A vanadyl Schiff base complex: {2,2′‐[1,1′‐(o‐phenylenedinitrilo)bis(ethan‐1‐yl‐1‐ylidene)]diphenolato}oxovanadium(IV)

The green crystals of the title compound, [V(C₂₂H₁₈N₂O₂)O], represent a mononuclear oxovanadium complex. The central V^IV centre has a distorted square‐pyramidal coordination. Two N atoms and two O atoms of the Schiff base ligand define the base of the pyramid, and the oxide O atom is in the apical position. Density functional theory (DFT) calculations were performed to analyse the changes in the geometry of the ligand during the complex formation. The most significant changes are observed in the values of the torsion angles in the vicinity of the donor N atoms. The HOMA index (Harmonic Oscillator Model of Aromaticity) has been calculated to compare the aromaticity of the benzene rings in the complex and its ligand.     

An instrumented vehicle for offroad dynamics testing

The paper presents an instrumented vehicle that was equipped with measuring systems to perform complete dynamics tests, especially in off-road conditions. The equipment consists of four wheel dynamometers, a steering robot, and a differential GPS system together with an inertial platform, a non-contact vehicle speed sensor, and an on-board computer with software to control the devices and collect experimental data. The four wheel dynamometers measure six elements; based on strain gage force transducers, it measures three orthogonal forces and three moments. The steering robot can control the steering wheel of the vehicle at a variety of excitation modes; it can carry out typical vehicle dynamics tests (ISO 7401, ISO 4138, ISO/TR3888, etc.) as well as custom engineered tests at a wide range of setting parameters (steer angle rate up to 1600 deg/s). The differential GPS system gives true time vehicle kinematics data (velocities, accelerations, angles, etc.) at 10-ns sample rate and 20-mm accuracy. The base vehicle, a Suzuki Vitara 4 × 4, required no special modifications or changes to install the measuring equipment. The paper also describes typical tests performed with the use of the instrumented vehicle together with sample results.     

Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs

General upper tail estimates are given for counting edges in a random induced subhypergraph of a fixed hypergraph ℋ, with an easy proof by estimating the moments. As an application we consider the numbers of arithmetic progressions and Schur triples in random subsets of integers. In the second part of the paper we return to the subgraph counts in random graphs and provide upper tail estimates in the rooted case.     

On typically real functions which are generated by a fixed typically real function

Let T be the family of all typically real functions, i.e. functions that are analytic in the unit disk Δ:= {z ∈ ℂ: |z| < 1}, normalized by f(0) = f′(0) − 1 = 0 and such that Imz Im f(z) ⩾ 0 for z ∈ Δ.     

Serre Problem for Unbounded Pseudoconvex Reinhardt Domains in ℂ<Superscript>2</Superscript>

We give a characterization of non-hyperbolic pseudoconvex Reinhardt domains in ℂ² for which the answer to the Serre problem is positive. Moreover, all non-hyperbolic pseudoconvex Reinhardt domains in ℂ² with non-compact automorphism group are explicitly described.     

K-subadditive and K-superadditive set-valued functions bounded on “large” sets

Aequationes mathematicae - We prove that every K–subadditive set–valued map weakly K–upper bounded on a “large” set (e.g.&nbsp;not null–finite, not...     

Comprehensive Characterisation of the Ketoprofen-β-Cyclodextrin Inclusion Complex Using X-ray Techniques and NMR Spectroscopy

Racemic ketoprofen (KP) and β-cyclodextrin (β-CD) powder samples from co-precipitation (1), evaporation (2), and heating-under-reflux (3) were analysed using X-ray techniques and nuclear magnetic resonance (NMR) spectroscopy. On the basis of NMR studies carried out in an aqueous solution, it was found that in the samples obtained by methods 1 and 2, there were large excesses of β-CD in relation to KP, 10 and 75 times, respectively, while the sample obtained by method 3 contained equimolar amounts of β-CD and KP. NMR results indicated that KP/β-CD inclusion complexes were formed and the estimated binding constants were approximately 2400 M⁻¹, showing that KP is quite strongly associated with β-CD. On the other hand, the X-ray single-crystal technique in the solid state revealed that the (S)-KP/β-CD inclusion complex with a stoichiometry of 2:2 was obtained as a result of heating-under-reflux, for which the crystal and molecular structure were examined. Among the methods used for the preparation of the KP/β-CD complex, only method 3 is suitable.     

1,3,5-Triazine Nitrogen Mustards with Different Peptide Group as Innovative Candidates for AChE and BACE1 Inhibitors

A series of new analogs of nitrogen mustards (4a–4h) containing the 1,3,5-triazine ring substituted with dipeptide residue were synthesized and evaluated for the inhibition of both acetylcholinesterase (AChE) and β-secretase (BACE1) enzymes. The AChE inhibitory activity studies were carried out using Ellman’s colorimetric method, and the BACE1 inhibitory activity studies were carried out using fluorescence resonance energy transfer (FRET). All compounds displayed considerable AChE and BACE1 inhibition. The most active against both AChE and BACE1 enzymes were compounds A and 4a, with an inhibitory concentration of AChE IC₅₀ = 0.051 µM; 0.055 µM and BACE1 IC₅₀ = 9.00 µM; 11.09 µM, respectively.     

Symmetry enforced gauge invariance of nuclear magnetic shielding constants

E.S.R. experiments performed at 1·3 K by optical detection are reported for the photo-excited triplet state of palladiumporphin in a single crystal of n-octane, and the observation of a level anticrossing signal is described.

In the crystal the orbital degeneracy of the ³ E _u state of the free molecule is lifted by the crystal field and in n-octane the energy difference between the two orbital components |x> and |y> is found to be 58 ± 2 cm^-1. The spinorbit coupling (SOC) and the orbital Zeeman interaction couple the triplet manifolds of |x> and |y>, and for a proper understanding of the magnetic properties of these states it is necessary to work in the basis of the six spin-orbit functions deriving from the ³ E _u state of the free molecule. It is shown that either of the two triplet states can be described by an effective spin hamiltonian of the common form and expressions for the zero-field parameters D and E and the principal values of the g tensor are given. The experimental values of the parameters in the lowest triplet state are D = -24·38 ± 0·03 GHz, |E| = 320 ± 60 MHz, g _‖ = 1·677 ± 0·001 and g _⊥ = 1·989 ± 0·002. The matrix element of the SOC connecting the |x> and |y> triplet manifolds amounts to qZ = 15 ± 3 cm^-1 and the vibronic orbital angular momentum (in units of ?) in the ³ E _u state of the free molecule to qΛ = 1·5 ± 0·3. A tentative value of 0·63 for the orbital reduction factor q is obtained by comparison with a theoretical estimate of Λ. The value of q is indicative of weak Jahn-Teller coupling.