Related papers: Hidden Convexity in the l0 Pseudonorm
Discrete Fenchel duality is one of the central issues in discrete convex analysis. The Fenchel-type min-max theorem for a pair of integer-valued M-natural-convex functions generalizes the min-max formulas for polymatroid intersection and…
We propose a set of convex low rank inducing norms for a coupled matrices and tensors (hereafter coupled tensors), which shares information between matrices and tensors through common modes. More specifically, we propose a mixture of the…
Lott-Sturm-Villani theory of curvature on geodesic spaces has been extended to discrete graph spaces by C. L{\'e}onard by replacing W2-Wasserstein geodesics by Schr{\"o}odinger bridges in the definition of entropic curvature [23, 25, 24].…
We introduce and study a new class of generalized convex functions termed star quasiconvex functions. This class includes convex, star-convex, quasiconvex, quasar-convex, and positively homogeneous functions of any degree $p>0$ as special…
We consider nonsmooth optimization problems under affine constraints, where the objective consists of the average of the component functions of a large number $N$ of agents, and we only assume access to the Fenchel conjugate of the…
The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the…
A conformal restriction system is a commutative, associative, unital algebra equipped with a representation of the groupoid of univalent conformal maps on connected open sets of the Riemann sphere, and a family of linear functionals on…
We deduce mixed quasi-norm estimates of Lebesgue types on semi-continuous convolutions between sequences and functions which may be periodic or possess a weaker form of periodicity in certain directions. In these directions, the Lebesgue…
An antinorm is a concave nonnegative homogeneous functional on a convex cone. It is shown that if the cone is polyhedral, then every antinorm has a unique continuous extension from the interior of the cone. The main facts of the duality…
The anomalous properties of High-$T_{{\rm c}}$ cuprates are investigated both in the normal state and in the superconducting state. In particular, we pay atte ntion to the pseudogap in the normal state and the phase transition from the pse…
We study pseudogap phenomena and Fermi-arc formation experimentally observed in typical two dimensional doped Mott insulators, namely, underdoped cuprate superconductors. To develop a physically unequivocal theory, we start from the…
This paper provides versions of classical results from linear algebra, real analysis and convex analysis in a free module of finite rank over the ring $L^0$ of measurable functions on a $\sigma$-finite measure space. We study the question…
We introduce pseudoconformal structures on 4--dimensional manifolds and study their properties. Such structures are arising from two different complex operators which agree in a 2--dimensional subbundle of the tangent bundle; this subbundle…
The paper deals with the optimal control problem described by second order evolution differential inclusions; to this end first we use an auxiliary problem with second order discrete and discrete-approximate inclusions. Then applying…
A $\lambda$-convex body in a three-dimensional space form $M^3(c)$ of constant curvature $c$ is a compact convex set $K$ whose boundary $\partial K$ has normal curvatures bounded below by a constant $\lambda>0$ (in a weak sense). Within…
A digraph is eulerian if it is connected and every vertex has its in-degree equal to its out-degree. Having a spanning eulerian subdigraph is thus a weakening of having a hamiltonian cycle. In this paper, we first characterize the pairs…
The smooth evolution of the tunneling gap of Bi_2Sr_2CaCu_2O_8 with doping from a pseudogap state in the underdoped cuprates to a superconducting state at optimal and overdoping reflects an underlying SO(6) instability structure of the…
We introduce the notion of relative pseudocoefficient for relative discrete series of real spherical homogeneous spaces of reductive groups. We prove that such relative pseudocoefficient does not exist for semisimple symmetric spaces of…
We prove new entropy inequalities for log concave and s-concave functions that strengthen and generalize recently established reverse log Sobolev and Poincare inequalities for such functions. This leads naturally to the concept of…
It is well-known that pseudo functors from bicategories of spans are equivalent to Beck-Chevalley bifibrations, and therefore capture the relationships underlying the adjunctions suitable as semantics for existential quantification. This…