On the Strong Law of Large Numbers and the Law of the Logarithm for Weighted Sums of Independent Random Variables with Multidimensional Indices

Let (X, X ; ^d} be a field of independent identically distributed real random variables, 0 < p < 2, and {a _, ; ( , ) ^d × ^d, ≤ } a triangular array of real numbers, where ^d is the d-dimensional lattice. Under the minimal condition that sup _, |a _, | < ∞, we show that | |^{− 1/p} ∑ _≤ a _, X → 0 a.s. as | | → ∞ if and only if E(|X|^p(L|X|)^{d − 1}) < ∞ provided d ≥ 2. In the above, if 1 ≤ p < 2, the random variables are needed to be centered at the mean. By establishing a certain law of the logarithm, we show that the Law of the Iterated Logarithm fails for the weighted sums ∑ _≤ a _, X under the conditions that EX = 0, EX² < ∞, and E(X²(L|X|)^{d − 1}/L₂|X|) < ∞ for almost all bounded families {a _, ; ( , ) ^d × ^d, ≤ of numbers.     

Fractional extensions of some boundary value problems in oil strata

In the present paper, we solve three boundary value problems related to the temperature field in oil strata — the fractional extensions of the incomplete lumped formulation and lumped formulation in the linear case and the fractional generalization of the incomplete lumped formulation in the radial case. By using the Caputo differintegral operator and the Laplace transform, the solutions are obtained in integral forms where the integrand is expressed in terms of the convolution of some auxiliary functions of Wright function type. A generalization of the Laplace transform convolution theorem, known as Efros’ theorem is widely used.     

高分子阳离子絮凝剂用于炼油废水处理研究

用聚二甲基二烯丙基氯化铵型高分子阳离子絮凝剂处理炼油废水考察了险油和化学耗氧量的动态变化规律。对产生的浮渣性质及滤饼的成份进行了研究。并且与聚合铝的处理效果进行对照。研究结果表明，ＨＣＡ除油和化学耗管氧量的性能优于ＰＡＣ，ＨＣＡ产生的浮渣是ＰＡＣ的三分之一，而浮渣中的含油量则是ＰＡＣ的三倍。     

Valence band and chemical interactions of Zn/CdSnAs2 interfaces

X-ray photoelectron spectroscopy (XPS) together with argon ion sputtering was used to investigate the interface of the Zn/CdSnAs₂ system at various temperatures. The formation of an intermediate compound between Zn and As is proposed. The surface enrichment of Cd and Sn at 200 and 400°C is explained in terms of bond breaking and lattice strain theories.NCL Communication No. 4352     

Effect of60Co gamma radiation on La2CuO4

The effect of⁶⁰Co -radiation on La₂CuO₄ solid catalyst prepared by the ceramic method has been studied. Gamma irradiation of La₂CuO₄ samples has been found to increase the Cu⁺ content, electrical conductivities and decrease the magnetic susceptibilities of the catalyst. The results have been interpreted on the basis of the crystal field model of the structure of La₂CuO₄.     

Potential energy curves: A simple and rapid method

The true potential energy curves for different electronic states of diatomic molecules have been constructed by a simplified and modified form of the Jarmain method. To check the validity of this new procedure potential energy curves are constructed for NO⁺, VO, Si₂, AsO, AsO⁺, PF⁺, CO and Bi₂. The results are in good agreement with the Jarmain, RKRV and Lakshman and Rao methods.     

Structural changes by sulfoxidation of phenothiazine drugs

Summary The side-chain conformations of psychoactive phenothiazine drugs in crystals are different from those of biologically inactive ring sulfoxide metabolites. This study examines the potential energies, molecular conformations and electrostatic potentials in chlorpromazine, levomepromazine (methotrimeprazine), their sulfoxide metabolites and methoxypromazine. The purpose of the study was to examine the significance of the different crystal conformations of active and inactive phenothiazine derivatives, and to determine why phenothiazine drugs lose most of their biological activity by sulfoxidation. Quantum mechanics and molecular mechanics calculations demonstrated that conformations with the side chain folded over the ring structure had lowest potential energy in vacuo, both in the drugs and in the sulfoxide metabolites. In the sulfoxides, side chain conformations corresponding to the crystal structure of chlorpromazine sulfoxide were characterized by stronger negative electrostatic potentials around the ring system than in the parent drugs. This may weaken the electrostatic interaction of sulfoxide metabolites with negatively charged domains in dopamine receptors, and cause the sulfoxides to be virtually inactive in dopamine receptor binding and related pharmacological tests.     

Amine-templated metal squarates

Two layered amine-templated cobalt squarates, [C₆N₂H₁₄]₂[Co₂(C₄O₄)₃(H₂O)₄], I, and [C₃N₂H₅]₂[Co₂(C₄O₄)₃(H₂O)₄], II, have been prepared under hydrothermal conditions. Both I and II contain chains formed by dimers comprising two cobalt atoms bound to the squarate units, the chains being connected through hydrogen bond interactions. An amine-templated cobalt squarate of the formula [C₄N₂H₁₂][Co(C₄O₄)₂(H₂O)₄][H₂O]₂, III, as well as its Ni, Zn and Cd analogues have been prepared by room temperature reactions. III has a layered architecture wherein the cobalt-squarate monomers are linked by the amine molecules. Co and Zn analogues of [Ni(C₄O₄)(H₂O)₂(C₃N₂H₄)] with ligating imidazole units have also been prepared and characterized.     

Non-isothermal thermogravimetric pyrolysis kinetics of waste petroleum refinery sludge by isoconversional approach

Pyrolysis of petroleum refinery sludge has received global acclamation as a clean conversion technique for providing solution of sludge disposal as well as efficient resource utilization. This communication reports the kinetics study of pyrolysis of petroleum refinery sludge. Experiments were carried out by means of thermogravimetric analysis at different heating rates of 5, 10 and 20°C min⁻¹. The pyrolytic reaction is significant in the temperature range of 200–350°C and analysis and evaluation of kinetic parameters is done in the 100–500°C region of non-isothermal TG curves obtained in nitrogen atmosphere. The activation energy is calculated by iso-conversional method, then other kinetic parameters are determined by considering single reaction and two reaction global kinetic model. Two-reaction model is found to fit satisfactorily the experimental results.