Suppose that (M, G) is a Riemannian manifold and f : M → R is a submersion. Then the complete lift of f, f : TM → R defined by f = ∂f ∂xi y is also a submersion. This interesting case leads us to the investigation of the level hypersurfaces of f as a submanifold of tangent bundle TM . In addition, we prolonge the level hypersurfaces of f to N̄ = (f)(0). Also, under the condition ∇̂f is a constant...

We develop a fusion of logical and metrical principles for reasoning about Markov processes. More precisely, we lift metrics from processes to sets of processes satisfying a formula and explore how the satisfaction relation behaves as sequences of processes and sequences of formulas approach limits. A key new concept is dynamically-continuous metric bisimulation which is a property of (pseudo)m...

In this paper we study a new technique we call post-bagging, which consists in resampling parts of a classification model rather then the data. We do this with a particular kind of model: large sets of classification association rules, and in combination with ordinary best rule and weighted voting approaches. We empirically evaluate the effects of the technique in terms of classification accura...

An earlobe that appears aged or malpositioned can sabotage the results of a well performed face lift. The most frequently noted sign of a naturally aged earlobe is increased length. Improper planning of face lift incisions may also result in disfigurement of the ear. The author suggests simple excisional techniques to correct the aged earlobe, as well as methods to avoid subsequent earlobe dist...

We consider the lift of a foliation to its conormal bundle and some transverse geometrical structures associated with this foliation are studied. We introduce a good vertical connection on the conormal bundle and, moreover, if the conormal bundle is endowed with a transversal Cartan metric, we obtain that the lifted foliation to its conormal bundle is a Riemannian one. Also, some transversally ...

Patients with thick skin mainly exhibit the aging processes of sagging, whereas patients with thin skin develop wrinkles or volume loss. Asian skin is usually thicker than that of Westerners; and thus, the sagging of skin due to aging, rather than wrinkling, is the chief problem to be addressed in Asians. Asian skin is also relatively large in area and thick, implying that the weight of tissue ...

Using a unique data set with 168 ski resorts located in France, this paper investigates the relationship between lift ticket prices and supply-related characteristics of ski resorts. A nonparametric analysis combined with a principal component analysis is used to identify the set of efficient ski resorts, defined as those where the lift ticket price is the cheapest for a given level of quality....

We introduce and study a new containment relation in graphs – lift contractions. H is a lift contraction of G if H can be obtained from G by a sequence of edge lifts and edge contractions. We show that a graph contains every n-vertex graph as a lift contraction, if (1) its treewidth is large enough, or (2) its pathwidth is large enough and it is 2-connected, or (3) its order is large enough and...