# MAM Seminars Autumn term 2017

Higher seminars in the subject Mathematics/Applied Mathematics, Autumn term 2017.

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

**Program for Mathematics and Applied Mathematics seminar. **

**Autumn term 2017**

*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.*

**P****rogram for Mathematics and Applied Mathematics seminar. **

**August 21, 2017, Monday, 15.30-16.30**

Location: U2-158, Västerås, UKK, Mälardalen University

Speaker: Dr. JIN Lu, University of Electro-Communications, Tokyo

__Title:__

Optimal Maintenance Policy for Deteriorating Systems Under a Variable Environment

__Abstract:__

In most research related to optimal decision policies, the system was assumed to operate in a non-variable environment. However, the deterioration of a system is affected by various factors, such as the environment and operating conditions. In such cases, the deterioration of the system should differ for different situations.

This talk will focus on the optimal maintenance policy for deteriorating systems operating in a variable environment with selectable operations. We assume that information about system deterioration and the surrounding environment are obtained by on-line monitoring. Using this information, the decision maker selects the operation that will minimize the total expected cost over an infinite horizon. Since there are strong dynamic interactions among a deteriorating system, its surrounding environment, and the operation being executed, we formulate the optimal decision-making problem for this system as a non-stationary Markov decision process with both environment and operation as parameters. The properties of the resulting optimal expected cost function are examined, and the optimal decision policy for operation selection is found to be given by a two-dimensional control limit policy under certain conditions. The optimal control limit policy reduces the total operating costs and enhances the dynamic decision-making process for deteriorating systems operating in a variable environment.

__About the Speaker:__

JIN Lu received her M.E. and Ph.D. degrees in engineering in 2003 and 2006 from the University of Electro-Communications (UEC), Tokyo. She is currently an Associate Professor in the Dept. of Informatics, University of Electro-Communications, Tokyo. Her current research interest is reliability engineering, condition monitoring maintenance and optimal decision-making. She received Literature Prize of the Japanese Society for Quality Control (2005). Also, she received the Outstanding Young Scientist of the Society (2006) and the Best Paper Award of IEEE Reliability Society, Japan Chapter (2006). She also received Nikkei Quality Control Literature Prize in 2014. She is a member of the Japanese Society for Quality Control (JSQC) and Reliability Engineering Association of Japan (REAJ), The Institute of Electronics, Information and Communication Engineers (IEICE), The Operation Research Society of Japan, IEEE.

**October 25, 2017, Wednesday, 15.30-16.30**

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

Speaker: Melanija Mitrović, University of Niš, Serbia

__Title:__

Semilattices of Archimedean Semigroups

__Abstract:__

Semigroups are the first mathematical object every human being has to deal with - even before attending school a child learns a ''language'', i.e. the child acquires ''words'' ( generators of a certain free semigroup) and ''sentences'' ( sequences of generators) formed by concatenation of words. Semigroup theory provides a convenient general framework for unifying and clarifying a number of topics and fields that seem, at first sight, unrelated. A *semigroup * is a set S together with an associative binary operation defined on it. Semigroups are, by definition, simple objects but, on the other hand, the very simplicity of their definition means that they can have a very complicated and intricate structure. Semigroup theorists agree that yet none of the powerful tools and ideas of today's mathematics has thrown much light on their structure. There are many different techniques for describing various kinds of semigroups. Four methods with general applications are ideal extensions, semilattice decompositions, subdirect decompositions, and group coextensions. The book *''Semilattices of Archimedean Semigroups' ' *(M. Mitrović) , provides a detail exposition of the approach to the structure theory of semigroups through semilattice decomposition. This talk will be based on material presented in that book.

**November ?, 2017, Wednesday, 15.30-16.30**

Location: R3-121, Västerås, UKK, Mälardalen University

Speaker: Dr. Yimin Xiao, Michigan State University

__Title:__

Fine Properties of Gaussian Random Fields on the Sphere

__Abstract:__

Let X = {X(t), t ∈ S^{2}} be a Gaussian random field on the sphere such as an isotropic spherical Gaussian field or a spherical fractional Brownian motion. This talk is concerned with sample path properties of X.

We provide a sufficient condition for X to have the property of strong local nondeterminism (SLND) in terms of the high-frequency behavior of its angular power spectrum. By applying SLND, we establish an exact uniform modulus of continuity for X and its local times. We also discuss the range of values of the spectral index for which the sample functions exhibit fractal or smooth behavior.

This talk is based on joint papers with Xiaohong Lan and Domenico Marinucci.