The new HMQC-based technique for the quantitative determination of heteronuclear coupling constants. Application for the measurement of 3J(H'(i),P(i+1)) in DNA oligomers

A new general J-HMQC-based technique is presented, which allows an accurate determination of heteronuclear coupling constants. The most important feature of this new approach includes acquisition of the two data sets with and without the additional pi(S)-pulse at the end of coupling evolution period. This enables preservation and separation of the two orthogonal terms of coupling evolution, which are manifested by in- and antiphase cross-peaks, respectively. The coupling magnitudes are evaluated by the nonlinear least-squares fitting of the ratios of integrated signal volumes for both kinds of signals. The effectiveness of the new sequence is demonstrated by determination of the 3J(H3'(i),P(i+1)) couplings in DNA octamer duplex d(GCGTACGC)(2) sample. Additionally, the ability of the new method for the measurement at the natural abundance level of 13C nuclei is presented for the beta-cyclodextrin.     

The Bolzano mean-value theorem and partial differential equations

We study the existence of solutions to abstract equations of the form $0=Au+F(u)$, $u\in K?E$, where A is an abstract differential operator acting in a Banach space E, K is a closed convex set of constraints being invariant with respect to resolvents of A and a perturbation F satisfies a certain tangency condition. Such problems are closely related to the so-called Poincaré–Miranda theorem, being the multi-dimensional counterpart of the celebrated Bolzano intermediate value theorem. In fact our main results should be regarded as infinite-dimensional variants of Bolzano and Miranda–Poincaré theorems. Along with single-valued problems we deal with set-valued ones, yielding the existence of the so-called constrained equilibria of set-valued maps. The abstract results are applied to show existence of (strong) steady state solutions to some weakly coupled systems of drift reaction–diffusion equations or differential inclusions of this type. In particular we get the existence of strong solutions to the Dirichlet, Neumann and periodic boundary problems for elliptic partial differential inclusions under the presence of state constraints of different type. Certain aspects of the Bernstein theory for bvp for second order ODE are studied, too. No assumptions concerning structural coupling (monotonicity, cooperativity) are undertaken.     

On uniformly bounded spherical functions in Hilbert space

Let G be a commutative group, written additively, with a neutral element 0, and let K be a finite group. Suppose that K acts on G via group automorphisms ${G \ni a \mapsto ka \in G}$ , ${k \in K}$ . Let ${{\mathfrak{H}}}$ be a complex Hilbert space and let ${{\mathcal L}({\mathfrak{H}})}$ be the algebra of all bounded linear operators on ${{\mathfrak{H}}}$ . A mapping ${u \colon G \to {\mathcal L}({\mathfrak{H}})}$ is termed a K-spherical function if it satisfies (1) ${|K|^{-1} \sum_{k\in K} u (a+kb)=u (a) u (b)}$ for any ${a,b\in G}$ , where |K| denotes the cardinality of K, and (2) ${u (0) = {\rm id}_{\mathfrak {H}},}$ where ${{\rm id}_{\mathfrak {H}}}$ designates the identity operator on ${{\mathfrak{H}}}$ . The main result of the paper is that for each K-spherical function ${u \colon G \to {\mathcal {L}}({\mathfrak {H}})}$ such that ${\| u \|_{\infty} = \sup_{a\in G} \| u (a)\|_{{\mathcal L}({\mathfrak{H}})} < \infty,}$ there is an invertible operator S in ${{\mathcal L}({\mathfrak{H}})}$ with ${\| S \| \, \| S^{-1}\| \leq |K| \, \| u \|_{\infty}^2}$ such that the K-spherical function ${{\tilde{u}} \colon G \to {\mathcal L}({\mathfrak{H}})}$ defined by ${{\tilde{u}}(a) = S u (a) S^{-1},\,a \in G,}$ satisfies ${{\tilde{u}}(-a) = {\tilde{u}}(a)^*}$ for each ${a \in G}$ . It is shown that this last condition is equivalent to insisting that ${{\tilde{u}}(a)}$ be normal for each ${a \in G}$ .     

In–Ga–Zn–O MESFET with transparent amorphous Ru–Si–O Schottky barrier

Rectifying transparent amorphous Ru–Si–O Schottky contacts to In–Ga–Zn–O have been fabricated by means of reactive sputtering without any annealing processes nor semiconductor surface treatments. The ideality factor, effective Schottky barrier height and rectification ratio are equal to 1.6, 0.9 eV and 10⁵ A/A, respectively. Ru–Si–O/In–Ga–Zn–O Schottky barriers were employed as gate electrodes for In–Ga–Zn–O metal–semiconductor field‐effect transistors (MESFETs). MESFET devices exhibiting on‐to‐off current ratio at the level of 10³ A/A in a voltage range of 2 V, with subthreshold swing equal to 420 mV/dec were demonstrated. A channel mobility of 7.36 cm²/V s was achieved. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Possibilities of Practical Use of Historical Distributions of Ash,Sulfur and Mercury Contents in Commercial Steam Coal of the USCB

In the process of extracting hard coal, extensive databases are created on its quality parameters. A statistical assessment was made of the ash, sulfur, and mercury content of commercial coals produced in the Upper Silesian Coal Basin (USCB). The statistical methods applied: non-parametric tests of compatibility for two populations, parametric significance tests, and non-parametric tests of compatibility for the three populations, showed that the distributions of ash and sulfur content in 2014 and 2015 are comparable and the average values are similar. Statistical tests indicated significant differences in the mercury content distributions and their variances. This demonstrates the need for ongoing monitoring of mercury content in commercial coals, as a prediction of mercury content from historical data is hardly possible.     

The semi-classical hopping model of the electrical conductivity of semiconductors

A model of localized carriers moving in a hopping manner from one crystallographic point to a neighbouring one is the starting point for the model presented here for the electrical conductivity in semiconductors. An effort is made to link this hopping type of motion of carriers with their mean uniform motion in the crystal. With an assumed shape for the potential barrier for a single hop of a carrier, the model permits the calculation of the effective mass, the mobility of a carrier with energy E, the mean mobility of all carriers in the band, and the electrical conductivity as a function of temperature, T. The model is presented and exemplified by a one-dimensional system.     

Structures and potential superconductivity in at high pressure: en route to "metallic hydrogen"

A way to circumvent the high pressures needed to metallize hydrogen is to "precompress" it in hydrogen-rich molecules, a strategy probed theoretically for silane. We show that phases with tetrahedral SiH4 molecules should undergo phase transitions with sixfold- and eightfold-coordinate Si appearing above 25 GPa. The most stable structure found can be metallized at under a megabar and at a compression close to the prediction of Goldhammer-Herzfeld criterion. According to a BCS-like estimate, metallic silane should be a high-temperature superconductor.     

SEM and TEM analysis of composite of ZrO2-Ti system

3Y-ZrO₂-Ti composites obtained by slip casting method were studied by means of X-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Moreover, the Vickers hardness was measured. The experiments show the complex microstructure of composites. The tetragonal zirconium dioxide (t-ZrO₂) and monoclinic zirconium dioxide (m-ZrO₂) as a composite matrix were detected at XRD analysis. SEM observations revealed that Ti -rich phase are uniform distributed in composites. Moreover, the large and very fine precipitations were found. The very fine Ti rich precipitations were located at ZrO₂ grain boundaries as well as in the triple-points. TEM experiments confirmed that in the sintered composites 3Y-ZrO₂ – 10%Ti the uniaxial ZrO₂ grains (100–600 nm), fine monoclinic martensitic plates and fine round monoclinic particles (20–40 nm) of ZrTiO₂ phase were exist. The complex microstructures of 3Y-ZrO₂-Ti composites have a high hardness as a result of existing fine ZrTiO₂ and other Ti oxides precipitations.     

Towards a metallic quasi‐d9 system without copper: AgO at high pressure

AgO is a prototypical mixed‐valence compound, with markedly different coordination environment of dumbbell Ag(1+) and low‐spin square‐planar Ag(3+) which render it a narrow band gap semiconductor. The hybrid HSE06 functional reproduces fairly well the band gap of its P 2₁/c form at ambient conditions (ΔE_exp = 1.0–1.1 eV, ΔE_theor = 0.94 eV) and suggest progressive band gap decrease with external pressure with metallization at 50 GPa via band overlap. Dynamic (phonon) instability appears at the onset of metallization leading to a structural phase transition to a more stable but still metallic $$P\stackrel{?}{1}$$ form. The density of electronic states at the Fermi level of the $$P\stackrel{?}{1}$$ polymorph is small and a pseudo‐gap at the Fermi level is preserved.

Illustration of the predicted P2₁/c → $$P\stackrel{?}{1}$$ transformation.     

Finite size effects in epidemic spreading: the problem of overpopulated systems

In this paper we analyze the impact of network size on the dynamics of epidemic spreading. In particular, we investigate the pace of infection in overpopulated systems. In order to do that, we design a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step, which can serve as a model for sexually transmitted diseases spreading in some student communes. Because of the highly discrete character of the process, the analysis cannot use the continuous approximation widely exploited for most models. Using a discrete approach, we investigate the epidemic threshold and the quasi-stationary distribution. The main results are two theorems about the mixing time for the process: it scales like the logarithm of the network size and it is proportional to the inverse of the distance from the epidemic threshold.