The spectrum of additive BIB designs

In this article, the existence of additive BIB designs is discussed with direct and recursive constructions, together with investigation of a property of resolvability. Such designs can be used to construct infinite families of BIB designs. In particular, we obtain a series of B(sⁿ, ts^m, λt (ts^m ? 1) (s^n‐m ? 1)/[2(s^m ? 1)]) for any positive integer λ, such that sⁿ (sⁿ ? 1) λ ≡ 0 (mod s^m (s^m ? 1) and for any positive integer t with 2 ≤ t ≤ s^n‐m, where s is an odd prime power. Connections between additive BIB designs and other combinatorial objects such as multiply nested designs and perpendicular arrays are discussed. A construction of resolvable BIB designs with v = 4k is also proposed. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 235–254, 2007     

The Strassen law of iterated logarithm for combinatorial assemblies

In [13], we investigated one-dimensional laws of iterated logarithm for additive functions defined on a class of combinatorial assemblies. In this paper, we obtain a functional law of iterated logarithm. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 2, pp. 211–219, April–June, 2007.     

The Limiting Spectra of Girko’s Block-Matrix

To analyze the limiting spectral distribution of some random block-matrices, Girko (Random Oper. Stoch. Equ. 8(2), 189–194, 2000) uses a system of canonical equations from (An Introduction to Statistical Analysis of Random Arrays. VSP, Utrecht, 1998). In this paper, we use the method of moments to give an integral form for the almost sure limiting spectral distribution of such matrices.     

CONVERGENCE RATE OF A GENERALIZED ADDITIVE SCHWARZ ALGORITHM

The convergence rate of a generalized additive Schwarz algorithm for solving boundaryvalue problems of elliptic partial differential equations is studied.A quantitative analysisof the convergence rate is given for the model Dirichlet problem.It will be shown that agreater acceleration of the algorithm can be obtained by choosing the parameter suitably.Some numerical tests are also presented in this paper.     

Estimates on the Transition Densities of Girsanov Transforms of Symmetric Stable Processes

In this paper, we first study a purely discontinuous Girsanov transform which is more general than that studied in Chen and Song [(2003), J. Funct. Anal. 201, 262–281]. Then we show that the transition density of any purely discontinuous Girsanov transform of a symmetric stable process is comparable to the transition density of the symmetric stable process. The same is true for the Girsanov transform introduced in Chen and Zhang [(2002), Ann. Inst. Henri poincaré 38, 475–505]. As an application of these results, we show that the Green function of Feynman–Kac type transforms of symmetric stable processes by continuous additive functionals of zero energy, when exists, is comparable to that of the symmetric stable process.      

Hydrogen production on iron–magnesium oxide in the high-temperature water-gas shift reaction

The effect of the structure of the achiral primary amine additive on the enantioselective heterogeneous catalytic hydrogenation of (E)-2-methyl-2-butenoic acid over cinchonidine modified Pd/Al₂O₃ was studied. It was found that a variety of amines increase the enantioselectivity, which was always accompanied by decrease in the initial rate of the hydrogenations. Based on these results, the participation of the amine additive in the formation of the intermediate complex responsible for enantioselection was suggested. A decrease in the reaction temperature resulted in further increase in the optical purity of the product up to 67%, the highest value reported in the hydrogenation of unsaturated aliphatic acids in this heterogeneous catalytic system so far.     

On the use of purely finitely additive multipliers in mathematical programming

In this paper, duality results are obtained for the problem of finding =inf{f(x):g(x)0,g(x)Y,xC}, where the constrainst spaceY is someL -space, by using the norm topology ofY. The corresponding multiplier is the sum of a countably additive part and a purely finitely additive part. Conditions are given such that the purely finitely additive part may be discarded.     

Effect of chromium residues on the stability of gas-phase high-density polyethylene produced by supported catalysts

The thermo-oxidative stability of high-density polyethylene (HDPE) prepared by silica supported Ziegler-Natta, bis(triphenylsilyl)chromate and bis(cyclopentadienyl)-chromium(II) catalyst systems was examined by chemiluminescence (CL) techniques and thermogravimetric (TG) analysis. In particular, the technique of dynamic CL in nitrogen allows the concentration of polymer hydroperoxides and the relative stability of these to be simultaneously determined. Polymer hydroperoxides in Ziegler-Natta catalyzed HDPE are relatively stable because titanium and aluminum residues are poor pro-oxidants compared with chromium residues. HDPE produced by bis(cyclopentadienyl)chromium(II) has a low intrinsic thermo-oxidative stability due to the chromium-catalyzed conversion of polymer hydroperoxides into degradation products during thermal aging. Concentrations of residual chromium as low as 1 ppm can profoundly affect the oxidative stability of the polymer and exert a much greater influence than either the extent of branching or the degree of unsaturation. The appearance of the silica catalyst support before and after gas-phase polymerization was studied by scanning electron microscopy. During polymerization the silica support shatters and the resulting submicron fragments are dispersed throughout the polymer particles. On exposure of the nascent polymer to the atmosphere, bis(cyclopentadienyl)chromium(II) is converted to a trivalent chromium species which remains associated with the silica substrate. The presence of trivalent chromium in the poisoned chromium catalyst was confirmed by UV/visible spectrophotometry and the nature of the Cr(III) species was investigated by diffuse reflectance Fourier transform infrared (FTIR) spectroscopy. The high surface area of the catalyst residue renders it a powerful pro-oxidant despite its low concentration. © 1992 John Wiley & Sons, Inc.     

The effect of Zn, Al layered double hydroxide on thermal decomposition of poly(vinyl chloride)

Poly(vinyl chloride)/layered double hydroxide (LDH) composite was prepared by mixing 4 wt% Zn₂Al-CO₃-LDH with PVC and fluxing at 180 °C. The thermal decomposition behaviour of the LDH + PVC composite in air and nitrogen environments was systematically investigated. We found that mixing Zn₂Al-CO₃-LDH into PVC facilitates dehydrochlorination from ca. 300 to 270 °C but reduces the reaction extent to leave more chlorine on the polyene backbones both in air and N₂. We have also found that at 400-550 °C, both in air and N₂, LDH assists the formation of char-like materials and decreases the release of volatile hydrocarbons. From 550 to 800 °C, the char-like materials are mostly retained in N₂ while they are almost completely thermo-oxidized (burned) in air. Thus, addition of Zn₂Al-CO₃-LDH to PVC does not increase the thermal stability, but does promote charring to retard the generation of flame. The influence of LDH on PVC thermal properties has been also addressed mechanically.