This paper generalizes the Aleksandrov problem, the Mazur–Ulam theorem and Benz theorem on n-normed spaces. It proves that a one-distance preserving mapping is an nisometry if and only if it has the zero-distance preserving property, and two kinds of n-isometries on n-normed spaces are equivalent.

Beckman and Quarles proved that a unit distance preserving mapping from a Euclidean space E into itself is necessarily an isometry. In this paper, we give an example of a (non-strictly convex) normed space H for which every unit distance preserving function from H into itself is an isometry. MSC 2000: 51M05, 52A10, 52A20, 52C05, 52C25

We study morphisms of the generalized quantum logic tripotents in JBW $$^*$$ -triples and von Neumann algebras. Especially, we establish a generalization celebrated Dye’s theorem on orthoisomorphisms between lattices to this new context. show existence one-to-one correspondence following maps: (1) posets preserving reflection $$u\rightarrow - u$$ (2) maps triples that preserve are real linear s...

The phase space of an integrable volume-preserving map with one action is foliated by a oneparameter family of invariant tori. Perturbations lead to chaotic dynamics with interesting transport properties. We show that near a rank-one resonant torus the mapping can be reduced to a volume-preserving standard map. This map is a twist map only when the frequency map crosses the resonance curve tran...

We consider the numerical integration of two types of systems of differential equations. We first consider Hamiltonian systems of differential equations with a Poisson structure. We show that symplectic Runge-Kutta methods preserve this structure when the Poisson tensor is constant. Using nonlinear changes of coordinates this structure can also be preserved for non-constant Poisson tensors, as ...

Various concepts of orthogonality on the real line are reviewed that arise in connection with quadrature rules. Orthogonality relative to a positive measure and Gauss-type quadrature rules are classical. More recent types of orthogonality include orthogonality relative to a sign-variable measure, which arises in connection with Gauss-Kronrod quadrature, and power (or implicit) orthogonality enc...

We present an analogue of Uhlhorn’s version of Wigner’s theorem on symmetry transformations for the case of indefinite inner product spaces. This significantly generalizes a result of Van den Broek. The proof is based on our main theorem, which describes the form of all bijective transformations on the set of all rank-one idempotents of a Banach space which preserve zero products in both direct...

We characterize bijective transformations on the set of all n-dimensional subspaces of a Hilbert space that preserve orthogonality in both directions. This extends Uhlhorn’s improvement of Wigner’s classical theorem on symmetry transformations.

A mapping f : Z → R is said to possess the direction preserving property if fi(x) > 0 implies fi(y) ≥ 0 for any integer points x and y with ‖x − y‖∞ ≤ 1. In this paper, a simplicial algorithm is developed for computing an integer zero point of a mapping with the direction preserving property. We assume that there is an integer point x with c ≤ x ≤ d satisfying that max1≤i≤n(xi − x 0 i )fi(x) > ...

Parameterizing a genus-0 mesh onto a unit sphere means assigning a 3D position on the unit sphere to each vertex of the mesh, such that the spherical mapping induced by the mesh connectivity is not too distorted and does not have overlapping areas. The non-overlapping requirement is technically the most difficult component also the most critical component of many spherical parametrization metho...