The autostigmatic microscope

The autostigmatic microscope is an instrument for measuring the line-of-sight distance to a reflecting surface and is used chiefly to measure the radii of lens surfaces. Special techniques can increase considerably its precision and its freedom from scattered light.     

Conversions by dimethyldioxirane of 1-alkylbenzotriazoles into their N-oxides and of 2-alkylbenzotriazoles into 2-alkyl-trans-4,5,6,7-diepoxy-4,5,6,7-tetrahydrobenzotriazoles

Dimethyldioxirane converted 1-alkylbenzotriazoles 4 to the corresponding 3-alkylbenzotriazole 1-oxides 5 in good yields, but transformed 2-alkylbenzotriazoles 12 into 2-alkyl-trans-4,5,6,7-diepoxy-4,5,6,7-tetrahydrobenzotriazoles 13.     

Regiospecific synthesis of 4-(2-oxoalkyl)pyridines

[reaction: see text]. A new and operationally simple method has been developed for the regiospecific syntheses of 4-(2-oxoalkyl)pyridines from ketones and pyridine in good yields, using triflic anhydride to activate the pyridine ring.     

Novel one-step synthesis of thiazolo[3,2-b]1,2,4-triazoles

[reaction: see text] Reactions of chalcones 3a-f with bis(1H-1,2,4-triazolyl) sulfoxide 4 formed the thiazolo[3,2-b]1,2,4-triazoles 5a-f, which resemble closely some previously prepared COX-2 inhibitors. The structure of 5a was confirmed by X-ray analysis.     

The maximality of the core model

Our main results are: 1) every countably certified extender that coheres with the core model is on the extender sequence of , 2) computes successors of weakly compact cardinals correctly, 3) every model on the maximal 1-small construction is an iterate of , 4) (joint with W. J. Mitchell) is universal for mice of height whenever , 5) if there is a such that is either a singular countably closed cardinal or a weakly compact cardinal, and fails, then there are inner models with Woodin cardinals, and 6) an -Erdös cardinal suffices to develop the basic theory of .

     

Synthesis of o-sulfamidotriazobenzenes from 1,1'-sulfonylbis(benzotriazole)

Easily accessible 1,1'-sulfonylbis(benzotriazole) (Bt2SO2, 1) reacts with secondary amines at room temperature to afford (i) the corresponding o-sulfamidotriazobenzenes 2a-d (53-75%) via concurrent substitution of the first and ring opening of the second benzotriazolyl group and (ii) N-sulfonylbenzotriazoles 3b,c,e,f (7-73%). 1-(Morpholine-4-sulfonyl)-1H-benzotriazole 3c reacts with piperidine, pyrolidine, and N-methylpiperazine under microwave irradiation (120 W) at 120 degrees C for 10 min to give the unsymmetrical sulfamides 4a-c (80-90%).     

Exploring Leishmania major inositol phosphorylceramide synthase (LmjIPCS): insights into the ceramide binding domain

The synthesis of set of ceramide analogues exploring hydrophobicity in the acyl chains and the degree and nature of hydroxylation is described. These have been assayed against the parasitic protozoan enzyme LmjIPCS. These studies showed that whilst the C-3 hydroxyl group was not essential for turnover it provided enhanced affinity. Reflecting the membrane bound nature of the enzyme a long (C(13)) hydrocarbon ceramide tail was necessary for both high affinity and turnover. Whilst the N-acyl chain also contributed to affinity, analogues lacking the amide linkage functioned as competitive inhibitors in both enzyme and cell-based assays. A model that accounts for this observation is proposed.     

Benzotriazole-mediated syntheses of depsipeptides and oligoesters

Reactions of O-Pg(α-hydroxyacyl)benzotriazoles with (a) unprotected α-hydroxycarboxylic acids, (b) amino acids, and (c) amines afforded, respectively, chirally pure (a) oligoesters, (b) depsidipeptides, and (c) amide conjugates (yields 52-94%). N-Pg(α-Aminoacyl)benzotriazoles reacted with α-hydroxycarboxylic acids to yield depsidipeptides (47-87%). N-Pg(depsidipeptidoyl)benzotriazoles, obtained from depsidipeptides, gave depsitripeptides (yields 55-78%) on reaction with amino acids and α-hydroxycarboxylic acids. O-Acylation of α-hydroxycarboxylic acids with N-Pg(α-aminoacyl)benzotriazoles followed by deprotection produced unprotected depsides useful for the preparation of depsitripeptides.     

Nonreciprocal photonic band structure of low-symmetry magnetic photonic crystals

We propose multicomponent magnetic photonic crystals as a basis component for nonreciprocal optical elements. It is shown that introduction of three or more components may provide violation of mirror reflection symmetry, which is a necessary condition for obtaining nonreciprocity in the dispersion of the structure's eigenmodes. Numerical simulations confirm that nonreciprocity indeed develops in the form of nonreciprocal photonic band structure of three-component low-symmetry photonic crystal. We find that symmetry constraints produce fine structure in the nonreciprocity at high-symmetry points of the Brillouin zone.