The controversy in theγγ →ρρ process: potential scattering or qq\bar q};\bar q}; resonance?; resonance?

Theγγ →ρ ⁰ ρ ⁰ → 4π reaction shows a broad peak at 1.5 GeV in the (J ^P ,J _z )=(2⁺,2) channel which has no counterpart in theρ ⁺ ρ ^? channel. This “resonance” is considered as a candidate for a qq $\bar q$ ; $\bar q$ state in the “s-channel”. We show, however, that it can also be explained by potential scattering ofρ ⁰ ρ ⁰ via theσ- exchange in the “t-channel”.     

Structural transition of nematic liquid crystal in cylindrical capillary as a result of the annihilation of two point defects

We study the annihilation of hedgehog-antihedgehog defects in confined nematic liquid crystals using Brownian molecular dynamics simulations. After the collision, merging of defects, and building a loop disclination structure, system can experience a structural transition into another nematic structure, triggered by a nucleation of loop disclination structure. In our rough theoretical approach we calculate the size of the emerged loop structure as the function of the typical size of the confining cavity. Attention is paid also to the dynamics of the loop structure after collision.     

Optimal Control in Autonomous Driving

Autonomous driving is no longer a subject of science fiction. Instead it has become a field of highly topical developments and has already reached numerous milestones. The Audi Autonomous Driving Cup provides a stage for students to participate in this development process. This competition, carried out in Germany, Austria and Switzerland, provides miniature vehicles of normed hardware to the participants which have the task of implementing algorithms for autonomous handling of problems such as lane tracking, obstacle detection, adaptive cruise control, overtaking, turning as well as entering and exiting parking spaces. To present the concept of optimal control based on a single track model in combination with image processing methods we focus in this paper on the parking manoeuvre only. Thereby we show that optimization and control techniques can play a key role in the design of autonomous vehicles. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Matrix semigroups whose ring commutators have real spectra are realizable

We introduce the numerical spectrum \(\sigma _n(A)\subseteq {\mathbb {C}}\) of an (unbounded) linear operator A on a Banach space X and study its properties. Our definition is closely related to the numerical range W(A) of A and always yields a superset of W(A). In the case of bounded operators on Hilbert spaces, the two notions coincide. However, unlike the numerical range, \(\sigma _n(A)\) is always closed, convex and contains the spectrum of A. In the paper we strongly emphasise the connection of our approach to the theory of \(C_0\)-semigroups.     

On finite-dimensional copointed Hopf algebras over dihedral groups

We classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero such that its coradical is isomorphic to the algebra of functions ${\mathbb{k}}^{{\mathbb{D}}_m}$ over a dihedral group ${\mathbb{D}}_m$, with $m=4a\ge 12$. We obtain this classification by means of the lifting method, where we use cohomology theory to determine all possible deformations. Our result provides an infinite family of new examples of finite-dimensional copointed Hopf algebras over dihedral groups.     

Thermodynamic characterization of aluminium corner of Al–Cu system with various Nd additions

Journal of Thermal Analysis and Calorimetry - The effect of various neodymium additions on the characteristic solidification temperatures and on the microstructure development of the...     

Separation and identification of some common isomeric plant triterpenoids by thin-layer chromatography and high-performance liquid chromatography

Chromatographic separation of 10 triterpenoids (α-amyrin, β-amyrin, δ-amyrin, lupeol, lupenon, lupeol acetate, cycloartenol, cycloartenol acetate, ursolic acid, oleanolic acid) and 2 sterols (stigmasterol and β-sitosterol) was studied. The chromatographic techniques included silica gel and reversed-phase (C₁₈ RP) thin-layer chromatography (TLC) and C₁₈ RP high-performance liquid chromatography (HPLC) using UV and mass spectrometric (MS) detection with atmospheric pressure chemical ionization (APCI). The TLC separation of the isomeric triterpenols lupeol, α-amyrin, β-amyrin and cycloartenol was achieved for the first time using C₁₈ RP-HPTLC plates. Cycloartenol could be separated from related compounds only on C₁₈ RP-TLC but not on the C₁₈ RP-HPLC. δ-Amyrin isolated from the tomato fruit surface extract could be separated from other amyrins only by HPLC. Tandem mass spectrometry allowed discrimination between the isomers lupeol, α-amyrin, β-amyrin, δ-amyrin, cycloartenol and between lupeol acetate and cycloartenol acetate. The combination of 3 TLC methods and 2 HPLC methods enables qualitative determination of all 12 compounds and proves to be useful for the analysis of plant extracts. It is recommended that TLC screening on silica gel and C₁₈ RP be performed before HPLC analysis.     

Extending dynamic convex risk measures from discrete time to continuous time: A convergence approach

We present an approach for the transition from convex risk measures in a certain discrete time setting to their counterparts in continuous time. The aim of this paper is to show that a large class of convex risk measures in continuous time can be obtained as limits of discrete time-consistent convex risk measures. The discrete time risk measures are constructed from properly rescaled (‘tilted’) one-period convex risk measures, using a d-dimensional random walk converging to a Brownian motion. Under suitable conditions (covering many standard one-period risk measures) we obtain convergence of the discrete risk measures to the solution of a BSDE, defining a convex risk measure in continuous time, whose driver can then be viewed as the continuous time analogue of the discrete ‘driver’ characterizing the one-period risk. We derive the limiting drivers for the semi-deviation risk measure, Value at Risk, Average Value at Risk, and the Gini risk measure in closed form.     

Nematic liquid crystal gyroids as photonic crystals

ABSTRACT

We demonstrate nematic and cholesteric liquid crystal (LC) gyroids and show their photonic properties as photonic crystals by using numerical modelling. The LC gyroids are designed as composite optical materials, where we take one labyrinth of passages to be a solid dielectric, whereas the other (complementing) labyrinth of passages is taken to be filled by chiral or achiral nematic LC, with the intermediate gyroid surface imposing homeotropic (perpendicular) surface anchoring. The nematic inside the gyroid matrix is shown to exhibit a variety of possible orientational profiles which are characterised by complex networks of topological defects – from ordered, semi-ordered, to completely disordered. The diversity of possible nematic states is shown to lead to a rich structure of photonic bands, which can be tuned by the LC volume fraction and the cholesteric pitch, including control over full – direct and indirect – band gaps.