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On a special function related to the Riemann zeta-function
Karlstads universitet, Fakulteten för teknik- och naturvetenskap, Avdelningen för matematik.
Karlstads universitet, Fakulteten för teknik- och naturvetenskap, Avdelningen för matematik.
(engelsk)Manuskript (preprint) (Annet vitenskapelig)
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
URN: urn:nbn:se:kau:diva-8712OAI: oai:DiVA.org:kau-8712DiVA, id: diva2:453609
Tilgjengelig fra: 2011-11-03 Laget: 2011-11-03 Sist oppdatert: 2011-11-07bibliografisk kontrollert
Inngår i avhandling
1. Some Problems in Kinetic Theory and Applications
Åpne denne publikasjonen i ny fane eller vindu >>Some Problems in Kinetic Theory and Applications
2011 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

This thesis consists of four papers. the first is devoted to discrete velocity models, the second to hydrodynamic equation beyond Navier-Stokes level, the third to a multi-linear Maxwell model for economic or social dynamics and the fourth is devoted to a function related to the Riemann zeta-function.

In Paper 1, we consider the general problem of construction and classification of normal, i.e. without spurious invariants, discrete velocity models (DVM) of the classical Boltzman equation. We explain in detail how this problem can be solved and present a complete classification of normal plane DVMs with relatively small number n of velocities (n≤10). Some results for models with larger number of velocities are also presented.

In Paper 2, we discuss hydrodynamics at the Burnett level. Since the Burnett equations are ill-posed, we describe how to make a regularization of these. We derive the well-posed generalized Burnett equations (GBEs) and discuss briefly an optimal choice of free parameters and consider a specific version of these equations. Finally we prove linear stability for GBE and present some numerical result on the sound propagationbased on GBEs.

In Paper 3, we study a Maxwell kinetic model of socio-economic behavior. The model can predict a time dependent distribution of wealth among the participants in economic games with an arbitrary, but sufficiently large, number of players. The model depends on three different positive parameters {γ,q,s} where s and q are fixed by market conditions and γ is a control parameter. In particular, we investigate the efficiency of control. Some exact solutions and numerical examples are presented.

In Paper 4, we study a special function u(s,x), closely connected to the Riemann zeta-function ζ(s), where s is a complex number. We study in detail the properties of u(s,x) and in particular the location of its zeros s(x), for various x≥0. For x=0 the zeros s(0) coincide with non-trivial zeros of ζ(s). We perform a detailed numerical study of trajectories of various zeros s(x) of u(s,x).

sted, utgiver, år, opplag, sider
Karlstad: Karlstad University, 2011. s. 22
Serie
Karlstad University Studies, ISSN 1403-8099 ; 2011:52
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
urn:nbn:se:kau:diva-8498 (URN)978-91-7063-388-1 (ISBN)
Disputas
2011-12-01, 21A 342, Karlstads universitet, Karlstad, 13:15 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2011-11-07 Laget: 2011-10-10 Sist oppdatert: 2011-11-07bibliografisk kontrollert

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