Chemical constituents from the leaves of Manglietia phuthoensis and their effects on osteoblastic MC3T3-E1 cells

Two new phenyl glycosides, mangliesides A and B (1, 2), a new ionol glycoside, manglieside C (3), two new lignan glycosides, mangliesides D and E (4, 5), were isolated from the leaves of Manglietia phuthoensis, along with two known lignans, 3-methoxymagnolol (6) and obovatol (7). Their structures were established by means of 1D and 2D NMR, electrospray ionization (ESI)-MS and HR-ESI-MS experiments. Among them, compounds 2 and 5 significantly (p<0.05) increased the growth and differentiation of osteoblastic MC3T3-E1 cells in vitro.     

Die Gaspermeabilität von Polybutylenterephthalat in der Umgebung der Einfriertemperatur

The permeability of poly(butylene terephthalate) was examined for He, Ne, Ar and CO₂ at the temperature range of 293–338 K and an upstream pressure to 1,2 bar. The energies of activation of permeation and diffusion in case of Ne, Ar and CO₂ are higher above glass transition temperature than below, while they are nearly constant in case of He. The dependence of temperature of solubility coefficients does not change at the glass transition temperature.     

The lattice of integer partitions and its infinite extension

In this paper, we use a simple discrete dynamical model to study integer partitions and their lattice. The set of reachable configurations of the model, with the order induced by the transition rule defined on it, is the lattice of all partitions of a positive integer, equipped with a dominance ordering. We first explain how this lattice can be constructed by an algorithm in linear time with respect to its size by showing that it has a self-similar structure. Then, we define a natural extension of the model to infinity, which we compare with the Young lattice. Using a self-similar tree, we obtain an encoding of the obtained lattice which makes it possible to enumerate easily and efficiently all the partitions of a given integer. This approach also gives a recursive formula for the number of partitions of an integer, and some informations on special sets of partitions, such as length bounded partitions.     

Heteroleptic FeII Complexes of 2,2′‐Biimidazole and Its Alkylated Derivatives: Spin‐Crossover and Photomagnetic Behavior

Three iron(II) complexes, [Fe(TPMA)(BIM)](ClO₄)₂?0.5H₂O ( 1 ), [Fe(TPMA)(XBIM)](ClO₄)₂ ( 2 ), and [Fe(TPMA)(XBBIM)](ClO₄)₂ ?0.75CH₃OH ( 3 ), were prepared by reactions of Fe^II perchlorate and the corresponding ligands (TPMA=tris(2‐pyridylmethyl)amine, BIM=2,2′‐biimidazole, XBIM=1,1′‐(α,α′‐o‐xylyl)‐2,2′‐biimidazole, XBBIM=1,1′‐(α,α′‐o‐xylyl)‐2,2′‐bibenzimidazole). The compounds were investigated by a combination of X‐ray crystallography, magnetic and photomagnetic measurements, and Mössbauer and optical absorption spectroscopy. Complex 1 exhibits a gradual spin crossover (SCO) with T_1/2=190 K, whereas 2 exhibits an abrupt SCO with approximately 7 K thermal hysteresis (T_1/2=196 K on cooling and 203 K on heating). Complex 3 is in the high‐spin state in the 2–300 K range. The difference in the magnetic behavior was traced to differences between the inter‐ and intramolecular interactions in 1 and 2 . The crystal packing of 2 features a hierarchy of intermolecular interactions that result in increased cooperativity and abruptness of the spin transition. In 3 , steric repulsion between H atoms of one of the pyridyl substituents of TPMA and one of the benzene rings of XBBIM results in a strong distortion of the Fe^II coordination environment, which stabilizes the high‐spin state of the complex. Both 1 and 2 exhibit a photoinduced low‐spin to high‐spin transition (LIESST effect) at 5 K. The difference in the character of intermolecular interactions of 1 and 2 also manifests in the kinetics of the decay of the photoinduced high‐spin state. For 1 , the decay rate constant follows the single‐exponential law, whereas for 2 it is a stretched exponential, reflecting the hierarchical nature of intermolecular contacts. The structural parameters of the photoinduced high‐spin state at 50 K are similar to those determined for the high‐spin state at 295 K. This study shows that N‐alkylation of BIM has a negligible effect on the ligand field strength. Therefore, the combination of TPMA and BIM offers a promising ligand platform for the design of functionalized SCO complexes.     

A parallel algorithm based on convexity for the computing of Delaunay tessellation

The paper describes a parallel algorithm for computing an n-dimensional Delaunay tessellation using a divide-conquer strategy. Its implementation (using MPI library for C) in the case n = 2, relied on restricted areas to discard non-Delaunay edges, is executed easily on PC clusters. We shows that the convexity is a crucial factor of efficiency of the parallel implementation over the corresponding sequential one.     

On Necessary Optimality Conditions with Higher-Order Complementarity Slackness for Set-Valued Optimization Problems

Set-Valued and Variational Analysis - We aim to establish Karush-Kuhn-Tucker multiplier rules involving higher-order complementarity slackness under Hölder metric subregularity. These rules...     

Regularity Index of S + 2 Fat Points not on a Linear (S − 1)-Space

We will give a formula to compute the regularity index of s + 2 fat points not lying on a linear (s ? 1)-space in ? ⁿ , s ≤ n (Theorem 3.4). Our result generalizes a formula to compute the regularity index of fat points in general position in ? ⁿ ([3 Catalisano , M. V. , Trung , N. V. , Valla , G. ( 1993 ). A sharp bound for the regularity index of fat points in general position . Proc. Amer. Math. Soc. 118 : 717 – 724 .[Crossref], [Web of Science ®] , [Google Scholar]], Corollary 8). Our result also shows that the Segre bound is attained by s + 2 points not lying on a linear (s ? 1)-space.