On averaging sets

For any set ={f ₁,f ₂,...,f _s} ofC ³-functions on the interval [–1, 1], and for any weight functionw(x) satisfyingL ₁w(x)L ₂(1–|x|)(L ₁,L ₂>0, 0) and , we give a constructive proof for the existence of quadrature formulas of the type

1, 4, 5, 6-Tetrahydro-ν-tetrazin-Derivate

1, 4, 5, 6-Tetrahydro-ν-tetrazin-Derivate The title compounds 2 and 13 are readily available from α-lithiated N-alkyl-nitrosoamines 1 (see Tables 1 and 2) which decompose at ? 73° to yield the N-oxides 2. The ESR. spectra of two derivatives 1 are recorded (Fig. 1), and tentative mechanisms are proposed for the head to head dimerizations ( la- 3- 4- 5- 2a and Scheme 1). Coupling of lithionitrosoamines with iodine (-6) and alternative decomposition routes of representatives of this class of organometallics with special substitution [equations (2)-(5)] are reported. The structures of the tetrazines are established by spectroscopic data [ESCA] (Fig. 2), IR., UV., ¹H- (cf. Fig. 9) and ¹³C-NMR., PE. (Scheme 2), by an X-ray analysis of 2a (Fig. 4-8 and Table 3), and by the chemical reactions. The crystal structure of 2a is a twisted boat with non planar terminal nitrogen atoms which reflects the electron repulsion in the 4-atom-6-electron N? N?N?N-system. Comparisons are made with 2-tetrazenes, the open chain analogues of 13 , wherever possible. Raney-Ni reductions of 2 or 13 gives diamines 14 to which is assigned the d, l-configuration through the ¹H-NMR. spectra of the aminals 7 and 15 . Neither the oxides 2 nor the tetrazines 13 undergo cycloaddition reactions [equation (6) and Section 4]. Compound 2a is dimerized to the bis (nitrosoamino)-2-tetrazene 18 by treatment with acid, Zn^II, Cu^I or iodomethane. 2a is oxidized at nitrogen to the ethylene diamine derivative 6a (through 20 , with H₂O₂), or at the CH₂-groups of the ring to give oxo-N-oxide 21 (with MnO₂ or the ring contracted oxo-tetrazoline-N-oxide 22 (with KMnO₄). Pyrolysis or photolysis of the dimethyl tetrahydrotetrazine 13a furnishes the trimer 26 of N-methylimine, but no diazetidine 27 . Silver and mercury complexes 29 are obtained from 13a , while Cr(CO)₅. THF does not furnish a complex as with azocompounds, but rather replaces N₂ in 13a by CO (→ 28). Oxidation with permanganate converts 13a into the oxalic acid derivative 30 with unchanged tetrazine structure.     

Analysis of the quorum-sensing regulon of the opportunistic pathogen Burkholderia cepacia H111 by proteomics

Burkholderia cepacia H111, an important pathogen for persons suffering from cystic fibrosis, employs a quorum-sensing (QS) system, cep, to control expression of virulence factors as well as the formation of biofilms. The QS system is thought to ensure that pathogenic traits are only expressed when the bacterial population density is high enough to overwhelm the host before it is able to mount an efficient response. In this study, we compared the protein pattern of the intracellular, extracellular, and surface protein fractions of an AHL-deficient cepI mutant with the one of the parent strain H111 by means of two-dimensional gel electrophoresis (2-DE). Our analysis showed that 55 proteins out of 985 detected spots were differentially expressed; these are expected to represent QS-controlled gene products. Addition of the respective signal molecules to the growth medium of the cep mutant fully restored the wild-type protein expression profile. In total about 5% of the B. cepacia proteome was downregulated and 1% upregulated in the cepI mutant, indicating that quorum sensing represents a global regulatory system. Nineteen proteins were identified with high confidence by N-terminal sequence analysis.     

Deep hydration of an Li7–3xLa3Zr2MIIIxO12 solid-state electrolyte material: a case study on Al- and Ga-stabilized LLZO

Single crystals of an Li-stuffed, Al- and Ga-stabilized garnet-type solid-state electrolyte material, Li₇La₃Zr₂O₁₂ (LLZO), have been analysed using single-crystal X-ray diffraction to determine the pristine structural state immediately after synthesis via ceramic sintering techniques. Hydrothermal treatment at 150 °C for 28 d induces a phase transition in the Al-stabilized compound from the commonly observed cubic Iad structure to the acentric I3d subtype. Li^I ions at the interstitial octahedrally (4 + 2-fold) coordinated 48e site are most easily extracted and Al^III ions order onto the tetrahedral 12a site. Deep hydration induces a distinct depletion of Li^I at this site, while the second tetrahedral site, 12b, suffers only minor Li^I loss. Charge balance is maintained by the incorporation of H^I, which is bonded to an O atom. Hydration of Ga-stabilized LLZO induces similar effects, with complete depletion of Li^I at the 48e site. The Li^I/H^I exchange not only leads to a distinct increase in the unit-cell size, but also alters some bonding topology, which is discussed here.     

Zur Kenntnis von Cr2H2(As2O7)(As4O12)

The crystal structure of Cr₂H₂(As₂O₇)(As₄O₁₂) has been determined by X-ray methods using single crystal diffractometer data (1,152 reflections,R=0.054, orthorhombic,Pmmn,a=1317.7 (7),b=1124.9 (6),c=494.3 (4) pm,Z=2). The crystal structure contains both diarsenate(V) and the hitherto unknown cyclo-tetraarsenate(V)-anions. The magnetic susceptibility follows theCurie-Weiss law (=3.86±0.01 _B/Cr³⁺, =–31 K).

     

On the reaction of aminobis(diorganylamino)phosphanes with halogenophosphanes—P-hydrogeno(iminophosphoranyl)-halogenophosphanes and P-hydrogeno(iminophosphoranyl)-σ2, λ3-iminophosphanes

Reactions of triaminophosphane (R₂N)₂P–NH₂, (R = ¹Pr) 1a, with aminodihalogenophosphanes ¹Pr₂N–PX₂, 2a–c [X = CL (a), Br (b), I(c)], in the presence of a base yielded the P-hydrogeno-iminophosphoranyl-halogenophosphanes (R₂N)₂PH = N–PX–N(¹Pr)₂ 4a–c [X = Cl (a), Br (b), I(c)]. Analogous reactions between 1a and 1b (b: R = c-hexyl) and chloroiminophosphane (Cl–P = N–Mes^*, (Mes^* = 2,4,6-^tBu₃C₆H₂) 6 , gave the P-hydrogeno(iminophosphoranyl)-σ²,λ³-iminophosphanes, (R₂N)₂PH = N–P = N–Mes^* 8a and 8b. In solution 8a, 8b eliminated amine, yielding σ², λ³-iminophosphanyl-substituted 1,3,2,4-diazadiphosphetidines [(R₂N)PN(P = N–Mes^*)]₂, 10a, 10b , and 11 ( 10a and 10b : cis; 11: trans). The X-ray structure analyses of compounds 4a, 4b, 8a, and 11 are discussed. © 1996 John Wiley & Sons, Inc.     

Externe Kristalljustierung für die Lang-Topographie

In dependence on crystal altitude, Bragg angle and distance focus-crystal the necessary accuracy of crystal adjustment is calculated on condition that with illumination of the full crystal height the Kα-doublet is separable. In this connection a critical crystal altitude for the Lang-topography is stated, which requires a faultless adjustment of the net plane. For the real altitude of crystal resp. film adequate demands for adjustment are derived. A simple diffractometer device for external crystal adjustment if described and the attainable accuracy is indicated.