Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales

The Fock transform recently introduced by the authors in a previous paper is applied to investigate convergence of generalized functional sequences of a discrete-time normal martingale $M$. A necessary and sufficient condition in terms of the Fock transform is obtained for such a sequence to be strong convergent. A type of generalized martingales associated with $M$ are introduced and their convergence theorems are established. Some applications are also shown.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1504.0500

Kenaf bast for fiber reinforced polymer composites

Cellulosic fibers sized from the macro-scale to the nano-scale were prepared hierarchically from kenaf bast fibers using chemicals. The process began with a hermetical alkaline retting followed by a bleaching treatment. The bleached fibers were hydrolyzed using inorganic acid, from which microfibers and cellulose nanowhiskers (CNWs) were fabricated. Inorganic nanoparticle impregnation (INI) was used to treat the retted fibers for the improvement of the interfacial compatibility between the fiber and polypropylene (PP) matrix. The retted fibers and INI-treated fibers were used as reinforcement for the PP polymer composites. Film casting process was used to make CNW/PVA composites. The hermetical retting process used in this study produced fibers with high cellulose contents (81-92%) by removing the lignin and hemicelluloses. Higher retting temperature resulted in higher fiber surface hardness and elastic moduli. The tensile strengths and tensile moduli of the fibers decreased as the temperature increased. The SEM images showed the micropores in the cell wall structure for the fibers retted at over 130°C, providing the possibility to anchor nanoparticles into the cell wall. Surface morphology of the INI-treated fibers was examined with SEM, and showed that the CaCO3 nanoparticle crystals grew onto the fiber surface. Energy-dispersive X-ray spectroscopy (EDS) was used to verify the CaCO3 particle deposits on the fiber surface. As the size scale of the fibers decreased, the fiber crystallinity increased from 49.9% (retted fibers) to 83.9% (CNWs). About 23% á-cellulose in the raw kenaf bast fibers had been converted into CNWs. The retted fibers without INI treatment had poor compatibility with the polypropylene matrix. The INI treatment improved the compatibility between the fibers and the PP matrix, resulting in an improvement in kenaf fiber/PP composite tensile moduli and tensile strengths. The CNWs prepared from kenaf bast fiber gave excellent reinforcement for PVA composites. A nine percent increase of CNWs in the CNW/PVA composites yielded significant improvements in tensile strength and modulus of about 46% and 152%, respectively, compared with pure PVA

Yukawa Corrections to gamma gamma --> b\bar{b} in the Topcolor Assisted Technicolor Models

We study the Yukawa corrections to the gamma gamma --> b\bar{b} corss section in the topcolor assisted technicolor models at the photon-photon colliders. We find that, for the favorable parameters, the relative corrections from pseudo Goldstone bosons give out a 3.2%--5.9% decrement of the cross section from the tree level when \sqrt{s}=500 GeV, the contributions from new extended technicolor gauge bosons Z* and colored gauge bosons B are negligibly small, and the relative correction arising from new color-singlet heavy gauge boson Z' is less than -3.2%. Therefore, the total relative corrections are significantly larger than the corresponding corrections in the standard model, the general two Higgs doublet model and the minimal supersymmetric standard model. Since these corrections are obvious for the International Linear Colliders, the process gamma gamma --> b\bar{b} is really interesting in testing the standard model and searching for the signs of technicolor.Comment: 24 pages, 6 figures, version appeared in PR