The mathematical sciences department graduate seminar is a venue for expository talks and presentations on research by undergraduate students, graduate students, and faculty members. Anyone interested is welcome to attend and participate.
The seminar is currently organized by Naveed Iqbal and Adam Prinkey. Please send an email to nchaudhrob@my.fit.edu with your suggestions for future talks, as well as any questions or comments.
Date and Time  Speaker  Title & Abstract 

Jan. 30
Mon. 910am MAC 
Evan Cosgrove
Math Sciences Department Florida Tech 
Title: On the Frechet Differentiability in Optimal Control of Coefficients in Parabolic Free Boundary Problems
Abstract: We consider the inverse Stefan type free boundary problem, where the coefficients, boundary heat flux, and density of the sources are missing and must be found along with the temperature and the free boundary. We pursue an optimal control framework where boundary heat flux, density of sources, and free boundary are components of the control vector. The optimality criteria consists of the minimization of the $L_2$norm declinations of the temperature measurements at the final moment, phase transition temperature, and final position of the free boundary. We prove the Frechet differentiability in BesovHölder spaces, and derive the formula for the Frechet differential under minimal regularity assumptions on the data. The result implies a necessary condition for optimal control and opens the way to the application of projective gradient methods in BesovHölder spaces for the numerical solution of the inverse Stefan problem. 
Feb. 06
Mon. 910am MAC 
Dr. Jonathan Goldfarb
Math Sciences Department Florida Tech 
Title: Some details of the proof of Frechet Differentiabilty in Optimal Control of Coefficients in Parabolic Free Boundary Problems
Abstract: We provide some details on certain technical results from our joint work on Frechet Differentiabilty in Optimal Control of Coefficients in Parabolic Free Boundary Problems. 
Feb. 27
Mon. 910am MAC 
Tsz Chung Ho
Math Sciences Department Florida Tech 
Title: Variational methods for nonlinear PDEs
Abstract: We apply basic tools from critical point theory to prove existence results for nonlinear PDEs. 
Mar. 13
Mon. 910am MAC 
Saleheh Seif
Math Sciences Department Florida Tech 
Title: Breast Cancer Detection via Electrical Impedance Tomography and Optimal Control Theory
Abstract: Electrical Impedance Tomography (EIT) is a rapidly developing noninvasive medical imaging technique with various applications for cancer detection and screening purposes. Electrical conductivity of the cancerous tumor is significantly different from healthy tissue. Mathematical formulation of recovering electrical conductivity of the body from the surface electrode measurements of electrical current is a nonlinear inverse problem for the second order elliptic partial differential equation, referred to as Calderon's inverse problem. In this project we use a variational approach and formulate the breast cancer detection as an optimal control problem for the second order elliptic PDE with bounded measurable coefficients. In this talk I will demonstrate proof of the existence and uniqueness of the solution to mixed problem for elliptic PDE through application of the LaxMilgram Theorem. Next I will discuss Frechet differentiability of the cost functional in HilbertSobolev spaces. 
Mar. 20
Mon. 910am MAC 
Shiqiu Fu
Math Sciences Department Florida Tech 
Title: Variational methods for nonlinear PDEs
Abstract: In this talk, I will speak about the Krasnoselskii Genus of an Index Theory. We will discuss some definitions, propositions, theorems and some proofs for the lemmas. Moreover, I will present some applications of Genus in PDE 
Mar. 27
Mon. 910am MAC 
Ali AlObaidi
Math Sciences Department Florida Tech 
Title: Modulated Random Measures in Topological Spaces
Abstract: In this seminar, we will introduce random measures in different topological spaces and give some examples of them. Moreover, we will define their stochastic integrals and go over relevant integral theory, such as Campbell's theorem and its application in Laplace functional. We will discuss the most significant issue: the fact that stochastic integrals are just a random measure. Next, we will present the concept of the stochastic integral of a function of two variables, where we will see how they are related to modulated random measures. We will talk about the construction of modulated random measures using measures or stochastic processes and drive the intensity and rates intensity of the constructions. 
Date and Time  Speaker  Title & Abstract 

Aug. 29
Mon. 910am MAC 
Naveed H. Iqbal
Math Sciences Department Florida Tech 
Title: On the Second Minimal Odd Periodic Orbits of the Continuous Endomorphisms on the Real Line
Abstract: This work introduces the notion of second minimal nperiodic orbit of the continuous map on the interval according as: $n$ is a successor of the minimal period of the map in Sharkovskii ordering. We pursue classification of second minimal $2k+1$orbits, $k\geq 3$, in terms of cyclic permutations and digraphs. It is proved that there are $4k3$ types of second minimal odd orbits with accuracy up to inverses. 
Sep. 12
Mon. 910am MAC 
Adam Prinkey
Math Sciences Department Florida Tech 
Title: Qualitative Properties of Solutions to Nonlinear Parabolic Partial Differential Equations with DoubleDegenerate Fast Diffusion
Abstract: We consider the Cauchy problem for the double degenerate parabolic partial differential equation.
\begin{equation} \nonumber\\
\frac{\partial u}{\partial t} = \frac{\partial}{\partial x}\left( \bigg\vert \frac{\partial u^m}{\partial x} \bigg\vert^{p1} \frac{\partial u^m}{\partial x} \right)  bu^\beta,~ x \in \mathbb{R}, ~t>0; ~u(x,0) = C(x)^\alpha_+, ~x \in \mathbb{R}
\end{equation}
where $C, \alpha, m,$ and $p$ are positive constants and $b \in \mathbb{R}$. We investigate the existence of an interface for this problem and the behavior of the solution near the interface, or the behavior of the solution at infinity if there is no interface. This equation arises in a variety of situations including heat transfer in plasma, spatial spread of populations in ecology, diffusion of chemicals through groundwater, and many others. We consider the case where $0 U. G. Abdulla. Evolution of Interfaces and Explicit Asymptotics at Infinity for the Fast Diffusion Equation with Absorption, Nonlinear Analysis: Theory, Methods and Applications, (4) 2002, 541560. From the structure of the equation, it is clear that the behavior of the interface is determined by the competition between diffusion and reaction. We found that if $\beta < mp$, the interface propagates with finite speed; in this case, we prove that the interface expands for $\alpha < \frac{1+p}{mp\beta}$ and shrinks for $\alpha > \frac{1+p}{mp\beta}$. In the critical case $\alpha = \frac{1+p}{mp\beta}$, we prove that there exists a critical value $C_*$ such that if $C=C_*$, the interface will remain stationary. In all of these cases, we rigorously prove explicit bounds for the interface and for the solution $u$ up to precise constants. If $\beta \geq mp$, we prove that the interface expands with infinite speed of propagation and we derive explicit asymptotic formulas for the solution at infinity. The rigorous methods we apply include scaling, construction of super and sub solutions to the problem, and special comparison theorems in general domains. We confirmed our results numerically with a WENO scheme and developed test problems for special cases of our equation for a new numerical interface tracking method. 
Sep. 26
Mon. 910am MAC 
Osita Onyejekwe
Math Sciences Department Florida Tech 
Title: MultiScale Signal Denoising, Feature Extraction and Signal Reconstruction Using NonParametric Regression Analysis
Abstract: Feature detection and signal reconstruction is an important aspect of digital signal processing. This task can be arduous and time consuming with varying results. Various feature extraction systems can be utilized to aid experts in this task. Signals are often corrupted with noise and signal denoising is needed prior to feature extraction. This presentation presents a general statistical approach using nonparametric regression analysis for smoothing and feature detection. The techniques proposed here include multiscale kernel regression alongside matched filtering. The optimal denoising bandwidth is selected for each point prediction by maximizing the Signal to Noise Ratio (SNR) through the process of matched filtering. From thence, the kernel bandwidth is selected based upon the estimated standard error of the estimated signal within the neighborhood window. 
Oct. 03
Mon. 910am MAC 
Roby Poteau
Math Sciences Department Florida Tech 
Title: TBA
Abstract: We consider the inverse problem for the identification of constant for systems of nonlinear ODEs arising in mathematical biology. We implement a numerical method suggested in U.G.Abdulla, Journal of Optimization Theory and Applications, 85, 3(1995), 509526. The method combines Bellman's quasilinearization with sensitivity analysis and Tikhonov's regularization. We apply the method to various biological models such as the classical LotkaVolterra system, models from systems biology and the Lorenz model. The numerical results show the accuracy of the method, applications to real data and confirm quadratic convergence.. 
Oct. 24
Mon. 910am MAC 
Roqia Jeli
Math Sciences Department Florida Tech 
Title: On the Qualitative Theory of the Nonlinear Parabolic $p$Laplacian Type ReactionDiffusion Equations
Abstract: We present a full classification of the shorttime behaviour of the interfaces and local solutions to the nonlinear parabolic $p$Laplacian type reactiondiffusion equation of nonNewtonian elastic filtration \[ u_t\Big(u_x^{p2}u_x\Big)_x+bu^{\beta}=0, \ p>2, \beta >0 \] The interface may expand, shrink, or remain stationary as a result of the competition of the diffusion and reaction terms near the interface, expressed in terms of the parameters $p,\beta, sign~b$, and asymptotics of the initial function near its support. In all cases, we prove the explicit formula for the interface and the local solution with accuracy up to constant coefficients. The methods of the proof are based on nonlinear scaling laws, and a barrier technique using special comparison theorems in irregular domains with characteristic boundary curves. 
Oct. 31
Mon. 910am MAC 
Jeremy Mandelkern
Math Sciences Department Florida Tech 
Title: An Integral Equation Method to Formulate Solutions Defined Near LP/N Irregular Singular Points For 2nd Order SL Equations
Abstract: In this talk, a fundamental system of solutions is obtained near the LP/N irregular singular point x = 0 for a 2nd order SturmLiouville equation with strongly singular potential & certain properties of these solutions are established. The crux of our method involves factoring away lambdaindependent singular behaviors of these solutions by the use of suitable changes of variables. The remaining nonsingular lambdadependent factors are then obtained by the solution of Volterra integral equations of the 2nd kind. Unlike the formal power series solution method which furnishes asymptotics of true solutions, our method appears to yield, by recursion, the true solutions for which these asymptotics correspond to. 
Date and Time  Speaker  Title & Abstract 

Feb. 3
Wed. 910am MAC 
Melissa S. Moreno, Megan Moreno, and Travaughn Bain
Math Sciences Department Florida Tech 
Title: Patternbased Classification and Survival Analysis of Chronic Kidney Disease
Abstract: This study integrates the principles of patternbased classification and KaplanMeier survival analysis to identify genes and clinical features associated with the rapid progression of chronic kidney disease. The methodology successfully determines the genegene survival interactions in the AfricanAmerican Study of Chronic Kidney Disease with Hypertension (AASK) genomic dataset. The results obtained from this study serves as a basis for the future studies on comparison of the disease progression in white patients with that in AfricanAmerican patients, both those with and those without apolipoprotein L1 (APOL1) highrisk variants. 
Feb. 17
Wed. 910am MAC 
Lamees Alzaki and Amna Abuweden
Math Sciences Department Florida Tech 
Title: Weighted Sobolev Spaces
Abstract: In this talk, we will give a summary of the main results in Chapter 1 of "Nonlinear Potential Theory of Degenerate Elliptic Equations" by J. Heinonen, T. Kilpelänen, and O. Martio, in which the theory of Weighted Sobolev spaces is developed. 
Date and Time  Speaker  Title & Abstract 

Sep. 2
Wed. 1011am MAC 
Jonathan Goldfarb
Math Sciences Department Florida Tech 
Title: Frechet Differentiability in Optimal Control of the Free Boundary Problems for the Second Order Parabolic PDEs
Abstract: We consider an optimal control of the Stefan type free boundary problem for the following general second order linear parabolic PDE: \(\frac{\partial}{\partial x}\Big( a\frac{\partial u}{\partial x} \Big )+b\frac{\partial u}{\partial x} +cu\frac{\partial u}{\partial t}=f~\text{in}~\Omega = \{(x,t):~0\lt x \lt s(t),~0 \lt t \leq T\}\) where $u(x,t)$ is the temperature function; the density of heat sources $f$, unknown free boundary $s$, and boundary heat flux are components of the control vector; and the cost functional consists of the $L_2$declination of the trace of the temperature at the final moment, temperature at the free boundary and final position of the free boundary from available measurements. This problem arises when considering a phase transition process with unknown temperature function, phase transition boundary, source term and boundary heat flux. A new variational formulation developed in
U. G. Abdulla, Inverse Problems and Imaging, 7, 2 (2013), 307340
which addresses the dual issues of possible measurement errors and large computational cost associated with classical variational formulations of ISP.In this project we prove Frechet differentiability of the cost functional in Hilbert space framework. Extension of the differentiable calculus to the infinitedimensional setting is the major mathematical challenge in this context, especially due to the fact that free boundary is the component of the control vector, and increment of the cost functional must take into account the variation of the domain of dependence. We apply the idea of decomposition of the domain, possibly into countably many subdomains depending of the sign oscillations of the free boundary increment, and carefully account for the effect of boundary integrals on the derivation of the first variation of the cost functional. The notion of the adjoint problem is introduced, as an infinite dimensional analogy of the classical Lagrange multipliers in finite dimensional constrained optimization problems. With the delicate use of sharp embedding theorems in fractional SobolevBesov spaces the Frechet differentiability is proven, and the formula for the Frechet gradient expressed in terms of the traces of the state vector and the solution of the adjoint problem. 
Sep. 9
Wed. 1011am MAC 
Adam Prinkey
Math Sciences Department Florida Tech 
Title: Evolution of Interfaces of the Double Degenerate Nonlinear
ReactionDiffusion Equation
Abstract: We consider the problem of interface development and local behavior of solutions near the interface in the following Cauchy problem for the nonlinear doubledegenerate parabolic PDE with reaction: $u_{t}=((u^{m})_{x}(\left\vert(u^{m})_{x}\right\vert^{p1}))_{x}bu^{\beta},~x\in\mathbb{R},~t>0;~u(x,0)=C(x)_{+}^{\alpha}$ The problem arises in applications such as heat radiation in plasma, spatial spread of populations, and chemical diffusion through groundwater. The structure of the PDE implies that interface behavior is determined by the competition between diffusion and reaction. The full solution for the reactiondiffusion equation ($p=1$) was given in 2000 [Abdulla and King, SIAM J. Math. Anal., 32, 2(2000), 235260] and 2002 [Abdulla, Nonlinear Analysis, 50, 4(2002), 541560]. Our aim is to apply the methods of these papers to solve the open problem for doubledegenerate reactiondiffusion equations ($p>1,~mp>1$). First we apply the nonlinear scaling method to identify which term dominates in various regions of the $(\alpha,\beta)$parameter space. We then construct super/subsolutions and apply special comparison theorems in irregular domains to prove explicit formulae for the interface and local solution, with precise estimations up to constant coefficients. A WENO scheme is applied and supports our estimates. 
Sep. 16
Wed. 1011am MAC 
Naveed Iqbal
Math Sciences Department Florida Tech 
Title: On the Fine Classification of Periodic Orbits of the Continuous Endomorphisms on the Real Line and Universality in Chaos
Abstract: We complete the classification of the periodic orbits of period $2^{n}(2k+1)$, $k>1$, of the continuous endomorphisms on the real line which are minimal with respect to Sharkovski ordering. By developing the new constructive method suggested recently by Abdulla et al. it is proved that independent of $k$, there are $2^{2^{n+1}2}$ types of digraphs (and cyclic permutations) with accuracy up to inverse digraphs. We advance outstanding open problem conjectured in JDEA paper on the structure of the second minimal odd orbits, which are defined as those that immediately follow the minimal orbits with respect to Sharkovski ordering. We pursue full analysis of the second minimal 7orbits. It is proved that there are 9 types of second minimal 7orbits with accuracy up to inverses. We apply this result to the problem on the distribution of superstable periodic windows within the chaotic regime of the bifurcation diagram of the oneparameter family of logistic type unimodal maps. It is revealed that by fixing the maximum number of appearances of the periodic windows there is a universal pattern of distribution. For example, by employing the notation $n_i$ for the $i$th appearance of the $n$orbit, all the superstable odd orbits up to 8th appearances while increasing the parameter are distributed according to the universal law \(\cdots\rightarrow (2k+3)_{1} \rightarrow (2k+9)_{5} \rightarrow (2k+7)_{3} \rightarrow (2k+9)_6 \rightarrow (2k+5)_{2} \rightarrow\) \(\rightarrow (2k+9)_{7} \rightarrow (2k+7)_{4} \rightarrow (2k+9)_{8} \rightarrow (2k+1)_1 \rightarrow \cdots\) where the branches successively follow from right to left as $k=1,2,\ldots$. The same universal route is continued to the left for all 8 appearances of the $2^n(2k+1)$orbits successfully for positive integers $n=1,2,\ldots$, and with the same order of appearance indices. Every orbit in (1) is universal, in the sense that it has a unique cyclic permutation and digraph independent of the unimodal map. In particular, the first appearance of all the orbits is always a minimal orbit, with precisely Type 1 digraph. It is observed that the second appearance of 7orbit is a second minimal 7orbit with Type 1 digraph. The reason for the relevance of the Type 1 minimal orbit is the fact that the topological structure of the unimodal map with single maximum is equivalent to the structure of the Type 1 piecewise linear endomorphism. Yet another important development of this research is the revelation of the pattern of the pattern dynamics with respect to increased number of appearances. Understanding the nature and characteristics of this fascinating universal route is an outstanding open problem for future investigations. 
Sep. 23
Wed. 1011am MAC 
Curtis Earl
Math Sciences Department Florida Tech 
Title: State Constrained Optimal Control of the Stefan Type Free Boundary Problems

Nov. 4
Wed. 1011am MAC 
Osita Onyejekwe
Math Sciences Department Florida Tech 
Title: NonParametric Kernel Regression with Application to MultiDimensional Data
Abstract: Kernel smoothing refers to a general class of techniques for nonparametric estimation of functions. It can be useful in two classes of problems; namely, (i) density function estimation and (ii) nonparametric regression estimation. Various techniques and kernels employed to denoise one dimensional functions will be analyzed. Two special cases of estimators studied include; the NadarayaWatson estimator and the local polynomial estimator. Expansion of these methods into in 2Dimensional settings along with an overview of future works will be looked into. Multidimensional kernel regression is used towards image processing and reconstruction. Proposed methods and development of tools will be used to denoise images to gain better understanding of its original features. 
Dec. 2
Wed. 1011am MAC 
Kenneth Iwezulu
Math Sciences Department Florida Tech 
Title: Operational Calculus in Stochastic Games
Abstract: In this talk, we shall consider an antagonistic stochastic game where two players $A$ and $B$ attack each other at some random times with strikes of random magnitude $X$ and $Y$ respectively and are observed by a third party. In particular, we consider three cases: Case 1, both players attack each other according to an ordinary Poisson process with intensities $\lambda$ and $\mu$, in case 2, one player attacks according to an ordinary Poisson process while the other attacks according to a marked Poisson process with position marks that are exponential with parameter $\nu$ and in case, we consider attacks according to an ordinary Poisson process but in bulk and are geometrically distributed while the other attacks according to a marked Poisson process which are exponentially distributed. In all three cases, the observation is said to be exponential. Both player $A$ and $B$ have predefined threshold $M$ and $N$ respectively which is considered to be their tolerance level, At the time either player crosses its threshold, that player is said to be defeated/ruined/overpowered. Our goal is to determine the first passage time i.e the time when the cumulative casualty of either player crosses its predefined threshold. To this end we shall employ the key fluctuation theorem to define such functional and use the Doperator/operational calculus to exhibit explicit results. This kind of game has applications in military warfare, politics, biology (cancer treatment) amongst others. 
Date and Time  Speaker  Title & Abstract 

September 9, 2014
4  5pm Evans Library 133 
Jonathan Goldfarb
Math Sciences Department Florida Tech 
Title: Numerical Methods for Solving Optimal Control Problems for the Second Order Parabolic PDEs

September 30, 2014
4  5pm Evans Library 133 
Ryan White
Math Sciences Department Florida Tech 
Title: An Operational Calculus Approach to Random Walks on Random Lattices
Abstract: In this talk, we discuss a particular class of stochastic processes for modeling the accumulation of damage to networks or systems experiencing a sequence of attacks that incapacitate random numbers of nodes (e.g. components), each with a random weight (e.g. a cost). Each component has threshold(s) whose crossing indicate the system entering a critical state. An operational calculus strategy is used to derive probabilistic information about the process within random vicinities of passage times. Necessary ideas from (measuretheoretic) probability theory are introduced. 
October 7, 2014
4  5pm Evans Library 133 
Joao Alberto de Faria
Math Sciences Department Florida Tech 
Title: Automorphism Groups of Rational Functions
Abstract: In this talk, we will discuss two algorithms to compute automorphism groups for single variable rational functions. These algorithms come directly from the paper "Computing Conjugating Sets and Automorphism Groups of Rational Functions", by Faber, Manes, and Viray. Throughout the talk, necessary ideas from algebra and dynamics will be introduced as needed. Afterwords, we will explain the connections between the current algorithms to my own work, which is making them work in higher dimensional cases. 
October 14, 2014
No talk (Holiday)  
November 4, 2014
4  5pm Evans Library 133 
Speaker TBA

Title: TBA

November 11, 2014
No talk (Holiday)  
November 18, 2014
4  5pm Evans Library 133 
Rana Haber
Math Sciences Department Florida Tech 
Title: Discriminative Interpolation for Functional Data Classification
Abstract: Functional Data, such as time series data, weather data, EEG data, handwritten data, and others, is assumed to have a smooth underlying function which can be represented using a basis expansion. Machine Learning’s traditional approach is to treat these datasets as feature vectors. In doing so, they do not leverage the fact that there is a smooth underlying function. We explore integrating this concept into machine learning algorithms starting with classification. 
November 25, 2014
4  5pm Evans Library 133 
Jeremy Mandelkern
Assistant Professor Eastern Florida State College Mathematics Department 
Title: Generating the Spectral Density Function for Bessel's Equation using the method of Fulton, Pearson, and Pruess
Abstract: Theory and application of eigenfunction expansions for the Bessel Equation will be presented. The Appell system and it's properties will be defined. The spectral density function will then be computed using this system and the recent method given by Fulton, Pearson, and Preuss. 
December 2, 2014
4  5pm Evans Library 133 
Roby Poteau
Math Sciences Department Florida Tech 
Title: Identification of Parameters in Mathematical Biology
Abstract: We consider inverse problems for the identification of parameters for systems of nonlinear ODEs arising in mathematical biology. We implement a numerical method suggested in U.G.Abdulla, Journal of Optimization Theory and Applications, 85, 3(1995), 509526. The idea of the method is based on the combination of Bellman's quasilinearization with sensitivity analysis and Tikhonov's regularization. We apply the method to various biological models such as LotkaVolterra system, the Pielou extension, bistable switch model in genetic regulatory networks, an angiogenesis model, a threestep pathway modelled by 8 nonlinear ordinary differential equations, etc. Numerical results confirm the quadratic convergence. Some challenges associated with the size of the system and unknown parameters, as well as the length of the time interval are discussed. 
Date and Time  Speaker  Title & Abstract 

Jan. 27, 2014
10  11am Skurla 106 
Jonathan Goldfarb
Math Sciences Department Florida Tech 
Title: Introduction to Sobolev Spaces I
Abstract: The seminar will introduce notation and concepts relevant to weak differentiation and Sobolev spaces, with applications to partial differential equations of mathematical physics. Source: Chapter 5 in Evans, Partial Differential Equations, with some others. 
Feb. 10, 2014
10  11am Quad 110 
Jonathan Goldfarb
Math Sciences Department Florida Tech 
Title: Introduction to Sobolev Spaces II
Abstract: We continue with properties of weak differentiation and basic facts of Sobolev spaces. Source: Chapter 5 in Evans, Partial Differential Equations, with some others. 
Feb. 24, 2014
10  11am Quad 111 
Bruno Poggi
Math Sciences Department Florida Tech 
Title: Introduction to Sobolev Spaces III
Abstract: We will discuss properties of Sobolev functions, and the completeness of the Sobolev space. Source: Chapter 5 in Evans, Partial Differential Equations. 
Mar. 17, 2014
10  11am Quad 111 
Noha Aljaber
Math Sciences Department Florida Tech 
Title: Introduction to Sobolev Spaces IV
Abstract: In this talk, we continue our exploration of Sobolev functions by showing that the space of smooth functions is a dense subset of the Sobolev space. Source: Chapter 5 in Evans, Partial Differential Equations. 
Mar. 24, 2014
10  11am Quad 111 
Noha Aljaber
Math Sciences Department Florida Tech 
Title: Convolution and Mollfication
Abstract: In this talk, we will look to the details of creating smooth approximations to badly behaved (integrable) functions. Source: Appendix C in Evans, Partial Differential Equations. 
Mar. 31, 2014
10  11am Quad 111 
Jeremy Mandelkern
Assistant Professor Eastern Florida State College Mathematics Department 
Title: A Novel Method for Frobenius Type Problems Utilizing 4x4 Matrix Multiplication Recurrence Relations
Abstract: In Balser [1, p. 1819] a matrix formulation of the Frobenius Theory, near a regular singular point, is given resulting in a 2x2 matrix of two linearly independent solutions together with their quasiderivatives. In this paper we apply Balser’s 2x2 matrix formulation to the Bessel equation, \( (xy')' + \left( \frac{v^2}{x} + \lambda x\right)y=0 \) We then show that with a slight reformulation of his 2x2 matrix recurrence relation, we can generate an equivalent recurrence relation through a “vectorization” procedure. This reformulated approach succeeds in overcoming the rather cumbersome coupling associated with Balser’s 2x2 matrix recursion. As a result of the vectorization procedure, the 2x2 matrix recurrence relation is replaced by a straightforward matrix multiplication of 4x4 matricies. 
Apr. 7, 2014
10  11am Quad 111 
Ryan White
Math Sciences Department Florida Tech 
Title: Introduction to Sobolev Spaces V
Abstract: In this talk, we continue our exploration of Sobolev functions by establishing how Sobolev functions can be extended to larger domains while satisfying appropriate inequalities. This extension allows results established with the domain of the whole space to be appropriately generalized to smaller domains. Source: Chapter 5 in Evans, Partial Differential Equations. 
Apr. 14, 2014
10  11am Quad 111 
Osita Onyejekwe
Math Sciences Department Florida Tech 
Title: Regression for Parametric and Nonparametric Estimation
Abstract: In this talk Linear, Polynomial, and Kernel Regression analysis will be introduced. It follows by application of regression method for parametric and nonparametric estimation through simulations. It will be concluded by addressing the important questions regarding selection of polynomial order in parametric estimation as well as selection of the bandwidth in nonparametric estimation. 
Apr. 21, 2014
10  11am Quad 111 
Elvira Erhardt
Math Sciences Department Florida Tech 
Title: Statistical Multiple Testing for Analysis of Imaging Response in Simulated Brain Images
Abstract: In this talk different methods of multiple testing will be introduced. Voxelwise test of significance will then be discussed by application of Bonferroni and FDR correction to imaging response in simulated brain images. It will be concluded by statistical estimation of background and standardizing the test statistics using the estimated parameters. 