Numerical Enclosures for Variational Inequalities

AbstractWe present a new method for proving the existence of a unique solution of variational inequalities within guaranteed close error bounds to a numerical approximation. The method is derived for a specific model problem featuring most of the difficulties of perfect plasticity. We introduce a finite element method for the computation of admissible primal and dual solutions which a posteriori guarantees the existence of a unique solution (by the verification of the safe load condition) and which allows determination of a guaranteed error bound. Finally, we present explicit existence results and error bounds in some significant specific configurations.

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Characterization of Degenerate Configurations in Attitude Determination of Three-Vehicle Heterogeneous Formations

Sensors ◽

10.3390/s21144631 ◽

2021 ◽

Vol 21 (14) ◽

pp. 4631

Author(s):

Pedro Cruz ◽

Pedro Batista

Keyword(s):

Unique Solution ◽

Multiple Solutions ◽

Attitude Determination ◽

Line Of Sight ◽

Number Of Solutions ◽

Relative Line ◽

Heterogeneous Formations ◽

Heterogeneous Formation

The existence of multiple solutions to an attitude determination problem impacts the design of estimation schemes, potentially increasing the errors by a significant value. It is therefore essential to identify such cases in any attitude problem. In this paper, the cases where multiple attitudes satisfy all constraints of a three-vehicle heterogeneous formation are identified. In the formation considered herein, the vehicles measure inertial references and relative line-of-sight vectors. Nonetheless, the line of sight between two elements of the formation is restricted, and these elements are denoted as deputies. The attitude determination problem is characterized relative to the number of solutions associated with each configuration of the formation. There are degenerate and ambiguous configurations that result in infinite or exactly two solutions, respectively. Otherwise, the problem has a unique solution. The degenerate configurations require some collinearity between independent measurements, whereas the ambiguous configurations result from symmetries in the formation measurements. The conditions which define all such configurations are determined in this work. Furthermore, the ambiguous subset of configurations is geometrically interpreted resorting to the planes defined by specific measurements. This subset is also shown to be a zero-measure subset of all possible configurations. Finally, a maneuver is simulated to illustrate and validate the conclusions. As a result of this analysis, it is concluded that, in general, the problem has one attitude solution. Nonetheless, there are configurations with two or infinite solutions, which are identified in this work.

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GAP FUNCTIONS AND GLOBAL ERROR BOUNDS FOR SET-VALUED MIXED VARIATIONAL INEQUALITIES

Taiwanese Journal of Mathematics ◽

10.11650/tjm.17.2013.2247 ◽

2013 ◽

Vol 17 (4) ◽

pp. 1267-1286 ◽

Cited By ~ 8

Author(s):

Nan-jing Huang ◽

Guo-ji Tang

Keyword(s):

Variational Inequalities ◽

Error Bounds ◽

Global Error ◽

Gap Functions ◽

Mixed Variational Inequalities

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Experience and prospects of religious organizations in Ukraine: prisma of independence

Ukrainian Religious Studies ◽

10.32420/2016.80.722 ◽

2016 ◽

pp. 58-62 ◽

Cited By ~ 1

Author(s):

Vita Tytarenko

Keyword(s):

Civil Religion ◽

Specific Model ◽

Self Determination ◽

Religious Organizations ◽

Political Events ◽

Ukrainian Society

In the article by Vita Titarenko «Experience and prospects of religious organizations in Ukraine: prisma of independence» on the basis of the analysis of the newest sociological researches the features of the post-Soviet religious society in Ukraine are considered. The formation of a specific model of religiosity of modern Ukrainian society, its new value matrix is noted. The distinctive characteristic is the nonconfessional self-determination of Ukrainians, the development of extra-religious religiosity during complex socio-political events in the country, the formation of such a phenomenon as a civil religion and a civil "ecclesia".

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