Search results for "convex"
showing 10 items of 389 documents
Existence and classification of critical points for nondifferentiable functions
2004
A general min-max principle established by Ghoussoub is extended to the case of functionals which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function. Some topological properties of the min-max-generated critical points in such a framework are then pointed out.
Canal transportation caused by a new instrumentation technique and three standard techniques
1996
The ability of three different enlarging techniques (balanced force concept, step-back, and recapitulation) and a prototype system to maintain the original canal path during root canal preparation were compared, in vitro, with a theoretical ideally prepared root canal. Measurements were made at the concave and convex sides of the canal at four different levels (1, 4, 5, and 7 mm from apical, respectively). Simulated root canals embedded in clear casting resin and an enlarging computer-supported device were used for this study. The results showed that none of the enlarging techniques used in this study was able to prepare a canal ideally. The prototype system, at level 1, showed an ideal amo…
Mappings of finite distortion between metric measure spaces
2015
We establish the basic analytic properties of mappings of finite distortion between proper Ahlfors regular metric measure spaces that support a ( 1 , 1 ) (1,1) -Poincaré inequality. As applications, we prove that under certain integrability assumption for the distortion function, the branch set of a mapping of finite distortion between generalized n n -manifolds of type A A has zero Hausdorff n n -measure.
On multivalued weakly Picard operators in partial Hausdorff metric spaces
2015
We discuss multivalued weakly Picard operators on partial Hausdorff metric spaces. First, we obtain Kikkawa-Suzuki type fixed point theorems for a new type of generalized contractive conditions. Then, we prove data dependence of a fixed points set theorem. Finally, we present sufficient conditions for well-posedness of a fixed point problem. Our results generalize, complement and extend classical theorems in metric and partial metric spaces.
Identifying and Assessing Inter-Muscular Fat at the Distal Diaphyseal Femur Measured by Peripheral Quantitative Computed Tomography (pQCT)
2021
INTRODUCTION Inter/intramuscular fat can be assessed with peripheral Quantitative Computed Tomography (pQCT) and is of interest as an indicator of ‘muscle quality’. Typical pQCT scan sites (forearm, lower leg) have a low amount of inter/intramuscular fat, however distal diaphyseal femur scan sites with conspicuous inter/intramuscular fat have been identified as potentially more prudent scan sites, even in healthy adolescents. However, current state of the art analysis methods require labour-intensive manual segmentation of the scan. The purpose of the present study was to evaluate the reliability of a novel open source automated enclosing convex polygon approach (source code https://github.…
An evolutionary Haar-Rado type theorem
2021
AbstractIn this paper, we study variational solutions to parabolic equations of the type $$\partial _t u - \mathrm {div}_x (D_\xi f(Du)) + D_ug(x,u) = 0$$ ∂ t u - div x ( D ξ f ( D u ) ) + D u g ( x , u ) = 0 , where u attains time-independent boundary values $$u_0$$ u 0 on the parabolic boundary and f, g fulfill convexity assumptions. We establish a Haar-Rado type theorem: If the boundary values $$u_0$$ u 0 admit a modulus of continuity $$\omega $$ ω and the estimate $$|u(x,t)-u_0(\gamma )| \le \omega (|x-\gamma |)$$ | u ( x , t ) - u 0 ( γ ) | ≤ ω ( | x - γ | ) holds, then u admits the same modulus of continuity in the spatial variable.
A sharp stability estimate for tensor tomography in non-positive curvature
2021
Funder: University of Cambridge
Postural and gestural synchronization, sequential imitation, and mirroring predict perceived coupling of dancing dyads
2023
Body movement is a primary nonverbal communication channel in humans. Coordinated social behaviors, such as dancing together, encourage multifarious rhythmic and interpersonally coupled movements from which observers can extract socially and contextually relevant information. The investigation of relations between visual social perception and kinematic motor coupling is important for social cognition. Perceived coupling of dyads spontaneously dancing to pop music has been shown to be highly driven by the degree of frontal orientation between dancers. The perceptual salience of other aspects, including postural congruence, movement frequencies, time-delayed relations, and horizontal mirrorin…
Topics in calculus and geometry on metric spaces
2022
In this thesis we present an overview of some important known facts related to topology, geometry and calculus on metric spaces. We discuss the well known problem of the existence of a lipschitz equivalent metric to a given quasiultrametric, revisiting known results and counterexamples and providing some new theorems, in an unified approach. Also, in the general setting of a quasi-metric doubling space, suitable partition of unity lemmas allows us to obtain, in step two Carnot groups, the well known Whitney’s extension theorem for a given real function of class C^m defined on a closed subset of the whole space: this result relies on relevant properties of the symmetrized Taylor’s polynomial…
Adaptive smoothing spline using non-convex penalties
2022
We propose a new adaptive penalty for smoothing via penalized splines. The new form of adaptive penalization is based on penalizing the differences of the coefficients of adjacent bases, using non-convex penalties. This makes possible to estimate curves with varying amounts of smoothness. Comparisons with respect to some competitors are presented.