Predavanje: Pakiranja malih grafova u fulerene i u druge poliedre

U petak, 09. srpnja 2021. u 12:00 u dvorani B3-17 PMF-a

prof. dr. sc. Tomislav Došlić

s Građevinskog fakulteta Sveučilišta u Zagrebu

održat će predavanje

Pakiranja malih grafova u fulerene i u druge poliedre

Predavanje je organizirano u sklopu redovitog kolokvija Znanstvenog razreda SMD-a.

Pozivamo sve zainteresirane da prisustvuju predavanju.

Sažetak:

Sparivanja i pakiranja u grafovima služe kao korisni modeli za procese adicije i adsorpcije malih molekula na strukturiranim supstratima. U predavanju ćemo promatrati takva pakiranja u fulerenskim grafovima i sličnim poliedrima. Posebno će nas zanimati granični slučajevi, tj. slučajevi najveće i najmanje efikasnosti te slučaj kad ostatak grafa dopušta savršeno sparivanje.

Predavanje: Spatial statistics in materials science

U petak, 18. lipnja 2021. u 12:00 u dvorani B3-17 PMF-a

Jakub Stanek, phd

sa Karlovog Sveučilišta u Pragu

održat će predavanje

Spatial statistics in materials science

Predavanje je organizirano u sklopu redovitog kolokvija Znanstvenog razreda SMD-a.

Pozivamo sve zainteresirane da prisustvuju predavanju.

Sažetak:

Spatial statistics is a special part of statistics which focuses on various geometrical objects of random shapes and/or positions. It has many practical applications, e.g. in biology (presence of plants or trees), medicine (distinguishing different types of tissues), material sciences (structures of various materials) etc. This talk concerns the last mentioned branch, namely three applications of spatial statistics in material science will be presented. First, there will be shown a parametric model of three phases in a material, where each phase forms a connected component. Such a kind of material occurs e.g. in anodes of solid oxide fuel cells. The second application introduces the mathematical definition of two structural characteristics which describe transport properties in porous or composite materials, the estimators of these two characteristics and their properties. The last application concerns a method of reconstruction of grains of polycrystalline materials based on incomplete 3DXRD data. The method uses cross-entropy optimization to find such a Laguerre tessellation that minimizes the discrepancy between centers of mass as well as sizes of the cells from the Laguerre tessellation and those of the grain data measured by 3DXRD. Although all the above-mentioned applications touch physics, the talk will focus mainly on their mathematical aspects.

Predavanje: The semigroup of metric measure spaces and its infinitely divisible probability measures

U petak, 13. rujna 2019. u 12:00 u dvorani B3-17 PMF-a

prof. Ilya Molchanov

Institute of Mathematical Statistics and Actuarial Science, University of Bern

održat će predavanje

The semigroup of metric measure spaces and its infinitely divisible probability measures

Predavanje je organizirano u sklopu redovitog kolokvija Znanstvenog razreda SMD-a.

 

Sažetak:

The semigroup of metric measure spaces and its infinitely divisible probability measures
(joint work with Steve Evans, Berkeley)

A metric measure space (also called Gromov triple) is a complete, separable metric space equipped with a probability measure that has full support. Two such spaces are equivalent if they are isometric as metric spaces via an isometry that maps the probability measure on the first space to the probability measure on the second. We consider the natural binary operation on this space that takes two metric measure spaces and forms their Cartesian product equipped with the sum of the two metrics and the product of the two probability measures. We show that the metric measure spaces equipped with this operation form a cancellative, commutative, Polish semigroup with a translation invariant metric. There is an explicit family of continuous semicharacters that is extremely useful for establishing that there are no infinitely divisible elements and that each element has a unique factorization into prime elements.

We investigate the interaction between the semigroup structure and the natural action of the positive real numbers on this space that arises from scaling the metric. We establish that there is no analogue of the law of large numbers and characterize the infinitely divisible probability measures and the L\’evy processes on this semigroup, characterize the stable probability measures and establish a counterpart of the LePage representation for the latter class.