A d-partite hypergraph is called fractionally balanced if there exists a non-negative, not identically zero, function on its edge set that has constant degrees in each vertex side. Using topological version of Hall’s theorem we prove lower bounds the matching number such hypergraphs. These yield rainbow versions KKM for products simplices, which turn are used to obtain some results multiple-cak...

This work investigates the Delaunay refinement for curved complexes. A manifold complex is defined as an unambiguous representation for the geometric objects required by a partial differential equation solver. The Chew’s and Ruppert’s Delaunay refinement algorithms, including an extension for curved complexes, are described under a new and arbitrary dimensional perspective. A theorem for strong...

Deguire and Lassonde [P. Deguire, M. Lassonde, Familles sélectantes, Topol. Methods Nonlinear Anal. 5 (1995) 261–269] extend the concept of continuous selection and introduce the notion of selecting family for a family of set-valued mappings. In this paper, we first establish a new existence theorem of selecting families. The existence of the selecting families will be then used in order to obt...

Topological semilattices with path-connected intervals are special abstract convex spaces. In this paper, we obtain generalized KKM type theorems and their analytic formulations, maximal element theorems and collectively fixed point theorems on abstract convex spaces. We also apply them to topological semilattices with path-connected intervals, and obtain generalized forms of the results of Hor...

We extend the concept of relaxed α-monotonicity to mixed relaxed α-β-monotonicity. The concept of mixed relaxed α-β-monotonicity is more general than many existing concepts of monotonicities. Finally, we apply this concept and well known KKM-theory to obtain the solution of generalized equilibrium problem.

We extend tropicalization and tropical compactification of subvarieties algebraic tori to spherical homogeneous spaces. Given a subvariety, we show that the support colored fan ambient variety agrees with subvariety. The proof is based on our equivariant version flattening by blow-up theorem. provide many examples.

Let V ⊗n be the n–fold tensor product of a vector space V. Following I. Schur we consider the action of the symmetric group Sn on V ⊗n by permuting coordinates. In the ‘super’ (Z2 graded) case V = V0 ⊕ V1, a ± sign is added [BR]. These actions give rise to the corresponding Schur algebras S(Sn, V ). Here S(Sn, V ) is compared with S(An, V ), the Schur algebra corresponding to the alternating su...