Bilipschitz homogeneous Jordan curves

We characterize bilipschitz homogeneous Jordan curves by utilizing quasihomogeneous parameterizations. We verify that rectifiable bilipschitz homogeneous Jordan curves satisfy a chordarc condition. We exhibit numerous examples including a bilipschitz homogeneous quasicircle which has lower Hausdorff density zero. We examine homeomorphisms between Jordan curves.

     

Generation of a Novel High-Affinity Monoclonal Antibody with Conformational Recognition Epitope on Human IgM

As IgM is the first isotype of antibody which appears in blood after initial exposure to a foreign antigen in the pattern of primary response, detection, and quantification of this molecule in blood seems invaluable. To approach these goals, generation, and characterization of a highly specific mAb (monoclonal antibody) against human IgM were investigated. Human IgM immunoglobulins were used to immunize Balb/c mice. Spleen cells taken from the immunized animals were fused with SP2/O myeloma cells using PEG (polyethylene glycol, MW 1450) as fusogen. The hybridomas were cultured in HAT containing medium and supernatants from the growing hybrids were screened by enzyme-linked immunosorbent assay (ELISA) using plates coated with pure human IgM and the positive wells were then cloned at limiting dilutions. The best clone designated as MAN-1, was injected intraperitoneally to some Pristane-injected mice. Anti-IgM mAb was purified from the animals’ ascitic fluid by protein-G sepharose followed by DEAE-cellulose ion exchange chromatography. MAN-1 interacted with human IgM with a very high specificity and affinity. The purity of the sample was tested by SDS-PAGE and the affinity constant was measured ( K_\texta = \text3.\text5 ×\text10^\text9\textM^{\text - 1} ) \left( {{K_{\text{a}}} = {\text{3}}.{\text{5}} \times {\text{1}}{0^{\text{9}}}{{\text{M}}^{{\text{ - 1}}}}} \right) . Immunoblotting and competitive ELISA were done and the results showed that the harvested antibody recognizes a conformational epitope on the μ chain of human IgM and there was no cross-reactivity with other subclasses of immunoglobulins. Furthermore, isotyping test was done and the results showed the subclass of the obtained mAb which was IgG₁κ.     

John disks and extension of maps

We show that a quasisymmetric map between the boundaries of two John disks can be extended to a quasiconformal map of the extended plane. Additional results on John disks are also given.With 2 Figures     

Toward design and fabrication of wind-driven vehicles: Procedure to optimize the threshold of driving forces

Wind energy has been continuously considered as a green, available, and economical alternative source of energy. For centuries, the transformed wind energy to drag-force has been used for transportation in watercrafts. With improvement of aerodynamics, the airfoil was invented to create and use a higher magnitude aerodynamic force, lift-force, in order to elevate airplanes. Later, the lift-force was horizontally applied as the thrust force in land/water wind-crafts. Whereas in airplanes horizontal airfoils (wing) create a vertical lift-force, installed vertical airfoils (wing-sail) produce a horizontal lift-force in wind-crafts. Therefore, this force can be used as thrust (driving) force in lift-based ice, water, and land vehicles. If the prevailing wind is constantly available, the vehicle speed can even exceed the wind velocity. Due to the complex kinematics of such vehicles, however, it should be noted that there would be always an optimum for the thrust force in order to control and navigate the vehicle to the destination point, and to avoid the severe undesired side-forces. This optimum is calculated in wind-craft trajectory software (WTS) which requires many inputs, including variable and constant parameters. Variable parameters consist of wind direction and magnitude in addition to vehicle’s position, velocities, and accelerations. On the other hand, design characteristics of the wind-driven vehicle are known as constant parameters. The land-yacht body’s drag is an unknown constant parameter which alters according to the relative wind. This implies that several wind tunnel experiment in different wind directions and speeds are required in order to obtain the drag coefficients.Therefore in order to bypass the wind tunnel measurements, this study aims to propose a fast and economical procedure to find the aforementioned drag coefficient by integration of a measurement and by a simulation approach. The obtained data can be later used in the optimization and control module of the WTS. The performance of this procedure has been investigated using a case study. For this purpose, a 1:4 prototype three-wheel land-yacht is first designed and fabricated. The land-yacht comprises of three major parts; horizontal airfoil (axle), vertical airfoil, and body. The dimensions of these elements are obtained after development of a code based on kinematics of the land-yacht. The axle is designed to increase the stability of the land-yacht, whereas the shape of the body is intended to produce a low drag coefficient in various directions. Furthermore, a set of experiments has been conducted to measure the body drag of the land-yacht in a direction parallel to the relative wind. This experiment is later used to develop and validate a computational fluid dynamics (CFD) model in order to estimate the drag of the land-yacht body in its various directions against the relative wind. The results show the adequate efficacy of this procedure to provide the required data for the optimization and control module of the WTS.     

A simple approach to designation of the intracavity resonator for second harmonic Nd:YAG laser

In this paper, the rate equation models, which have been used for describing the high repetitive Q-switched intracavity doubling of Nd:YAG laser, are represented. According to these models and onthe basis of resonator length as the most important parameter for designation of the laser system, a computational procedure (block diagram), which is applied for determination of the doubling intracavity resonator specifications of the Nd:YAG laser, has been provided. According to the resonator length the beam quality inside the resonator for second harmonic generation of Nd:YAG laser in different output powers has been calculated. The results for several green output powers of the laser are compared with the experimental data, and good agreement is obtained.     

New bounds for the chromatic number of graphs

In this article we first give an upper bound for the chromatic number of a graph in terms of its degrees. This bound generalizes and modifies the bound given in 11 . Next, we obtain an upper bound of the order of magnitude for the coloring number of a graph with small K_2,t (as subgraph), where n is the order of the graph. Finally, we give some bounds for chromatic number in terms of girth and book size. These bounds improve the best known bound, in terms of order and girth, for the chromatic number of a graph when its girth is an even integer. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:110–122, 2008     

On Anti-Hermitian Metric Connections Preserving a Bicomplex Structure

We give a characterization of bicomplex-holomorphic anti-Hermitian manifolds by using pure metric connection     

Ru(II) complexes bearing tertiary phosphine ligands: a novel and efficient homogeneous catalyst for one‐pot synthesis of dihydropyrano[3,2‐c]chromene and tetrahydrobenzo[b]pyran derivatives

A number of ruthenium complexes were prepared and their catalytic activities in three‐component one‐pot condensation of aldehydes, malononitrile and 4‐hydroxycoumarin or dimedone was considered to afford dihydropyrano[3,2‐c]chromenes and tetrahydrobenzo[b]pyran derivatives under optimum reaction conditions. We found that a catalytic amount of RuBr₂(PPh₃)₄ efficiently promotes the reaction in a short time (3–15 min) and with high yield (75–88%). Copyright © 2012 John Wiley & Sons, Ltd.