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Physical Sciences and Mathematics Commons™
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Articles 1 - 10 of 10
Full-Text Articles in Physical Sciences and Mathematics
Mathematical Relativity And The Nature Of The Universe, Priscila Reyes
Mathematical Relativity And The Nature Of The Universe, Priscila Reyes
Mathematics Colloquium Series
In this talk, I will be discussing certain space-times, which can be used to model celestial objects and events in the universe. These are solutions to Einstein's field equations, which roughly describe the relation between matter, energy and the geometry of the universe. The concept of time in relation to an observer will be demonstrated. I will also include some interesting phenomena that arise out of the unusual mathematical structure of space-times , such as Lorentz contraction, reverse Cauchy-Schwarz, and the twin paradox.
Mathematical Optimization And Applications, Teodora Suciu
Mathematical Optimization And Applications, Teodora Suciu
Mathematics Colloquium Series
This talk centers on mathematical optimization in the context of Calculus of Variations. Optimization involves choosing the best element from a set of choices, usually through mathematical approaches. Solving these kinds of problems is considered an essential tool in many areas of science and engineering. Additionally, various mathematics and business applications are discussed. Also explored is a real-life example with a detailed algorithm that is closely related to the Traveling Salesman problem.
Minimum Number Of Distinct Eigenvalues Of Graphs, Shahla Nasserasr
Minimum Number Of Distinct Eigenvalues Of Graphs, Shahla Nasserasr
Mathematics Colloquium Series
For a simple graph G on n vertices, a real symmetric nxn matrix A is said to be compatible with G, if for different i and j, the (i; j) entry of A is nonzero whenever there is an edge between the vertices i and j, it is zero otherwise. The minimum number of distinct eigenvalues, when minimum is taken over all compatible matrices with G, is denoted by q(G). In this talk, a survey of some known and new results about q(G) is presented.
Continuous Dependence And Differentiating Solutions Of A Second Order Boundary Value Problem With Average Value Condition, Samantha A. Major
Continuous Dependence And Differentiating Solutions Of A Second Order Boundary Value Problem With Average Value Condition, Samantha A. Major
Mathematics Colloquium Series
Using a few conditions, continuous dependence, and a result regarding smoothness of initial conditions, we show that derivatives, with respect to each of the boundary data, of solutions to a second order boundary value problem with an average value integral condition solve the associated variational equation with interesting boundary conditions.
Spatial Population Models With Fitness Based Dispersal, Chris Cosner
Spatial Population Models With Fitness Based Dispersal, Chris Cosner
Mathematics Colloquium Series
Traditional continuous time models in spatial ecology typically describe movement in terms of linear diffusion and advection, which combine with nonlinear population dynamics to produce semi-linear parabolic equations and systems. In environments that are favorable everywhere in the sense that the local population growth rate is always positive, organisms can use linear advection and diffusion to achieve an optimal spatial distribution. (Here optimal means evolutionarily stable.) In regions where there are environmental “sinks” where the local growth rate is negative, it does not seem possible to achieve an optimal distribution via linear dispersal. It is possible for organisms using advection …
Modeling And Methods Of Signal Separations With Applications In Spectroscopic Sensing, Yuanchang Sun
Modeling And Methods Of Signal Separations With Applications In Spectroscopic Sensing, Yuanchang Sun
Mathematics Colloquium Series
Spectroscopic sensing is a powerful and a widely used family of techniques for detecting and identifying chemical and biological substances. For example, nuclear magnetic resonance (NMR) relies on the magnetic properties of the atomistic nucleus to determine the molecular structures. Raman spectroscopy (RS) uses laser light scattering and the resulting energy shift of photons to sense the vibrational modes of a sample. In remote sensing, hyperspectral imaging (HSI) makes use of hundreds of contiguous spectral bands to identify nearly invisible objects at subpixel level. Differential optical absorption spectroscopy (DOAS) is based on the light absorption property of matter to identify …
Geometric Flows, Ming-Liang Cai
Geometric Flows, Ming-Liang Cai
Mathematics Colloquium Series
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.
Asymptotic Stability Of Non-Unique Solutions Of Initial Value Problems, Muhammad Islam
Asymptotic Stability Of Non-Unique Solutions Of Initial Value Problems, Muhammad Islam
Mathematics Colloquium Series
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.
Periodicity In Quantum Calculus, Jeffrey T. Neugebauer
Periodicity In Quantum Calculus, Jeffrey T. Neugebauer
Mathematics Colloquium Series
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 …
Existence Results For Functional Dynamic Equations With Delay, Gnana Bhaskar Tenali
Existence Results For Functional Dynamic Equations With Delay, Gnana Bhaskar Tenali
Mathematics Colloquium Series
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 …