Rotatory phase in a system of hard cyclic hexamers; an experimental modelling study2

A system of N = 169 hard cyclic hexamers is studied by an experimental modelling method. Results obtained suggest phase transitions connected with the rotational degree of freedom.     

Catalytic isomerization of 1-hexene on hy zeolite

The isomerization of 1-hexene on 70/80 mesh HY zeolite was studied at 200°C. The observed reaction products are formed via a variety of processes including double bond shift, cis–trans isomerization, skeletal rearrangement, cracking, hydrogen transfer, polymerization, cyclization, and coke formation. By applying the time-on-stream theory, the products have been classified as primary, secondary, or both, according to their OPE curves on product selectivity plots. 2-Ethyl-1-butene, which is present as an impurity in the feed, is found to react about 30 times faster than 1-hexene. Both 2-hexenes and 3 hexenes are formed primarily from 1-hexene, while 3 methyl 2 pentenes and 3-methyl-1-pentene formed from 2-ethyl-1-butene. The ratio of the initial rate of deprotonation to that of hydrogen shift in these reactions is ～15 and ～100, respectively. All products of skeletal rearrangement are observed to be secondary. Cracking products are produced mainly from precoke, which is also the source of hydrogen in the formation of paraffins. A detailed reaction network along with its associated mechanisms are presented and discussed.     

Infinite Matroidal Version of Hall's Matching Theorem

Hall's theorem for bipartite graphs gives a necessary and sufficientcondition for the existence of a matching in a given bipartitegraph. Aharoni and Ziv have generalized the notion of matchabilityto a pair of possibly infinite matroids on the same set andgiven a condition that is sufficient for the matchability ofa given pair (M, W) of finitary matroids, where the matroidM is SCF (a sum of countably many matroids of finite rank).The condition of Aharoni and Ziv is not necessary for matchability.The paper gives a condition that is necessary for the existenceof a matching for any pair of matroids (not necessarily finitary)and is sufficient for any pair (M, W) of finitary matroids,where the matroid M is SCF.     

Electron spin polarisation in laser induced autoionisation

The electron spin polarisation in the strong laser light induced autoionisation is discussed in the simple model. It is shown that confluence of coherences manifests itself in the dependence of polarisation on the laser detuning as a field strength dependent resonance, which enables verification of the phenomenon by means of the spin polarisation measurement. The separation of the confluence of coherences point and the point at which the maximal slowing down of the ionisation process (population trapping) occurs is showed.     

Gas chromatographic determination of the interconversion energy barrier for dimethyl-2,3-pentadienedioate enantiomers

The enantiomers of dimethyl-2,3-pentadienedioate undergo interconversion during gas chromatographic separation on 2,6-di-O-methyl-3-O-pentyl-beta-, 2,6-di-O-methyl-3-O-pentyl-gamma-, and 2,3-di-O-methyl-6-O-tert butyldimethylsilyl-beta-CD chiral stationary phases. The combination of a deconvolution method with an internal standard was used to determine individual enantiomer peak areas and retention times needed for the calculation of the interconversion rate constants and the energy barrier for dimethyl-2,3-pentadienedioate enantiomers. The kinetic and thermodynamic data obtained for the interconversion data (rate constants, energy barriers, enthalpies, and entropies) were in good agreement with the published data (Trapp, O., Schurig, V., Chirality 2002, 14, 465-470) using permethylated-beta-CD (Chirasil-beta-Dex).     

Size determination of Acipenser ruthenus spermatozoa in different types of electron microscopy

In this study three types of scanning electron microscopes were used for the size determination of spermatozoa of sterlet Acipenser ruthenus – high vacuum scanning electron microscope (SEM, JEOL 6300), environmental scanning electron microscope (ESEM, Quanta 200 FEG), field emission scanning electron microscope (FESEM, JEOL 7401F) with cryoattachment Alto 2500 (Gatan) and transmission electron microscope (TEM, JEOL 1010). The use of particular microscopes was tied with different specimen preparation techniques. The aim of this study was to evaluate to what degree the type of used electron microscope can influence the size of different parts of spermatozoa. For high vacuum SEM the specimen was prepared using two slightly different procedures. After chemical fixation with 2.5% glutaraldehyde in 0.1 M phosphate buffer and post-fixation by 1% osmium tetroxide, the specimen was dehydrated by acetone series and dried either by critical point method or by means of t-butylalcohol. For ESEM fresh, unfixed material was used, which was dropped on microscopic copper grids. In FESEM working in cryo-mode the specimen was observed in a frozen state. Ultrathin sections from chemically fixed and Epon embedded specimens were prepared for TEM observation. Distinct parts of sterlet spermatozoa were measured in each microscope and the data obtained was statistically processed. Results confirmed that the classical chemical procedure of specimen preparation for SEM including critical point drying method led to a significant contraction of all measured values, which could deviate up to 30% in comparison with values measured on the fresh chemically untreated specimen in ESEM. Surprisingly sperm dimensions determinated on ultrathin sections by TEM are comparable with values obtained in ESEM or FESEM.     

The lattice of congruence lattices of algebras on a finite set

The congruence lattices of all algebras defined on a fixed finite set A ordered by inclusion form a finite atomistic lattice \(\mathcal {E}\). We describe the atoms and coatoms. Each meet-irreducible element of \(\mathcal {E}\) being determined by a single unary mapping on A, we characterize completely those which are determined by a permutation or by an acyclic mapping on the set A. Using these characterisations we deduce several properties of the lattice \(\mathcal {E}\); in particular, we prove that \(\mathcal {E}\) is tolerance-simple whenever \(|A|\ge 4\).     

The lattice of convexities of partial monounary algebras

A class of partial monounary algebras is called a convexity if it is closed under homomorphic images, direct products and convex relative subalgebras. We prove that the collection of all convexities of partial monounary algebras forms a countable set. Further, each convexity can be generated by at most two algebras.     

Constant factor approximation for ATSP with two edge weights

We give a constant factor approximation algorithm for the Asymmetric Traveling Salesman Problem on shortest path metrics of directed graphs with two different edge weights. For the case of unit edge weights, the first constant factor approximation was given recently by Svensson. This was accomplished by introducing an easier problem called Local-Connectivity ATSP and showing that a good solution to this problem can be used to obtain a constant factor approximation for ATSP. In this paper, we solve Local-Connectivity ATSP for two different edge weights. The solution is based on a flow decomposition theorem for solutions of the Held–Karp relaxation, which may be of independent interest.