Subgraphs with Restricted Degrees of Their Vertices in Planar 3-Connected Graphs

We have proved that every 3-connected planar graph G either contains a path on k vertices each of which has degree at most 5k or does not contain any path on k vertices; the bound 5k is the best possible. Moreover, for every connected planar graph H other than a path and for every integer m ≥ 3 there is a 3-connected planar graph G such that each copy of H in G contains a vertex of degree at least m.     

Improved synthesis of arachno-6,9-C2B8H14 and its halogenation under electrophilic conditions

A convenient synthesis of arachno-6,9-C₂B₈H₁₄, based on the reduction of nido-5,6-C₂B₈H₁₂ with sodium tetrahydroborate, is reported. Electrophilic halogenation of the former carborane produced a series of 1-X-6,9-C₂B₈H₁₃ (X = Cl, Br and I) derivatives whose constitution was established on the basis of their ¹H and ¹¹B NMR spectra.     

Spectroscopic evidence of polymorphism in vitreous B2O3

Brillouin and Raman spectroscopy were performed on B2O3 glass compressed to 57 GPa at 273 K. Upon compression the sound velocities increase smoothly and the boroxol ring Raman mode vanishes by 11 GPa. Upon decompression the sound velocities follow a different path and at 3 GPa a discontinuity of 3 km/s in V(p) and 2 km/s in V(s) returns the velocities to the values seen on compression. After the transition, the boroxol ring Raman mode reappears. A second pressure cycle produces the same behavior, suggesting the 3 GPa transition occurs between vitreous polymorphs with different boron coordination.     

Are J(Si-H) NMR coupling constants really a probe for the existence of nonclassical H-Si interactions?

A series of hydridosilyl complexes of tantalum, Cp(ArN)Ta(PMe3)(H)(SiClnR3-n) (n = 0-3), was prepared and studied by 29Si NMR, X-ray diffraction, and DFT calculations. An unprecedented increase of the J(Si-H) coupling constant between the hydride and silyl ligands from 14 Hz for n = 0 to 50 Hz n = 3 was observed, which however, according to DFT calculations, does not correspond to stronger bonding interaction between silicon and hydride ligands, with the strongest interaction being for n = 1.     

Linear resolvent growth test for similarity of a weak contraction to a normal operator

It is proved in Benamara-Nikolski [1] that if the spectrum σ(T) of a contractionT with finite defects (rank(I−T ^* T)=rank (I−TT ^*)<∞) does not coincide with , then the contraction is similar to a normal operator if and only if

Solar-blind MSM-photodetectors based on Al<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ga<Subscript>1-<Emphasis Type="Italic">x</Emphasis></Subscript>N heterostructures

Solar-blind MSM photodetectors based on the AlGaN heterostructures have been fabricated and investigated. The influence of material properties on device parameters is discussed. Effect of different buffer layers on the detector performances has been examined. Detectors exhibit low dark currents and high sensitivity within the range of 250–290 nm. Effect of optical excitation energy on GaN-based MSM-detector performance is analyzed and discussed. At high excitation level the detector speed of response is limited by the field screening caused by the space-charge of the holes. The impulse response of GaN-based MSM-detector is compared favorably with GaAs MSM-device.     

A study of Ga layers on Si(1 0 0)-(2 × 1) by SR-PES: Influence of adsorbed water

Results for deposition and thermal annealing of gallium on the Si(1 0 0)-(2 × 1) surface achieved by synchrotron radiation photoelectron spectroscopy (SR-PES) and low energy electron diffraction (LEED) are presented. In addition to deposition of Ga on a clean surface, the influence of water adsorption on the arrangement of gallium atoms was also studied. The results on Ga deposition at a higher temperature (490 °C) are consistent with a Ga ad-dimer model showing equivalent bond arrangement of all Ga atoms for coverages up to 0.5 ML. The deposition onto a surface with adsorbed water at room temperature led to a disordered gallium growth. In this case gallium atoms bind to silicon dimers already binding fragments of adsorbed water. A subsequent annealing of these layers leads to a surface structure similar to the Ga-(2 × 2), however, it is less ordered, probably due to the presence of silicon oxides formed from water fragments.