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https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events
Recent Events in en-usTue, 12 Feb 2019 13:51:37 PST3600The HRT Conjecture
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/14
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/14Thu, 01 Dec 2016 12:00:00 PST
Stated more than 20 years ago by C. Heil, J. Ramanathan, and P. Topiwala, the HRT conjecture is about the linear independence of a collection of finitely many time-frequency shifts of an arbitrary nonzero square integrable function. Despite the simplicity of its statement, the conjecture is still open for the general case. In this talk the author will present results based on a paper by Dr. J. Benedetto and the author. The paper proves HRT conjecture for a class of functions with certain behavior at infinity. This class includes some square integrable functions built by combining polynomial, exponential, and logarithmic functions. For example, we prove HRT for any finite collection of time-frequency shifts of e{-|x|}.
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Abdelkrim BourouihiyaPeriodicity in Quantum Calculus
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/13
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/13Tue, 15 Mar 2016 12:00:00 PDT
After a brief introduction to time scales, we will explore periodic functions on time scales. We will discuss how periodicity is defined on time scales that are not periodic. In particular, we will look at periodicity in the quantum case. Two definitions of periodicity have recently been introduced. One definition is based on the equality of areas lying below the graph of the function at each period; the other regards a periodic function to be one that repeats its values after a certain number of steps. We will show a relation between these two definitions and then use this relation to show the existence of a periodic solution in both senses of a quantum Volterra integral equation.
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Jeffrey T. NeugebauerBehind the Numbers
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/12
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/12Wed, 03 Feb 2016 12:00:00 PST
Number Theory, which is typically referred to as “The Queen of Mathematics” is a branch of pure mathematics that investigates the properties of the integers. In this talk we provide a historical overview of classical number theory and examine various real world applications of number theory. Lastly, if time permits, we will discuss how technology has contributed to the development and advancement of number theory.
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Ricardo CarreraA Novel Hands-On Way to Teach Introductory Statistics
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/11
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/11Tue, 19 Jan 2016 12:00:00 PST
We plan to present the novel approach to teaching intro-Stat classes. This technique has been implemented at FAU for several years and based on a few thousand students, it was very well received. We greatly simplified the material by eliminating much of redundant and tedious computations by hand, as well as formula memorization. Instead, via Excel, we introduce the hands-on data analysis on real data. And we do this on the very first week! As the semester progresses, we add the necessary computer skills as well as Statistical tools; as needed. By the completion of semester, the students learn to effortlessly open and manipulate data files containing tens of thousands data point, to perform multiple regression as well as t-tests.
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Dragan RadulovicExistence Results for Functional Dynamic Equations with Delay
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/10
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/10Thu, 18 Feb 2016 12:00:00 PST
Time scale, arbitrary nonempty closed subset of the real numbers (with the topology and ordering inherited from the real numbers) is an efficient and general framework to study different types of problems to discover the commonalities and highlight the essential differences. Sometimes, we may need to choose an appropriate time scale to establish parallels to known results. We present a few recent results from existence theory of funcational dynamic equations including a few (counter) examples. In particular, we discuss first order functional dynamic equations with delay xDelta(t)=f(t,xt) on a time scale. Here, xt is in Crd([-tau,0],Rn) and is given by xt(s)=x(t+s), -tau < s< 0. We consider an appropriate timescale on which such delay equations can be studied meaningfully. We establish an existence result for the solutions of such problems. We also present a few examples.
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Gnana Bhaskar TenaliAsymptotic stability of non-unique solutions of Initial Value Problems
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/9
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/9Thu, 31 Mar 2016 12:00:00 PDT
We consider an initial value problem (I. V. P.) of a first order nonlinear ordinary differential equations. We assume that the I. V. P. can have more than one solution. We study a new type of stability property of these solutions. This stability is not the standard Liapunov stability, commonly studied in the field of differential equations.
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Muhammad Islam*CANCELLED* Predictive Accuracy Measures for Binary Outcomes: Relationships and Impact of Incidence Rate
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/8
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/8Thu, 21 Apr 2016 12:00:00 PDT
Evaluating the performance of models predicting a binary outcome can be done using a variety of measures. While some measures intend to describe the model's overall fit, others more accurately describe the model's ability to discriminate between the two outcomes. A desirable model would be one that both fit the data and could discriminate between the two outcomes well. In this presentation, the relationships among the measures of discrimination and overall fit will be examined under general conditions and also controlling for the incidence rate in the data used to build the model. The measures of interest include the area under the ROC curve (auc), Brier score, discrimination slope, log loss and r-squared. Presented analysis includes the use of real data from common medical research studies and simulated data controlling for the incidence rate.
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Ryan C. ScolnikGeometric Flows
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/7
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/7Tue, 12 Apr 2016 12:00:00 PDT
A geometric flow is a process which is defined by a differential equation and is used to evolve a geometric object from a general shape to a one with more symmetries. For example, the curve-shortening flow deforms a simple closed curve to a round one ; the Ricci flow deforms a simply connected surface (say, a football shaped one) to a round sphere. In this talk, we will give an overview of some of these geometric flows, in particular, some discussions on singularities that these flows often run into.
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Ming-Liang CaiComputing Invariant Dynamics for Differential Equations: Spectral Methods, Errors, and Computer Assisted Proof
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/6
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/6Thu, 10 Sep 2015 12:00:00 PDT
The qualitative theory of dynamical systems is concerned with studying the long time behavior discrete and continuous time models such as nonlinear differential equations. The long time behavior of such models is organized by landmarks called invariant sets. For complicated nonlinear equations these invariant sets are difficult to study via pen and paper analysis, and we typically employ numerical simulations to gain insights into the dynamics. If we now think of these computer assisted insights as mathematical conjectures, then it is natural to ask how we might obtain proofs. Since the conjectures themselves originate with the computer it is not surprising that computer assistance is sometimes needed to prove the desired theorems. In this talk I will discuss some numerical methods for computing invariant sets for nonlinear differential equations, and indicate how these computations can be distilled into mathematical theorems. A byproduct of this discussion is that we obtain `validated' a posteriori error bounds on our scientific computations.
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J. D. Mireles JamesCURVATURE: A geometric villain that ruins our instinctive perception of nature
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/5
https://nsuworks.nova.edu/mathematics_colloquium/ay_2015-2016/events/5Wed, 02 Dec 2015 12:00:00 PST
Our perception of nature is based on evolutionary wiring of our brain and observations we make via our senses. But, in reality, many scientific and technological advancements are based on non-intuitive rules and principles that can only be explained by the ultimate abstraction that is embedded in mathematics. In this talk, I will discuss the concept of curvature and argue how it explains the “unexplainable”. We will see how the curvature proves that the earth is rotating, how good the soap bubbles are at proving profound mathematical results, and if the two dimensional residents can determine the shape of their world . Get ready to see some interesting applications of the curvature in engineering, medical sciences and even architecture.
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Vehbi Emrah Paksoy