Generalized Toponogov’s theorem for manifolds with radial curvature bounded below

A natural requirement to impose upon the life distribution of a component is that after inspection at some randomly chosen time to check whether it is still functioning, its life distribution from the time of checking should be bounded below by some specified distribution which may be defined by external considerations. Furthermore, the life distribution should ideally be minimal in the partial ordering obtained from the conditional probabilities. We prove that these specifications provide an apparently new characterization of the DFRA class of life distributions with a corresponding result for IFRA distributions. These results may be transferred, using Slepian's lemma, to obtain bounds for the boundary crossing probabilities of a stationary Gaussian process.

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An alternative approach to study irrotational periodic gravity water waves

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/s00033-021-01578-8 ◽

2021 ◽

Vol 72 (4) ◽

Author(s):

Biswajit Basu ◽

Calin I. Martin

Keyword(s):

Free Surface ◽

Water Waves ◽

Water Wave ◽

Wave Problem ◽

Water Wave Problem ◽

Stagnation Points ◽

Alternative Approach ◽

New Formulation ◽

Bounded Below ◽

Surface Dynamic

AbstractWe are concerned here with an analysis of the nonlinear irrotational gravity water wave problem with a free surface over a water flow bounded below by a flat bed. We employ a new formulation involving an expression (called flow force) which contains pressure terms, thus having the potential to handle intricate surface dynamic boundary conditions. The proposed formulation neither requires the graph assumption of the free surface nor does require the absence of stagnation points. By way of this alternative approach we prove the existence of a local curve of solutions to the water wave problem with fixed flow force and more relaxed assumptions.

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THE NATURAL PARTIAL ORDER ON LINEAR SEMIGROUPS WITH NULLITY AND CO-RANK BOUNDED BELOW

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972714000793 ◽

2014 ◽

Vol 91 (1) ◽

pp. 104-115 ◽

Cited By ~ 1

Author(s):

SUREEPORN CHAOPRAKNOI ◽

TEERAPHONG PHONGPATTANACHAROEN ◽

PONGSAN PRAKITSRI

Keyword(s):

Semigroup Forum ◽

Partial Order ◽

Lower Bounds ◽

Partial Orders ◽

Natural Partial Order ◽

Linear Transformations ◽

Bounded Below

AbstractHiggins [‘The Mitsch order on a semigroup’, Semigroup Forum 49 (1994), 261–266] showed that the natural partial orders on a semigroup and its regular subsemigroups coincide. This is why we are interested in the study of the natural partial order on nonregular semigroups. Of particular interest are the nonregular semigroups of linear transformations with lower bounds on the nullity or the co-rank. In this paper, we determine when they exist, characterise the natural partial order on these nonregular semigroups and consider questions of compatibility, minimality and maximality. In addition, we provide many examples associated with our results.

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Complete hypersurfaces in cylinders

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

10.1017/s1446788700030792 ◽

1989 ◽

Vol 46 (2) ◽

pp. 313-318

Author(s):

Thomas Hasanis

Keyword(s):

Euclidean Space ◽

Scalar Curvature ◽

Sectional Curvature ◽

Positive Scalar Curvature ◽

Positive Scalar ◽

Coordinate Functions ◽

Bounded Below ◽

Complete Hypersurfaces

AbstractWe consider the extent of certain complete hypersurfaces of Euclidean space. We prove that every complete hypersurface in En+1 with sectional curvature bounded below and non-positive scalar curvature has at least (n − 1) unbounded coordinate functions.

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Farthest points on most Alexandrov surfaces

Advances in Geometry ◽

10.1515/advgeom-2019-0010 ◽

2020 ◽

Vol 20 (1) ◽

pp. 139-148

Author(s):

Joël Rouyer ◽

Costin Vîlcu

Keyword(s):

Distance Functions ◽

Farthest Points ◽

Baire Categories ◽

Bounded Below

AbstractWe study global maxima of distance functions on most Alexandrov surfaces with curvature bounded below, where most is used in the sense of Baire categories.

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