In this paper the existence of minimal lattice-subspaces of a vector lattice E containing a subset B of E+ is studied (a lattice-subspace of E is a subspace of E which is a vector lattice in the induced ordering). It is proved that if there exists a Lebesgue linear topology τ on E and E+ is τ -closed (especially if E is a Banach lattice with order continuous norm), then minimal lattice-subspace...

Let R be a commutative ring, q a unit of R and P a multiplicatively antisymmetric matrix with coefficients which are integer powers of q. Denote by SE(q,P) the multiparameter quantum matrix bialgebra associated to q and P. Slightly generalizing [H-H], we define a multiparameter deformation Lλ/μVP of the classical skew Schur module. In case R is a field and q is not a root of 1, arguments like t...

We obtain a generalization of Furstenberg’s Diophantine Theorem on non-lacunary multiplicative semigroups. For example we show that the sets of sums {(p1 qm 1 + p2 qm 2 )α : n, m ∈ N} and {(p1 qm 1 + 2n)α : n, m ∈ N} are dense in the circle T = R/Z for all irrational α, where (pi, qi) are distinct pairs of multiplicatively independent integers for i = 1, 2.

We show that the knowledge of Dirichlet-to-Neumann maps given on an arbitrary open non-empty portion boundary a smooth domain in $${\mathbb {R}}^n$$ , $$n\ge 2$$ for classes semilinear and quasilinear conductivity equations, determines nonlinear conductivities uniquely. The main ingredient proof is certain $$L^1$$ -density result involving sums products gradients harmonic functions which vanish...

We show that the variational inequality V I(C,A) has a unique solution for a relaxed (γ, r)-cocoercive, μ-Lipschitzian mapping A : C → H with r > γμ, where C is a nonempty closed convex subset of a Hilbert space H . From this result, it can be derived that, for example, the recent algorithms given in the references of this paper, despite their becoming more complicated, are not general as they ...

A time scale, T, is a nonempty, closed subset of the real numbers, R. Several methods of solution exist for second order linear equations on a time scale. An advantage of these methods is that we can obtain solutions on a system comprising of continuous and/or discrete elements. After restricting the time scale to be R, these solutions are equivalent to those obtained using differential equatio...

We show that local deformations, near closed subsets, of solutions to open partial differential relations can be extended global provided all but the highest derivatives stay constant along subset. The applicability this general result is illustrated by a number examples, dealing with convex embeddings hypersurfaces, forms, and lapse functions in Lorentzian geometry. main application approximat...