Abstract We investigate the relations between normalized critical points of nonlinear Schrödinger energy functional and corresponding action on associated Nehari manifold. Our first general result is that ground state levels are strongly related by following duality result: (negative) level Legendre–Fenchel transform level. Furthermore, whenever an exists at a certain frequency, then all states...

Let $f$ be a locally univalent function on the unit disk $U$. We consider the normalized extensions of $f$ to the Euclidean unit ball $B^nsubseteqmathbb{C}^n$ given by $$Phi_{n,gamma}(f)(z)=left(f(z_1),(f'(z_1))^gammahat{z}right),$$  where $gammain[0,1/2]$, $z=(z_1,hat{z})in B^n$ and $$Psi_{n,beta}(f)(z)=left(f(z_1),(frac{f(z_1)}{z_1})^betahat{z}right),$$ in which $betain[0,1]$, $f(z_1)neq 0$ a...

Goal-oriented error estimates (GOEE) have become popular tools to quantify and control the local error in quantities of interest (QoI), which are often more pertinent than local errors in energy for design purposes (e.g. the mean stress or mean displacement in a particular area, the stress intensity factor for fracture problems). These GOEE are one of the key unsolved problems of advanced engin...

Let S be an orientable surface. Let Diff(S) be the group of all diffeomorphisms of S, and Diff(S) its identity component. Then Mod±S = Diff(S)/Diff (S) is called the extended mapping class group or the extended Teichmüller modular group of S. Let Diff(S) be the subgroup of orientation preserving diffeomorphisms of S. Then Mod(S) = Diff(S)/Diff(S) is called the mapping class group or the Teichmü...

The mapping class group of a topological space is the group of self-homeomorphisms modulo the equivalence relation of isotopy. For 2-manifolds (of finite type), it is a discrete group which is known (see [M, HI, H2, H3, H4]) to share many of the properties of arithmetic subgroups of linear algebraic groups, although it is not arithmetic. In this note we describe the results of [Ml], which show ...

Let V be a finite-dimensional vector space, and let G be a subgroup of GL( V). Set D( V) equal to the algebra of differential operators on V with polynomial coefficients and D( V) G equal to the G invariants in D( V). If 9 is a reductive Lie algebra over C then ~ egis a Cartan subgroup of g, and if G is the adjoint group of 9 then W is the Weyl group of (g, ~) , Harish-Chandra introduced an alg...

the objective of this paper is to deal with the fuzzy conic program- ming problems. the aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. toward this end, the convexity-like concept of fuzzy mappings is introduced and then a speci c ordering cone is established based on the parameterized representation of fuzzy numbers. un- der this setting, duality t...

A polyhedron is a graph G which simple, planar and 3-connected. In this note, we classify the family of strongly involutive self-dual polyhedra. The latter done by using well-known result due to Tutte characterizing 3-connected graphs. We also show that special class polyhedra self-duality behaves topologically as antipodal mapping. These are related with several problems in convex discrete geo...