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Castelnuovo–Mumford Regularity And Arithmetic Cohen–Macaulayness Of Complete Bipartite Subspace Arrangements, Zach Teitler, Douglas A. Torrence 2015 Boise State University

Castelnuovo–Mumford Regularity And Arithmetic Cohen–Macaulayness Of Complete Bipartite Subspace Arrangements, Zach Teitler, Douglas A. Torrence

Mathematics Faculty Publications and Presentations

We give the Castelnuovo–Mumford regularity of arrangements of (n−2)-planes in Pn whose incidence graph is a sufficiently large complete bipartite graph, and determine when such arrangements are arithmetically Cohen–Macaulay.


Video Event Understanding With Pattern Theory, Fillipe Souza, Sudeep Sarkar, Anuj Srivastava, Jingyong Su 2015 University of South Florida

Video Event Understanding With Pattern Theory, Fillipe Souza, Sudeep Sarkar, Anuj Srivastava, Jingyong Su

MODVIS Workshop

We propose a combinatorial approach built on Grenander’s pattern theory to generate semantic interpretations of video events of human activities. The basic units of representations, termed generators, are linked with each other using pairwise connections, termed bonds, that satisfy predefined relations. Different generators are specified for different levels, from (image) features at the bottom level to (human) actions at the highest, providing a rich representation of items in a scene. The resulting configurations of connected generators provide scene interpretations; the inference goal is to parse given video data and generate high-probability configurations. The probabilistic structures are imposed using energies ...


Global Holomorphic Functions In Several Noncommuting Variables, Jim Agler, John E. McCarthy 2015 University of California - San Diego

Global Holomorphic Functions In Several Noncommuting Variables, Jim Agler, John E. Mccarthy

Mathematics Faculty Publications

We define a free holomorphic function to be a function that is locally, with respect to the free topology, a bounded nc-function. We prove that free holomorphic functions are the functions that are locally uniformly approximable by free polynomials. We prove a realization formula and an Oka-Weil theorem for free analytic functions.


Is Heyser Still Relevant?, Douglas R. Jones 2015 Columbia College Chicago

Is Heyser Still Relevant?, Douglas R. Jones

Douglas R Jones

The author, highlighting excerpts from the writings of Richard C. Heyser, argues that Heyser continues to be relevant in the field of audio engineering nearly three decades after his death. Using material from the Richard C. Heyser Collection, held in the Columbia College Chicago Archives & Special Collections, the author chose comments from the collection, both published and unpublished "which should be at least intriguing and possibly down right shocking."


Tables For Dihedral Angles Between The Adjacent Faces Of Platonic Solids & Various Uniform Polyhedra, Harish Chandra Rajpoot Rajpoot HCR 2015 M.M.M. University of Technology, Gorakhpur-273010 (UP) India

Tables For Dihedral Angles Between The Adjacent Faces Of Platonic Solids & Various Uniform Polyhedra, Harish Chandra Rajpoot Rajpoot Hcr

Harish Chandra Rajpoot H.C. Rajpoot

These data tables have been prepared by the author Mr H.C. Rajpoot by using his data tables of the various polyhedra for determining the dihedral angle between any two adjacent faces with a common edge of different uniform polyhedra or polyhedral shells. These are very useful for the construction & preparing the wire-frame models of the uniform polyhedral shells having different regular polygonal faces. A polyhedral shell can be easily constructed/framed by continuously fixing all its adjacent (flat) faces each two as a pair at their common edge at an angle equal to the dihedral angle between them. These ...


Mathematical Analysis Of Uniform Polyhedra Having 2 Congruent Regular N-Gonal Faces, 2n Congruent Trapezoidal Faces, 5n Edges & 3n Vertices Lying On A Spherical Surface (Generalized Formula By H.C. Rajpoot), Harish Chandra Rajpoot Rajpoot HCR 2015 M.M.M. University of Technology, Gorakhpur-273010 (UP) India

Mathematical Analysis Of Uniform Polyhedra Having 2 Congruent Regular N-Gonal Faces, 2n Congruent Trapezoidal Faces, 5n Edges & 3n Vertices Lying On A Spherical Surface (Generalized Formula By H.C. Rajpoot), Harish Chandra Rajpoot Rajpoot Hcr

Harish Chandra Rajpoot H.C. Rajpoot

All the formula have been generalized by the author which are applicable to calculate the important parameters, of any uniform polyhedron having 2 congruent regular n-gonal faces, 2n congruent trapezoidal faces each with three equal sides, 5n edges & 3n vertices lying on a spherical surface, such as solid angle subtended by each face at the centre, normal distance of each face from the centre, inner radius, outer radius, mean radius, surface area & volume. These are useful for analysis, designing & modeling of different uniform polyhedra.


Real Linear Maps Preserving Some Complex Subspaces, Adam Coffman 2015 Indiana University - Purdue University Fort Wayne

Real Linear Maps Preserving Some Complex Subspaces, Adam Coffman

Mathematical Sciences Faculty Publications

We find configurations of subspaces of a complex vector space such that any real linear map with sufficiently high rank that maps the subspaces into complex subspaces of the same dimension must be complex linear or antilinear.


Pseudospherical Surfaces And Evolution Equations In Higher Dimensions, Innovative Research Publications IRP India, M.F. El-Sabbagh, K.R. Abdo 2015 Innovative Research Publications

Pseudospherical Surfaces And Evolution Equations In Higher Dimensions, Innovative Research Publications Irp India, M.F. El-Sabbagh, K.R. Abdo

Innovative Research Publications IRP India

In this paper, the study of evolution equations with two independent variables which are related to pseudospherical surfaces in R3 , is extended to evolution equations with more than two independent variables. Equations of the type 𝒖𝒙𝒕 = 𝝍(𝒖, 𝒖𝒙 , … … . . , 𝝏 𝒌𝒖 𝝏 𝒙 𝒌 , 𝒖𝒚, … … … , 𝝏 𝒌ʹ𝒖 𝝏 𝒚 𝒌ʹ ) are studied and characterized. Some features and results on properties of these equations are given via this study.


Session B-1: Pipelines And Oil Spills!, Patrick Young 2015 Illinois Mathematics and Science Academy

Session B-1: Pipelines And Oil Spills!, Patrick Young

Professional Learning Day

Don’t miss this hands-on approach to middle school math. Participants will construct an actual pipeline from inexpensive materials and record evidence of leakage. They will then conduct an experiment and create a model relating liquid volume and spill area. They will apply their model to determine how much liquid leaked from their pipeline.


Session B-2: The “Roll” Of Statistics In Modeling - It All Adds Up, Richard Stalmack, Janice Krouse 2015 Illinois Mathematics and Science Academy

Session B-2: The “Roll” Of Statistics In Modeling - It All Adds Up, Richard Stalmack, Janice Krouse

Professional Learning Day

The common core practice standards ask us to teach students to propose mathematical models and test their viability. Participants will do an experiment, collect data and use technological tools to combine modeling, analysis and basic statistics. Participants should bring a laptop, if possible; otherwise, bring a graphing calculator.


Session B-3: Mathematical Games, Puzzles, And Diversions, Steven M. Condie 2015 Illinois Mathematics and Science Academy

Session B-3: Mathematical Games, Puzzles, And Diversions, Steven M. Condie

Professional Learning Day

Delve into the exciting world of math through games, puzzles and other sources! Participants shall try their luck and test their skill at these diversions. Participants will leave this session with a wealth of mathematical activities appropriate for students of all ages.


Session A-2: From Polynomial To Rational Functions: Flip!, Ruth Dover 2015 Illinois Mathematics and Science Academy

Session A-2: From Polynomial To Rational Functions: Flip!, Ruth Dover

Professional Learning Day

Ah HA! Making the connection between polynomial functions, rational functions and using reciprocals! Join us to flip, not flop, with trig for your classroom.


Session A-1: Implementing Common Core In Middle School Math, Karen Togliatti 2015 Illinois Mathematics and Science Academy

Session A-1: Implementing Common Core In Middle School Math, Karen Togliatti

Professional Learning Day

This session will focus on implementing Common Core Middle-School Mathematics Standards using student-centered activities. Participants will receive three hands-on activities (one each at grades six, seven, and eight) to take back to their classrooms.


Session C-2: Problem-Based Mathematics: You Reap What You Sow, Nicole Ross, Lindsey Herlehy 2015 Illinois Mathematics and Science Academy

Session C-2: Problem-Based Mathematics: You Reap What You Sow, Nicole Ross, Lindsey Herlehy

Professional Learning Day

Approach problem-based mathematics through a historical perspective! Join us to learn a fun, hands-on approach to examining the science behind crop rotation systems originally implemented during the Medieval Period. This activity requires students to mathematically evaluate the efficiency of a crop rotation system, strategically complete an integers-based crop puzzle, and evaluate crop yield and profit through data analysis. This activity integrates a variety of middle school mathematics concepts.


Non-Isomorphic Real Simple Lie Algebras Of The Same Complex Type And Character, Ian M. Anderson 2015 ian.anderson@usu.edu

Non-Isomorphic Real Simple Lie Algebras Of The Same Complex Type And Character, Ian M. Anderson

Tutorials on... in 1 hour or less

Complex simple Lie algebras are classified by their root types. The type of a real simple Lie algebra is the root type of the associated complex algebra. The character of a real simple Lie algebra is the signature of its Killing form.

For many root types, the character is sufficient to uniquely classify the corresponding real Lie algebras. However, one should not take this statement to be literally true – there are a few cases where the character does not suffice to distinguish all possible real forms.

In this worksheet we will show that the 2 real non-isomorphic Lie algebras so ...


Spontaneous Dimension Reduction And The Existence Of A Local Lagrange-Hamilton Formalism For Given N-Dimensional Newtonian Equations Of Motion, Piotr W. Hebda, Beata A. Hebda 2015 University of North Georgia

Spontaneous Dimension Reduction And The Existence Of A Local Lagrange-Hamilton Formalism For Given N-Dimensional Newtonian Equations Of Motion, Piotr W. Hebda, Beata A. Hebda

Faculty Publications

A partially explicit construction of a Lagrange-Hamiltonian formalism for an arbitrary n -dimensional Newtonian system of equations of motion is given. Additional variables used in the construction are spontaneously reduced by the Dirac’s constraints resulting from degeneracy of the proposed Lagrangian, so that only the variables that appear in the original system of equations remain. A Hamiltonian and dynamical Dirac’s brackets are calculated.


Spontaneous Dimension Reduction And The Existence Of A Local Lagrangian For Given N-Dimensional Newtonian Equations Of Motion, Piotr W. Hebda, Beata A. Hebda 2015 University of North Georgia

Spontaneous Dimension Reduction And The Existence Of A Local Lagrangian For Given N-Dimensional Newtonian Equations Of Motion, Piotr W. Hebda, Beata A. Hebda

Faculty Publications

A partially explicit construction of a Lagrangian for an n -dimensional Newtonian system of equations of motion is given. Extra variables used in the construction are spontaneously reduced by the constraints resulting from degeneracy of the proposed Lagrangian, so that only the variables that appear in the original system of equations remain. An explicit example of a Lagrangian for a system not satisfying Helmholtz conditions is given.


Transition To Higher Mathematics: Structure And Proof (Second Edition), Bob A. Dumas, John E. McCarthy 2015 University of Washington - Seattle Campus

Transition To Higher Mathematics: Structure And Proof (Second Edition), Bob A. Dumas, John E. Mccarthy

Books and Monographs

This book is written for students who have taken calculus and want to learn what “real mathematics" is. We hope you will find the material engaging and interesting, and that you will be encouraged to learn more advanced mathematics.

This is the second edition of our text. It is intended for students who have taken a calculus course, and are interested in learning what higher mathematics is all about. It can be used as a textbook for an "Introduction to Proofs" course, or for self-study.

Chapter 1: Preliminaries, Chapter 2: Relations, Chapter 3: Proofs, Chapter 4: Principles of Induction, Chapter ...


My Finite Field, Matthew Schroeder 2015 Idaho State University

My Finite Field, Matthew Schroeder

Journal of Humanistic Mathematics

A love poem written in the language of mathematics.


Prisoner's Dilemma, Raymond N. Greenwell 2015 Hofstra University

Prisoner's Dilemma, Raymond N. Greenwell

Journal of Humanistic Mathematics

No abstract provided.


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