Notes Lichénologiques N° X

Notes on Big-n Problems

where α is a step size. If the gradient of f is Lipschitz-continuous with constant L, then using the step size α = 1/L guarantees that f(x) < f(x) (provided ∇f(x) 6= 0), and if f is convex that the distance to the optimal value f(x∗) as a function of k is O(1/k). Nesterov [1983] proposes a simple modification, referred to as the accelerated gradient method, that improves this to O(1/k), and und...

The Nature of Halogen Bonds in [N∙∙∙X∙∙∙N]+ Complexes: A Theoretical Study

     The effects of substituents on the symmetry and the nature of halogen bonds in [N∙∙∙X∙∙∙N]+-type systems are presented for the YC5H4N∙∙∙X∙∙∙NC5H5 (Y = NO2, CN, H, CH3, OCH3, OH, NH2, X = Cl, Br, I) complexes. Some structural parameters, energy data and electronic properties were explored with...

BC530 Class notes on X-ray Crystallography

Arithmetical Notes. X. a Class of Totients1

NOTES ON CONGRUENCE n-PERMUTABILITY AND SEMIDISTRIBUTIVITY

In [1] T. Dent, K. Kearnes and Á. Szendrei define the derivative, Σ′, of a set of equations Σ and show, for idempotent Σ, that Σ implies congruence modularity if Σ′ is inconsistent (Σ′ |= x ≈ y). In this paper we investigate other types of derivatives that give similar results for congruence n-permutable for some n, and for congruence semidistributivity. In a recent paper [1] T. Dent, K. Kearne...