Highly stereoselective synthesis of peracylated α-aldopyranosyl chlorides from aldopyranose peracetates and thionyl chloride catalyzed by BiCl3 generated in situ from the procatalyst BiOCl

Aldopyranose peracetates react with thionyl chloride and BiCl₃, generated in situ from a substoichiometric amount of the procatalyst BiOCl, producing the corresponding peracylated aldopyranosyl chlorides in very good to excellent yields (82–97%) with exclusive α-anomeric selectivity.     

Thickness of the hydration layer of a protein from molecular dynamics simulation

Water molecules around a protein exhibit slow dynamics with respect to that of pure bulk water. One important issue in protein hydration is the thickness of the hydration layer (i.e., the distance from the protein surface up to which the water dynamics is influenced by the protein). Estimation of thickness is crucial to understand better the properties of "biological water" and the role that it plays in guiding the protein's function. We have performed an atomistic molecular dynamics simulation of an aqueous solution of the protein villin headpiece subdomain or HP-36 to estimate the thickness of its hydration water. In particular, several dynamical properties of water around different segments (three alpha-helices) of the protein have been calculated by varying the thickness of the hydration layers. It is found that in general the influence of the helices on water properties extends beyond the first hydration layer. However, the heterogeneous nature of water among the first hydration layers of the three helices diminishes as the thickness is increased. It indicates that, for a small protein such as HP-36, the thickness of "biological water" is uniform for different segments of the protein.     

Stable Pfaffian state in bilayer graphene

Here, we show that the incompressible Pfaffian state originally proposed for the 5/2 fractional quantum Hall states in conventional two-dimensional electron systems can actually be found in a bilayer graphene at one of the Landau levels. The properties and stability of the Pfaffian state at this special Landau level strongly depend on the magnetic field strength. The graphene system shows a transition from the incompressible to a compressible state with increasing magnetic field. At a finite magnetic field of ~10 T, the Pfaffian state in bilayer graphene becomes more stable than its counterpart in conventional electron systems.     

Thermodynamics of Lema$$\hat{i}$$ tre−Tolman−Bondi Model

Here we consider our universe as inhomogeneous spherically symmetric Lema [^(i)]{\hat{i}} tre−Tolman−Bondi Model and analyze the thermodynamics of this model of the universe. The trapping horizon is calculated and is found to coincide with the apparent horizon. The Einstein field equations are shown to be equivalent with the unified first law of thermodynamics. Finally assuming the first law of thermodynamics validity of the generalized second law of thermodynamics is examined at the apparent horizon for the perfect fluid and at the event horizon for holographic dark energy.     

Ti(III)-mediated opening of 2,3-epoxy alcohols to build five-membered carbocycles with multiple chiral centres

Stereoselective construction of highly substituted five-membered carbocycles with multiple chiral centres is described. Sharpless kinetic resolution was applied as the key step to prepare the required 2,3-epoxy alcohols and a Ti(III) radical mediated opening of the epoxide ring followed by intramolecular trapping of the generated radical with a suitably placed α,β-unsaturated ester resulted in the formation of five-membered carbocycles with up to three consecutive new chiral centres stereoselectively fixed.     

A simple mathematical model for seasonal planktonic blooms

We show how the inclusion of the defense strategy by different species can alter the prediction of simple models. One of the defense strategy by the phytoplankton population against their grazer is the release of toxic chemicals. In turn the zooplankton population reduces there predation rate over toxin producing phytoplankton (TPP) to protect themselves from those toxic chemicals. Thus, when the level of toxicity is high, the grazing pressure is low and when the level of toxicity is low or when the toxin is absent, the grazing pressure is high. Here we have considered a TPP–zooplankton system where the rate of toxin liberation and the predation rate vary with zooplankton abundance. We observe that our proposed model has the potential to show different dynamical behaviour that are similar to that seen in real‐world situations. Further, we consider three different functional forms for the distribution of the toxins and compare them using latin hypercube sampling technique and found that the functional forms seem to have no effect in determining the final outcome of the system. Copyright © 2009 John Wiley & Sons, Ltd.     

Production lot sizing with process deterioration and machine breakdown

The paper presents a generalized economic manufacturing quantity model for an unreliable production system in which the production facility may shift from an ‘in-control’ state to an ‘out-of-control’ state at any random time (when it starts producing defective items) and may ultimately break down afterwards. If a machine breakdown occurs during a production run, then corrective repair is done; otherwise, preventive repair is performed at the end of the production run to enhance the system reliability. The proposed model is formulated assuming that the time to machine breakdown, corrective and preventive repair times follow arbitrary probability distributions. However, the criteria for the existence and uniqueness of the optimal production time are derived under general breakdown and uniform repair time (corrective and preventive) distributions. The optimal production run time is determined numerically and the joint effect of process deterioration, machine breakdowns and repairs (corrective and preventive) on the optimal decisions is investigated for a numerical example.     

Class numbers with many prime factors

Here, we construct infinitely many number fields of any given degree d>1 whose class numbers have many prime factors.     

Liouville Type Dilatonic Potential in Locally Rotationally Symmetric Bianchi I Model

Exact solutions are obtained for a special case of locally rotationally symmetric Bianchi I models consisting of a dilaton scalar field and a Liouville type dilatonic potential interacting with an electromagnetic field coupled with gravity, and the corresponding properties of the space-time are discussed.