On Distributions of Runs in the Compound Binomial Risk Model

This paper is concerned with the distribution of runs associated with claim indicators in a compound binomial risk model. We study the total number of claims, the longest run without claim, the shortest run without claim and the total number of runs up to a fixed period before the occurrence of a ruin. These quantities are potentially useful for an investment strategy of an insurance company and for understanding the behavior of a specific portfolio over time. We obtain recursive equations for the exact distributions of these random variables. We also illustrate the theoretical results with numerical computations.     

Heat transfer effects on the stability of low speed plane Couette-Poiseuille flow

The stability problem of low-speed plane Couette-Poiseuille flow of air under heat transfer effects is solved numerically using the linear stability theory. Stability equations obtained from two-dimensional equations of motion and their boundary conditions result in an eigenvalue problem that is solved using an efficient shoot-search technique. Variable fluid properties are accounted for both in the basic flow and the perturbation (stability) equations. A parametric study is performed in order to assess the roles of moving wall velocity and heat transfer. It is found that the moving wall velocity and the location of the critical layers play decisive roles in the instability mechanism. The flow becomes unconditionally stable whenever the moving wall velocity exceeds half of the maximum velocity in the channel. With wall heating and Mach number effects included, the flow is stabilized.     

Novel red-emitting phosphors, (Mg(1−x−y)MnxDyy)Al2Si2O8 and (Mg(1−x−y)MnxTmy)Al2Si2O8

Mn⁴⁺ doped and Dy³⁺, Tm³⁺ co-doped MgAl₂Si₂O₈-based phosphors were prepared by conventional solid state reaction at 1,300 °C. They were characterized by thermogravimetry, differential thermal analysis, X-ray powder diffraction, photoluminescence, and scanning electron microscopy. The luminescence mechanism of the phosphors, which showed broad red emission bands in the range of 600–715 nm and had a different maximum intensity when activated by UV illumination, was discussed. Such a red emission can be attributed to the ²E → ⁴A₂ transitions of Mn⁴⁺.     

Effect of the TiC content on microstructure and thermal properties of Cu–TiC composites prepared by powder metallurgy

Copper matrix with an individual addition of TiC particles was prepared by means of powder metallurgy and hot pressing process, and the effect of TiC addition on microstructure, thermal properties, and electrical conductivity of Cu–TiC composites was investigated. The TiC quantity was changed as 1, 3, 5, 10, and 15 Cu (in mass%), and Cu–TiC powder mixtures were hot-pressed for 4 min at 700 °C under an applied pressure of 50 MPa. Microstructure studies revealed that TiC particles were distributed uniformly in the Cu matrix. Thermal Analysis result showed that there were two exothermic peaks and with rising TiC rate, oxidation amount of Cu composite decreased. With the increasing addition of TiC, hardness of composites changed between 58.6 HV_0.1 and 87.8 HV_0.1. The highest electrical conductivity for Cu–TiC composites was obtained in the Cu-1 mass% TiC composite, with approximately 81.2 % IACS.     

Direct enantioselective aldol reactions catalyzed by calix[4]arene-based l-proline derivatives in the water

Two novel p-tert-butylcalix[4]arene-based chiral organocatalysts derived from l-proline have been developed to catalyze direct aldol reactions between cyclohexanone and aromatic aldehydes in water. Under the optimal conditions, high yields (up to 95%), enantioselectivities (up to 90%), and moderate diastereoselectivities (up to 65:35) were obtained. Considering the catalytic inefficiency of sole proline for the aldol reaction in water, these results clearly display the enormous effect of the hydrophobic part of calix[4]arene of compound A.     

Poly(caprolactone) containing highly branched segmented poly(ester urethane)s via A2 with oligomeric B3 polymerization

Highly branched, poly(caprolactone) (PCL) containing segmented poly(ester urethane)s were synthesized via polymerization of A₂ and oligomeric B₃ type monomers. An isocyanate functional butanediol‐based A₂ hard segment was synthesized and immediately reacted with a poly(caprolactone)‐based trifunctional (B₃) soft segment. Characterization of thermal properties using DMA and DSC analysis demonstrated that the PCL segment remained amorphous in branched poly(ester urethane)s. Conversely, the crystallinity of PCL segment was retained to some extent in a linear analogue with equivalent soft segment molecular weight. Tensile testing revealed a slight decrease in Young's modulus and tensile strength for the highly branched polymers compared with a linear analogue. However, highly branched poly(ester urethane)s demonstrated lower hysteresis. In addition to synthesis of highly branched polymers, poly(ester urethane) networks were synthesized from a highly branched hydroxyl‐terminated precursor and a low molar mass diisocyanate as the crosslinking agent. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6285–6295, 2008     

A note on runs of geometrically distributed random variables

Recently, Grabner et al. [Combinatorics of geometrically distributed random variables: run statistics, Theoret. Comput. Sci. 297 (2003) 261-270] and Louchard and Prodinger [Ascending runs of sequences of geometrically distributed random variables: a probabilistic analysis, Theoret. Comput. Sci. 304 (2003) 59-86] considered the run statistics of geometrically distributed independent random variables. They investigated the asymptotic properties of the number of runs and the longest run using the corresponding probability generating functions and a Markov chain approach. In this note, we reconsider the asymptotic properties of such statistics using another approach. Our approach of finding the asymptotic distributions is based on the construction of runs in a sequence of m-dependent random variables. This approach enables us to find the asymptotic distributions of many run statistics via the theorems established for m-dependent sequence of random variables. We also provide the asymptotic distribution of the total number of non-decreasing runs and the longest non-decreasing run.     

Effect of hexane on magnetic blocking behavior of FePt nanoparticles

In this work effect of the carrier fluid, hexane, on the magnetic properties of 4.7 nm sized FePt nanoparticles is investigated. Nanoparticles are synthesized by chemical method. Structural and magnetic characterizations confirmed that samples are monodispersed with disordered face centered cubic (fcc) crystal structure and, magnetically, exhibit two blocking behaviors; the first is at 27 K and second at 110 K. Carrier fluid of particles, hexane, is found to influence the blocking of 7% of the total magnetic moments in the system by freezing at low temperatures resulting in a two blocking phenomena even for nanoparticles that are monodispersed with narrow particle size distribution.     

Comparative Evaluation of the Effects of Bone Powder and Calcium Phosphate on Plant Growth and Development

The present study aimed to elucidate the effectiveness of inorganic element composition (except for calcium and phosphorus) of bone powder (BP) on some morphological (root and shoot length and dry weight) and biochemical (protein, sugar, chlorophyll, and inorganic element contents) parameters in bean seedlings. For this, BP was compared with calcium phosphate (CP), which is used as calcium and phosphorus source. Bone powder solutions (BPS) (0.5, 1, 1.5, and 2%) and CP solution (0.1 M) were applied to growing media of 12-day bean seedlings. Seedlings were harvested on 20th day. Both BPS and CP treatments significantly stimulated plant growth and increased dry weight, pigment, protein, and sugar contents compared to control seedlings; however, BPS treatments were found to be more effective than CP treatment. The best stimulatory effect on plant growth was determined at 1.5% concentration of BPS. Besides, BP treatment significantly increased contents of K, S, Fe, Zn, Mg, Mn, and Cu compared to control and CP-treated seedlings. This result clearly elucidated that the other elements existing in structure of BP also participated in plant structure, and they played important roles on growth and development in bean seedlings. It is possible to say that BP

may be used as an important source of the other inorganic elements as well as Ca and P in agriculture studies for improving of plant growth and productivity. This is the first report revealing the effect of BP on inorganic element content of plants.     

Novel pH‐responsive mixed‐charge copolymer brushes based on carboxylic acid and quaternary amine monomers

In this study, we report on the fabrication of tunable mixed‐charged copolymer brushes consisting of negatively charged carboxylic acid monomer (4‐vinylbenzoic acid, VBA) and positively charged quaternary amine monomer ((ar‐vinylbenzyl)trimethylammonium chloride) via reversible addition–fragmentation chain transfer‐mediated polymerization. The copolymer brushes have negative charge under neutral and basic conditions, and are positively charged under acidic conditions owing to the protonation of the carboxylate groups. The copolymer brushes revealed a unique reversible wetting behavior with pH. The reversible properties of the copolymer brushes can be employed to regulate the adsorption of charged biomacromolecules such as DNA and proteins. © 2013 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013