On Weak Solutions of Stochastic Differential Equations II

In the first part of this article a new method of proving existence of weak solutions to stochastic differential equations with continuous coefficients having at most linear growth was developed. In this second part, we show that the same method may be used even if the linear growth hypothesis is replaced with a suitable Lyapunov condition.     

Controlling the Assembly of Cellulose-Based Oligosaccharides through Sequence Modifications

Peptides and nucleic acids with programmable sequences are widely explored for the production of tunable, self-assembling functional materials. Herein we demonstrate that the primary sequence of oligosaccharides can be designed to access materials with tunable shapes and properties. Synthetic cellulose-based oligomers were assembled into 2D or 3D rod-like crystallites. Sequence modifications within the oligosaccharide core influenced the molecular packing and led to the formation of square-like assemblies based on the rare cellulose IV_II allomorph. In contrast, modifications at the termini generated elongated aggregates with tunable surfaces, resulting in self-healing supramolecular hydrogels.     

The solvophobic effect in simple fluid mixtures

The “solvophobic” effect is the tendency of solute particles to cluster as the attractive interaction between solvent particles is strengthened. The potentials of mean force in the hypernetted chain approximation have been obtained for a simple fluid mixture consisting of two hard spheres immersed in a hard core/Yukawa tail solvent. The results clearly exhibit features attributable to the “solvophobic” effect.     

Two-stage weighted PROMETHEE II with results’ visualization

Central European Journal of Operations Research - Multicriteria decision-making methods are widely spread and used to assist the decision-makers to resolve problems. Many of the methods are simple...     

Classical phase space revealed by coherent light

We study the far-field characteristics of oval-resonator laser diodes made of an GaAs/Al(x)Ga(1-x)As quantum well. The resonator shapes are various oval geometries, thereby probing chaotic and mixed classical dynamics. The far-field pattern shows a pronounced fine structure that strongly depends on the cavity shape. Comparing the experimental data with ray-model simulations for a Fresnel billiard yields convincing agreement for all geometries and reveals the importance of the underlying classical phase space for the lasing characteristics.     

Application of Linear and Branched Poly(Ethylene Glycol)‐Poly(Lactide) Block Copolymers for the Preparation of Films and Solution Electrospun Meshes

Poly(ethylene glycol)‐poly(lactide) (PEG‐PLA) block copolymers are processed to solvent cast films and solution electrospun meshes. The effect of polymer composition, architecture, and number of anchoring points for the plasticizer on swelling, degradation, and mechanical properties of these films and meshes is investigated as potential barrier device for the prevention of peritoneal adhesions. As a result, adequate properties are achieved for the massive films with a longer retention of the plasticizer PEG for star‐shaped block copolymers than for the linear triblock copolymers and consequently more endurable mechanical properties during degradation. For electrospun meshes fabricated using the same polymers, similar trends are observed, but with an earlier start of fragmentation and lower tensile strengths. To overcome the poor mechanical strengths and an occurring shrinkage during incubation, which may impair the coverage of the wound, further adaptions of the meshes and the fabrication process are necessary.

     

Lie algebra type noncommutative phase spaces are Hopf algebroids

For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite-dimensional Lie algebra, it is known how to introduce an extension playing the role of the corresponding noncommutative phase space, namely by adding the commuting deformed derivatives in a consistent and nontrivial way; therefore, obtaining certain deformed Heisenberg algebra. This algebra has been studied in physical contexts, mainly in the case of the kappa-Minkowski space-time. Here, we equip the entire phase space algebra with a coproduct, so that it becomes an instance of a completed variant of a Hopf algebroid over a noncommutative base, where the base is the enveloping algebra.