A determinantal inequality involving the Moore-Penrose inverse

Let A be a rectangular matrix of complex numbers whose rows are partitioned into r arbitrary blocks:

The Moore-Penrose inverses of each of these blocks are used to form the matrix B = (A₁⁺,…, A_r⁺). It is shown that 0 ? det (AB) ? 1. This is a generalized version of Hadamard's inequality.     

In Situ Deprotection and Incorporation of Unnatural Amino Acids during Cell‐Free Protein Synthesis

The S30 extract from E. coli BL21 Star (DE3) used for cell‐free protein synthesis removes a wide range of α‐amino acid protecting groups by cleaving α‐carboxyl hydrazides; methyl, benzyl, tert‐butyl, and adamantyl esters; tert‐butyl and adamantyl carboxamides; α‐amino form‐, acet‐, trifluoroacet‐, and benzamides; and side‐chain hydrazides and esters. The free amino acids are produced and incorporated into a protein under standard conditions. This approach allows the deprotection of amino acids to be carried out in situ to avoid separate processing steps. The advantages of this approach are demonstrated by the efficient incorporation of the chemically intractable (S)‐4‐fluoroleucine, (S)‐4,5‐dehydroleucine, and (2S,3R)‐4‐chlorovaline into a protein through the direct use of their respective precursors, namely, (S)‐4‐fluoroleucine hydrazide, (S)‐4,5‐dehydroleucine hydrazide, and (2S,3R)‐4‐chlorovaline methyl ester. These results also show that the fluoro‐ and dehydroleucine and the chlorovaline are incorporated into a protein by the normal biosynthetic machinery as substitutes for leucine and isoleucine, respectively.     

Development of an electrospray ionization mass spectrometric method for the quantification of theophylline in horse serum

A rapid and selective method has been developed for the determination of theophylline in horse serum by LC-ESI/MS/MS. The analytical method includes a protein precipitation extraction for sample preparation, liquid chromatography separation technique and ionspray tandem mass spectrometry. The drug was extracted from serum using a protein precipitation with acetonitrile and the supernatants were analyzed using an LC-ESI/MS/MS instrument. The chromatography was performed using a 50 x 2.1 mm C(8) analytical column and an isocratic mobile phase composes of 60:40 acetonitrile-0.5% formic acid in water with a flow rate fixed at 350 microL/min. A linear (weighted 1/concentration) relationship was used to perform the calibration over an analytical range of 0.1-20 ppm. The intra-batch precision and accuracy at LLOQ, medium and high concentration were 11.7, 6.9 and 5.4% and 95.8, 107.8 and 95.8%, respectively, and the inter-batch precision and accuracy at LLOQ, medium and high concentration were 10.4, 7.9 and 7.3% and 97.3, 105.2 and 95.9%, respectively. This LC-ESI/MS/MS method for the determination of theophylline in horse serum has been proved to within generally accepted criteria used for bioanalytical assay and was used successfully during clinical investigation.     

A new triterpene glycoside from fruit of <Emphasis Type=Italic>Phytolacca americana</Emphasis>

Glycosides H and I, the structures of which were established by modern physicochemical analytical methods (PMR, ¹³C NMR, COSY, TOCSY, HMBC, MS) and acid-base hydrolysis, were isolated from the purified total saponins from fruit of Phytolacca americana containing at least 10 triterpene glycosides by rechromatography of enriched fractions over a column of silica gel. Glycoside H was a bidesmoside of phytolaccageninic acid, which was isolated earlier from cell culture of Phytolacca acinosa. Glycoside I was 3-O-(β-D-xylopyranosyl-(1 → 3)-β-D-galactopyranosyl-(1 → 3)- β -D-xylopyranosyl)-28-O- β -D-glucopyranosyl phytolaccagenin, which was isolated by us for the first time.     

A CRUSH TEST FIXTURE FOR INVESTIGATING ENERGY ABSORPTION OF FLAT COMPOSITE PLATES

A flat plate crush test fixture was designed and qualified to meet the need for a cost effective method for screening material systems, laminate stacking sequence, and trigger mechanism in the design of energy absorbing composite structures. The effect of scale on energy absorption is important to understand before cost-saving sub-scale plates are used in place of full scale plates. Therefore, the capability to test two different sizes of plates was designed into the fixture.     

The rodrigues type representations for a certain class of special functions

Summary An attempt is made here to present a systematic introduction to and several applications of a certain method of obtaining Rodrigues type representations for a fairly wide variety of sequences of special functions. The main results, contained in Theorems2 and3 below, are shown to apply not only to the Bessel polynomials, the classical orthogonal polynomials including, for instance, Hermite, Jacobi (and, of course, Gegenbauer, Legendre, and Tchebycheff), and Laguerre polynomials, and to their various generalizations studied in recent years, but also to such other special functions as the Bessel function and a certain class of generalized hypergeometric functions. Entrata in Redazione il 25 giugno 1977. This work was partially supported by the National Research Council of Canada under grants A-7353 and A-4027. For a preliminary report of this paper see Notices Amer. Math. Soc.,24 (1977), p. A-238, Abstract no. 77T-B43.     

Effect of a small axisymmetric contraction on grid turbulence

Measurements downstream of a grid followed by a contraction with an area ratio of 1.36 have been made with a one-component vorticity probe. The velocity data indicate that there is indeed an improvement in isotropy of the large scales when such a contraction is used. In particular, the spectrum of u loses a significant amount of low frequency energy and its peak is shifted towards that of v. Although the v spectrum is less affected than the u spectrum, the relative magnitudes of the u and v spectra satisfy isotropy more closely with than without the contraction. In particular, isotropy is most closely approximated when the contraction is used in combination with a grid designed to minimise vortex shedding. The lateral vorticity spectrum is essentially unaffected, irrespective of the grid that is used or the magnitude of the wavenumber.