Orientations of Hamiltonian cycles in bipartite digraphs

The main result of the paper is the following Theorem. Let D=(X,Y,A) be a bipartite, balanced digraph of order 2n and size at least 2n²–2n+3. Then D contains an almost symmetric Hamiltonian cycle (i.e. a Hamiltonian cycle in which at least 2n–1 arcs are symmetric edges), unless D has a vertex which is not incident to any symmetric edge of D.This theorem implies a number of results on cycles in bipartite, balanced digraphs, including some recent results of N. Chakroun, M. Manoussakis and Y. Manoussakis.     

Are linear algorithms always good for linear problems?

We exhibit linear problems for which every linear algorithm has infinite error, and show a (mildly) nonlinear algorithm with finite error. The error of this nonlinear algorithm can be arbitrarily small if appropriate information is used. We illustrate these examples by the inversion of a finite Laplace transform, a problem arising in remote sensing.     

First production of ultracold neutrons with a solid deuterium source at the pulsed reactor TRIGA Mainz⋆

The production rates of ultracold neutrons (UCN) with a solid deuterium converter have been measured at the pulsed reactor TRIGA Mainz. Exposed to a thermal neutron fluence of n·cm^-2·pulse^-1, the number of detected very cold and ultracold neutrons ranges up to 200 000 at 7mol of solid deuterium (sD₂) in combination with a pre-moderator (mesitylene). About 50% of the measured neutrons can be assigned to UCN with energies E of where V _F(sD ₂) = 105 neV and V _F(guide) = 190 neV are the Fermi potentials of the sD₂ converter and our stainless steel neutron guides, respectively. Thermal cycling of solid deuterium, which was frozen out from the gas phase, considerably improved the UCN yield, in particular at higher amounts of sD₂.     

New properties of a certain method of summation of generalized hypergeometric series

In a recent paper (Appl. Math. Comput. 215:1622–1645, 2009), the authors proposed a method of summation of some slowly convergent series. The purpose of this note is to give more theoretical analysis for this transformation, including the convergence acceleration theorem in the case of summation of generalized hypergeometric series. Some new theoretical results and illustrative numerical examples are given.     

Boundary and initial fluctuation effect on dynamic behaviour of a laminated solid

Two problems will be studied in this contribution. First, we analyse some phenomena which take place in a laminated solid and are caused by a fluctuation of time-dependent boundary tractions. Second, we investigate the transient effect of initial displacement fluctuations on the behaviour of a laminate. To solve the above problems we propose a new macroscopic 3D model for investigations of initial-boundary value problems in elastodynamics of a laminated medium.     

On the modelling of dynamic problems for plates with a periodic structure

Summary The subject of analysis is the bending of elastic plates exhibiting a nonhomogeneous periodic structure and/or a periodically variable thickness in a certain direction parallel to the plate's midplane. The fundamental modelling problem is how to obtain an effective 2D-model of a plate under consideration, i.e., a 2D-model represented by PDEs with constant coefficients. This problem for periodic plates has been solved independently in [5] and [10], using asymptotic homogenization. However, homogenization neglects dynamic phenomena related to the plate's rotational inertia and cannot be applied to the analysis of higher-order vibration frequences. The main aim of this contribution is to formulate a new non-asymptotic effective 2D-model of a periodic plate which is free from the mentioned drawbacks and describes the dynamic behaviour of plates having the thickness of the order of the period length. The proposed model is applied to the analysis of some vibration problems.     

Synthesis,molecular characterisation,and in vivo study of platinum(IV) coordination compounds against B16 mouse melanoma tumours

A novel platinum(IV) coordination compound with 6-mercaptopurine (6-Hmp) has been synthesised and characterised by IR and NMR spectroscopy. Spectroscopic parameters indicate the presence of two chelate (S-6, N-7) monodeprotonated ligands and two chloride ions in the coordination sphere of [PtCl₂(6-mp)₂] · H₂O (I). Two Pt(IV) coordination compounds, [PtCl₂(6-mp)₂] · H₂O (I) and [PtCl₄(dbtp)₂] (II), were used in the in vivo test against B16 mouse melanoma tumours. Cytotoxic activity of compound II against the tumour cells was found to be high (LC₁₀ = 2.6 μM, LC₅₀ = 17.0 μM, LC₉₀ = 58.0 μM) compared to that of cisplatin.     

Inclusion Complex Formation Between Modified Cyclodextrins and Riboflvin and Alloxazine in Aqueous Solution

Inclusion complex formation of hydroxypropylated α-, β- and γ-cyclodextrins with riboflavin (vitamin B₂) and alloxazine was studied by spectroscopic and solubility methods. Alloxazine, which is a structural analog of riboflavin, was considered in order to evaluate the role of ribityl and methyl substituents in complexation. Thermodynamic parameters for 1:1 complex formation were obtained and analyzed in terms of influence of the reagent structure on the binding process. It was shown that the cavity of hydroxypropyl-β-cyclodextrin is more appropriate for formation of stable complexes. The complexes are enthalpy stabilized, due to prevalence of van der Waals interactions and possible hydrogen bonding. The partial insertion of riboflavin into the cyclodextrin cavity was revealed by ¹H NMR and computer modeling. The ribityl side chain, which prevents deep inclusion, is located nearby the wider rim of the cyclodextrin molecule and can undergo destruction. Penetration of the alloxazine molecule into the macrocyclic cavity is deeper and accompanied by formation of more stable inclusion complexes. Hydroxypropyl-β-cyclodextrin was found to be the more efficient solubilizing agent for riboflavin and alloxazine, whereas a stabilization action of cyclodextrins towards riboflavin was not observed.     

Ring-expanded bicyclic β-lactams: a structure-chiroptical properties relationship investigation by experiment and calculations

In the present work, the validity of the helicity rule relating the absolute configuration of the bridgehead carbon atom in bicyclic β-lactams to the sign of the 220 nm band observed in their electronic circular dichroism (ECD) spectra is examined for ring-expanded cephalosporin analogues. To this end, a series of model compounds with a seven-membered ring condensed with the β-lactam unit was synthesized. A key step of their synthesis was either the ring-closing metathesis (RCM) or the free radical cyclization leading to the seven-membered ring with an S, O, or C atom at the 6 position in the bicyclic skeleton. To investigate the scope and limitations of the simple, empirically established helicity rule, a combination of ECD spectroscopy, variable-temperature ECD measurements, X-ray analysis, and time-dependent density functional theory (TD-DFT) calculations was used. A comparison of the experimental ECD spectra with the spectra simulated by TD-DFT calculations gives a reasonable interpretation of the Cotton effects observed in the 240-215 nm spectral range. The results suggest that the helicity rule does not apply to the investigated compounds because of the planarity of their amide chromophore. Thus, these compounds do not constitute an exception to the rule that was established for bi- and polycyclic β-lactams with the nonplanar amide chromophore only.