Search results for "convexity"
showing 7 items of 57 documents
Covarying shell growth parameters and the regulation of shell shape in marine bivalves: a case study on Tellinoidea.
2014
Specific parameters characterising shell shape may arguably have a significant role in the adaptation of bivalve molluscs to their particular environments. Yet, suchfunctionally relevantshape parameters (shell outline elongation, dissymmetry, and ventral convexity) are not those parameters that the animal may directly control. Rather than shell shape, the animal regulates shell growth. Accordingly, an alternative,growth-baseddescription of shell-shape is best fitted to understand how the animal may control the achieved shell shape. The key point is, in practice, to bring out the link between those two alternative modes of shell-shape descriptions, that is, to derive the set of equations whi…
Vector Well-posedness of Optimization Problems and Variational Inequalities
2008
In this paper, a new sufficient condition is given in order a vector variational inequality is well-posed. This condition uses generalized convexity assumptions and can be also used in order to prove the well-posedness of a vector optimization problem.
Logarithmic mean inequality for generalized trigonometric and hyperbolic functions
2015
In this paper we study the convexity and concavity properties of generalized trigonometric and hyperbolic functions in case of Logarithmic mean. peerReviewed
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.
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…
Envelopes for sets and functions II: generalized polarity and conjugacy
2018
International audience; Let X,Y be two nonempty sets, Φ an extended real-valued bivariate coupling function on X × Y and Γ a subset of X × Y. The present paper provides extensions to the well-known generalized Φ-conjugacy and Γ-polarity of diverse results of our previous work [2] related to φ-conjucacy and Λ-polarity, where Λ is a subset of a vector space E and φ is a function on E defining the particular coupling function (x,y)→φ(x−y) on E × E. A particular attention is devoted to the conjugacy functions (resp. polarity sets) which are mutually generating. Finally, for a superadditive conjugacy function Φ, we obtain a full description of the class of Φ-envelopes.
COMPLEX CONVEXITY AND VECTOR-VALUED LITTLEWOOD–PALEY INEQUALITIES
2003
Let 2 p 0s uch thatfHp(X) (� f(0)� p + λ (1 −| z| 2 ) p−1 � f � (z)� p dA(z)) 1/p ,f or all f ∈ H p (X). Applications to embeddings between vector-valued BMOA spaces defined via Poisson integral or Carleson measures are provided.