On disjoint matchings in cubic graphs

For $i=2,3$ and a cubic graph $G$ let ${\nu }_i\left(G\right)$ denote the maximum number of edges that can be covered by $i$ matchings. We show that ${\nu }_2\left(G\right)\ge \frac{4}{5}\left|V\left(G\right)\right|$ and ${\nu }_3\left(G\right)\ge \frac{7}{6}\left|V\left(G\right)\right|$. Moreover, it turns out that ${\nu }_2\left(G\right)\le \frac{\left|V\left(G\right)\right|+2{\nu }_3\left(G\right)}{4}$.     

High-precision X-ray diffractometer on the base of acoustic monochromator

A new scheme for X-ray difractometer based on acoustic monochromator has been developed and created. The advantages of the new diffractometer are high-level of X-ray monochromaticity, high intensity of diffracted waves, high density of energy flow, and the absence of background.     

Entropy and the Shannon-McMillan-Breiman Theorem for Beta Random Matrix Ensembles

We show that beta ensembles in Random Matrix Theory with generic real analytic potential have the asymptotic equipartition property. In addition, we prove a Central Limit Theorem for the density of the eigenvalues of these ensembles.     

The dual nature of the transverse vibrations of an elastic rod

The transverse vibrations of an elastic rod, to one of which displacements are applied while the other end is free, are investigated. It is assumed that the propagation velocity of the perturbations in the rod is finite. The unperturbed part performed rotational motion around the centre line. The angle of rotation is expressed by the angle of curvature of the centre line of the perturbed part of the rod. Two types of elastic vibrations are obtained: (1) the rod vibrates elastically due to displacements applied at the end, and (2) when performing rotational motion elastic vibrations and additional forces occur in the rod due to elasticity [1].     

Four-Step Spin Crossover in a New Cyano-Bridged Iron-Silver Coordination Polymer

Spin-crossover complexes with multistep transitions attract much attention due to their potential applications as multi-switches and for data storage. A four-step spin crossover is observed in the new iron(II)-based cyanometallic guest-free framework compound Fe(2-ethoxypyrazine)₂{Ag(CN)₂}₂ during the transition from the low-spin to the high-spin state. A reverse process occurs in three steps. Crystallographic studies reveal an associated stepwise evolution of the crystal structures. Multiple transitions in the reported complex originate from distinct Fe^II sites which exist due to the packing of the ligand with a bulky substituent.     

Study of Features of the Diffraction of X Rays in a Quartz Crystal Modulated by Longitudinal and Transverse Ultrasonic Vibrations

JETP Letters - Features of the simultaneous action of longitudinal and transverse ultrasonic vibrations in the quartz crystal on the parameters of reflected X-rays are studied. It is shown that...     

Highly Emissive Self‐Trapped Excitons in Fully Inorganic Zero‐Dimensional Tin Halides

The spatial localization of charge carriers to promote the formation of bound excitons and concomitantly enhance radiative recombination has long been a goal for luminescent semiconductors. Zero‐dimensional materials structurally impose carrier localization and result in the formation of localized Frenkel excitons. Now the fully inorganic, perovskite‐derived zero‐dimensional Sn^II material Cs₄SnBr₆ is presented that exhibits room‐temperature broad‐band photoluminescence centered at 540 nm with a quantum yield (QY) of 15±5 %. A series of analogous compositions following the general formula Cs_4?xA_xSn(Br_1?yI_y)₆ (A=Rb, K; x≤1, y≤1) can be prepared. The emission of these materials ranges from 500 nm to 620 nm with the possibility to compositionally tune the Stokes shift and the self‐trapped exciton emission bands.     

Synthesis of 3,4-benzo-7-hydroxy-2,9-diazabicyclo[3.3.1]non-7-enes by cyclization of 1,3-bis(silyl enol ethers) with quinazolines

A variety of functionalized 3,4-benzo-7-hydroxy-2,9-diazabicyclo[3.3.1]non-7-enes were prepared by one-pot cyclizations of 1,3-bis(silyl enol ethers) with quinazolines. The mechanism of the cyclization was studied by B3LYP/6-31G(d) density functional theory computations. The products could be functionalized by Suzuki cross-coupling reactions. The reaction of 1,3-bis(silyl enol ethers) with phthalazine afforded open-chain rather than cyclization products.