Crystallization of Arthrobacter sp. strain 1C N-(1-D-carboxyethyl)-L-norvaline dehydrogenase and its complex with NAD+

The novel NAD+-linked opine dehydrogenase from a soil isolate Arthrobacter sp. strain 1C belongs to an enzyme superfamily whose members exhibit quite diverse substrate specificites. Crystals of this opine dehydrogenase, obtained in the presence or absence of co-factor and substrates, have been shown to diffract to beyond 1.8 ? resolution. X-ray precession photographs have established that the crystals belong to space group P21212, with cell parameters a = 104.9, b = 80.0, c = 45.5 ? and a single subunit in the asymmetric unit. The elucidation of the three-dimensional structure of this enzyme will provide a structural framework for this novel class of dehydrogenases to enable a comparison to be made with other enzyme families and also as the basis for mutagenesis experiments directed towards the production of natural and synthetic opine-type compounds containing two chiral centres.     

Extremal problems for certain analytic (Nevanlinna) functions

We obtain sharp bounds on some basic functionals defined on the sets of all analytic functions having the representations \(f\left( z \right) \equiv \int\limits_{ - 1}^1 {\frac{{d\mu \left( t \right)}}{{z - t}}} \) and \(\varphi \left( z \right) \equiv \int\limits_{ - 1}^1 {\frac{{z\mu \left( t \right)}}{{1 - tz}}} \) ; respectively. Here μ is a probability measure.     

The Hardy classes for functions in the class MV[α, k]

Suppose that f(z) = z + a₂z² + ··· + a_nz_n + ··· is regular in the unit disc $\text{D}\text{with}\text{[f(z) f′}\text{(z)}\text{z] ≠ 0}\text{in}\text{D}$, and further let α ? 0 and k ? 2. If $\text{∝}{}^{\mathrm{2\pi }}{}_{\mathrm{o}}\text{¦}\text{Re}\text{{(1 ? α)z[}\text{f′(z)}\text{f(z)}\text{] + α(1 + z[}\text{f″(z)}\text{f′(z)}\text{])}¦ dθ ? kπ}\text{for}\text{z ? D}$, then f(z) is said to belong to the class MV[α, k]. This class contains many of the special classes of regular and univalent functions. The authors determine the Hardy classes of which f(z), f′(z) and f″(z) belong and obtain growth estimates of a_n.     

On the univalence of functions defined by certain integral transforms

The integral transform $\text{F(z) = ∝}{}_0{}^{\mathrm{z}}\text{(f′(t))}{}^{\mathrm{\alpha }}\text{(}\text{g(t)}\text{t}\text{)}{}^{\mathrm{\beta }}\text{dt}$, where α and β are real, of pairs of special analytic functions f(z) = z + ···, g(z) = z + ···, univalent in the open unit disc Δ is studied. The transform and our results extend some recent results due to Shirakova.     

Large-deviation analysis of Burgers turbulence with white-noise initial data

The statistics of the solution to the inviscid Burgers equation are investigated when the initial velocity is a white-noise function. Explicit representations for the probability distribution functions (PDFs) of the velocity and the distance between two successive shocks are found in terms of the solution to a PDE system. By using these expressions and large-deviation theory, tight bounds are found for the tails of these distributions and for that of the shock-strength distribution. These bounds give the exact rates of decay for the tails. © 1998 John Wiley & Sons, Inc.     

On a linear combination of some expressions in the theory of the univalent functions

LetH(α) denote the class of regular functionsf(z) normalized so thatf(0)=0 andf′(0)=1 and satisfying in the unit discE the condition $$\operatorname{Re} \left\{ {(1 - \alpha )f'(z) + \alpha (1 + zf''(z)/f'(z))} \right\} > 0$$ for fixed α. It is known thatH(0) is a particular class NW of close-to-convex univalent functions. The authors show the following results:Theorem 1. Letf(z)∈H(α). Thenf(z)∈NW if α≤0 andz∈E.Theorem 2. Letf(z)∈NW. Thenf(z)∈H(α) in |z|=r<r _α where i) \(r_\alpha = (1 + \sqrt {2\alpha } )^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}}\) , α≥0 and ii) \(r_\alpha = \sqrt {\frac{{1 - \alpha - \sqrt {\alpha (\alpha - 1)} }}{{1 - \alpha }}}\) , α<0. All results are sharp.Theorem 3. Iff(z)=z+a ₂ z ²+a ₃ z ³+... is inH(α) and if μ is an arbitrary complex number, then $$\left| {1 + \alpha } \right|\left| {a_3 - \mu a_2^2 } \right| \leqslant ({2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3})\max \left[ {1,\left| {1 + 2\alpha - {3 \mathord{\left/ {\vphantom {3 {2\mu }}} \right. \kern-\nulldelimiterspace} {2\mu }}(1 + \alpha )} \right|} \right].$$ .     

A gas-phase electron-diffraction study of trvinylborane

Trivinylborane has been studied by standard electron-diffraction techniques. The best agreement with experiment is obtained with a planar dynamic model in which steric strain within the molecule is reduced by distortion of the vinyl groups, and shrinkages simulate considerable torsional motion about the B-C bonds. The following parameters (r_a basis) and e.s.d. were obtained: C-H = 1.092± 0.003 Å; C-C = 1.370 ± 0.006 Å; B-C = 1.558± 0.003 Å; ∠BCH = 116.5 ± 0.9 °; ∠BCC = 122.4 ± 0.9°; ∠CCH (trans to B) = 124.0 ± 1.6°; ∠CCH (cis to B) = 132.2 ± 2.3°. A static non-planar model has also been considered.The probable planarity of the molecule and the length of the C C bond are interpreted as evidence for π-electron delocalisation from carbon to boron.     

Estimates for the Norm of the nth Indefinite Integral

Let T be the Volterra operator on L²[0, 1] where f L²[0, 1], 0 x 1. It is well known that||n!Tⁿ|| = O(1/n!). In a recent paper [1], D. Kershaw has provedthat a result which wasfirst conjectured by Lao and Whitley in [2]. It is easy to provethat For completeness, wegive the proof using the familiar Schmidt norm estimate forthe norm of an integral operator (see Section 2 below). Kershawproves that by analysingthe special positivity preserving properties of T*T. He usesone of the many abstract theorems on eigenvalues and eigenfunctionsof compact operators which preserve a cone. In this paper weshall reprove (1), giving a short and direct proof of (2). 1991Mathematics Subject Classification 47G10, 45-04.