Noether's Theorem on Surfaces

In this article we prove a version of Noether's Theorem (of Calculus of Variations) which is valid for a general regular (compact) surface. As a special feature, the Lie group of transformations is allowed to act on the Cartesian product of the surface and the functional space. Additionally, we apply the Theorem to a problem in Classical Differential Geometry of surfaces. The given application is actually an example showing how Noether's Theorem can be used to construct invariant properties of the solutions to variational problems defined on surfaces, or equivalently, of the solutions to the associated Euler-Lagrange equations resulting from them.     

Homodiselenacalix[4]arenes: Molecules with Unique Channelled Crystal Structures

A synthetic route towards homodiselenacalix[4]arene macrocycles is presented, based on the dynamic covalent chemistry of diselenides. The calixarene inner rim is decorated with either alkoxy or tert‐butyl ester groups. Single‐crystal X‐ray analysis of two THF solvates with methoxy and ethoxy substituents reveals the high similarity of their molecular structures and alterations on the supramolecular level. In both crystal structures, solvent channels are present and differ in both shape and capacity. Furthermore, the methoxy‐substituted macrocycle undergoes a single‐crystal‐to‐single‐crystal transformation during which the molecular structure changes its conformation from 1,3‐alternate (loaded with THF/water) to 1,2‐alternate (apohost form). Molecular modelling techniques were applied to explore the conformational and energetic behaviour of the macrocycles.     

New aspects of gold nanorod formation via seed-mediated method

Gold nanorods (AuNRs) were obtained via a wet chemistry technique, in aqueous medium, employing crystallisation seeds. The kinetics of formation, the aspect ratio, and the selectivity of the particles were evaluated according to the parameters of synthesis: the growth-driving agent, seed, and gold precursor concentrations. In 2–4 h, the rod particles attained the expected size and shape under kinetic control, and were stable for at least 2 days. In order to obtain good quality AuNRs in good yields, without enrichment, we suggest keeping the growth-driving agent/gold molar ratio, the Au^I/seed ratio, and the concentration of the reagents in the final solution within specific ranges. For example, even if good molar ratios between the reagents are maintained, relatively highly concentrated reaction solutions lead to AuNRs with lower aspect ratios. The main properties of the prepared colloidal systems and the nanoparticles were evaluated by UV–vis spectroscopy and transmission electron microscopy, respectively.     

A New Ent-Kaurane from the Roots of Lasianthaea aurea

Chemistry of Natural Compounds - A known kaurenoic acid (1), together with a new kaurane derivative named 3α-isobutyryloxykaurenoic acid (2), was isolated from the roots of Lasianthaea aurea,...     

Memoryless near-collisions via coding theory

We investigate generic methods to find near-collisions in cryptographic hash functions. We introduce a new generic approach based on methods to find cycles in the space of codewords of a code with low covering radius. We give an analysis of our approach and demonstrate it on the SHA-3 candidate TIB3.