Low frequency internal modes of 1,2,4,5-tetramethylbenzene, tetramethylpyrazine and tetramethyl-1,4-benzoquinone INS, Raman, infrared and theoretical DFT studies

The results of inelastic neutron scattering (INS), Raman and infrared (IR) studies on 1,2,4,5-tetramethylbenzene (durene), tetramethylpyrazine (TMP) and tetramethyl-1,4-benzoquinone (TMBQ) in the solid state are reported. The observed frequencies are analyzed on the basis of DFT calculations. The low frequency region, below 400 cm(-1), related to the torsional and bending out-of-plane vibrations of the CH(3) groups, is of particular interest. The detailed analysis is possible due to the simulation of the INS spectra by using the auntie-CLIMAX program. It is shown that the observed low frequency INS bands are dramatically shifted, compared to the calculated ones, towards higher frequencies. Although one cannot exclude deficiencies of theoretical methods as applied to low frequency modes, it seems more probable the interpretation based on an existence of non-conventional CH(...)pi, CH(...)N, CH(...)O hydrogen bonds formed by the methyl groups in crystalline phases.     

Hydride affinities of some substituted alkynes: prediction by DFT calculations and rationalization by triadic formula

Hydride affinities (HAs) of the ethynes substituted by a wide range of different substituents are considered by using the B3LYP methodology. The computed values are in fair agreement with available experimental data, which are unfortunately scarce. The trend of changes of the HAs is rationalized by trichotomy formula. One of the important results of this analysis is a finding that similar HA values might result from completely different effects. Alternative sites of the H- attack are examined and the difference in energies relative to the most susceptible positions is interpreted. Structural features of substituted ethyne hydrides are briefly discussed.     

Reactivity and biological activity of the marine sesquiterpene hydroquinone avarol and related compounds from sponges of the order Dictyoceratida

A review of results of bioactivity and reactivity examinations of marine sesquiterpene (hydro)quinones is presented. The article is focused mostly on friedo- rearranged drimane structural types, isolated from sponges of the order Dictyoceratida. Examples of structural correlations are outlined. Available results on the mechanism of redox processes and examinations of chemo- and regioselectivity in addition reactions are presented and, where possible, analyzed in relation to established bioactivities. Most of the bioactivity examinations are concerned with antitumor activities and the mechanism thereof, such as DNA damage, arylation of nucleophiles, tubulin assembly inhibition, protein kinase inhibition, inhibition of the arachidonic cascade, etc. Perspectives on marine drug development are discussed with respect to biotechnological methods and synthesis. Examples of the recognition of validated core structures and synthesis of structurally simplified compounds retaining modes of activity are analyzed.     

The unsaturated flow in porous media with dynamic capillary pressure

In this paper we consider a degenerate pseudoparabolic equation for the wetting saturation of an unsaturated two-phase flow in porous media with dynamic capillary pressure-saturation relationship where the relaxation parameter depends on the saturation. Following the approach given in [13] the existence of a weak solution is proved using Galerkin approximation and regularization techniques. A priori estimates needed for passing to the limit when the regularization parameter goes to zero are obtained by using appropriate test-functions, motivated by the fact that considered PDE allows a natural generalization of the classical Kullback entropy. Finally, a special care was given in obtaining an estimate of the mixed-derivative term by combining the information from the capillary pressure with the obtained a priori estimates on the saturation.     

On the scattering problem for infinitely many fermions in dimensions d ≥ 3 at positive temperature

In this paper, we study the dynamics of a system of infinitely many fermions in dimensions $d\ge 3$ near thermal equilibrium and prove scattering in the case of small perturbation around equilibrium in a certain generalized Sobolev space of density operators. This work is a continuation of our previous paper [11], and extends the important recent result of M. Lewin and J. Sabin in [19] of a similar type for dimension $d=2$. In the work at hand, we establish new, improved Strichartz estimates that allow us to control the case $d\ge 3$.     

Multi-set neighbor distinguishing 3-edge coloring

Let $G$ be a graph without isolated edges, and let $c:E\left(G\right)\to \{1,\dots ,k\}$ be a coloring of the edges, where adjacent edges may be colored the same. The color code of a vertex $v$ is the ordered $k$-tuple $(a_1,a_2,\dots ,a_k)$, where $a_i$ is the number of edges incident with $v$ that are colored $i$. If every two adjacent vertices of $G$ have different color codes, such a coloring is called multi-set neighbor distinguishing. In this paper, we prove that three colors are sufficient to produce a multi-set neighbor distinguishing edge coloring for every graph without isolated edges.     

A fixed point theorem of Jungck in $$b_v(s)$$-metric spaces

In this paper, we prove the common fixed point theorem of Jungck in \(b_v(s)\)-metric spaces. As a corollary, a common fixed point theorem in the rectangular b-metric space and the well known common fixed point theorem in b-metric spaces are obtained.     

On graded nil clean rings

In this paper we introduce and study the notion of a graded (strongly) nil clean ring which is group graded. We also deal with extensions of graded (strongly) nil clean rings to graded matrix rings and to graded group rings. The question of when nil cleanness of the component, which corresponds to the neutral element of a group, implies graded nil cleanness of the whole graded ring is examined. Similar question is discussed in the case of groupoid graded rings as well.     

New results on (b,c)–inverses

In this paper, we present some necessary and sufficient conditions for the existence of the (b, c)-inverse and several representations for the (b, c)-inverse related to the group inverse. Since Mary inverse, core inverse, dual core inverse and Bott–Duffin (e, f)-inverse are all the special cases of the (b, c)-inverse, related results for these inverses are obtained.     

The error bounds of Gauss-Kronrod quadrature formulae for weight functions of Bernstein-Szegő type

We consider the Gauss-Kronrod quadrature formulae for the Bernstein-Szeg? weight functions consisting of any one of the four Chebyshev weights divided by the polynomial \(\rho (t)=1-\frac {4\gamma }{(1+\gamma )^{2}}\,t^{2},\quad t\in (-1,1),\ -1<\gamma \le 0\). For analytic functions, the remainder term of this quadrature formula can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points ? 1 and sum of semi-axes ρ > 1, for the given quadrature formula. Starting from the explicit expression of the kernel, we determine the locations on the ellipses where maximum modulus of the kernel is attained. So we derive effective error bounds for this quadrature formula. An alternative approach, which has initiated this research, has been proposed by S. Notaris (Numer. Math. 103, 99–127, 2006).