Synthesis of N-phthalimido β-aminoethanesulfonyl chlorides: the use of thionyl chloride for a simple and efficient synthesis of new peptidosulfonamide building blocks

N-Phthalimido β-aminoethanesulfonyl chlorides, new building blocks for the synthesis of peptidosulfonamide peptidomimetics, were prepared in a straightforward manner from amino acids. In the crucial synthetic step, sulfonic acids or their sodium salts were converted into the corresponding sulfonyl chlorides using an excess of refluxing thionyl chloride or thionyl chloride/DMF. This simple and effective chlorinating method is also applicable to β-aminoethane sulfonic acids and their sodium salts with other N-protecting groups.     

Absolutely continuous functions of several variables and diffeomorphisms

In [4], a class of absolutely continuous functions of d-variables, motivated by applications to change of variables in an integral, has been introduced. The main result of this paper states that absolutely continuous functions in the sense of [4] are not stable under diffeomorphisms. We also show an example of a function which is absolutely continuous with respect cubes but not with respect to balls.     

Dynamical stability of an elastic column and the phenomenon of bifurcation

The article studies the stability of rectilinear equilibrium shapes of a non-linear elastic thin rod (column or Timoshenko's beam), the ends of which are pressed. Stability is studied by means of the Lyapunov direct method with respect to certain integral characteristics of the type of norms in Sobolev spaces. To obtain equations of motion, a model suggested in [16] is used. Furta [6] solved the problem of stability for all values of the parameter except bifurcational ones. When values of the system's parameter become bifurcational, the study of stability is more complicated already in a finite-dimensional case. To solve a problem like that, one often has to use a procedure of solving the singularities described in [1], for example. In this paper a change of variables is made which, in fact, is the first step of the procedure mentioned. To prove instability, we use a Chetaev function which can be considered as an infinite-dimensional analogue of functions suggested in [14, 9]. The article also investigates a linear problem on the stability of adjacent shapes of equilibrium when the parameter has supercritical values (post-buckling).     

On some properties of 4-regular plane graphs

The d-distance face chromatic number of a connected plane graph is the minimum number of colors in such a coloring of its faces that whenever two distinct faces are at the distance at most d, they receive distinct colors. We estimate 1-distance chromatic number for connected 4-regular plane graphs. We show that 0-distance face chromatic number of any connected multi-3-gonal 4-regular plane graphs is 4. © 1995, John Wiley & Sons, Inc.     

A quantum chemical investigation of pyrolysis reactions of glyoxylic acid ethylester

Two possible reaction paths for the pyrolysis of the ethylester of glyoxylic acid have been studied by ab initio molecular orbital calculations. The basis sets 3-21G and 6-31G * have been used, and electron correlation has been included by Møller–Plesset calculations up to fourth order. Our calculations indicate that the reaction leading to acid and ethylene through a 6-membered ring transition state is favored relative to a process involving a formyl hydrogen transfer via a 5-membered ring to the alkyl unit leading to ethane, CO, and CO₂. The predicted activation energies for these two reactions obtained at the highest level of calculation, MP 4(SDTQ )/6–31G *, are 50.4 and 71.7 kcal/mol, respectively. The transition states have RHF wave functions that are stable relative to UHF solutions using the 3–21G basis. The geometry of the transition states and IRC following indicate that both reactions are strongly asynchronous: The C? O bond rupture is virtually completed before hydrogen transfer occurs. For comparative purposes, analogous calculations have been performed for the ethylester of formic acid, where it is confirmed that a 6-membered ring transition state is preferred relative to a 4-membered one by around 42 kcal/mol at the highest level of calculation.     

Tensor train completion: Local recovery guarantees via Riemannian optimization

In this work, we estimate the number of randomly selected elements of a tensor that with high probability guarantees local convergence of Riemannian gradient descent for tensor train completion. We derive a new bound for the orthogonal projections onto the tangent spaces based on the harmonic mean of the unfoldings' singular values and introduce a notion of core coherence for tensor trains. We also extend the results to tensor train completion with auxiliary subspace information and obtain the corresponding local convergence guarantees.     

On modes and criteria of ABS melt failure in extension

Melt failure of a commercial ABS polymer in uniaxial extension over ranges of elongation rate ([(e)\dot] = 0.01 - 1.0 s ^{- 1}\dot \varepsilon = 0.01 - 1.0\,{\rm s}^{ - 1} ) and temperature (140-200 °C) was investigated. Four methods of experimental and numerical calculation for determination of modes and criteria of melt failure in uniaxial extension were investigated: 1) visual observation of necking; 2) visual observation of non-uniform flow during stress relaxation after cessation of steady elongation; 3) calculation of the Considère criterion from the measured elongational stress-strain curve; 4) numerical calculation of inflection point (‘C²/‘)²=0) from the tensile stress-strain curve. In addition, under higher Deborah number conditions the critical Hencky strains at Considère criterion were calculated using PSM model parameters (! and #) and were compared with those obtained from the measured elongational stress-strain curve. The relationship between these failure modes is discussed in terms of rheological properties of the polymer, putting emphasis on the relationship with the thermoforming process. The Considère criterion appears to be the most effective indicator of the non-uniform deformation of ABS melt in uniaxial extension under conditions where cohesive fracture does not occur. The rheological properties such as elongational viscosity, strain hardening and/or strain softening, and their temperature dependence play an important role in determining the growth and transition of melt failure of ABS polymer in uniaxial extension.     

Perovskites with the Framework‐Forming Xenon

The Group 18 elements (noble gases) were the last ones in the periodic system to have not been encountered in perovskite structures. We herein report the synthesis of a new group of double perovskites KM(XeNaO₆) (M=Ca, Sr, Ba) containing framework‐forming xenon. The structures of the new compounds, like other double perovskites, are built up of the alternating sequence of corner‐sharing (XeO₆) and (NaO₆) octahedra arranged in a three‐dimensional rocksalt order. The fact that xenon can be incorporated into the perovskite structure provides new insights into the problem of Xe depletion in the atmosphere. Since octahedrally coordinated Xe^VIII and Si^IV exhibit close values of ionic radii (0.48 and 0.40 Å, respectively), one could assume that Xe^VIII can be incorporated into hyperbaric frameworks such as MgSiO₃ perovskite. The ability of Xe to form stable inorganic frameworks can further extend the rich and still enigmatic chemistry of this noble gas.     

Antioxidative properties of <Emphasis Type="Italic">Sambucus nigra</Emphasis> extracts

Potential protective effects of elderberry (Sambucus nigra) extracts against oxidative degradation of hyaluronan (HA) were detected in vitro. To induce free-radical-mediated HA degradation, Weissberger’s biogenic oxidative system, which mimics the situation of acute inflammation, was applied. Time- and dose-dependent changes of dynamic viscosity of the HA solutions in the presence and absence of two elderberry extracts produced in 2006 and 2012 were recorded by rotational viscometry (RV). Radical scavenging capacity of both extracts was investigated by the spectrocolorimetric ABTS [2,2′-azinobis(3-ethylbenzothiazoline-6-sulfonic acid) diammonium salt] assay and the “inverted” ABTS assay. Oxygen consumption of the system oxidizing HA either in the absence or presence of the elderberry extracts was determined. The results of RV revealed that an addition of the newer extract (2012) promoted the inhibition of HA degradation more markedly compared to the older extract (2006). The same effect of both extracts on ABTS^·+ scavenging was observed. Inverted ABTS assay demonstrated that colorful substances were not responsible for the radical-scavenging activity. Results of oximetry demonstrated that the effect of the extract from 2006 was more significant than that of the extract from 2012.