Robustness Of Synchronization In A System With A Diffusive-Time-Lag Coupling

Lattice differential equations have been studied with a view of establishing their long time behavior. Normal Hyperbolicity has been used to establish conditions for stability and persistence of the synchronization manifold. In most cases, Lattice structures can take different topological structures depending on the nature of coupling. The degree of structural stability and persistence depends on the coupling configuration; whether it is all-to-all, coupling on a circle, or simple Bravis structure. We use Hausdorff measure to demontrate the robustness of these topological structures.

Some New Results Related to Lorentz GΓ-Spaces and Interpolation

We give definition of a new generalized Weighted Lorentz GΓ-spaces. Some properties of these spaces will presented. We will show that these paces are interpolation space in the sense of Peetre between classical Lorentz spaces. These spaces are obtained also from weighted Cesàro and Copson spaces by so call “symmetrisation”. We give a characterization of the interpolation space in the sense of Peetre for some couple of spaces as small or classical Lebesgue space or Lorentz-Marcinkiewicz spaces. It happens that the result is always a GΓ- space, since this last space covers many spaces.

Abstract Omega Algebra that Subsumes Tropical Min and Max Plus Algebras

In this talk abstract omega algebra is introduced and the definition is modeled in such a way that it subsumes almost all so called tropical min and max plus algebras. Concrete examples of distinct nature of these algebras are presented. As applications, symmetrized omega algebras are constructed and matrices with basic operations and some topological distances over them are defined.

Classes Of Systems Of Differential Equations Of High Dimension

In this talk, we establish new connections between solutions to classes of systems of nonlinear ordinary differential equations of high dimension and solutions to delay differential equations. These connections make it possible to find approximate solutions to the systems of high dimension by reducing theirs to delay differential equations. Examples of such systems are systems arising when modeling some biological processes; moreover, the dimensions of these systems may be so large that their solving by a computer may constitute a very complicated problem. Such high-dimensional problems in mathematical biology originated authors studies in this direction.
The author was supported by the Russian Foundation for Basic Research (project no. 18-29-10086).

Linear Algebra without Determinant

A brief description of the structure of a standard undergraduate course of linear algebra is given. This course uses only concepts which are relevant from the point of view of computing with finite accuracy. Thus, the spectral theory and the theory of linear equations do not use concept of determinant.
(with Christoph Zenger, Technical University of Munich, Germany)

Mathemata, A Concept Between the Known and Unknown: Rereading the History of Mathematics in the Islamic Civilization within the Context of the Term 'Hisab'

The paper will focus on the transformation of the concept of ‘mathemata’ after the invention of the term 'Ḥisab' which is a calculation technique based on the ‘relations’ between numbers and the ‘relations’ between the magnitudes. Mathemata is inherited by the Islamic civilisation from the ancient civilisations and derives from two terms: arithmos (number) and megethos (magnitude). It is considered to be the study of ‘essence’. Additionally, the paper will examine how this new concept arithmetizates the known (sexagesimal, mental, and Indian) and unknown (algebra) quantities. Moreover, it will deal with how the science of surveying (misāḥa) is conducted by using the quantitative representation of the concept magnitude. It will introduce the Seljuk, Ottoman, and Andalusian scholars and treatises that had role in canonization of the taḥrīr movement on mathematical sciences which was began in Marw.

Analyses For Inverse Problems Related To The Fukushima Daiichi Nuclear Disaster: An Application Of Mathematics

The Fukushima Daiichi Nuclear Disaster in March 2011 has released cesium-137 etc. into environments. The long-standing prediction of the diffusion is important and for it, the starting point is inverse problems of determining unknown physical parameters on the basis of model equations. Moreover some extrapolation procedure of measured data is a kind of inverse problems. I discuss the following three related inverse problems and present numerical results for field data as well as theoretical results such as the uniqueness and the stability: • Determination of amplitude of explosion • Diffusion of radioactive substances in the soil related to the decontamination of farm- lands and estimation of air dose rate of radioactive substances • air dose rate of radioactive substances at the human height level by high-altitude data by drones The incident was very serious but the needed mathematical analysis is quite standard. I intend to demonstrate that the talk is a case study where mathematics is effective also for such serious real-world problems.

Mathematics Teacher Educators: Current Situation and Future Projections

In this presentation, findings of a recent research study on the present situation of mathematics teacher educators who are actively involved in teacher preparation programs will be shared. The important issues that the findings indicate will be addressed with reference to above-cited questions. The future projection of mathematics teacher educators will be presented and the areas that require further research will be discussed with the participants.

Importance Of Mathematical Modeling And Optimization in Industrial Applications

Generally speaking, the importance of mathematical modeling and optimization in real industry applications and its benefits will be discussed. In various applications carried out in industry, the way of implication, results achieved, the advantages provided of the mathematical modeling and optimization works will be explained.

Maximal and Singular Integral Operators and Their Commutators in Variable Exponent Generalized Weighted Morrey Spaces

We consider the generalized weighted Morrey spaces Mp(·),φ ω (R n) with variable exponent p(x) and a general function φ(x, r) defining the Morrey- type norm. We prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel, in such spaces. We also prove the boundedness of the commutators of max- imal operator and Calderon-Zygmund singular operators in the variable exponent generalized weighted Morrey spaces.