Dissecting a brick into bars

Consider the set of all lengths of sides of an N-dimensional parallelepiped. If this set has no more than k elements, the parallelepiped will be called a bar (the definition of a bar depends on k). We prove that a parallelepiped can be dissected into a finite number of bars if and only if the lengths of its sides span a linear space of dimension at most k over \mathbb Q{{\mathbb Q}} . This extends and generalizes a well-known theorem of Max Dehn about the splitting of rectangles into squares. Several other results about dissections of parallelepipeds are obtained.     

Synthesis and Photophysical Properties of Alkoxysilyl Derivatives of Dibenzoylmethanatoboron Difluoride

Alkoxysilyl derivatives of dibenzoylmethanatoboron difluoride (DBMBF₂) are synthesized by the hydrosilylation reaction of the corresponding O‐allyl derivatives of DBMBF₂ with triethoxysilane. The photophysical properties of the synthesized O‐allyl and alkoxysilyl derivatives are investigated. It is found that the absorption and fluorescence spectra of the DBMBF₂ derivatives essentially depend on the position of the O‐allyl or O‐propyl alkoxysilyl substituent. The highest fluorescence quantum yield is obtained for the para‐position, whereas the substitution at the meta‐position gives the largest bathochromic shift in the fluorescence spectrum. Density functional theory calculations of the structures and time‐dependent density functional theory calculations of the gas‐phase excitation and emission energies of alkoxysilyl derivatives are performed at the PBE0/SVP level of theory. Some spectral features of para‐, ortho‐, and meta‐substituted derivatives can be adequately explained by the overlapping of two absorption bands.     

Magnetic resonance imaging of mouse Ehrlich carcinoma growth inhibition by thiacarpine, an analogue of cytotoxic marine alkaloid polycarpine

The anticancer effect of thiacarpine, a synthetic analogue of the known cytotoxic alkaloid polycarpine isolated from the Pacific ascidian Polycarpa aurata, was investigated in vivo in experiments using mouse solid Ehrlich carcinoma tumor as the target. A high-resolution magnetic resonance imaging (MRI) technique using a MR tomograph "PharmaScan" US70/16 (Bruker, Ettlingen, Germany) was used for visualization and quantification of tumor size. Fluorescence microscopy and image analysis were applied to determine Ehrlich carcinoma cell chromatin condensing (apoptosis) and necrosis in Ehrlich carcinoma cells at the action of thiacarpine in in vitro experiments. The scan and size calculations of the tumor and some mouse organs were carried out during the experiments. Thiacarpine in a total dose of 100 mg/kg was found to exhibit the delay in growth of the mouse tumor. The antineoplastic effect of this compound was accompanied by an increase in the lifetime of experimental mice in comparison with the control group of animals. Our data show that the ability of thiacarpine to induce apoptosis in carcinoma cells may contribute to thiacarpine anticancer effects against mice solid Ehrlich carcinoma in vivo detected by MRI.     

Effect of Parameters of Pulse Electrolysis on Electrodeposition of Copper–Tin Alloy from Sulfate Electrolyte

Russian Journal of Electrochemistry - The effect of pulsed electrolysis on the electrodeposition of Cu–Sn alloy from the sulfate–sulfuric acid electrolyte is studied. It is shown that...     

Numerical Study of the Influence of Anisotropy of Physicomechanical Properties on the Impact Fracture of Orthotropic Composites

Russian Physics Journal - The influence of orientation of elastic and strength properties of an orthotropic organoplastic on the behavior of the material upon dynamic loading is considered. The...     

Tandem rearrangements of a cyclic bis-allene

Reaction of the bis-dibromocarbene adduct of cyclonona-1,4,7-triene with methyllithium leads to a mixture of meso and racemic cycloundeca-1,2,5,6,9-pentaenes; the former rearranges at ambient temperature through a set of pericyclic reactions.     

Utilization of (p, 4n) reaction for <Superscript>86</Superscript>Zr production with medium energy protons and development of a <Superscript>86</Superscript>Zr → <Superscript>86</Superscript>Y radionuclide generator

Utilization of (p, 4n) reaction channel for the production of medical radionuclides became very attractive with commercial availability of medium energy cyclotrons. Significantly higher yields and radionuclidic purity may open new perspectives for several novel and some of the radionuclides previously have not been considered due to production difficulties. In present work, we show the proof-of-principle study on the production of ⁸⁶Y for Positron Emission Tomography imaging via radionuclide generator ⁸⁶Zr → ⁸⁶Y. Production suitability of ⁸⁶Zr from natural yttrium target and radiochemical separation strategies were tested. In addition, two generator systems were proposed and evaluated.     

Colloidal dynamics: influence of diffusion, inertia and colloidal forces on cluster formation

Computer simulations of colloidal suspensions are discussed. The simulations are based on the Langevin equations, pairwise interaction between colloidal particles and take into account Brownian, hydrodynamic and colloidal forces. Comparison of two models, one taking into account inertial term in Langevin equation and another based on diffusional approximation proposed in [D.L. Ermak, J.A. McCammon, J. Chem. Phys. 69 (1978) 1352], has shown that both models enable the prediction of the correct values of the diffusion coefficient and residence time of particle in a doublet and are therefore suitable to study the dynamics of formation and breakage of clusters in colloidal suspensions. It is shown that the appropriate selection of the time step and taking into account inertia of particles provides also the correct value of the average kinetic energy of each particle during the simulations, what allows to use the model based on full Langevin equations as a reference model to verify the validity of the numerical scheme for simulation using diffusion approximation.     

Delivering Structural Information on the Polar Face of Membrane‐Active Peptides: 19F‐NMR Labels with a Cationic Side Chain

Conformationally constrained non‐racemizing trifluoromethyl‐substituted lysine isosteres [(E)‐ and (Z)‐TCBLys] with charged side chains are presented as a new type of ¹⁹F‐NMR labels for peptide studies. Design of the labels, their synthesis, incorporation into peptides and experimental demonstration of their application for solid state NMR studies of membrane‐active peptides are described. A series of fluorine‐labeled analogues of the helical amphipathic antimicrobial peptide PGLa(Nle) was obtained, in which different lysine residues in the original peptide sequence were replaced, one at a time, by either (E)‐ or (Z)‐TCBLys. Antimicrobial activities of the synthesized analogues were practically the same as those of the parent peptide. The structural and orientational parameters of the helical PGLa(Nle) peptide in model bilayers, as determined using the novel labels confirmed and refined the previously known structure. (E)‐ and (Z)‐TCBLys, as a set of cationic ¹⁹F‐NMR labels, were shown to deliver structural information about the charged face of amphipathic peptides by solid state ¹⁹F‐NMR, previously inaccessible by this method.