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1

Characterizing Stable and Deriving Valid Inequalities of Petri Nets

Triebel M., Sürmeli J.

Fundamenta Informaticae

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2016

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Vol. 146, nr 1

1--34

EN

One way to express correctness of a Petri net N is to specify a linear inequality U, requiring each reachable marking of N to satisfy U. A linear inequality U is stable if it is preserved along steps. If U is stable, then verifying correctness reduces to checking U in the initial marking of N. In this paper, we characterize classes of stable linear inequalities of a given Petri net by means of structural properties. We generalize classical results on traps, co-traps, and invariants. We show how to decide stability of a given inequality. For a certain class of inequalities, we present a polynomial time decision procedure. Furthermore, we show that stability is a local property and exploit this for the analysis of asynchronously interacting open net structures. Finally, we study the summation of inequalities as means of deriving valid inequalities.

2

On invariants of fluid mechanics tensors

Tesch K.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2013

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Vol. 17, No 3-4

223--230

EN

This paper presents physical interpretations of the first and second invariants of tensors of fluid mechanics. Some examples of elementary applications and meanings are also given.

3

Modelling of orthotropic masonry structures

Jemioło S., Gajewski M., Małyszko L.

Logistyka

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2011

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nr 6

EN

A class of constitutive models of orthotropic non-homogeneous masonry materials in the framework of elasto-plasticity theory of small displacements with energetic hardening/softening is proposed. Analysed class of constitutive models reduces to the classical one for ideal elasto-plasticity with well-known Hoffman yield condition for orthotropic homogeneous materials. Proposed class of models is implemented in FEM system ABAQUS. Constitutive relationships are implemented in FORTRAN in user procedure UMAT. The numerical tests are proposed to check correctness of the implementation, and some boundary value problems are also solved.

PL

W artykule przedstawiono sformułowanie teorii sprężysto plastyczności niejednorodnych ortotropowych materiałów murowych z tzw. Energetycznym wzmocnieniem/osłabieniem. Analizowana klasa modeli redukuje się do znanych modeli idealnej sprężysto-plastyczności w warunkiem plastyczności Hoffmana. Zaproponowaną klasę modeli zaimplementowano w programie MES ABAQUS. Relacje konstytutywne zaprogramowano w języku FORTRAN w procedurze użytkownika UMAT. Przydatność zaimplementowanego modelu zaprezentowano na przykładzie zadania brzegowego ścinania ściany z otworem.

4

Curvatures of single-input control systems

Jakubczyk B.

Control and Cybernetics

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2009

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Vol. 38, no 4B

1375-1391

EN

We introduce invariants of control-affine systems which we call curvatures. They are defined by the drift and the control distribution, given by the system. The curvatures allow us to analyse the variational equation along a given trajectory, as well as existence of conjugate points.

5

On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity

Bogoliubov N. N. (Jr.), Blackmore D. L., Somoylenko V. Hr., Prykarpatsky A. K.

Opuscula Mathematica

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2007

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Vol. 27, no. 2

187-195

EN

A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.

6

Phase portraits of planar control-affine systems

Jakubczyk B., Respondek W.

Control and Cybernetics

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2005

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Vol. 34, no 3

819-847

EN

We study nonlinear control systems in the plane, affine with respect to control. We introduce two sets of feedback equivariants forming a phase portrait PP and a parameterized phase portrait PPP of the system. The phase portrait PP consists of an equilibrium set E, a critical set C (parameterized, for PPP), an optimality index, a canonical foliation and a drift direction. We show that under weak generic assumptions the phase portraits determine, locally, the feedback and orbital feedback equivalence class of a system. The basic role is played by the critical set C and the critical vector field on C. We also study local classification problems for systems and their families.

7

Możliwości pomiaru niezmienników tensora i dewiatora naprężenia metodami dyfraktometrii rentgenowskiej

Senczyk D., Sokołowski M.

Zeszyty Naukowe Politechniki Poznańskiej. Mechanika

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2002

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Nr 48

121-128

PL

Opracowano sposób pomiaru niezmienników tensora i dewiatora naprężenia metodą dyfraktometrii rentgenowskiej oraz program komputerowy wspomagający te pomiary .Umożliwi to badania związane z problematyką przejścia materiału polikrystalicznego ze stanu sprężystego w plastyczny w przypadku obciążenia go złożonym stanem naprężenia. Opracowaną metodykę zastosowano do badania stanu naprężenia w szlifowanych próbkach stali 55. Stwierdzono pełną jej przydatność i uzyskano ważne rezultaty .

EN

Stress tensor and stress deviator invariants measurement by X -ray diffraction and computer program is implemented. This makes possible investigation of polycrystalline material transition from elastic state into plastic one when complex stress state is applicated. The methodology is used for investigation of stress state for grinded samples of steel 55 and important resu1ts are obtained