In 1937, Von Neumann [1] established the famous coincidence theorem. Since then, the coincidence theorem was generalized in many directions. Browder [2] first proved some basic coincidence theorems for a pair of set-valued mappings in compact setting of topological vector spaces and gave some applications to minimax inequalities and variational inequalities. Recently, Ding [3] established some ...

A cumbersome hypothesis for Viro patchworking of real algebraic curves is the convexity of the given subdivision. It is an open question in general to know whether the convexity is necessary. In the case of trigonal curves we interpret Viro method in terms of dessins d’enfants. Gluing the dessins d’enfants in a coherent way we prove that no convexity hypothesis is required to patchwork such cur...

We prove complex interpolation theorems for analytic families of multilinear operators defined on quasi-Banach spaces, with explicit constants on the intermediate spaces. We obtain analogous results for analytic families of operators defined on spaces generated by the Calderón method applied to couples of quasi-Banach lattices with nontrivial lattice convexity. As an application we derive a mul...

Using a result linking convexity and irreducibility of matrix sets it is shown that the generalized spectral radius of a compact set of matrices is a strictly increasing function of the set in a very natural sense. As an application some consequences of this property in the area of time-varying stability radii are discussed. In particular, using the implicit function theorem sufficient conditio...

In the present paper, slightly modifying the topological KKM Theorem of Park and Kim (1996), we obtain a new existence theorem for generalized vector equilibrium problems related to an admissible multifunction. We work here under the general framework of G-convex space which does not have any linear structure. Also, we give applications to greatest element, fixed point and vector saddle point p...

Given a complex semisimple Lie algebra g = k+ ik, we consider the converse question of Kostant’s convexity theorem for a normal x ∈ g. Let π : g → h be the orthogonal projection under the Killing form onto the Cartan subalgebra h := t+it where t is a maximal abelian subalgebra of k. If π(Ad(K)x) is convex, then there is k ∈ K such that each simple component of Ad(k)x can be rotated into the cor...

The bipotential theory is based on an extension of Fenchel’s inequality (see section 1 and example 1 in section 2). Despite several powerful applications (frictional contact [6], non-associated Drucker-Prager model [1], or Lemaitre plastic ductile damage law [2], to cite a few), the bipotentials don’t have yet a complete mathematical treatment. This is a second paper on the mathematics of the b...

We review the mathematics of the theory of entanglement measures. As well as giving proofs from first principles for some well-known and important results, we provide a sharpened version of a uniqueness theorem which gives necessary and sufficient conditions for an entanglement measure to coincide with the reduced von Neumann entropy on pure states. We also prove several versions of a theorem o...

(i) Gromov’s Compactness Theorem for pseudo-holomorphic curves in symplectic manifolds ([23]) and the topology of symplectomorphism groups of rational ruled surfaces (sections 2 and 3, references [1, 2]). (ii) Atiyah-Guillemin-Sternberg’s Convexity Theorem for the moment map of Hamiltonian torus actions ([9, 25]) and Kähler geometry of toric orbifolds in symplectic coordinates (sections 4 and 5...