The convergent syntheses of pyrazinyl and quinoxalinyl phenylmethanones from 2-lithio pyrazines and quinoxalines

Pyrazines and quinoxalines bearing 2-substituents that direct ortho metalation reacted with lithium 2,2,6,6-tetramethylpiperidide to produce 2-substituted-3-lithiopyrazines and quinoxalines. These lithio reagents reacted with N-methoxy-N-methylbenzamide to give good to moderate yields of 3-substituted pyrazinyl or quinoxalinylphenylmethanones. The 3-methylthio substituents of some ketone products were oxidized to methylsulfonyl groups that were susceptible to nucleophilic displacement.     

On the dynamics of radially symmetric granulomas

A granuloma is a collection of macrophages that contains bacteria or other foreign substances that the body?s immune response is unable to eliminate. In this paper we present a simple mathematical model of radially symmetric granuloma dynamics. The model consists of a coupled system of two semi-linear parabolic equations for the macrophage density, and the bacterial density. The boundary of the granuloma is free. This simple framework makes it possible to conduct a mathematical analysis of the system dynamics. In particular, we show that the model system has a unique solution, and that, depending on the biological parameters; the bacterial load either disappears over time or persists. We use numerical methods to establish the existence of stationary solutions and examine how a stationary solution changes with the reproductive rate of the bacteria. These simulations show that the structure of the granuloma breaks down as the reproductive rate of the bacteria increases.     

Gold(III) chloride catalysed synthesis of 5-alkylidene-dihydrothiazoles

A two step synthesis of dihydrothiazoles is presented. First, the previously unknown N-propargylic dithiocarboimidates are produced in good yields from easily available, cheap starting materials. The subsequent gold catalysed ring closure is fast and efficient, leading to dihydrothiazoles through a cascade of 5-exo-dig cyclisation and 1,3-alkyl migration. The yields range from 74% to 95%.     

Counting all bent functions in dimension eight 99270589265934370305785861242880

Based on the classification of the homogeneous Boolean functions of degree 4 in 8 variables we present the strategy that we used to count the number of all bent functions in dimension 8. There are $$99270589265934370305785861242880 \approx 2^{106}$$ such functions in total. Furthermore, we show that most of the bent functions in dimension 8 are nonequivalent to Maiorana?CMcFarland and partial spread functions.     

1,3-Cyclobutandionderivate aus Keten

1,3-Cyclobutanedione derivatives from ketene The dimerisation of ketene leads mainly to the methylidene-β-lactone ‘Diketene’ 2c . It is shown, that also a small amount of the symmetrical dimer, 1,3-cyclobutadione 1c is produced, which under the reaction conditions is acetylated to 3-acetoxycyclo-butenone (5) .     

Augmentation of the barrier for prompt μ− induced fusion

The lowest muon energy levels in heavy muonic atoms are calculated for a sequence of distortions describing nuclear shapes on the way to fission. Higher multipole distortions are found to be of minor importance.     

The breaking of intrinsic reflection symmetry in nuclear ground states

Negative-parity excited states of doubly even nuclei have earlier been attributed to vibrational excitations. This paper shows that an interpretation starting from a reflection asymmetric intrinsic state is more appropriate for certain nuclei in the radium region. Theoretical evidence for stable octupole deformation comes from a deformed shell-model calculation in which we use a single-particle potential with a realistic radial shape and a finite-range interaction for the surface energy. The octupole effect systematically improves the agreement between theoretical and experimental masses. The low-lying O⁺ excitations observed in experiment are compatible with the calculated collective octupole potentials. The possibility of obtaining further evidence from the spectroscopy of odd-mass nuclei is considered in an exactly solvable model, which shows that the smaller energy splitting observed in odd-A parity doublets mainly reflects single-particle fragmentation of the collective mode. The systematics of theoretical shell structure and experimental spectroscopy suggests the presence of other regions of octupole collectivity near the limits of stability.