Normalizers and self-normalizing subgroups II

Let \mathbbK\mathbb{K} be a field, G a reductive algebraic \mathbbK\mathbb{K}-group, and G ₁ ≤ G a reductive subgroup. For G ₁ ≤ G, the corresponding groups of \mathbbK\mathbb{K}-points, we study the normalizer N = N _G (G ₁). In particular, for a standard embedding of the odd orthogonal group G ₁ = SO(m, \mathbbK\mathbb{K}) in G = SL(m, \mathbbK\mathbb{K}) we have N ≅ G ₁ ⋊ μ _m ( \mathbbK\mathbb{K}), the semidirect product of G ₁ by the group of m-th roots of unity in \mathbbK\mathbb{K}. The normalizers of the even orthogonal and symplectic subgroup of SL(2n, \mathbbK\mathbb{K}) were computed in [Širola B., Normalizers and self-normalizing subgroups, Glas. Mat. Ser. III (in press)], leaving the proof in the odd orthogonal case to be completed here. Also, for G = GL(m, \mathbbK\mathbb{K}) and G ₁ = O(m, \mathbbK\mathbb{K}) we have N ≅ G ₁ ⋊ \mathbbK\mathbb{K} ^×. In both of these cases, N is a self-normalizing subgroup of G.     

Compactification with Respect to a Generalized-net Convergence on Constructs

We introduce and deal with a convergence on (objects of) constructs which is expressed in terms of generalized nets. The generalized nets used are obtained from the usual nets by replacing the construct of directed sets and cofinal maps by an arbitrary construct. Convergence separation and convergence compactness are then introduced in a natural way. We study the convergence compactness and compactification and show that they behave in much the same way as the compactness and compactification of topological spaces.     

Experimental investigation of integral and local flow field properties on rotating porous disc

Flow field through rotating porous disc was investigated with experimental fluid dynamics and compared with computational fluid dynamics. Open cell aluminum metal foam with 88% porosity was used. On rotating porous disc, integral measurements of static pressure difference in dependence of air volume flow rate were performed. Local measurements of velocity profiles close to disc circumference were performed with hot-wire anemometry. The airflow visualization method using smoke generator and digital camera was performed. Flow structures through porous disc were visualized at three different air volume flow rates. Numerical simulation of homogenous rotating porous disc was performed. Experimental and numerical results were compared. The results showed appropriate comparison of integral and local properties. The presented experimental approach can be used for the investigation and understanding of flow field phenomena on rotating porous materials. The proposed conclusions can be applied for variable applications on rotating porous materials.     

Peculiarities of TiH<Subscript>2</Subscript> decomposition

The eventual competition between the dehydrogenation and oxidation of TiH₂ powder in the argon, oxygen, and static air atmospheres has been examined in the regime of linear heating using differential thermal analysis (DTA), X-ray diffraction, transmission and scanning electron microscopy coupled to energy dispersive spectroscopy techniques. Three stages of dehydrogenation, R1, R2, and R3, and two different oxidation reactions, O1 and O2, have been identified. The kinetics of individual reactions has been investigated by the Kissinger and Suriñach curve fitting procedures. While the kinetics of O1, O2, and R1 reactions depends on the diffusivities of the external reagent gas, being oxygen, and internal product gas, being hydrogen, the main dehydrogenation stage R2 is controlled by the combined nucleation-and-growth and coalescence kinetics. The effect of pre-annealing of TiH₂ on its subsequent degradation has also been studied. Due to the huge overheating accompanying both oxidation reactions in the DTA set-up, substantial thermal losses have been demonstrated and the method to obtain the true heat of oxidation reactions in metals has been described.     

Recombinant Single-Chain Antibody with the Trojan Peptide Penetratin Positioned in the Linker Region Enables Cargo Transfer Across the Blood–Brain Barrier

Delivery of therapeutic proteins into tissues and across the blood–brain barrier (BBB) is limited by the size and biochemical properties of the proteins. Efficient delivery across BBB is generally restricted to small, highly lipophilic molecules. However, in the last decades, several peptides that can pass cell membranes have been identified. It has been shown that these peptides are also capable of delivering large hydrophilic cargoes into cells and are therefore a powerful biological tool for transporting drugs across cell membranes and even into the brain. We designed and prepared a single-chain antibody fragment (scFvs), specific for the pathological form of the prion protein (PrP^Sc), where a cell-penetrating peptide (CPP) was used as a linker between the two variable domains of the scFv. The intravenously administered recombinant scFv-CPP was successfully targeted to and delivered into mouse brain cells. Our single-chain antibody fragments are of special interest in view of possible therapeutic reagents design not only for prion diseases but also for other neurodegenerative diseases.     

Design,synthesis and activity evaluation of mannose-based DC-SIGN antagonists

In this article, we describe the design, synthesis and activity evaluation of glycomimetic DC-SIGN antagonists, that use a mannose residue to anchor to the protein carbohydrate recognition domain (CRD). The molecules were designed from the structure of the known pseudo-mannobioside antagonist 1, by including additional hydrophobic groups, which were expected to engage lipophilic areas of DC-SIGN CRD. The results demonstrate that the synthesized compounds potently inhibit DC-SIGN-mediated adhesion to mannan coated plates. Additionally, in silico docking studies were performed to rationalize the results and to suggest further optimization.     

Influence of deposition temperature on amorphous structure of PECVD deposited a-Si:H thin films

The effect of deposition temperature on the structural and optical properties of amorphous hydrogenated silicon (a-Si:H) thin films deposited by plasma-enhanced chemical vapour deposition (PECVD) from silane diluted with hydrogen was under study. The series of thin films deposited at the deposition temperatures of 50–200°C were inspected by XRD, Raman spectroscopy and UV Vis spectrophotometry. All samples were found to be amorphous with no presence of the crystalline phase. Ordered silicon hydride regions were proved by XRD. Raman measurement analysis substantiated the results received from XRD showing that with increasing deposition temperature silicon-silicon bond-angle fluctuation decreases. The optical characterization based on transmittance spectra in the visible region presented that the refractive index exhibits upward trend with increasing deposition temperature, which can be caused by the densification of the amorphous network. We found out that the scale factor of the Tauc plot increases with the deposition temperature. This behaviour can be attributed to the increasing ordering of silicon hydride regions. The Tauc band gap energy, the iso-absorption value their difference were not particularly influenced by the deposition temperature. Improvements of the microstructure of the Si amorphous network have been deduced from the analysis.     

Logarithmic Finite-Size Correction in Non-neutral Two-Component Plasma on Sphere

We consider a general two-component plasma of classical pointlike charges \(+e\) (e is say the elementary charge) and \(-Z e\) (valency \(Z=1,2,\ldots \)), living on the surface of a sphere of radius R. The system is in thermal equilibrium at the inverse temperature \(\beta \), in the stability region against collapse of oppositely charged particle pairs \(\beta e^2 < 2/Z\). We study the effect of the system excess charge Qe on the finite-size expansion of the (dimensionless) grand potential \(\beta \varOmega \). By combining the stereographic projection of the sphere onto an infinite plane, the linear response theory and the planar results for the second moments of the species density correlation functions we show that for any \(\beta e^2 < 2/Z\) the large-R expansion of the grand potential is of the form \(\beta \varOmega \sim A_V R^2 + \left[ \chi /6 - \beta (Qe)^2/2\right] \ln R\), where \(A_V\) is the non-universal coefficient of the volume (bulk) part and the Euler number of the sphere \(\chi =2\). The same formula, containing also a non-universal surface term proportional to R, was obtained previously for the disc domain (\(\chi =1\)), in the case of the symmetric \((Z=1)\) two-component plasma at the collapse point \(\beta e^2=2\) and the jellium model \((Z\rightarrow 0)\) of identical e-charges in a fixed neutralizing background charge density at any coupling \(\beta e^2\) being an even integer. Our result thus indicates that the prefactor to the logarithmic finite-size expansion does not depend on the composition of the Coulomb fluid and its non-universal part \(-\beta (Qe)^2/2\) is independent of the geometry of the confining domain.     

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.