# MAM Seminars 2019

Higher seminars in the subject Mathematics/Applied Mathematics, 2019

Mathematics and Applied Mathematics Research Environment MAM, Division of Applied Mathematics,

School of Education, Culture and Communication (UKK), Mälardalen University.

**Program for Mathematics and Applied Mathematics seminar (MAM seminar) **

(lited in reverse chronological order from new to old, thus forthcomming listed first)

*Wednesdays afternoon 15.15-17.00 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 *

*Professor Sergei Silvestrov sergei.silvestrov@mdh.se.*

### 2019 Autumn term

**September 12, 2019, Thursday, 15.15-17.00**

__Location:__ U3-083 (Hilbert room), Västerås, Mälardalen University

**OBS! Two talks**

__Speakers:__

**15.15-16.05:** Siyang Wang, MAM, Division of Applied Mathematics, Mälardalen University

**16.10-17.00:** Doghonay Arjmand, MAM, Division of Applied Mathematics, Mälardalen University

**Siyang Wang talk ****title and abstract**

__Title:__ Efficient wave solvers by the finite difference method

__Abstract:__

We consider a class of finite difference methods for solving time-dependent hyperbolic partial difference equations. The finite difference operators satisfy a summation-by-parts (SBP) property, which is the discrete analogue of the integration-by-parts principle. Together with the simultaneous-approximation-term (SAT) method to impose boundary conditions, the SBP-SAT technique provides a recipe for constructing provably stable and high-order accurate finite difference discretizations. In this talk, we first discuss the SBP-SAT methodology, with a focus on the stability and accuracy analysis when applied to wave propagation problems. Then we generalize the method to solve problems with complicated geometry, and use local mesh refinement to further improve efficiency. In the end, we present numerical experiments and practical applications, and discuss future research topics.

**Doghonay ****Arjmand ****talk title and abstract**

__Title:__ Multiscale methods for numerical homogenization problems: overview and recent advances

__Abstract:__

In a multiscale problem several scales interact with each other to form a system which has variations over a wide range of scales. A direct numerical simulation of such problems requires resolving the small scales over a computational domain, typically much larger than the microscopic scales. This demands a tremendous computational cost as the microscopic variations need to be resolved over the entire computational geometry. In this talk, we will overview a class of multiscale methods for numerical homogenization problems considering applications from steady heat conduction and wave propagation problems in microscopically non-homogeneous media.

### --

### 2019 Spring term

**May 29, 2019, Wednesday, 15.30-16.30**

__Location__: U3-083 (Hilbert room), Västerås, Mälardalen University

__Speaker__: Thomas Westerbäck, Division of Applied Mathematics, Mälardalen University

__Title:__

Matroids, polymatroids and generalizations thereof via cyclic flats, and some connections to different algebraic structures

__Abstract:__

Matroid theory, a branch of algebraic combinatorics, has been successfully used to solve problems in many areas of mathematics and computer science. The theory has links to areas such as algebra, combinatorics, geometry and topology. For example, graphs and matrices over fields give rise to matroids. Polymatroids, a generalization of matroids, can be considered both as a set-combinatorial object and as a special class of polytopes. The theory of polymatroids has especially been important for combinatorial optimization when submodular functions are considered. Polymatroids can be used in connection with concepts such as Shannon entropy and hypergraphs .

In this talk, we will present how we have developed the theory of cyclic flats for matroids, polymatroids and generalizations thereof and how this can be used in order to capture certain properties of different algebraic structures. Further, we will also present some applications to distributed storage, network coding and machine learning.

**April 26, 2019, Wednesday, 15.30-16.30**

__Location__: U3-083 (Hilbert room), Västerås, Mälardalen University

__Speaker__: Andrii Dmytryshyn, Mathematics, School of Science and Technology, Örebro University

__Title:__

Reducing collections of matrices

__Abstract:__

We present Roth-type theorems for systems of matrix equations including an arbitrary mix of Sylvester and $*$-Sylvester equations, in which the transpose or conjugate transpose of the unknown matrices also appear. In full generality, we derive consistency conditions by proving that such a system has a solution if and only if the associated set of $2 \times 2$ block matrix representations of the equations are block diagonalizable by linked equivalence transformations.

We also describe the class of all possible sets of complex matrices that can be reduced to an upper-triangular form by associated unitary transformations, and the class of all possible sets of real matrices that can be reduced to a quasi-upper-triangular form by associated orthogonal transformations. Here one may think of Schur forms for a single matrix, a matrix pencil, and matrices associated with the periodic eigenvalue problem which all are frequently used and studied representatives of this class. Schur forms are the key ingredient for solving systems of Sylvester matrix equations by generalizations of the Bartels-Stewart algorithm.

**April 24, 2019, Wednesday, 15.30-16.30**

__Location__: U3-083 (Hilbert room), Västerås, Mälardalen University

__Speaker__: Thomas Westerbäck, Division of Applied Mathematics, Mälardalen University

__Title:__

Matroids, polymatroids and generalizations thereof via cyclic flats, and some connections to different algebraic structures

__Abstract:__

Matroid theory, a branch of algebraic combinatorics, has been successfully used to solve problems in many areas of mathematics and computer science. The theory has links to areas such as algebra, combinatorics, geometry and topology. For example, graphs and matrices over fields give rise to matroids. Polymatroids, a generalization of matroids, can be considered both as a set-combinatorial object and as a special class of polytopes. The theory of polymatroids has especially been important for combinatorial optimization when submodular functions are considered. Polymatroids can be used in connection with concepts such as Shannon entropy and hypergraphs .

In this talk, we will present how we have developed the theory of cyclic flats for matroids, polymatroids and generalizations thereof and how this can be used in order to capture certain properties of different algebraic structures. Further, we will also present some applications to distributed storage, network coding and machine learning.

**March 14, 2019, Wednesday, **

**Lecture 1, 15.15- 16.05, break 5 minutes, Lecture 2, 16.10-17.00**

__Location__: R2-605, Västerås, Mälardalen University

**MAM research frontier lecture series.**

**Intensive PhD course for PhD students and researchers.**

__Speaker__: Predrag Rajković, Department for Mathematics and Informatics, Faculty of Mechanical Engineering, University of Niš, Serbia

__Title:__

**Lecture 1:** *q*-Calculus - from basics to differential and integral operators

**Lecture 2:** **Elements of fractional q-calculus**

__Abstract:__

**Lecture 1:** *q*-Calculus - from basics to differential and integral operators

The theory of *q*-calculus starts with a real parameter *q* in purpose to define the discrete mathematical objects such that they are connected with well-known mathematical notions. It has its full justification in the fact that many continuous scientific problems have their discrete versions. In accordance to the basics of *q*-calculus, analogs of the numbers and operations, elementary functions, differential and integral operator, the whole structure of mathematical analysis is developed. In special, we gave contributions in the mean-value theory, *q*-Taylor formula, integral inequalities. These results are used in considering some new iterative methods for solving equations and systems.

**Lecture 2:** **Elements of fractional q-calculus**

The fractional calculus is used in various sciences because of its ability to describe memory effects. Today there are a number of concepts with different definitions of fractional integrals and derivatives and their applications in mathematics and other sciences. Several types of fractional *q*-integral operators and fractional *q*-derivatives were developed, always with the lower limit of integration equal to zero. However, in some considerations, such as solving of *q*-differential equation of fractional order with initial values in nonzero point, it is of interest to allow that the lower limit of integration is variable. In our papers, we succeeded to generalize this theory in that direction. We introduced a *q*-Taylor-like formula which had included fractional *q*-derivatives of the function. Also, the application of these derivatives to *q*-exponential functions allowed us to introduce *q*-analogues of the Mittag-Leffler function. Vice versa, those functions could be used for defining generalized operators in the fractional *q-*calculus.

**Dr Predrag Rajković, full professor, ****head of the Department for Mathematics and Informatics, ****Faculty of Mechanical Engineering, University of Niš, Serbia**

*Professor Dr Predrag Rajković is a mathematician doing his research mostly in the Special Functions and Numerical Analysis, but also with contributions in various scientific areas and good cooperation with numerous coauthors. His papers are published in the respectable journals and conference proceedings. He lectured a lot of different courses at his institution (special functions, numerical analysis, operational research, programming and graphics) and lead young scientists to their thesis*

**March 13, 2019, Wednesday, 15.15-17.00**

__Location__: R2-605, Västerås, Mälardalen University

__Speaker__:
Pasha Zusmanovich
, University of Ostrava, Czech Republic

__Title:__ Variations on the Hom-Lie theme: Hom-Lie structures and the Ado theorem

__Abstract:__

I will discuss recent results about Hom-Lie structures on various classes of Lie algebras: current Lie algebras, affine Kac-Moody algebras (joint work with Abdenacer Makhlouf), and Extended Affine Lie Algebras (work in progress with Chad Mangum). Time permitting, I will also discuss the Ado theorem in various classes of Hom-Lie algebras.

**Thursday, March 7, 2019, 15.15-17.00**

__Location__: **R2-605****, Västerås, Mälardalen University**

**Monday, March 11, 2019, 15.15-17.00**

__Location__: **U2-016****, Västerås, Mälardalen University**

**MAM research frontier lecture series.**

**Intensive PhD course for PhD students and researchers.**

**Quantitative Estimation of Characteristic Parameters in Demography: Methods, Models, Techniques and Simulations with Computer Programs**

**Christos H Skiadas, **ManLab, Technical University of Crete, Chania, Greece**, **Email: skiadas@cmsim.net

__Abstract:__

We provide methods, models and estimation techniques along with stochastic simulations and the appropriate computer programs to estimate and simulate from Life Tables the main characteristic parameters in Demography Research.

The seminar includes:

- Life Tables and basic parameters estimation (Life Expectancy)
- The death probability density
- The Gompertz and the Weibull models
- The Stochastic models
- Stochastic simulations
- Heath State and Deterioration
- Healthy Life Expectancy
- The optimal retirement age
- Health Expenditure allocation per age group
- Various estimations

**References**

1. New Book on: “Demography and Health Issues: Population Aging, Mortality and Data Analysis” (Skiadas & Skiadas, Eds, 2018). This is the 46 Volume of the Springer Series on Demographic Methods and Population Analysis.

2. New Book on: “Exploring the Health State of a Population by Dynamic Modeling Methods” (Skiadas & Skiadas, Monograph, 2018). This is the 45 Volume of the Springer Series on Demographic Methods and Population Analysis.

**March 6, 2019, Wednesday, 15.15-17.00**

__Location__: U2-016, Västerås, Mälardalen University

__Speaker__: Christos H Skiadas, ManLab, Technical University of Crete, Chania, Greece

__Title:__ Mathematical statistics methods in Demographic research

__Abstract:__

Quantitative Demographic Methods go back to the construction of Life Tables by Graunt (1662) and Halley (1693). These Life Tables, with the appropriate reformulations are the important part of quantitative demography until nowadays.

It follows a model by De Moivre (1725) and later on the famous Gompertz (1825) model. Makeham (1860) provided an extension of the Gompertz model and later appeared the Weibull (1951) model. The stochastic methodology inserted new models and forms in the demography area.

Of particular importance are also the population models starting from the Malthus (1798) model and later with the Logistic model from Verhulst (1838).

The new modeling approaches include the stochastic models and the stochastic reconstruction of health state models, the deterioration models and the finding of the healthy life expectancy estimation along with the healthy life years lost to disability. The stochastic methodologies include stochastic calculus, solution of Fokker-Planck partial differential equations and finding the death probability density functions.

**References**

1. New Book on: “Demography and Health Issues: Population Aging, Mortality and Data Analysis” (Skiadas & Skiadas, Eds, 2018). This is the 46 Volume of the Springer Series on Demographic Methods and Population Analysis.

2. New Book on: “Exploring the Health State of a Population by Dynamic Modeling Methods” (Skiadas & Skiadas, Monograph, 2018). This is the 45 Volume of the Springer Series on Demographic Methods and Population Analysis.