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.)     

CeO2和Pd在Ni/γ-Al2O3催化剂中的助剂作用

采用脉冲微反技术研究了添加n型半导体氧化物CeO2及贵金属Pd对Ni/γ Al2O3催化剂上CH4积炭/CO2消炭反应性能的影响,并运用BET、TPR、CO2 TPSR及氢吸附等技术对催化剂进行了表征.结果表明, n型半导体氧化物CeO2的添加可以降低Ni/γ Al2O3催化剂上CH4裂解积炭活性,提高CO2消炭活性,添加少量贵金属Pd可以进一步改变载体Al2O3、助剂CeO2和活性组分Ni之间的相互作用,从而改善Ni/γ Al2O3催化剂的抗积炭性能.通过Ni Ce Pd/γ Al2O3催化剂上CH4积炭/CO2消炭模型对上述作用机制作出了新的解释.     

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].     

钴(II)-联吡啶-α-氨基酸的热力学和动力学研究

关于联吡啶为第一配体的二元、三元配合物的热力学和动力学性质的研究,以铜（Ⅱ）作为中心离子最为多见,而以钴（Ⅱ）作为中心离子的报导较少．实验表明,过渡金属钻（Ⅱ）能与大多数的生物配体、大π共轭体系形成相当稳定的二元、三元配合物,是生物功能模拟的一个具有应用价值的中心离子·钴（Ⅱ）卟啉可以代替铁（Ⅱ）卟啉,模拟血红蛋白、肌红蛋白[1],在生物体内起到输送氧的作用．为了充分了解钴（Ⅱ）与生物配体的配伍能力、配位方式以及其配位过程的动态行为,为推动钴（Ⅱ）配合物及其生物功能的模拟研究,本文分别采用PH电位法…     

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.

     

ImmobilizedE. coli Alkaline Phosphatase

We have immobilized E.coli alkaline phosphatase (EC 3.1.3.1) by linking it covalently to sepharose 4B. This preparation has several advantages over the soluble enzyme. The immobilized enzyme is easily separable from other constituents in incubation mixtures. The immobilized enzyme can be reused repeatedly and is more stable than the soluble enzyme to heat treatment in the presence of 10 mM Mg²⁺. The insoluble and soluble phosphatases removed 75 and77%, respectively, of the inorganic phosphorus from casein. The immobilized enzyme inactivated two enzymes believed to be active in the phosphorylated state, acyl-CoA : cholesterol acyltransferase (ACAT) by 39% and NADPH-cytochrome P-450 reductase by 89%. The utility of immobilized alkaline phosphatase for studying the phosphorylation and dephosphorylation of soluble or membrane-bound enzymes and proteins is discussed.     

Quantum-mechanical exploration of the properties of the sugar rings

Theab initio SCF method is used for computing the main electronic properties of the ribose unit of the nucleic acids. The present study is devoted to the ribose in the C₃-endo,gg conformation. The properties investigated include the distribution of the electronic charges, the electrostatic molecular potential around the four oxygens of the unit, the hydration and the Na⁺ binding schemes studied in the supermolecule approximation. The possibilities of through-water binding of the cation to the sugar are also explored. The predictions of the computation in particular with regard to cation binding to the ribose ring are correlated with recent experimental results.     

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.     

Coordination around thorium(IV) in aqueous perchlorate,chloride and nitrate solutions

The coordination around the thorium(IV) ion in aqueous perchlorate, chloride and nitrate solutions has been determined from large angle X-ray scattering measurements. In perchlorate solutions, where inner-sphere complexes are not formed, the first coordination sphere contains 8.0±0.5 water molecules with Th-H₂O bond lengths of 2.48₅ Å. In chloride solutions inner-sphere complexes are formed, which lead to an increase in the coordination number. In nitrate solutions the nitrate ions are bonded as bidentate ligands to the thorium ion. The bond lengths are similar to those found in crystalline hydrates of thorium nitrate. The coordination numbers found for thorium(IV) in solution are compared with previously reported values for lower charged ions of similar size.On leave from Department of Inorganic Chemistry Royal Institute of Technology S-10044 Stockholm Sweden