Central Limit Theorems for dependent variables. I

Summary This paper gives a flexible approach to proving the Central Limit Theorem (C.L.T.) for triangular arrays of dependent random variables (r.v.s) which satisfy a weak mixing condition called -mixing. Roughly speaking, an array of real r.v.s is said to be -mixing if linear combinations of its past and future are asymptotically independent. All the usual mixing conditions (such as strong mixing, absolute regularity, uniform mixing, -mixing and -mixing) are special cases of -mixing. Linear processes are shown to be -mixing under weak conditions. The main result makes no assumption of stationarity. A secondary result generalises a C.L.T. that Rosenblatt gave for strong mixing samples which are nearly second order stationary.     

Solid-phase oligosaccharide and glycopeptide synthesis using glycosynthases

Enzymatic approaches for the preparation of oligosaccharides are interesting alternatives to traditional chemical synthesis, the main advantage being the regio- and stereoselectivity offered without the need for protecting groups. The use of solid-phase techniques offers easy workup procedures and the prospect of automatability. Here, we report the first application of glycosynthases to solid-phase oligosaccharide synthesis by use of the 51 kDa serine and glycine mutants of Agrobacterium sp. beta-glucosidase, Abg E358S and E358G. Acceptors were linked to PEGA resin through a backbone amide linker (BAL), and using these mutated enzymes, a galactose moiety was transferred from a donor sugar, alpha-D-galactosyl fluoride, with high efficiency (>90%) together with excellent recovery of material. Furthermore, it was demonstrated that a resin-bound model glycopeptide was also an acceptor for the glycosynthase.     

A TEM, XRD, and crystal chemical investigation of oxygen/vacancy ordering in (Ba1−xLax)2In2O5+x, 0x0.6

A careful TEM and XRD study of the (Ba_1−xLa_x)₂In₂O_5+x, 0x0.6, ‘defect-perovskite’-type solid solution has been carried out. A well-defined structural phase transition is shown to occur between x=0.1 and 0.2 from the orthorhombic brownmillerite structure type on the low x side to a multiple twinned, tetragonal 1×1×2 perovskite-related superstructure phase on the high x side at x=0.2. This phase transition correlates with an important phase transition previously observed in electrical conductivity versus temperature measurements. The existence of additional satellite reflections close to the regions of reciprocal space was found to be typical of all (Ba_1−xLa_x)₂In₂O_5+x specimens, although their intensity relative to the parent Bragg reflections systematically reduces as x increases. As x increases beyond 0.2, the -type satellite reflections initially become weaker and rather more diffuse for x=0.3 before splitting into pairs of rather weak and somewhat diffuse incommensurate satellite reflections for x=0.4 and beyond. An interpretation in terms of oxygen vacancy ordering and associated structural relaxation is given. Additional structured diffuse scattering is also observed and a tentative explanation in terms of Ba/La ordering and associated local strain distortions put forward.     

An unusual mechanism of glycoside hydrolysis involving redox and elimination steps by a family 4 beta-glycosidase from Thermotoga maritima

Among the numerous well-characterized families of glycosidases, family 4 appears to be the anomaly, requiring both catalytic NAD+ and a divalent metal for activity. The unusual cofactor requirement prompted the proposal of a mechanism involving key NAD+-mediated redox steps as well as elimination of the glycosidic oxygen. Primary kinetic isotope effects for the 2- and 3-deutero substrate analogues, isotopic exchange with solvent, and structural analysis of a 6-phospho-beta-glucosidase, BglT (E.C. 3.2.1.6), provided evidence in support of the proposed mechanism, which has striking resemblances to that of the sugar dehydratases. Furthermore, analysis of the stereochemical outcome indicated that family 4 enzymes are retaining glycosidases.     

The metastable Ni7±xS6, and mixed Ni6±x(S1−ySey)5, phases

The closely related, narrowly non-stoichiometric, metastable as well as thermodynamically stable “phases” in the metal-rich part of the Ni–S phase diagram near the nominal composition Ni_7±xS₆ have been carefully re-investigated via electron diffraction and transmission electron microscope imaging. Two quite distinct polymorphs have been identified, a minority incommensurate interface-modulated polymorph and a (heavily twinned) majority I1a1, a=2a_p, b=2b_p, c=−a_p+c_p superstructure (of an underlying Bmmb, a_p3.3, b_p16.4, c_p11.3 Å parent structure) polymorph. The incommensurate polymorph is shown to be very closely related to the only known polymorph of Ni_6±xSe₅ and is rapidly stabilized to room temperature upon doping of the sulfide compounds with selenium.     

D-Gluconhydroximo-1,5-lactam and Related N-Arylcarbamates Theoretical Calculations,Structure, Synthesis,and Inhibitory Effect on β-Glucosidases

The known D -gluconhydroximo-1,5-lactam (= D -glucono-1,5-lactam oxime) 7a , its nitrogen isotopomers 7b and 7c , and the N-arylcarbamates 26–29 were synthesized from 2,3,4,6-tetra-O-benzyl-D -glucono-1,5-lactam ( 11a ) and its nitrogen isotopomer 11b to establish the controversial structure of 7a and to study the inhibition of β-glucosidases by the N-arylcarbamates 26–29 . Conversion of 11a with Lawesson's reagent yielded a mixture of the thionolactam 15a and its manno-configurated isomer 16a , which was transformed into a mixture of the benzylated hydroximo-lactam 13a and the manno-isomer 17a . Debenzylation (Na/NH₃) and acetylation of this mixture led to the gluco-configurated pentaacetate 14a and the manno-isomer 18a . Treatment of 11a with Et₃O·BF₄ and then with H₂NOH gave exclusively the benzylated D -gluconhydroximo-1,5-lactam (benzylated D-nojirilactam oxime) 13a , which was transformed into 14a . Deacetylation of 14a yielded the hydroximo-lactam 7a . The isotopomers 7b and 7c were obtained by analogous reaction sequences, using either ¹⁵NH₃ or ¹⁵NH₂OHHCl. To prepare the acetylated N-arylcarbamates 20–25 , 13a was debenzylated and acetylated (→ 14a ), followed by selective deacetylation to the tetraacetate 19a and treatment with the appropriate isocyanates. The structure of the 2-chlorophenyl carbamate 21 was established by X-ray analysis. Deacetylation of 20–23 led to the N-arylcarbamates 26–29 . The ¹⁵N-NMR spectra of 7b , 7c , and of their precursors 13b , 13c , 14b , and 14c , show that the C?N bond in all these lactam oximes is exocyclic as predicted from semiempirical and ab initio SCF-MO calculations on the structure of acetamide oxime and 5-pentanelactam oxime. According to these calculations, 5-pentanelactam oxime is a (Z)-configurated, flattened chair. X-ray analysis established the structure of D -glucono-1,5-lactam oxime ( 7a ) in the solid state, where it adopts a conformation between ⁴C₁ and ⁴H₃. In H₂O, 7a is a flattened ⁴C₁. The calculations also predict that protonation at the exocyclic N-atom strengthens the conjugation between the endocyclic N-atom and the hydroxyimino group, and leads to a half-chair conformation. This is evidenced by the chemical shift differences in the ¹⁵N-NMR spectra observed upon protonation of 7b and 7c . The hydroximolactam 7a and the N-arylcarbamates 26–29 are competitive inhibitors of the β-glucosidases from sweet almond (emulsin) and from Agrobacterium faecalis (= Abg), with K_I values between 8 and 21·10^?6M against emulsin (at pH 6.8) and between 0.15 and 1.2·10^?6M against Abg (at pH 7.0).     

A universally applicable composite modulated structure approach to ordered BaxMyTi8−yO16 hollandite-type solid solutions

A wide range of barium titanate hollandites of the form (M=Zn, Co, Mg, Fe and Mn) and (M=Fe) with nominal x ranging from 1.0 to 1.4 have been synthesized and examined to investigate the solid solution range and the nature of the ordering of the Ba ions. Electron diffraction studies confirm that the barium titanate hollandites are composite modulated single phase solid solutions made up of mutually incommensurable (along b) framework and Ba ion sub-structures. The overall superspace group symmetry was found to be I′2/m(0,,0)1. The symbol I′ here refers to the superspace centering operation (see below). Both the framework and the Ba sub-structures have the same I2/m average structure space group symmetry. The solid solution ranges for the hollandites were calculated from the positions of well-defined superlattice peaks in X-ray diffraction patterns. The effect of cooling rate on Ba ion ordering is also examined.     

The Interactive Development of Visual Simulation Models

Visual interactive simulation has been shown to have advantages over conventional ‘batch’ simulation. This paper suggests that further gains could be made by providing the facilities necessary for the interactive development of such models. An experimental system is described which embodies some of these facilities.