Note on Geometrical Products

Note on Cup-products

Geometrical Evaluation of Star Products

The geometric picture of the star-product based on its Fourier representation kernel is utilized in the evaluation of chains of star-products and the intuitive appreciation of their associativity and symmetries. Such constructions appear even simpler for a variant asymmetric product, and carry through for the standard star-product supersymmetrization. §1. Groenewold’s noncommutative ⋆-product [...

Note on Distance Magic Products G ∘ C4

A distance magic labeling of a graph G = (V, E) of order n is a bijection l : V → {1, 2, . . . , n} with the property that there is a positive integer k (called magic constant) such that w(x) = k for every x ∈ V . If a graph G admits a distance magic labeling, then we say that G is a distance magic graph. In the case of non-regular graph G, the problem of determining whether there is a distance...

Some Geometrical Bases for Incremental-Iterative Methods (RESEARCH NOTE)

Finding the equilibrium path by non-linear structural analysis is one of the most important subjects in structural engineering. In this way, Incremental-Iterative methods are extremely used. This paper introduces several factors in incremental steps. In addition, it suggests some control criteria for the iterative part of the non-linear analysis. These techniques are based on the geometric of e...

A Note on the Boundary Shape of Matrix Polytope Products

Motivated by interval matrix multiplication we consider (matrix) polytopes A ⊆ R, B ⊆ R, m,n, k ∈ N, and investigate the boundary shape of their pointwise product AB := {AB | A ∈ A, B ∈ B}. We prove that AB cannot have outward curved boundary sections while inward curved sections may exist. This is achieved by a simple local extreme point analysis. Results are proved in a more general abstract ...