Mathematics Commons^™

Session D-3: The Mathematical Wonders Of Pascal's Triangle, Donald Porzio

Professional Learning Day

Most mathematics teachers are aware of the some of the more straightforward connections Pascal's Triangle has to mathematics. Come explore some of the lesser known connections that can be used to peak your students' interest and entice them into exploring the mathematics behind these connections.

Session A-4: It’S A Wrap, Lindsey Herlehy, David Hernandez

Professional Learning Day

Investigate the concepts of surface area, measurement, ratio and proportion through a visual and kinesthetic mathematical investigation. Participants will be presented with the challenge of calculating how many sheets of toilet paper it would take to wrap one of their group members using a limited selection of tools. This session will provide teachers with a wonderful hands-on, minds-on activity that could easily be implemented into any classroom!

Session A-3: The Box Problem – An Introduction, Ruth Dover

Professional Learning Day

Create some simple boxes with paper and scissors. Then we'll measure the height, area of the base, and the volume. Find formulas, find regressions, and graph the functions. It's a simple activity to engage students and combine many different aspects of mathematics.

Session C-2: “It Is Easy As Pi”, Christine L. Moskalik, Carmela Jones

Professional Learning Day

Participants will work together using pi to try to open an ancient chest filled with treasure!! The chest is protected by a passcode that can only be determined through the activities within the lesson. Enjoy a progressive exposure to pi through this two-part lesson (total 110 minutes) offering a FUN storyline within the context of geometry and circles. With "pi-day" right around the corner, this hands-on, fun, inquiry-based lesson is sure to be a hit with your budding mathematicians.

Experimental Demonstration Of Topological Effects In Bianisotropic Metamaterials, Alexey P. Slobozhanyuk, Alexander B. Khanikaev, Dmitry S. Filonov, Daria A. Smirnova, Andrey E. Miroshnichenko, Yuri S. Kivshar

Publications and Research

Existence of robust edge states at interfaces of topologically dissimilar systems is one of the most fascinating manifestations of a novel nontrivial state of matter, a topological insulator. Such nontrivial states were originally predicted and discovered in condensed matter physics, but they find their counterparts in other fields of physics, including the physics of classical waves and electromagnetism. Here, we present the first experimental realization of a topological insulator for electromagnetic waves based on engineered bianisotropic metamaterials. By employing the near-field scanning technique, we demonstrate experimentally the topologically robust propagation of electromagnetic waves around sharp corners without backscattering effects.

Interplay Between Anomalous Transport And Catalytic Reaction Kinetics In Single-File Nanoporous Systems, Dajiang Liu, Jigang Wang, David Ackerman, Igor I. Slowing, Marek Pruski, Hung-Ting Chen, Victor S.-Y. Lin, James W. Evans

Jigang Wang

Functionalized nanoporous materials have broad utility for catalysis applications. However, the kinetics of catalytic reaction processes in these systems can be strongly impacted by the anomalous transport. The most extreme case corresponds to single-file diffusion for narrow pores in which species cannot pass each other. For conversion reactions with a single-file constraint, traditional mean-field-type reaction-diffusion equations fail to capture the initial evolution of concentration profiles, and they cannot describe the scaling behavior of steady-state reactivity. Hydrodynamic reaction-diffusion equations accounting for the single-file aspects of chemical diffusion can describe such initial evolution, but additional refinements are needed to incorporate fluctuation effects …

The Jin And Jang Of Quantum Physics Truth Tables, Shannon Lieb, Jeremiah Farrell

Scholarship and Professional Work - LAS

No abstract provided.

Kate Jones – A Tribute, Karen Farrell, Jeremiah Farrell

Scholarship and Professional Work - LAS

Kate is also an accomplished recreational mathematician and poet. To try to match in a small way her creative ability, we offer three puzzle-games in her honor: O'BEIRNE's TRI-HEX, PAPPUS and "KATe JONES". These three are specific examples of (9,3) symmetric configurations. More generally an (n,r) configuration is a collection of n "points"and n "lines" subject to the following requirements:

Rl: Any two points belong to at most one line.

R2: Each line has r points, and each point belongs to r lines.

A New 12-Puzzle, Todd Estroff, Jeremiah Farrell

Scholarship and Professional Work - LAS

This puzzle is a continuation of the tribute to the magician Paul Swinford. The following 18 two-letter words use each of the 12 letters of PAUL SWINFORD exactly three times each. The words are to be placed on the nodes of the grid so that each hexagon and each of the three diagonals contain the 12 letters of our honoree's name.

The White Rabbit 12-Puzzle, Chris Morgan, Jeremiah Farrell

Scholarship and Professional Work - LAS

Martin Gardner's fondness for the characters and themes of Lewis Carroll's "Alice" is well-known and to honor Gardner we offer two word puzzles to be played on the 12-node diagram of the WHITE RABBIT.

Paul Swinford – A Tribute, Jeremiah Farrell

Scholarship and Professional Work - LAS

No abstract provided.

Time-Dependent Neutral Stochastic Functional Differential Equations Driven By A Fractional Brownian Motion, B Boufoussi, S Hajji, E Lakhel

Communications on Stochastic Analysis

No abstract provided.

A Stochastic Transport Theorem, Pedro Catuogno, Simão N Stelmastchuk

Communications on Stochastic Analysis

No abstract provided.

Mean-Field Limit Versus Small-Noise Limit For Some Interacting Particle Systems, Samuel Herrmann, Julian Tugaut

Communications on Stochastic Analysis

No abstract provided.

Stochastic Integral Representations Of F-Selfdecomposable And F-Semi-Selfdecomposable Distributions, Nadjib Bouzar

Communications on Stochastic Analysis

No abstract provided.

Solution Of The Dirichlet Problem For A Linear Second-Order Equation By The Monte Carlo Method, José Villa-Morales

Communications on Stochastic Analysis

No abstract provided.

Moments Estimates For Local Times Of A Class Of Gaussian Processes, Olga Izyumtseva

Communications on Stochastic Analysis

No abstract provided.

Probability Distributions And Orthogonal Polynomials Associated With The One-Parameter Fibonacci Group, Andreas Boukas, Philip Feinsilver, Anargyros Fellouris

Communications on Stochastic Analysis

No abstract provided.

On The Second Fundamental Theorem Of Asset Pricing, Rajeeva L Karandikar, B V Rao

Communications on Stochastic Analysis

No abstract provided.

Limitations Of Realistic Monte-Carlo Techniques, Andrzej Pownuk, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Because of the measurement errors, the result Y = f(X1, ..., Xn) of processing the measurement results X1, ..., Xn is, in general, different from the value y = f(x1, ..., xn) that we would obtain if we knew the exact values x1, ..., xn of all the inputs. In the linearized case, we can use numerical differentiation to estimate the resulting difference Y -- y; however, this requires >n calls to an algorithm computing f, and for complex algorithms and large $n$ this can take too long. In situations when for each input xi, we know the probability distribution …