LPTMS Publications

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Colloquium and seminar talks will normally be on a Wednesday usually in UNA from 3: Send an e-mail to jmclaughlin2 wcupa.

In this presentation the different phases of clinical trials will be compared and contrasted in terms of the broad clinical objectives of each phase. Attention will be especially directed to translating the clinical objectives into statistical concepts that will inform the selection of a design at each phase. He received an M. In this role, he collaborated with clinical investigators, epidemiologists, and basic scientists throughout the medical school, and he taught biostatistics to medical students and to students in the Master of Public Health program.

In he retired and moved to Chester County; he now enjoys auditing courses at West Chester University. The category's three identity morphisms 1X, 1Y and 1Z, if explicitly represented, would appear as three arrows, from the letters X, Y, and Z to themselves, respectively. It will be easy to read along with the textbook so one need not know any category theory ahead of time to be a presenter. Solute transport in streams and rivers is governed by several differential equations for the hydrologic and geochemical processes.

Knowledge of solute fate and transport is needed to aid estimating nutrient uptake in streams, estimating particulate transport, and assessing the fate of contaminants that are released into surface waters. OTIS is a mathematical simulation model used in conjunction with field-scale data to quantify hydrologic processes advection, dispersion, and transient storage affecting solute transport and certain chemical reactions sorption and first-order decay.

With given quantities, such as, the mass of the solute and the distance of the reach in the stream, OTIS determines the solute concentrations that result from hydrologic transport and chemical transformation. Our experimental work on the streams and the data analysis using OTIS will help scientists to better understand the solute transport in the local streams and help estimating contamination in the local streams if it happens in the future.

The theory of quantum cohomology was initially developed in the early s by physicists working in the field of superstring theory. In this talk, we will explore the "rim hook rule" which provides a fun and efficient way to compute the quantum cohomology of the Grassmannian of k-dimensional planes in complex n-space.

This talk will be very concrete and completely self-contained, assuming only a background in basic linear algebra. She earned her B. Liz has also participated as a scientific committee member and co-organizer in many other regional, national, and international conferences, including the weekly Combinatorics, Algebra, and Geometry CAGE seminar at the University of Pennsylvania, as well as the annual international workshop on Formal Power Series and Algebraic Combinatorics FPSAC.

In two weeks, March 21, we will have a continuation of this seminar model various growths processes like stock prices and predator-models. We will introduce stochastic differential equations, which are ordinary differential equations with a random component. We could use this random component in many manners, one in particular is modeling an error term. So you could think of SDE stochastic differential equations as an ode ordinary differential equation with a built in error term.

This lecture will develop what is called stochastic calculus which will be used to solve some SDEs.

We will continue this discussion next spring to include numerical solutions to SDEs with many examples. In standard decimal notation, we write each integer as the linear combination of powers of In binary, we use powers of 2. What if we used factorials instead of exponentials? How can we express each integer as the sum of factorials in a minimal way? She earned her Ph. Her research interests include curriculum and materials development and directing undergraduate research in combinatorics.

She enjoys teaching mathematics at all levels using pedagogies that support active and inquiry-based learning. An avid gardener, cook, and designer, she appreciates the importance of getting her hands dirty, and not just in mathematics. Modeling is one application that most people associate to mathematics, something that the non-mathematician can see, use and appreciate.

This noise can be used in a number of ways, one being the natural error in the usual models. We will introduce how to modified sonine approximation for granular binary mixtures journal of fluid mechanics cambridge core populations using stochastic differential equations with analytic and numerical examples an emphasis on the numerical models.

We only assume that the student knows the main ideas from calculus and a little statistics mainly the standard normal random variable which we will review. Talks will be added to the schedule throughout the semester. Check back for updates. A deep understanding of fractions is a gateway to algebra, probability and statistics, the calculus, real analysis, and so on.

However, a response to the challenge needs to offer an alternative and prior conception of fractions as numbers before students are able to arrange them on a number line. In ending my talk, I will discuss the implication of the alternative conception and new instructional model for modified sonine approximation for granular binary mixtures journal of fluid mechanics cambridge core teaching and learning of school mathematics. Powell earned his B.

As a PI on a collaborative, five-year NSF Discovery Research K grant, modified sonine approximation for granular binary mixtures journal of fluid mechanics cambridge core has been working with researchers from Drexel University and the Math Forum at the National Council of Teachers of Mathematics to design, implement, and assess the teaching and learning of dynamic geometry through an online collaborative environment, Virtual Mat Teams with GeoGebra His books co-edited and co-authored are Math: You have certainly been told that it is good to draw pictures when thinking about math.

We will show several examples that will convince you that visualization is amazingly powerful, both for understanding things as well as for discovering new things that we don't understand. Paul Zeitz was an undergraduate at Harvard University and he earned his Ph. After completing his Ph. Before graduate school, Dr. Zeitz taught high school for six years.

Paul is a graduate of Stuyvesant High School in NY and he was a member of the first American IMO team in and coached several IMO teams in the s, including the "Dream Team" of which received a perfect score, for the first and only time in history. We say that a permutation p contains the shorter permutation q as a pattern if p contains q entries, not necessarily in consecutive positions, whose pairwise relations to each other are the same as those of the entries of q.

In the first part of this talk, we will review the early results of this fascinating and rapidly growing topic, including modified sonine approximation for granular binary mixtures journal of fluid mechanics cambridge core celebrated Marcus-Tardos theorem from In the second part, we discuss some more recent developments, such as a sequence of results on the extremely tenacious patterna surprising connection to stack-sortable permutations, and the disproof of numerous long-standing conjectures.

Many open problems will also be discussed. Sincehe has taught at the University of Florida, where in he was inducted to the Academy of Distinguished Teaching Scholars. Sincehe has been one of the editors-in-chief of the Electronic Journal of Combinatorics.

So you could think of sde stochastic differential equations as an ode ordinary differential equation with a built in error term. This lecture will develop what is called stochastic calculus which will be used to solve some sdes. We will continue this discussion next spring to include numerical solutions to sdes with many examples.

The notion of negative refraction goes back to the work of V. In modified sonine approximation for granular binary mixtures journal of fluid mechanics cambridge core talk, I will discuss certain refraction problems in the setting of metamaterials.

Along the way, I will show that surfaces possessing a certain uniform refraction property, in the setting of metamaterials, are in general neither convex nor concave, modified sonine approximation for granular binary mixtures journal of fluid mechanics cambridge core greatly contrasts with the case of positive refractive indices.

In this talk, we shall discuss what is known as John H. The only pre-requisite to understand this algorithm is addition and subtraction of natural numbers below German Lorenz cipher machine, used in World War II to encrypt very-high-level general staff messages source: In this talk the mathematics behind some modern public key cryptosystems are examined in a public key cryptosystem, the enciphering key is public knowledge, and anyone can encipher and send a message, but only someone with deciphering key can decipher an enciphered message.

This talk will require little mathematics beyond multiplication of integers, and the concept of a remainder when one integer is divided by another. We shall discuss this phenomenon and also give a method to create such polynomials and give several examples. In thein modified sonine approximation for granular binary mixtures journal of fluid mechanics cambridge core book, Foundations of GeometryDavid Hilbert set forth a modern treatment of triangle congruence by postulating by Side-Angle-Side axiom.

In this talk we will discuss the questions: After teaching mathematics in high school for ten years, he moved to SUNY Geneseo where he held a faculty position in the Mathematics Department.

During his thirty years at Geneseo he coordinated their highly successful secondary mathematics certification program, served as Chair of Mathematics and was promoted to the rank of Distinguished Teaching Professor of Mathematics.

Throughout his career, Dr. West has contributed to the improvement of mathematics teaching with his professional service. In addition, he has served the National Council of Teachers of Mathematics as both member and chair of the Regional Services Committee. In his retirement, Dr. West is a T3 National Instructor and continues to do mathematics, work on his old cars, read avidly and most importantly, watch modified sonine approximation for granular binary mixtures journal of fluid mechanics cambridge core ten grandchildren grow!

Fitness is environment-specific, and many organisms have evolved the ability to alter resource allocation based on perceived environmental cues e. We are developing an optimization model that examines relative resource allocation into growth, reproduction, and defensive morphology under varying conditions. Specifically, we are investigating how reproductive investment in terms of rate and amount changes as a function of predation risk.

The survival function utilizes a modified Gompertz-Makeham law for mortality. The fecundity function is the product of the reproductive schedule and output. The reproductive schedule utilizes a gamma distribution and the output is modeled exponentially. Optimizing the fitness model yields the optimal resource allocation and resulting reproductive schedule. This allows us to understand the effects of phenotypic plasticity in life-history traits on the evolution of a post-reproductive period.

As predation risk increases, more resources are allocated towards defenses. However, once predation risk is sufficiently high, it becomes more beneficial for the individuals to allocate all their resource towards reproduction. A model is being developed that simulates the dorsal closure process, a stage of drosophila embryogenesis. The apical side of the amnioserosa a cell monolayer- wound like region on the surface of the embryo is being represented through polygonal two dimensional representations of cells, with forces acting on their edges and nodes.

Those forces are being regulated by the action of actin and myosin. The model is granular enough so various subregions can be studied to the level of the individual cell.

Various equations are being tested, describing the evolution of forces generated by the action of the actomyosin network, which itself might be biochemically driven. Eventually, the model may be used to understand mechanisms of dorsal closure that are not easily analyzed in the lab or produce simulation results that might drive new experiments.

Microbes modified sonine approximation for granular binary mixtures journal of fluid mechanics cambridge core a large and central part of the global ecosystem. As a consequence of their short reproductive time and their proficiency at exchange of genetic material, it seems plausible that microbes in communities operate at high efficiency in terms of free energy and nutrient usage in many contexts.

One obvious issue of interest would be the description of species within a microbial community and its dependence on the local environment. Description of niche structure of organisms and how that structure impacts competitiveness has long been a topic of interest among ecologists. Here, in the context of Yellowstone National Park microbial mat, we discuss influence of temporal environment on microbial community species structure.

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