Linear combination of concomitants of order statistics with application to testing and estimation

Summary Let (X ₁,Y ₁), (X ₂,Y ₂),…, (X _n,Y _n) be i.i.d. as (X, Y). TheY-variate paired with therth orderedX-variateX _rn is denoted byY _rn and terms the concomitant of therth order statistic. Statistics of the form are considered. The asymptotic normality ofT _n is established. The asymptotic results are used to test univariate and bivariate normality, to test independence and linearity ofX andY, and to estimate regression coefficient based on complete and censored samples.     

Derivation of the transport equation for electrons moving through random impurities

A single (nonrelativistic, spinless) electron subject to a constant external electric field interacts with impurities located on an infinitely extended lattice by a potential of random strength. The random strength is given by a field of Gaussian random variables. We show the existence of the averaged dynamics and prove that in the weak coupling limit, 0, ₂ t= fixed, one obtains the usual transport equation for the velocity distribution.Work supported by a Max Kade Foundation fellowship.On leave of absence of the Fachbereich Physik der Universität München.     

A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)     

Effect of conformational control of chiral oxazaborolidine by π-π stacking interaction of a pentafluorophenyl group toward asymmetric borane reduction

A pentafluorophenyl group can act as a stereo-controlling group in oxazaborolidine-catalyzed asymmetric borane reduction through intramolecular π-π stacking interaction with a phenyl group. The intramolecular π-π interaction in oxazaborolidine bearing pentafluorophenyl group is confirmed by calculations and ¹H NMR study. The interaction affects the enantioselectivity of the asymmetric reduction of acetophenone while the extent is small.     

Reaktive E = C(p-p)π-Systeme. XLII [1]. Neue Koordinationsverbindungen des 2-(Diisopropylamino)-1-phosphaethins: [{η4-(iPr2NCP)2}Ni{η2-(iPr2NCP)}], [(Ph3P)2Pt{η2-(iPr2NCP)}] und [Co2(CO)6{η2-η2-(iPr2NCP)}]

Reactive E = C(pp)π-Systems. XLII [1]. Novel Coordination Compounds of 2-(Diisopropylamino)-1-phosphaethyne: [{η⁴-(iPr₂NCP)₂}Ni{η²-(iPr₂NCP)}], [(Ph₃P)₂Pt{η²-(iPr₂NCP)}], and [Co₂(CO)₆{η²-μ²-(iPr₂NCP)}] 2-(Diisopropylamino)-phosphaethyne iPr₂N? C?P ( 2 ) reacts with the Ni(0)-complexes [Ni(1,5-cyclooctadiene)₂] and [Ni(CO)₃(1-azabicyclo[2.2.2]octane)], respectively, to give the novel complex [{η⁴-(iPr₂NCP)₂}Ni{η²-(iPr₂NCP)}] ( 5 ), with the 1,3-diphosphacyclobutadiene derivative and 2 (side-on) as π-ligands. The molecular structure of 5 determined by X-ray diffraction on single crystals proves the spin systems and rotational barriers deduced from NMR-data (¹H, ¹³C-, ³¹P). The PC distances of the four-membered ring of 1.817(2) and 1.818(2) Å – as expected – are considerably longer than the PC bond of the η²-coordinated phosphaalkyne 2 [1.671(2) Å]. – In the reactions of 2 with [(Ph₃P)₂Pt(C₂H₄)] or [Co₂(CO)₈] the ligand properties of 2 resemble those of alkynes affording the complexes [(Ph₃P)₂Pt{η²-(iPr₂NCP)}] ( 7 ) with side-on coordinated 2 and [Co₂(CO)₆{η²-μ²-(iPr₂NCP)}] with 2 acting as a 4e donor bridge in quantitative yield. In attempts to prepare copper(I) complexes of the aminophosphaalkyne 2 by reaction with CuCl or CuI the only isolable product formed in reasonable amounts under the influence of air and moisture is the 1 λ³, 3 λ⁵-diphosphetene (iPr₂N) ( 10 ) (isolated yield: ca. 20%). The crystal structure analysis of 10 indicates a strong structural relationship to the diamino-2-phosphaallyl cation [Me(iPr₂N)]⁺ ( 12 ), the 1,3-diphosphacyclobutadiene ligand (iPr₂NCP)₂ in the binuclear complex [{η¹, μ²-(iPr₂NCP)₂}Ni₂(CO)₆] ( 3a ) as well as to the heterocycles (dme)₂LiOE₂′ (E′ = S, 11a ; E′ = Se, 11b ) prepared by Becker et al. [11b, 35].     

Synthese von Clathratverbindungen des Typs Cd(mea) m [Pd(CN)4] ·nG

The preparation, identification and some properties of three new clathrate compounds Cd(mea)[Pd(CN)₄] · 2C₆H₆, Cd(mea)₂[Pd(CN)₄] · C₄H₄S and Cd(mea)₂[Pd(CN)₄] · C₄H₄NH (mea = HO-CH₂-CH₂-NH₂) are described.

     

Synthesis and Crystal Structur of (4,4''-H2bipy)[CdBr4]·H2O

The title compound (4,4'-H2bipy)[CdBr4]·H2O 1 has been synthesized via hydrothermal reaction and characterized by X-ray diffraction. The crystal belongs to monoelinic,space group P21/c with a=8.260(3), b=23.926(7), c=9.774(2) (A), β=106.777(9)°,C10H12Br4CdN2O, Mr=608.26, V=1849.4(9)(A)3, Z=4, Dc=2.185 g/cm3, S=1.005, μ(MoKα)=9.814 mm-1, F(000)=1128, R=0.0646 and wR=0.0989. The crystal structure analysis of 1reveals that the title compound features an isolated structure, based on discrete 4,4'-H2bipy moieties and lattice water molecules which are linked by hydrogen bonds together with tetrahedral cadmium atoms terminally coordinated by four bromine atoms.     

Optimization of the Microwave-Assisted Saponification and Extraction of Organic Pollutants from Marine Biota Using Experimental Design and Artificial Neural Networks

Several improvements in sample pretreatment for the determination of organic pollutants (i.e. n-alkanes, polycyclic aromatic hydrocarbons, PAHs) in marine biota (mussels) are presented. The use of liquid nitrogen and homogenization of the samples are shown to be an alternative to the time consuming liophilization step required for the analysis of biota samples. Microwave-assisted hydrolysis and extraction are combined to isolate organic pollutants (19 n-alkanes and 27 PAHs) from biota matrices. Experimental design (ED) and artificial neural networks (ANNs) were used to optimize the experimental conditions. NIST-CRM 2978 was used to test the validity of the developed method which shows a good agreement with certified values.     

A sequential reaction process to assemble polysubstituted indolizidines, quinolizidines and quinolizidine analogues

The ω-iodo-α,β-alkynoates and their ketone, sulfone or phosphonate analogues react with δ-chloropropylamines in MeCN assisted with K₂CO₃ to undergo a sequential S_N2/Michael addition/S_N2/S_N2 reaction process, giving polysubstituted indolizidines or quinolizidines in good to excellent yields. This sequential reaction process is also compatible with three other substituted α,β-alkynoates, affording quinolizidine analogues in moderate to good yields.     

High performance liquid chromatographic determination of metoclopramide in plasma and urine and its application to biopharmaceutical investigations

An optimized HPLC method for the quantification of metoclopramide (MCP) in human plasma and urine is described. MCP and internal standard are extracted from alkalinized substrate into diethyl ether and back-extracted into dilute acid. The analytes are separated with a ternary mobile phase at cyanopropyl-silica and detected at 312 nm (UV detection). The lower limit of quantification is 0.5 ng/ml in plasma and 50 ng/ml in urine. Optimization of extraction, chromatography, and detection is discussed. The method is selective to numerous common drug substances with excellent accuracy and precision data. After validation, the method is applied to the samples of a pharmacokinetic study. Pharmacokinetic parameters indicate the need for a sophisticated method as tool for optimization of metoclopramide formulations.