Approximations 3,
2016
Illinois Mathematics and Science Academy
Approximations 3, Ruth Dover
Integrals
Understanding Riemann sum approximations, including technology.
2. Population,
2016
Illinois Mathematics and Science Academy
2. Population, Ruth Dover
Differential Equations
Introduction to logistic population growth.
More Limits,
2016
Illinois Mathematics and Science Academy
Limits1,
2016
Illinois Mathematics and Science Academy
2. Intro To Concavity,
2016
Illinois Mathematics and Science Academy
2. Intro To Concavity, Ruth Dover
More on Derivatives
Looking at changes in ƒ’ to understand concavity.
3: Drugs And De's,
2016
Illinois Mathematics and Science Academy
3: Drugs And De's, Ruth Dover
Differential Equations
Making a connection between discrete recursion and differential equations.
Rate Of Change 3,
2016
Illinois Mathematics and Science Academy
The Diameter Of A Rouquier Block,
2016
The University of Akron
The Diameter Of A Rouquier Block, Andrew Mayer
Williams Honors College, Honors Research Projects
For my Honors Research Project, I will be researching special properties of Rouquier blocks that represent the partitions of integers. This problem is motivated by ongoing work in representation theory of the symmetric group. For each integer n and each prime p, there is an object called a Rouquier block; this block can be visualized as a collection of points in a plane, each corresponding to a partition. In this group of points, we say a pair of points is “connected” if certain conditions on the partitions are met. We compare each partition with each other partition, add edges when …
1. Measuring Speed,
2016
Illinois Mathematics and Science Academy
1. Coffee,
2016
Illinois Mathematics and Science Academy
Approximations 2,
2016
Illinois Mathematics and Science Academy
Approximations 2, Ruth Dover
Integrals
Drawing rectangles and calculating Riemann sums.
Limits3,
2016
Illinois Mathematics and Science Academy
Rate Of Change 1,
2016
Illinois Mathematics and Science Academy
Approximations 1,
2016
Illinois Mathematics and Science Academy
Multi-Type Display Calculus For Propositional Dynamic Logic,
2016
Aix-Marseille Université
Multi-Type Display Calculus For Propositional Dynamic Logic, Sabine Frittella, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano
Engineering Faculty Articles and Research
We introduce a multi-type display calculus for Propositional Dynamic Logic (PDL). This calculus is complete w.r.t. PDL, and enjoys Belnap-style cut-elimination and subformula property.
Tool Support For Reasoning In Display Calculi,
2016
University of Oxford
Tool Support For Reasoning In Display Calculi, Samuel Balco, Sabine Frittella, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano
Engineering Faculty Articles and Research
We present a tool for reasoning in and about propositional sequent calculi. One aim is to support reasoning in calculi that contain a hundred rules or more, so that even relatively small pen and paper derivations become tedious and error prone. As an example, we implement the display calculus D.EAK of dynamic epistemic logic. Second, we provide embeddings of the calculus in the theorem prover Isabelle for formalising proofs about D.EAK. As a case study we show that the solution of the muddy children puzzle is derivable for any number of muddy children. Third, there is a set of meta-tools, …
Characterizations Of Rectangular (Para)-Unitary Rational Functions,
2016
Chapman University
Characterizations Of Rectangular (Para)-Unitary Rational Functions, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz
Mathematics, Physics, and Computer Science Faculty Articles and Research
We here present three characterizations of not necessarily causal, rational functions which are (co)-isometric on the unit circle:
(i) through the realization matrix of Schur stable systems,
(ii) the Blaschke-Potapov product, which is then employed to introduce an easy-to-use description of all these functions with dimensions and McMillan degree as parameters,
(iii) through the (not necessarily reducible) Matrix Fraction Description (MFD).
In cases (ii) and (iii) the poles of the rational functions involved may be anywhere in the complex plane, but the unit circle (including both zero and infinity). A special attention is devoted to exploring the gap between the …
Real Complex Functions,
2016
University of Richmond
Real Complex Functions, Stephan Ramon Garcia, Javad Mashreghi, William T. Ross
Department of Math & Statistics Faculty Publications
We survey a few classes of analytic functions on the disk that have real boundary values almost everywhere on the unit circle. We explore some of their properties, various decompositions, and some connections these functions make to operator theory.
Subgroups Of Finite Wreath Product Groups For P=3,
2016
University of Akron
Subgroups Of Finite Wreath Product Groups For P=3, Jessica L. Gonda
Williams Honors College, Honors Research Projects
Let M be the additive abelian group of 3-by-3 matrices whose entries are from the ring of integers modulo 9. The problem of determining all the normal subgroups of the regular wreath product group P=Z9≀(Z3 × Z3) that are contained in its base subgroup is equivalent to the problem of determining the subgroups of M that are invariant under two particular endomorphisms of M. In this thesis we give a partial solution to the latter problem by implementing a systematic approach using concepts from group theory and linear algebra.
Wiener Algebra For The Quaternions,
2016
Chapman University
Wiener Algebra For The Quaternions, Daniel Alpay, Fabrizio Colombo, David P. Kimsey, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener-Lévy type theorem and a factorization theorem. We give applications to Toeplitz and Wiener-Hopf operators.
