509 research outputs found
Energy properness and Sasakian-Einstein metrics
In this paper, we show that the existence of Sasakian-Einstein metrics is
closely related to the properness of corresponding energy functionals. Under
the condition that admitting no nontrivial Hamiltonian holomorphic vector
field, we prove that the existence of Sasakian-Einstein metric implies a
Moser-Trudinger type inequality. At the end of this paper, we also obtain a
Miyaoka-Yau type inequality in Sasakian geometry.Comment: 27 page
Calculus of Tangent Sets and Derivatives of Set Valued Maps under Metric Subregularity Conditions
In this paper we intend to give some calculus rules for tangent sets in the
sense of Bouligand and Ursescu, as well as for corresponding derivatives of
set-valued maps. Both first and second order objects are envisaged and the
assumptions we impose in order to get the calculus are in terms of metric
subregularity of the assembly of the initial data. This approach is different
from those used in alternative recent papers in literature and allows us to
avoid compactness conditions. A special attention is paid for the case of
perturbation set-valued maps which appear naturally in optimization problems.Comment: 17 page
Interaction of Cutibacterium (formerly Propionibacterium) acnes with bone cells: a step toward understanding bone and joint infection development
Cutibacterium acnes (formerly Propionibacterium acnes) is recognized as a pathogen in foreign-body infections (arthroplasty or spinal instrumentation). To date, the direct impact of C. acnes on bone cells has never been explored. The clade of 11 C. acnes clinical isolates was determined by MLST. Human osteoblasts and osteoclasts were infected by live C. acnes. The whole genome sequence of six isolates of this collection was analyzed. CC36 C. acnes strains were significantly less internalized by osteoblasts and osteoclasts than CC18 and CC28 C. acnes strains (p ≤ 0.05). The CC18 C. acnes ATCC6919 isolate could survive intracellularly for at least 96 hours. C. acnes significantly decreased the resorption ability of osteoclasts with a major impact by the CC36 strain (p ≤ 0.05). Genome analysis revealed 27 genes possibly linked to these phenotypic behaviors. We showed a direct impact of C. acnes on bone cells, providing new explanations about the development of C. acnes foreign-body infections
Conjugate times and regularity of the minimum time function with differential inclusions
This paper studies the regularity of the minimum time function, ,
for a control system with a general closed target, taking the state equation in
the form of a differential inclusion. Our first result is a sensitivity
relation which guarantees the propagation of the proximal subdifferential of
along any optimal trajectory. Then, we obtain the local regularity of
the minimum time function along optimal trajectories by using such a relation
to exclude the presence of conjugate times
Computing domains of attraction for planar dynamics
In this note we investigate the problem of computing the
domain of attraction of a
ow on R2 for a given attractor. We consider
an operator that takes two inputs, the description of the
ow and a cover
of the attractors, and outputs the domain of attraction for the given
attractor. We show that: (i) if we consider only (structurally) stable
systems, the operator is (strictly semi-)computable; (ii) if we allow all
systems de ned by C1-functions, the operator is not (semi-)computable.
We also address the problem of computing limit cycles on these systems
Nonlinear porous medium flow with fractional potential pressure
We study a porous medium equation, with nonlocal diffusion effects given by
an inverse fractional Laplacian operator. We pose the problem in n-dimensional
space for all t>0 with bounded and compactly supported initial data, and prove
existence of a weak and bounded solution that propagates with finite speed, a
property that is nor shared by other fractional diffusion models.Comment: 32 pages, Late
Moving constraints as stabilizing controls in classical mechanics
The paper analyzes a Lagrangian system which is controlled by directly
assigning some of the coordinates as functions of time, by means of
frictionless constraints. In a natural system of coordinates, the equations of
motions contain terms which are linear or quadratic w.r.t.time derivatives of
the control functions. After reviewing the basic equations, we explain the
significance of the quadratic terms, related to geodesics orthogonal to a given
foliation. We then study the problem of stabilization of the system to a given
point, by means of oscillating controls. This problem is first reduced to the
weak stability for a related convex-valued differential inclusion, then studied
by Lyapunov functions methods. In the last sections, we illustrate the results
by means of various mechanical examples.Comment: 52 pages, 4 figure
The Cauchy problems for Einstein metrics and parallel spinors
We show that in the analytic category, given a Riemannian metric on a
hypersurface and a symmetric tensor on , the metric
can be locally extended to a Riemannian Einstein metric on with second
fundamental form , provided that and satisfy the constraints on
imposed by the contracted Codazzi equations. We use this fact to study the
Cauchy problem for metrics with parallel spinors in the real analytic category
and give an affirmative answer to a question raised in B\"ar, Gauduchon,
Moroianu (2005). We also answer negatively the corresponding questions in the
smooth category.Comment: 28 pages; final versio
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