Algebraic properties of classes of path ideals of posets

We consider path ideals associated to special classes of posets such as tree posets and cycles. We express their property of being sequentially Cohen–Macaulay in terms of the underlying poset. Moreover, monomial ideals, which arise in algebraic statistics from the Luce-decomposable model and the ascending model, can be viewed as path ideals of certain posets. We study invariants of these so-called Luce-decomposable monomial ideals and ascending ideals for diamond posets and products of chains. In particular, for these classes of posets, we explicitly compute their Krull dimension, their projective dimension, their Castelnuovo–Mumford regularity and their Betti numbers.     

Numerical test of Born–Oppenheimer approximation in chaotic systems

We study the validity of the Born–Oppenheimer approximation in chaotic dynamics. Using numerical solutions of autonomous Fermi accelerators, we show that the general adiabatic conditions can be interpreted as the narrowness of the chaotic region in phase space.     

Asymmetric benzoin reaction catalyzed by benzoylformate decarboxylase

Aromatic aldehydes are converted into benzoins by benzoylformate decarboxylase catalyzed C–C bond formation. The reaction affords (R)-benzoins with high enantiomeric excess and in good chemical yields. A broad range of aromatic aldehydes can be used as substrates in aqueous buffer or buffer/DMSO-solutions.     

Hyperbranched polymers as scaffolds for multifunctional reversible addition–fragmentation chain‐transfer agents: A route to polystyrene‐core‐polyesters and polystyrene‐block‐poly(butyl acrylate)‐core‐polyesters

Polydisperse hyperbranched polyesters were modified for use as novel multifunctional reversible addition–fragmentation chain‐transfer (RAFT) agents. The polyester‐core‐based RAFT agents were subsequently employed to synthesize star polymers of n‐butyl acrylate and styrene with low polydispersity (polydispersity index < 1.3) in a living free‐radical process. Although the polyester‐core‐based RAFT agent mediated polymerization of n‐butyl acrylate displayed a linear evolution of the number‐average molecular weight (M_n) up to high monomer conversions (>70%) and molecular weights [M_n > 140,000 g mol^?1, linear poly(methyl methacrylate) equivalents)], the corresponding styrene‐based system reached a maximum molecular weight at low conversions (≈30%, M_n = 45,500 g mol^?1, linear polystyrene equivalents). The resulting star polymers were subsequently used as platforms for the preparation of star block copolymers of styrene and n‐butyl acrylate with a polyester core with low polydispersities (polydispersity index < 1.25). The generated polystyrene‐based star polymers were successfully cast into highly regular honeycomb‐structured microarrays. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3847–3861, 2003     

Synthesis of semi-biodegradable crosslinked microspheres for the delivery of 1,25 dihydroxyvitamin D3 for the treatment of hepatocellular carcinoma

It has been demonstrated that 1,25 dihydroxyvitamin D₃ (1,25(OH)₂VD₃) can inhibit the proliferation of cancer cells, including colorectal and hepatocellular cells which are mainly responsible for liver cancer. However, the use of 1,25(OH)₂VD₃ is hampered due to the development of hypercalcaemia. We hereby report a promising technique in liver cancer treatment by utilizing crosslinked microspheres prepared by polymerization as a carrier to control the release of 1,25(OH)₂VD₃ or hydrophobic drug in general at targeted sites over a long period. Microspheres in the size range of 35 μm were prepared and the drug was loaded to these poly(vinyl neodecanoate-crosslinked-ethyleneglycol dimethacrylate) microspheres after polymerization. The release study has shown that up to 1% of the drug was released after 40 days. MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) assay and direct contact cytotoxicity assay using HT-20 and L929 confirm the non-toxicity of these spheres.     

Production and hydrolysis of 3,4-dimethyl-2,5-diphenyl-1,3-oxazolidine

Summary Condensation of ephedrine with benzaldehyde, an acid catalyzed reversible reaction, producing 3,4-dimethyl-2,5-diphenyl-1,3-oxazolidine, was studied. If the starting reaction mixture contained acetic acid, it quantitatively reacted with ephedrine and produced a salt functioning as an acid catalyst. On the contrary, ephedrine hydrochloride had no catalytic effect.     

Unexpected high ordering of a [60]Fullerene nitroxide in the nematic phase of 4-4'-azoxyanisole

A nitroxide [60]fullerene adduct containing a pyrrolidine-1-oxyl group has been synthesized. Its orientational order in the nematic phase of the liquid crystal solvent 4,4'-azoxyanisole (PAA) has been measured from the variation of the EPR spectral parameters on passing from the isotropic to the nematic phase. Highly resolved EPR lines allow for precise evaluation of the shifts of the g , a N and a H values. Since the g and the hyperfine tensors are known, the order matrix could be obtained. This is compared with the one calculated with a theoretical model based on short range solute-solvent interactions, which predicts a considerable degree of orientation of the molecular axes, despite the almost spherical shape of the molecule. The agreement with experimental findings is quite good and it is further improved if a bent structure of the pyrrolidine ring is taken into account.