Conservation laws for non-potential operators

The aim of this work is to study the conservation laws of continuous means mechanics and also to extend the Hamiltonian method for these kind of systems in order to valid for non-potential operators through variational approach. Besides illustrating with various examples of mechanical applications we also introduce in this work the new technique in order to treat such problems as the non-potential problem.

Conservation laws for non-potential operators

A study was developed in order to build a function M invariant in time, by means of Hamiltonian's formulation, taking into account the equation associated to the problem, showing that starting from this function the equation of motion of the system with the contour conditions for non-conservative considered problems can be obtained. The Hamiltonian method is extended for these kind of systems in order to validate for non-potential operators through variational approach.

Riesz potential operators and inverses via fractional centred derivatives

International Journal of Mathematics and Mathematical Sciences, Vol.2006

Fractional Powers of Almost Non-Negative Operators

Mathematics Subject Classification: Primary 47A60, 47D06.

Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators

2000 Mathematics Subject Classification: Primary 47A20, 47A45; Secondary 47A48.

Condition number estimates for combined potential boundary integral operators in acoustic scattering

We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panic, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition numbers for these formulations, emphasising dependence on the frequency, the geometry of the scatterer, and the coupling parameter. Of independent interest we also obtain upper and lower bounds on the norms of two oscillatory integral operators, namely the classical acoustic single- and double-layer potential operators.

Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.

Folner sequences and finite operators

This article analyzes Folner sequences of projections for bounded linear operators and their relationship to the class of finite operators introduced by Williams in the 70ies. We prove that each essentially hyponormal operator has a proper Folner sequence (i.e. a Folner sequence of projections strongly converging to 1). In particular, any quasinormal, any subnormal, any hyponormal and any essentially normal operator has a proper Folner sequence. Moreover, we show that an operator is finite if and only if it has a proper Folner sequence or if it has a non-trivial finite dimensional reducing subspace. We also analyze the structure of operators which have no Folner sequence and give examples of them. For this analysis we introduce the notion of strongly non-Folner operators, which are far from finite block reducible operators, in some uniform sense, and show that this class coincides with the class of non-finite operators.

Accumulation of complex eigenvalues of an indefinite Sturm--Liouville operator with a shifted Coulomb potential

For a particular family of long-range potentials V, we prove that the eigenvalues of the indefinite Sturm–Liouville operator A = sign(x)(−Δ+V(x)) accumulate to zero asymptotically along specific curves in the complex plane. Additionally, we relate the asymptotics of complex eigenvalues to the two-term asymptotics of the eigenvalues of associated self-adjoint operators.

Novel algorithms for electronic structure based molecular dynamics with linear system-size scaling

Die vorliegende Arbeit behandelt die Entwicklung und Verbesserung von linear skalierenden Algorithmen für Elektronenstruktur basierte Molekulardynamik. Molekulardynamik ist eine Methode zur Computersimulation des komplexen Zusammenspiels zwischen Atomen und Molekülen bei endlicher Temperatur. Ein entscheidender Vorteil dieser Methode ist ihre hohe Genauigkeit und Vorhersagekraft. Allerdings verhindert der Rechenaufwand, welcher grundsätzlich kubisch mit der Anzahl der Atome skaliert, die Anwendung auf große Systeme und lange Zeitskalen. Ausgehend von einem neuen Formalismus, basierend auf dem großkanonischen Potential und einer Faktorisierung der Dichtematrix, wird die Diagonalisierung der entsprechenden Hamiltonmatrix vermieden. Dieser nutzt aus, dass die Hamilton- und die Dichtematrix aufgrund von Lokalisierung dünn besetzt sind. Das reduziert den Rechenaufwand so, dass er linear mit der Systemgröße skaliert. Um seine Effizienz zu demonstrieren, wird der daraus entstehende Algorithmus auf ein System mit flüssigem Methan angewandt, das extremem Druck (etwa 100 GPa) und extremer Temperatur (2000 - 8000 K) ausgesetzt ist. In der Simulation dissoziiert Methan bei Temperaturen oberhalb von 4000 K. Die Bildung von sp²-gebundenem polymerischen Kohlenstoff wird beobachtet. Die Simulationen liefern keinen Hinweis auf die Entstehung von Diamant und wirken sich daher auf die bisherigen Planetenmodelle von Neptun und Uranus aus. Da das Umgehen der Diagonalisierung der Hamiltonmatrix die Inversion von Matrizen mit sich bringt, wird zusätzlich das Problem behandelt, eine (inverse) p-te Wurzel einer gegebenen Matrix zu berechnen. Dies resultiert in einer neuen Formel für symmetrisch positiv definite Matrizen. Sie verallgemeinert die Newton-Schulz Iteration, Altmans Formel für beschränkte und nicht singuläre Operatoren und Newtons Methode zur Berechnung von Nullstellen von Funktionen. Der Nachweis wird erbracht, dass die Konvergenzordnung immer mindestens quadratisch ist und adaptives Anpassen eines Parameters q in allen Fällen zu besseren Ergebnissen führt.

Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

Australian veterinarians who work with horses: views of the future

Objective To give an account of the views held by Australian veterinarians who work with horses on the future of their professional field. Method Questionnaires were mailed to 866 veterinarians who had been identified as working with horses, and 87% were completed and returned. Data were entered onto an Excel spreadsheet, and analysed using the SAS System for Windows. Results Their future prospects were believed to be very good or excellent by >60% of equine veterinarians but by only 30% of mixed practitioners seeing < 10% horses. The main factors believed likely to affect these prospects were the strength of the equine industries and the economic climate affecting horse owners, followed by the encroachment of cities into areas used for horses, competition from other veterinarians including specialist centres and from non-veterinary operators, and their ability to recruit and retain veterinarians with interest, experience and skill with horses. Urban encroachment, competition and recruitment were especially important for those seeing few horses. Concerns were also expressed about the competence and ethical behaviour of other veterinarians, the physical demands and dangers of horse work, the costs of providing equine veterinary services and of being paid for them, the regulatory restrictions imposed by governments and statutory bodies, the potential effects of litigation, and insurance issues. For many veterinarians in mixed practice these factors have reduced and are likely to reduce further the number of horses seen, to the extent that they have scant optimism about the future of horse work in their practices. Conclusion Economic and local factors will result in an increasing proportion of equine veterinary work being done in specialised equine centres, and the future of horse work in many mixed practices is, at best, precarious. A key factor influencing future prospects will be the availability of competent veterinarians committed to working with horses.

Susceptibility of Anopheles campestris-like and Anopheles barbirostris species complexes to Plasmodium falciparum and Plasmodium vivax in Thailand

Nine colonies of five sibling species members of Anopheles barbirostris complexes were experimentally infected with Plasmodium falciparum and Plasmodium vivax. They were then dissected eight and 14 days after feeding for oocyst and sporozoite rates, respectively, and compared with Anopheles cracens. The results revealed that Anopheles campestris-like Forms E (Chiang Mai) and F (Udon Thani) as well as An. barbirostris species A3 and A4 were non-potential vectors for P. falciparum because 0% oocyst rates were obtained, in comparison to the 86.67-100% oocyst rates recovered from An. cracens. Likewise, An. campestris-like Forms E (Sa Kaeo) and F (Ayuttaya), as well as An. barbirostris species A4, were non-potential vectors for P. vivax because 0% sporozoite rates were obtained, in comparison to the 85.71-92.31% sporozoite rates recovered from An. cracens. An. barbirostris species A1, A2 and A3 were low potential vectors for P. vivax because 9.09%, 6.67% and 11.76% sporozoite rates were obtained, respectively, in comparison to the 85.71-92.31% sporozoite rates recovered from An. cracens. An. campestris-like Forms B and E (Chiang Mai) were high-potential vectors for P. vivax because 66.67% and 64.29% sporozoite rates were obtained, respectively, in comparison to 90% sporozoite rates recovered from An. cracens.

A logic programming framework for possibilistic argumentation: formalization and logical properties

In the last decade defeasible argumentation frameworks have evolved to become a sound setting to formalize commonsense, qualitative reasoning. The logic programming paradigm has shown to be particularly useful for developing different argument-based frameworks on the basis of different variants of logic programming which incorporate defeasible rules. Most of such frameworks, however, are unable to deal with explicit uncertainty, nor with vague knowledge, as defeasibility is directly encoded in the object language. This paper presents Possibilistic Logic Programming (P-DeLP), a new logic programming language which combines features from argumentation theory and logic programming, incorporating as well the treatment of possibilistic uncertainty. Such features are formalized on the basis of PGL, a possibilistic logic based on G¨odel fuzzy logic. One of the applications of P-DeLP is providing an intelligent agent with non-monotonic, argumentative inference capabilities. In this paper we also provide a better understanding of such capabilities by defining two non-monotonic operators which model the expansion of a given program P by adding new weighed facts associated with argument conclusions and warranted literals, respectively. Different logical properties for the proposed operators are studied

Konenäköjärjestelmien ostokriteerit ja laitetoimittajien asiakashankinta

Työn tavoitteena oli edesauttaa Euroelektro International Oy:tä kasvattamaan asiakaskuntaansa löytämällä oikeat lähtökohdat yrityksen markkinoinnin ja myynnin tehostamiselle sekä kannattavien kohdesegmenttien valinnalle. Työssä tehtiin tutkimus, jolla määritettiin yrityksen tyypillinen asiakas, asiakastarpeet, konenäköjärjestelmien ostokriteerit ja –preferenssit sekä ostopäätöksen tekijät ja siihen vaikuttavat henkilöt. Lisäksi selvitettiin, mitkä ovat Euroelektron potentiaalisia ja ei-potentiaalisia teollisuuden aloja. Tutkimuksen tulosten perusteella laadittiin lopuksi yrityksen markkinoinnin ja myynnin kehittämisehdotelma. Tutkimus rajattiin konenäköä jo käyttäviin yrityksiin, konenäön käyttöä suunnitteleviin yrityksiin, yrityksiin, joiden ajateltiin voivan tulevaisuudessa käyttää konenäköä ja yrityksiin, jotka ovat tekemisissä konenäköasiakkaiden kanssa. Markkinointi- ja myyntiprosessien hallintaan yrityksen tulisi kehittää oma seurantaohjelma, jonka avulla valitun markkinointistrategian onnistuneisuutta voitaisiin helposti seurata, sekä laatukäsikirja, mistä löytyisivät standardoidut toimenpidemallit asiakashankintaan, kenttämyyntiin ja myyntiprojektien läpiviemiseen sekä eri toimihenkilöiden toimenkuvaukset ja vastuualueet.