Windmill polynomials over fields of characteristic two

Chambers andSmeets [3] have designed a windmill arrangement of linear feedback shift registers (LFSRs) to generate pn-sequences overGF(2) with high speed. When the windmill hasv vanes, the associated minimal feedback polynomial (having degreen, relatively prime tov) can be taken to have the shapef ₁(x ^v )+x ⁿ f ₂(x ^–v ), where the polynomialsf ₁ andf ₂ have degree [n/v]. Their numerical evidence, whenv is divisible by 4, suggests that, surprisingly, there areno such windmill polynomials which are irreducible ifn±3 (mod 8), while about twice as many irreducible and primitive windmill polynomials as they expected occur ifn±1 (mod 8). A discussion of this behaviour is presented here with proofs. The brief explanation is that the Galois group of the underlying generic windmill polynomial overGF (4) is equal to the alternating groupA _n .     

Geometric techniques in representation theory

A discussion of results and conjectures, focussed around the extension of the modular representation theory for finite Lie-type groups to more general groups that act on building-like geometries.Based on a lecture given at the conference Groups and Geometries-Finite and Algebraic, on 26 March 1986 at Noordwijkerhout, Netherlands (a NATO Advanced Research Workshop).Partially supported by NSF Grant MCS 83-00855.     

The vibrational spectra of some 1,3-dimethyl-1,3-diaza-2-boracyclopentanes

A detailed vibrational assignment is proposed for 1,3-dimethyl-1,3-diaza-2-boracyclopentanes:

where X = Cl, Br or NMe₂. The assignments are generally in accord with C_2v symmetry, but there is some evidence for a slight breakdown, as some A₂ modes appear in the IR. The BN₂ stretches are near 1500 cm^?1, (antisymmetric) and 1300 cm^?1 (symmetric), consistent with a large degree of π-bonding.     

Fluorimetric determination of acidity constants of naphthoic and anthroic acids

A fluorimetric method of determining the acidity constants (pK_a values) of some naphthoic and anthroic acids is presented, based on the changes in fluorescence of solutions of these acids in water on changing the pH. The method is useful in the absence as well as in the presence of excited-state proton transfer. In the latter case, when the excited-state protonation occurs in the same pH region as the ground-state dissociation, resolution of the two processes can be accomplished by addition of a suitable quencher such as iodide. The method permits the accurate determination of the pK_a value of fluorescent compounds, even when they are poorly soluble in water, because of the high sensitivity of the spectrofluorimetry.     

Synthesis of pyrimido[4,5-e][1,4]oxazepin-5-ones

Eighteen novel pyrimido[4,5-e][1,4]oxazepin-5-ones were prepared directly via the reaction of either ethyl 4-chloro-2-phenyl-5-pyrimidinecarboxylate (Ia) or ethyl 4-chloro-2-m-chlorophenyl-5-pyrimidinecarboxylate (Ib) with a variety of substituted 2-(alkylamino)ethanols. A typical example was the preparation of 8,9-dihydro-9-methyl-2-phenylpyrimido[4,5-e][1,4]-oxazepin-5(7H)-one (IIa) from the reaction of Ia with 2-(methylamino)ethanol. Hydrolytic cleavage of the lactone ring in IIa with sodium hydroxide solution, followed by acidification with hydrochloric acid afforded 4-[(2-hydroxyethyl)methylamino]-2-phenyl-5-pyrimidinecarboxylic acid (IV). Reactions of IIa with concentrated ammonium hydroxide or hydrazine also caused cleavage of the lactone ring, giving the corresponding amide (V) or hydrazide (VI), respectively. Structural assignments were supported by infrared and nuclear magnetic resonance spectra.     

S)-(+)-2-(p-tolylsulfinyl)-2-buten-4-olide: an enantiomerically pure Michael acceptor for asymmetric synthesis of 3-substituted 4-butanolides. (—)-podorhizon.

A short, reliable, and practical synthesis of ($\text{S}$)-(+)-2-($\text{p}$-tolylsulfinyl)-2-buten-4-olide has been developed, and the utility of this Michael acceptor for highly enantiocontrolled synthesis of 3-substituted 4-butanolides has been demonstrated.     

Formamidino and carbamoyl-formamidino complexes of manganese and rhenium carbonyls

Lithio-1,3-diarylformamidines undergo reaction with the monomeric and dimeric carbonyl chlorides of manganese and rhenium, [M(CO)₅Cl] and [M(CO)₄Cl₂] to yield respectively the carbamoyl-formamidino [M(CO)₄-CON(R)CHNR] and the formamidino [M(CO)₄RNCHNR] types of complex. The carbamoyl complexes undergo decarbonylation to produce the formamidino complexes in low yield.     

Capillary isoelectric focusing-mass spectrometry: analysis of protein mixtures from human body fluids

Isoelectric focusing within a fused silica capillary (cIEF) has proved to be a powerful and practical method for high-resolution separation of analytes from complex biological mixtures. This technique overcomes many of the problems of isoelectric focusing within slab gel media. However current cIEF systems commonly utilize UV detection which limits the detail of analyte structural information that is obtained during analysis. The use of mass spectrometry (MS) as the detection system provides much greater structural information about the detected analytes allowing accurate relative molecular mass (M(r)) determination for proteins and polypeptides. We have constructed a cIEF-MS interface and compared the separation of standard proteins analyzed by cIEF-UV with cIEF-MS. This allowed rapid optimization of the cIEF-MS system performance. Further we have demonstrated the use of MS as a detection system provides accurate M(r) information and can provide analyte modification details. These factors increase the likelihood of absolute identification for physiological proteins within complex in vivo-derived mixtures. To demonstrate the value of cIEF-MS in such analyses we have undertaken an examination of cerebrospinal fluid (CSF), and tentatively identified a number of constituent proteins. We have also analyzed whole blood from control and diabetic patients. We show that glycated alpha- and beta- chains of hemoglobin are found in almost equal abundance in diabetic patient blood. From these results we suggest cIEF-MS is an efficient and useful tool for the separation and examination of in vivo-derived analytes within physiological fluids.     

Microwave and infrared spectra of deuterium-substituted germyl halides and the structures of the germyl halides

We have obtained microwave spectra of fully and partially deuterated germyl halides GeD₃X and GeHD₂X (X = F, Cl, Br, I) and analysed the infrared spectra in the GeH stretching region of the asymmetric species. The resulting A_o and B_o values have been combined with existing data on GeH₃X to give improved structures for the germyl halides. The values of the HGeX angles obtained show a correlation with GeH stretching frequencies, as in methyl compounds, but there appears to be no such correlation between stretching frequencies and GeH bond lengths.