Frobenius properties and Maschke-type theorems for entwined modules

Entwined modules arose from the coalgebra-Galois theory. They are a generalisation of unified Doi-Hopf modules. In this paper, Frobenius properties and Maschke-type theorems known for Doi-Hopf modules are extended to the case of entwined modules.

     

Reaction of some strong N-bases with chloropentafluorobenzene in the presence of water molecules

Products of reactions between chloropentafluorobenzene and strong N-bases (DBN, DBU, TBD, and MTBD) in polar aprotic solvents and in the presence of water were isolated and identified by analytical and spectroscopic methods. The products of these dehydrohalogenation reactions are apropriate lactams, and if the TBD N-base is used, a condensation occurs with formation of benzimidazole derivative. All the products are not formed directly in the nucleophilic substitution by N-bases but after the hydrolyses of the N-bases with formation of amines known as hard nucleophiles.     

Volume estimates for sections of certain convex bodies

This paper deals with volume estimates for hyperplane sections of the simplex and for m‐codimensional sections of powers of m‐dimensional Euclidean balls. In the first part we consider sections through the centroid of the n‐dimensional regular simplex. We state a volume formula and give a lower bound for the volume of sections through the centroid. In the second part we study the extremal volumes of m‐codimensional sections “perpendicular” to of unit balls in the space for all . We give volume formulas and use them to show that the normal vector (1, 0, …, 0) yields the minimal volume. Furthermore we give an upper bound for the ‐dimensional volumes for natural numbers . This bound is asymptotically attained for the normal vector as .     

Design,Sustainable Synthesis and Biological Evaluation of a Novel Dual α2A/5-HT7 Receptor Antagonist with Antidepressant-Like Properties

The complex pathophysiology of depression, together with the limits of currently available antidepressants, has resulted in the continuous quest for alternative therapeutic strategies. Numerous findings suggest that pharmacological blockade of α₂-adrenoceptor might be beneficial for the treatment of depressive symptoms by increasing both norepinephrine and serotonin levels in certain brain areas. Moreover, the antidepressant properties of 5-HT₇ receptor antagonists have been widely demonstrated in a large set of animal models. Considering the potential therapeutic advantages in targeting both α₂-adrenoceptors and 5-HT₇ receptors, we designed a small series of arylsulfonamide derivatives of (dihydrobenzofuranoxy)ethyl piperidines as dually active ligands. Following green chemistry principles, the designed compounds were synthesized entirely using a sustainable mechanochemical approach. The identified compound 8 behaved as a potent α_2A/5-HT₇ receptor antagonist and displayed moderate-to-high selectivity over α₁-adrenoceptor subtypes and selected serotonin and dopaminergic receptors. Finally, compound 8 improved performance of mice in the forced swim test, displaying similar potency to the reference drug mirtazapine.     

Sensitivity considerations in polarization transfer and filtering using dipole-dipole couplings: implications for biomineral systems

The robustness and sensitivities of different polarization-transfer methods that exploit heteronuclear dipole-dipole couplings are compared for a series of heterogeneous solid systems, including polycrystalline tetrakis(trimethylsilyl)silane (TKS), adamantane, a physical mixture of doubly (13)C,(15)N-enriched and singly (13)C-enriched polycrystalline glycine, and a powder sample of siliceous marine diatoms, Thalossiosira pseudonana. The methods were analyzed according to their respective frequency-matching spectra or resultant signal intensities. For a series of (13)C{(1)H} cross-polarization experiments, adiabatic passage Hartmann-Hahn cross-polarization (APHH-CP) was shown to have several advantages over other methods, including Hartmann-Hahn cross-polarization (HHCP), variable-amplitude cross-polarization (VACP), and ramped-amplitude cross-polarization (RACP). For X-Y systems, such as (13)C{(15)N}, high and comparable sensitivities were obtained by using APHH-CP with Lee-Goldburg decoupling or by using the transferred-echo double resonance (TEDOR) experiment. The findings were applied to multinuclear (1)H, (13)C, (15)N, and (29)Si CP MAS characterization of a powder diatom sample, a challenging inorganic-organic hybrid solid that places high demands on NMR signal sensitivity.     

Predictive tracking of an object by a pan–tilt camera of a robot

Nonlinear Dynamics - Moving-object tracking using a pan–tilt camera setup is quite a well-known task in robotics. However, the presented research addresses specific properties of the tracked...