scholarly journals Resolvents of equilibrium problems on a complete geodesic space with curvature bounded above

2021 ◽  
Vol 37 (3) ◽  
pp. 463-476
Author(s):  
YASUNORI KIMURA ◽  
◽  

We consider equilibrium problems on a complete geodesic space with curvature bounded above by one and propose the notion of resolvents for this problem. We prove its well-definedness as a single-valued mapping whose domain is the whole space, and its geometric properties.

2018 ◽  
Vol 12 (01) ◽  
pp. 169-207 ◽  
Author(s):  
Žiga Virk

Given a compact geodesic space [Formula: see text], we apply the fundamental group and alternatively the first homology group functor to the corresponding Rips or Čech filtration of [Formula: see text] to obtain what we call a persistence object. This paper contains the theory describing such persistence: properties of the set of critical points, their precise relationship to the size of holes, the structure of persistence and the relationship between open and closed, Rips and Čech induced persistences. Amongst other results, we prove that a Rips critical point [Formula: see text] corresponds to an isometrically embedded circle of length [Formula: see text], that a homology persistence of a locally contractible space with coefficients in a field encodes the lengths of the lexicographically smallest base, and that Rips and Čech induced persistences are isomorphic up to a factor [Formula: see text]. The theory describes geometric properties of the underlying space encoded and extractable from persistence.


2017 ◽  
Vol 5 (2) ◽  
pp. 73-78
Author(s):  
Jay Prakash Singh ◽  

In this paper author present an investigation of some differential geometric properties of Para-Sasakian manifolds. Condition for a vector field to be Killing vector field in Para-Sasakian manifold is obtained. Mathematics Subject Classification (2010). 53B20, 53C15.


2020 ◽  
pp. 026010602097524
Author(s):  
Darren G Candow ◽  
Philip D Chilibeck ◽  
Julianne Gordon ◽  
Emelie Vogt ◽  
Tim Landeryou ◽  
...  

Background: The combination of creatine supplementation and resistance training (10–12 weeks) has been shown to increase bone mineral content and reduce a urinary indicator of bone resorption in older males compared with placebo. However, the longer-term effects (12 months) of creatine and resistance training on bone mineral density and bone geometric properties in older males is unknown. Aim: To assess the effects of 12 months of creatine supplementation and supervised, whole-body resistance training on bone mineral density, bone geometric properties, muscle accretion, and strength in older males. Methods: Participants were randomized to supplement with creatine ( n = 18, 49–69 years, 0.1 g·kg-1·d-1) or placebo ( n = 20, 49–67 years, 0.1 g·kg-1·d-1) during 12 months of supervised, whole-body resistance training. Results: After 12 months of training, both groups experienced similar changes in bone mineral density and geometry, bone speed of sound, lean tissue and fat mass, muscle thickness, and muscle strength. There was a trend ( p = 0.061) for creatine to increase the section modulus of the narrow part of the femoral neck, an indicator of bone bending strength, compared with placebo. Adverse events did not differ between creatine and placebo. Conclusions: Twelve months of creatine supplementation and supervised, whole-body resistance training had no greater effect on measures of bone, muscle, or strength in older males compared with placebo.


Author(s):  
Habib ur Rehman ◽  
Aviv Gibali ◽  
Poom Kumam ◽  
Kanokwan Sitthithakerngkiet

2020 ◽  
Vol 10 (1) ◽  
pp. 450-476
Author(s):  
Radu Ioan Boţ ◽  
Sorin-Mihai Grad ◽  
Dennis Meier ◽  
Mathias Staudigl

Abstract In this work we investigate dynamical systems designed to approach the solution sets of inclusion problems involving the sum of two maximally monotone operators. Our aim is to design methods which guarantee strong convergence of trajectories towards the minimum norm solution of the underlying monotone inclusion problem. To that end, we investigate in detail the asymptotic behavior of dynamical systems perturbed by a Tikhonov regularization where either the maximally monotone operators themselves, or the vector field of the dynamical system is regularized. In both cases we prove strong convergence of the trajectories towards minimum norm solutions to an underlying monotone inclusion problem, and we illustrate numerically qualitative differences between these two complementary regularization strategies. The so-constructed dynamical systems are either of Krasnoselskiĭ-Mann, of forward-backward type or of forward-backward-forward type, and with the help of injected regularization we demonstrate seminal results on the strong convergence of Hilbert space valued evolutions designed to solve monotone inclusion and equilibrium problems.


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