Graphs, 2009 Occidental College

#### List Coloring And N-Monophilic Graphs, Ramin Naimi, Radoslav Kirov

*Ramin Naimi*

In 1990, Kostochka and Sidorenko proposed studying the smallest number of list-colorings of a graph G among all assignments of lists of a given size n to its vertices. We say a graph G is n-monophilic if this number is minimized when identical n-color lists are assigned to all vertices of G. Kostochka and Sidorenko observed that all chordal graphs are n-monophilic for all n. Donner (1992) showed that every graph is n-monophilic for all suﬃciently large n. We prove that all cycles are n-monophilic for all n; we give a complete characterization of 2-monophilic graphs (which turns out to ...

Mathematica In Action: Problem-Solving Through Visualization And Computation, 2009 Macalester College

#### Mathematica In Action: Problem-Solving Through Visualization And Computation, Stan Wagon

*Stan Wagon, Retired*

No abstract provided.

Stacking Blocks And Counting Permutations, 2009 Valparaiso University

#### Stacking Blocks And Counting Permutations, Lara Pudwell

*Lara K. Pudwell*

No abstract provided.

Categorical Approaches To Non-Commutative Fuzzy Logic, 2009 Illinois Wesleyan University

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

*Lawrence N. Stout*

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 ...

Combinatorial Analysis, 2009 Macalester College

College Algebra In Context With Applications To The Managerial, Life, And Social Sciences, 2009 University of South Carolina - Beaufort

#### College Algebra In Context With Applications To The Managerial, Life, And Social Sciences, Ronald Harshbarger, Lisa Yocco

*Lisa S. Yocco*

Harshbarger/Yocco’s College Algebra in Context with Applications for the Managerial, Life, and Social Sciences, Third Edition uses modeling and real-data problems to develop the skills that students will need for their future courses and careers. Applications anticipate the math that students will encounter in their professional lives, giving them the practice they need to become adept problem-solvers. Every chapter begins with the Algebra Toolbox, which reviews the skills and concepts necessary to master the material ahead. This new full-color edition offers a greater number of technology tips, and the content has been reorganized to accommodate a wide range ...

On K4 Of The Gaussian And Eisenstein Integers, 2009 University of Massachusetts - Amherst

#### On K4 Of The Gaussian And Eisenstein Integers, Mathieu Dutour Sikiric, Herbert Gangl, Paul Gunnells, Jonathan Hanke, Achill Schürmann, Dan Yasaki

*Paul Gunnells*

Abstract. In this paper we investigate the structure of the algebraic K-groups K4(Z[i]) and K4(Z[ρ]), where i := √ −1 and ρ := (1 + √ −3)/2. We exploit the close connection between homology groups of GLn(R) for n 6 5 and those of related classifying spaces, then compute the former using Voronoi’s reduction theory of positive definite quadratic and Hermitian forms to produce a very large finite cell complex on which GLn(R) acts. Our main results are (i) K4(Z[i]) is a finite abelian 3-group, and (ii) K4(Z[ρ]) is trivial.

Quantifying The Effect Of Performance-Enhancing Drug Use On Fastball Velocity In Major League Baseball, 2009 Macalester College

#### Quantifying The Effect Of Performance-Enhancing Drug Use On Fastball Velocity In Major League Baseball, Vittorio Addona, J. Roth

*Vittorio Addona*

No abstract provided.

A Categorical Semantics For Fuzzy Predicate Logic, 2009 Illinois Wesleyan University

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

*Lawrence N. Stout*

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 ...

Spectral Decomposition Of Kac-Murdock-Szego Matrices, 2009 Trinity University

#### Spectral Decomposition Of Kac-Murdock-Szego Matrices, William F. Trench

*William F. Trench*

No abstract provided.

Characterization And Properties Of Matrices With $K$-Involutory Symmetries Ii, 2009 Trinity University

#### Characterization And Properties Of Matrices With $K$-Involutory Symmetries Ii, William F. Trench

*William F. Trench*

No abstract provided.

Phase-Linking And The Perceived Motion During Off-Vertical Axis Rotation, 2009 Portland State University

#### Phase-Linking And The Perceived Motion During Off-Vertical Axis Rotation, Jan E. Holly, Scott J. Wood, Gin Mccollum

*Gin McCollum*

Human off-vertical axis rotation (OVAR) in the dark typically produces perceived motion about a cone, the amplitude of which changes as a function of frequency. This perception is commonly attributed to the fact that both the OVAR and the conical motion have a gravity vector that rotates about the subject. Little-known, however, is that this rotating-gravity explanation for perceived conical motion is inconsistent with basic observations about self-motion perception: (a) that the perceived vertical moves toward alignment with the gravito-inertial acceleration (GIA) and (b) that perceived translation arises from perceived linear acceleration, as derived from the portion of the GIA ...

Asymptotic Behavior Of The Finite-Size Magnetization As A Function Of The Speed Of Approach To Criticality, 2009 University of Massachusetts - Amherst

#### Asymptotic Behavior Of The Finite-Size Magnetization As A Function Of The Speed Of Approach To Criticality, Richard S. Ellis, Jonathan Machta, Peter Tak-Hun Otto

*Richard S. Ellis*

The main focus of this paper is to determine whether the thermodynamic magnetization is a physically relevant estimator of the finite-size magnetization. This is done by comparing the asymptotic behaviors of these two quantities along parameter sequences converging to either a second-order point or the tricritical point in the mean-field Blume–Capel model. We show that the thermodynamic magnetization and the finite-size magnetization are asymptotic when the parameter α governing the speed at which the sequence approaches criticality is below a certain threshold α0. However, when α exceeds α0, the thermodynamic magnetization converges to 0 much faster than the finite-size ...

Phase-Linking And The Perceived Motion During Off-Vertical Axis Rotation, 2009 Portland State University

#### Phase-Linking And The Perceived Motion During Off-Vertical Axis Rotation, Jan E. Holly, Scott J. Wood, Gin Mccollum

*Gin McCollum*

Human off-vertical axis rotation (OVAR) in the dark typically produces perceived motion about a cone, the amplitude of which changes as a function of frequency. This perception is commonly attributed to the fact that both OVAR and the conical motion have a gravity vector that rotates about the subject. Little-known, however, is that this rotating-gravity explanation for perceived conical motion is inconsistent with basic observations about self-motion perception: (a) that the perceived vertical moves toward alignment with the gravitoinertial acceleration (GIA) and (b) that perceived translation arises from perceived linear acceleration, as derived from the portion of the GIA not ...

Gibbs Sampling For A Bayesian Hierarchical General Linear Model, 2009 University of Minnesota - Twin Cities

#### Gibbs Sampling For A Bayesian Hierarchical General Linear Model, Alicia A. Johnson, Galin L. Jones

*Alicia A. Johnson*

No abstract provided.

A Closer Look At The Relative Age Effect In The National Hockey League, 2009 Macalester College

#### A Closer Look At The Relative Age Effect In The National Hockey League, Vittorio Addona, P. A. Yates

*Vittorio Addona*

No abstract provided.

The 1905 Einstein Equation In A General Mathematical Analysis Model Of Quasars, 2009 DePaul University and Columbia College Chicago

#### The 1905 Einstein Equation In A General Mathematical Analysis Model Of Quasars, Byron E. Bell

*Byron E. Bell*

No abstract provided.

Forced Patterns Near A Turing-Hopf Bifurcation, 2009 Macalester College

#### Forced Patterns Near A Turing-Hopf Bifurcation, Chad M. Topaz, Anne Catlla

*Chad M. Topaz*

We study time-periodic forcing of spatially-extended patterns near a Turing-Hopf bifurcation point. A symmetry-based normal form analysis yields several predictions, including that (i) weak forcing near the intrinsic Hopf frequency enhances or suppresses the Turing amplitude by an amount that scales quadratically with the forcing strength, and (ii) the strongest effect is seen for forcing that is detuned from the Hopf frequency. To apply our results to specific models, we perform a perturbation analysis on general two-component reaction-diffusion systems, which reveals whether the forcing suppresses or enhances the spatial pattern. For the suppressing case, our results explain features of previous ...