New Dolabellane Derivatives from the Brown Alga Dictyota pardalis

Reinvestigation of the brown alga Dictyota pardalis f. pseudohamata CRIBB led to the crystallization of 1 and to the isolation of the two new dolabellane derivatives 2 and 3 . X-Ray analysis of 1 and 2 , together with detailed 1D-and 2D-NMR studies on 2 and 3 , allowed their structures to be elucidated as (1R*,3S*,7S*,11R*,4Z)-dolabella-4,8(17), 12(18)-triene-3,7-diol ( 1 ), (1R*,3S*,4S*,7S*,8S*,11R*,14R*,12E)-3,4:7,8-diepoxydolabe11-12-ene-14, 18-diol ( 2 ), and (1R*,3S*,4S*,7S*,8S*,11R*,14R*)-3,4:7,8-diepoxy-l,4,8,12,12-pentamethylbicyclo[9. 3. 0]tetra-decan-14-ol( 3 ).     

Untersuchungen an Natriumtrifluormethylsulfonat – Kristallstruktur und Phasenumwandlung des Monohydrats und Natriumionenleitfähigkeit des wasserfreien Salzes

Studies on Sodium Trifluormethanesulfonate – Crystal Structure and Phase Transition of Sodium Trifluormethanesulfonate Monohydrate and Sodium Ion Conductivity of Anhydrous Sodium Trifluormethanesulfonate According to the results of temperature dependent powder diffractometry (Guinier-Simon-technique) sodium trifluormethanesulfonate monohydrate is dimorphous. The phase transition occurs at ?35°C. The room-temperature modification crystallizes monoclinic in space group P2₁/c with the lattice parameters a = 941.6(5) pm, b = 654.3(2) pm, c = 1062.4(5) pm and β = 107.73(2)°. The crystal structure consists of double layers of trifluormethanesulfonate anions, the lipophilic CF₃-groups pointing at each other. Sodium is coordinated by four oxygen atoms from four different anions and by two molecules of crystal water. The resulting polyhedron may be addressed as a distorted octahedron. The low-temperature modification crystallizes orthorhombic in space group Pnma with the lattice parameters a = 645.31(9) pm, b = 538.03(9) pm, c = 1745.3(3) pm. The loss of crystal water occurs at 136°C. Anhydrous sodium trifluormethanesulfonate shows a phase transition at 252°C. The high-temperature modification is a good sodium ionic conductor (σ = 4.1 · 10^?1 Ω^?1 cm^?1 at 250°C).     

Quantitative Local Bounds for Subcritical Semilinear Elliptic Equations

The purpose of this paper is to prove local upper and lower bounds for weak solutions of semilinear elliptic equations of the form ???u =?cu ^p , with 0 < p < p _s = (d + 2)/(d - 2), defined on bounded domains of ${{\mathbb{R}^d}, d \geq 3}$ , without reference to the boundary behaviour. We give an explicit expression for all the involved constants. As a consequence, we obtain local Harnack inequalities with explicit constants, as well as gradient bounds.     

Quasi-hereditary covers of higher zigzag algebras of type A

In this paper we define and study some quasi-hereditary covers for higher zigzag algebras of type A. We show how these algebras satisfy three different Koszul properties: they are Koszul in the classical sense, standard Koszul and Koszul with respect to the standard module Δ, according to the definition given in [24]. This last property gives rise to a well defined duality and we compute the Δ-Koszul dual as the path algebra of a quiver with relations.     

The Group Ring ofSL2(p) over thep-adic Integers

This paper describes the ring-theoretic structure of the group rings ofSL₂(p²) over thep-adic integers.     

Optimal Elements in Vector Optimization with a Variable Ordering Structure

Optimality concepts for vector optimization problems with a variable ordering structure are examined. These considerations are motivated by an application in medical image registration, where the preferences vary depending on the element in the image space.     

On the equivalence of quadratic APN functions

Establishing the CCZ-equivalence of a pair of APN functions is generally quite difficult. In some cases, when seeking to show that a putative new infinite family of APN functions is CCZ inequivalent to an already known family, we rely on computer calculation for small values of n. In this paper we present a method to prove the inequivalence of quadratic APN functions with the Gold functions. Our main result is that a quadratic function is CCZ-equivalent to the APN Gold function x^2r+1{x^{2^r+1}} if and only if it is EA-equivalent to that Gold function. As an application of this result, we prove that a trinomial family of APN functions that exist on finite fields of order 2 ⁿ where n ≡ 2 mod 4 are CCZ inequivalent to the Gold functions. The proof relies on some knowledge of the automorphism group of a code associated with such a function.