MAM Seminars Autumn term 2015
Higher seminars in the subject Mathematics/Applied Mathematics, Autumn term 2015.
School of Education, Culture and Communication (UKK), Mälardalen University.
Program for Mathematics and Applied Mathematics seminar.
Autumn term 2015
Wednesdays afternoon is the normal time for MAM seminars with deviations when necessary. The program is always provisional. The information about each specific talk at MAM seminar becomes final the day before. Suggestions for talks at MAM seminar are very welcome to Prof. Sergei Silvestrov sergei.silvestrov@mdh.se.
September 2, 2015, Wednesday, 16.0017.00 (Obs! starts at 16.00 not 15.30)
Location: U3083 (Hilbert room), Västerås, UKK, Mälardalen University
Speaker:
Emanuel Guariglia, University of Salerno, Italy
Title:
Special functions in Number Theory: a noconventional approach
Abstract:
Many special functions find wide application in Number Theory and Physics: through a noconventional approach (using Fractional Calculus, Wavelet Analysis and Fractal Geometry), we can describe a family of them. It is well know that almost all special functions are functions of complex variable: Ortigueira, defines a generalized Caputo derivative for complex functions with respect to a given direction of the complex plane: so the fractional derivative of a Dirichlet series, Hurwitz zeta function and Riemann zeta function can be easily computed as a complex series. Some interesting properties of the fractional derivative of the Riemann zeta function are also investigated to show that there is a chaotic decay to zero.
September 9, 2015, Wednesday, 15.3016.30
Location: U3083 (Hilbert room), Västerås, UKK, Mälardalen University
Speaker: Prof. Ola Hössjer, Division of Mathematical Statistics, Department of Mathematics, Stockholm University, Stockholm, Sweden
Title:
September 16, 2015, Wednesday, 15.3016.30
Location: U3083 (Hilbert room), Västerås, UKK, Mälardalen University
Speaker: Lars Hellström, Division of Applied Mathematics, MAM, UKK, Mälardalen University
Title:
Valuations on universal enveloping algebras: employing skew field embedding with generalised PBW property
Abstract:
September 30, 2015, Wednesday, 15.3016.30
Location: U3083 (Hilbert room), Västerås, UKK, Mälardalen University
Speaker:
Kibret Sigstam, Division of Applied Mathematics, Mälardalens University
Title:
Optimization and Estimation of Solutions of Riccati Equations
Abstract:
We are concerned with the initial value problem:
y'' r^{2}y=0, y(0)1=y'(0)=0, (1)
on the interval [0,T].
Riccati substitution f=y'/y of (1) gives a nonlinear first degree equation
f'+f^{2}= r^{2}, f(0)=0, (2)
on the same interval. Clearly the solution f of (2) is nonnegative. We studied the problems of optimizing the area under the function f on the interval [0,T], when r is allowed to vary over (i) all its equimeasurable rearrangements (ii) the convex hull of all its equimeasurable rearrangements.
We give a new and very short proof of the infimum problems. We also set conditions characterizing the solvability of the supremum problems.
October 7, 2015, Wednesday, 15.3016.30
Location: U3083 (Hilbert room), Västerås, UKK, Mälardalen University
Speaker: John Bondestam Malmberg, Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg
Title:
A Twostage Numerical Procedure for an Inverse Scattering Problem for Maxwell's Equations
Abstract:
We study a numerical procedure for the solution of the inverse problem of reconstructing location, shape and material properties (in particular refractive indices) of scatterers located in a known background medium. The data consist of timeresolved backscattered radar signals from a single source position. This relatively small amount of data and the illposed nature of the inversion are the main challenges of the problem. Mathematically, the problem is formulated as a coefficient inverse problem for a system of partial differential equations derived from Maxwell's equations.
The numerical procedure is divided into two stages. In the first stage, a good initial approximation for the unknown coefficient is computed by an approximately globally convergent algorithm. This initial approximation is refined in the second stage, where an adaptive finite element method is employed to minimize a Tikhonov functional. An important tool for the second stage is a posteriori error estimates  estimates in terms of known (computed) quantities  for the difference between the computed coefficient and the true minimizing coefficient.
October 14, 2015, Wednesday, 16.0017.00
Location: U2158 (Hilbert room), Västerås, UKK, Mälardalen University
Speaker: Prof. Kanhaiya Jha, School of Science, Kathmandu University, Kathmandu, Nepal
Email: jhakn(at)ku.edu.np; jhaknh(at)yahoo.co.in
Title:
Some Applied Aspects of fixed point results in Generalized Metric Spaces
Abstract:
Inspired from the impact and utility of metric space, several generalizations of this notion have been introduced in the literature such as semimetric space, fuzzy metric space, dislocated metric space, probabilistic metric (Menger) space, Gmetric space, cone metric space. The fixed point theory as a part of nonlinear analysis is a study of function equation in metric or nonmetric setting. It provides necessary tools for the existence of theorems in nonlinear problems. The classical Banach contraction principle is one of the fundamental results in metric space with wide applications. This principle has also a vital role on establishing fixed point results for nonexpansive mappings in Banach and Hilbert spaces. The main purpose of this presentation is to discuss some developments of classical metric subspaces and contractive definitions with applications to other disciplines.
Key words and phrases: metric space, contraction mapping, fuzzy sets
Mathematics Subject Classification: 47 H 10, 54 H 25
October 21, 2015, Wednesday, 15.3016.30
MAM doctoral students workshop
"Selected topics on Integratoin theory connected to PhD course in Integration Theory"
Orgeniser: Linus Carlsson , Division of Applied Mathematics, Mälardalen University,
Location: R1142, Västerås, Mälardalen University
November 4, 2015, Wednesday, 15.3016.30
Location: U3083 (Hilbert room), Västerås, UKK, Mälardalen University
Speaker: Marta Leniec, PhD Student, Department of Mathematics, Uppsala University
Title:
American options and counterparty risk
Abstract:
We study a problem of pricing a contract consisting of two perpetual American options between two defaultable counterparties. We show that the problem reduces to an optimal stopping game. Moreover, we show that a Nash equilibrium as well as the value of the game exist and we state and prove a verification theorem. Then, we calculate Credit Valuation Adjustment (CVA) of this contract. This paper can be considered as the first step in pricing larger volumes of contracts between two defaultable counterparties.
November 18, 2015, Wednesday, 15.3016.30
Location: U3104 (Turing room), Västerås, UKK, Mälardalen University
Speaker: Johan Richter, Division of Applied Mathematics, MAM, UKK, Mälardalen University
Title:
Centralizers and valuations
Abstract:
I will describe a generalization of certain results by Hellström and Silvestrov on centralizers in graded algebras. More precisely I have studied centralizers in certain algebras with valuations. I have proven that the centralizer of an element in theses rings is a free module over a certain ring. Under further assumptions we obtain that the centralizer is also commutative.
November 25, 2015, Wednesday, 15.3016.30
Location: U3083 (Hilbert room), Västerås, UKK, Mälardalen University
Speaker: Emanuel Guariglia, University of Salerno, Italy. Division of Applied Mathematics, MAM, UKK, Mälardalen University, Sweden
Title:
Reducibility of the wavelet representations associated to the Cantor set
Abstract:
This work is devoted to interplay between wavelets, fractals, operator theory and representations. An introductory review of the article on the subject by Sergei Silvestrov and Dorin Dutkay and some related works will be given.
Sergei Silvestrov, Dorin E. Dutkay, Reducibility of the wavelet representations associated to the Cantor set, Proceedings of the American Mathematical Society, Vol. 139, No. 10, 3657–3664
http://arxiv.org/abs/1008.4349
http://www.ams.org/journals/proc/201113910/S000299392011109134/S000299392011109134.pdf
December 2, 2015, Wednesday, 15.3017.00
Location: U2158, Västerås, Mälardalen University
OBS! Fractals and Geometry in Antennas technology!
Two guests talks in one MAM seminar 90 = 45+45 minutes!
Talk 1:
Speaker: Emanuel Guariglia, University of Salerno, Italy and Division of Applied Mathematics, MAM, UKK, Mälardalen University, Sweden
Title:
Fractal antennas: theory and application
Abstract:
Fractal antennas represent a surprising application of the theory developed by Mandelbrot to antenna theory. The two fundamental properties of a fractal (i.e. selfsimilarity and spacefilling) allow these antennas to have an efficient miniaturization and an excellent multiband behaviour. Fractal antennas have different fields of application, like defence, cultural heritage conservation and spatial communications: in addition, they may be used to obtain the socalled broadband invisibility cloak.
Talk 2:
Speaker: Dr. Pushpanjali G. Metri, Dept. of Physics, School of Physical Sciences, Central university of Karnataka, Gulbarga, India
Title:
Enhancement of Impedance Bandwidth of Equilateral Triangular Microstrip Antenna Using Different Feeding Techniques
Abstract:
Novel design of equilateral triangular microstrip antenna is proposed at Xband frequency. The antenna is designed, fabricated and tested for single and multiband operation. The experimental impedance bandwidth of conventional equilateral triangular microstrip antenna (CEMA) is found to be 5.02%. The CEMA is simulated using HFSS software.The study is continuedwith array technique and the radiating patches are fed by corporate feeding technique. An optimized wide slot is inserted at the centre of radiating patches of array antennas to enhance the impedance bandwidth and other antenna parameters. It is observed from the results that the impedance bandwidth of proposed antennas is enhanced up to 9.11 % which is 80.08% more when compared to the impedance bandwidth of CEMA. Theoretical results of the proposed antennas are well agreed with the experimental results. Input impedance, gain, azimuthal radiation patterns and VSWR of proposed antennas have been studied and reported. The obtained experimental results and theoretical study of the proposed antennas are given and discussed in detail.
Key words: equilateral triangular microstrip antenna, array antenna, corporate feeding technique
December 9, 2015, Wednesday, 15.3016.30
Location: U3104 (Turing room), Västerås, UKK, Mälardalen University
Speaker: Jens Fjelstad, Uppsala University
Title:
Finite dimensional representations of mapping class groups of surfaces from finite groups
Abstract:
Mapping class groups of surfaces constitute a class of infinite discrete groups that is on the one hand interesting for a number of applications and on the other hand notoriously difficult to get a good handle on. Some theories from Physics describing lowdimensional systems produce finite dimensional representations of mapping class groups which have proved useful to investigate properties of mapping class groups themselves. I will discuss recent results (obtained in collaboration with Jürgen Fuchs) partly characterising a certain class of such representations constructed from any finite group G. The class of representations that we consider is a generalisation of certain representations of the modular group appearing in finite group theory (in work by Drinfeld) as well as in the socalled Moonshine programme.
December 16, 2015, Wednesday, 15.3016.30
Location: U3083 (Hilbert room), Västerås, UKK, Mälardalen University
Speaker: Urban Larsson, Dalhousie University, Halifax, Canada
Title:
Selforganization in combinatorial games
Abstract:
By generalizing the classical heap game of Wythoff Nim (a.k.a CornertheLady), we have various empirical evidence of selforganization of the generalized outcomes. Moreover, a new diamond shaped Cellular Automaton emulates these patterns. This is joint work with Matthew Cook, Turlough Neary, Adam Landsberg, Scott Garrabrant, Eric Friedman and Ilona PhippsMorgan.
