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1
Content available Hybrid-optional effectiveness functions entropy conditional extremization doctrine contributions into engineering systems reliability assessments
Goncharenko Andriy Viktorovich
Transactions on Aerospace Research
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2019
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Nr 2 (255)
96--106
EN
In this publication a Doctrine for the Conditional Extremization of the Hybrid-Optional Effectiveness Functions Entropy is discussed as a tool for the Reliability Assessments of Engineering Systems. Traditionally, most of the problems having been dealt with in this area relate with the probabilistic problem settings. Regularly, the optimal solutions are obtained through the probability extremizations. It is shown a possibility of the optimal solutions “derivation”, with the help of a model implementing a variational principle which takes into account objectively existing parameters and components of the Markovian process. The presence of an extremum of the objective state probability is observed and determined on the basis of the proposed Doctrine with taking into account the measure of uncertainty of the hybrid-optional effectiveness functions in the view of their entropy. Such approach resembles the well known Jaynes’ Entropy Maximum Principle from theoretical statistical physics adopted in subjective analysis of active systems as the subjective entropy maximum principle postulating the subjective entropy conditional optimization. The developed here with Doctrine implies objective characteristics of the process rather than subjective individual’s preferences or choices, as well as the states probabilities maximums are being found without solving a system of ordinary linear differential equations of the first order by Erlang corresponding to the graph of the process. Conducted numerical simulation for the proposed mathematical models is illustrated with the plotted diagrams.
2
Content available A continuum description of failure waves
Said H., Glimm J.
Journal of Theoretical and Applied Mechanics
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2018
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Vol. 56 nr 3
657—674
EN
Shattering of a brittle material such as glass occurs dynamically through a propagating failure wave, which however, can not be assigned to any of the classical wave. In this paper, we build a thermodynamically consistent theory based on the idea that a failure wave is analogous to a deflagration wave. Our theory admits, as special cases, the classical models of Feng and Clifton. Two fundamental thermodynamic functions form the basis of our theory. This approach allows for the construction of a new variational principle and a Lagrangian formulation. Finally, the theory is linearized to interpret specific experimental observations.
3
Content available remote Zasada wariacyjna magnetostrykcji
Wyrwał J., Haberecht M.
Roczniki Inżynierii Budowlanej
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2014
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z. 14
69--74
EN
The paper shows how to transform a given nonlinear boundary problem of magnetostriction into a variational formulation. A sufficient condition for the construction of variational principle is formulated in the theorem of VAINBERG. The results obtained in this work can become the theoretical basis to formulate the numerical solutions of different scientific and engineering problems connected with magnetostrictive materials.
4
Content available remote Zasada wariacyjna elektrostrykcji
Wyrwał J.
Roczniki Inżynierii Budowlanej
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2013
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z. 13
7--12
EN
The paper shows how to transform a given nonlinear boundary problem of electrostriction into a variational formulation. A sufficient condition for the construction of variational principle is formulated in the theorem of VAINBERG. The results obtained in this work can become the theoretical basis to formulate the numerical solutions of different scientific and engineering problems connected with electrostrictive materials.
5
Content available A particular case of a variational problem of control in an active aviation system
Goncharenko A. V.
Prace Instytutu Lotnictwa
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2013
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Nr 1 (228)
3--12
EN
It is theoretically considered one of the simplest particular cases of a variational problem of control in an active aviation system acting in conditions of multi-alternativeness and conflicts. With the help of the Euler-Lagrange equations it is obtained the canonical distributions of the subjective preferences for the given functional; differential equation of the second order for finding extremals of the controlled functions of the functional The differential equation satisfies the conditions of existence and unique solution. Mathematical modeling is fulfilled with the help of the hybrid pseudo-entropy function. Plotted corresponding diagrams.
6
Content available remote A Remark on Variational Principles of Choban, Kenderov and Revalski
Królak A.
Bulletin of the Polish Academy of Sciences. Mathematics
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2013
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Vol. 61, no 3-4
257--261
EN
We consider some variational principles in the spaces C*(X) of bounded continuous functions on metrizable spaces X, introduced by M. M. Choban, P. S. Kenderov and J. P. Revalski. In particular we give an answer (consistent with ZFC) to a question stated by these authors.
7
Content available remote Stationary action principle and particular solutions for long line equations
Grochowicz B., Kosiński W.
Przegląd Elektrotechniczny
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2012
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R. 88, nr 12b
39-42
EN
The recently developed by both authors a method for deriving telegraph equation from the stationarity principle of the action functional I[u], under a particular form of the non-commutativity of operations od partial differentiation and taking variation, is further elaborated. The variational principle applied for field equations gives the availability of analytical or approximate solution of the equations. In the paper particular forms of solutions of the long line equation are searched.
PL
Wartykule kontynuuje sie ostatnio rozwijana przez dwójkę autorów metodę wyprowadzania równań linii długiej z zasady stacjonarności działania I[u] przy szczególnej postaci nieprzemienności operacji różniczkowania i brania wariacji. Zasada wariacyjna zastosowana do równań pola pozwala uzyskać warunki na analityczne albo przybliżone rozwiązania. W artykule poszukuje się rozwiązań szczególnych i przybliżonych. (Zasada stacjonarnosci działania i rozwiązania szczególne równań linii długiej)
8
Content available remote Holomorphons on spheres
Milewski J.
Commentationes Mathematicae
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2008
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Vol. 48, [Z] 1
13-22
EN
We consider Euler–Lagrange equations of families of nonnegative functionals defined on tensor fields of the type (1, 1), which are equal to zero only for complex structures tensor fields.
9
Content available remote Variational Approach to Nonlinear Coupled Oscillators Arising in Sirospun Yarn Spinning
He J. H.
Fibres & Textiles in Eastern Europe
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2007
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Vol. 15, no. 1 (60)
31--34
EN
A description of stable working conditions for spinning two-strand yarn is given. A theoretical model underlying Sirospun yarn spinning is also given. Based on the variational formulation established for the coupled oscillators arising in two-strand yarn spinning, a simple analytical model for the forces that determine the nonlinear oscillation during the yarn spinning, as a function of inlet velocities, strand-spacing, and forces acting on the strands is proposed, which reveals that resonance occurs when the convergence angle is near 127 degrees.
PL
Opisano stabilne warunki pracy dla przędzenia dwóch wiązek włókien. Przytoczono teoretyczny model opisujący przędzenie typu Sirospun. Na podstawie układów równań opisujących sprzężone oscylatory, powstające przy formowaniu przędzy z dwóch wiązek, zaproponowano zastosowanie prostego analitycznego modelu działania sił, które określają nieliniowe oscylacje, powstające przy przędzeniu nitki, jako funkcje prędkości wejściowych, odległości pomiędzy wiązkami i sił działających na wiązki. Stwierdzono, że rezonans występuje przy kącie zbieżności wiązek 127°.
10
Content available remote Holomorphons and the standard almost complex structure on S^6
Milewski J.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2006
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Vol. 46, [Z] 2
245-254
EN
We consider Euler–Lagrange equations of families of nonnegative functionals defined on tensor fields of the type (1, 1), which are equal to zero only for complex structures tensor fields. As a solution of the equations we define the notion of holomorphon to distinguish a new class of tensor fields on Riemannian manifolds. Next, as our main result, we construct a holomorphon on the 6–dimensional sphere S^6.
11
Content available Modelowanie powierzchni terenu zawierającej linie nieciągłości na podstawie danych skaningu laserowego
Borkowski A.
Archiwum Fotogrametrii, Kartografii i Teledetekcji
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2003
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Vol. 13b
307--314
PL
Wzrost rozdzielczości techniki skaningu laserowego w ostatnich latach pozwala na modelowanie linii nieciągłości powierzchni terenu na podstawie informacji punktowej. W pracy przedstawiono metodę aproksymacji powierzchni będącą rozwiązaniem zadania wariacyjnego (uogólnienie techniki snake), w którym minimalizowana jest energia wewnętrzna powierzchni i zewnętrzna opisująca defekt danych. Energia wewnętrzna opisuje nachylenie i naprężenie powierzchni i jest sumą składowych gradientu i krzywizny powierzchni. Poszczególne składniki energii wewnętrznej są wzajemnie ważone za pomocą swobodnych parametrów, poprzez które możliwe jest lokalne modelowanie właściwości geometrycznych powierzchni. Zadanie wariacyjne rozwiązano metoda Ritza z funkcją bazową typu Gaussa. Parametry modelowanej powierzchni otrzymuje się z rozwiązania układu równań liniowych. Podano przykład modelowania danych skaningu laserowego.
EN
The resolution increase of the laser-scanning technique within the last few years enables on modeling of terrain discontinuities considering only discrete information. In the paper there has been presented the method of surface approximation which was a solution of variational principle (generalization of the snakes technique) where the internal – and external energy of surface describing the data defect are minimized. The internal energy describes an inclination and tension of surface and presents a sum of gradient and curvature components. Particular components of internal energy have been weighted by the use of free parameters enabling a modeling of geometrical properties of surface. The variational problem has been solved by the use of the Ritz method with the base Gaussian-type function. Parameters of modeled surface are obtained by solving the linear equations system. Furthermore, a modeling example of laser-scanning data has been presented.
12
Micropolar model of high-temperature superconductors
Radzikowska E.
Journal of Technical Physics
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2001
|
Vol. 42, no 4
419-435
EN
The micropolar continuum theory is applied to superconductors of type II containing a vortex lattice. The classical electrodynamic theory of micropolar continua is supplemented by quantum-mechanical notions describing the phenomenon of superconductivity. A variational principle for dissipative processes taking place in high-temperature superconductors is formulated. The electromagnetic, mechanical and thermal fields interactions in superconductors are considered. Finally, the complete system of field equations describing these interactions is obtained together with the constitutive relations and the jump conditions on the discontinuity surface.
13
Content available remote Some results related to Caristi's fixed point theorem and Ekeland's variational principle
Pathak H., Mishra S.
Demonstratio Mathematica
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2001
|
Vol. 34, nr 4
859-872
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