A note on the tangent bundle of <Emphasis Type="Italic">G/P</Emphasis>

Let P be a parabolic subgroup of a complex simple linear algebraic groupG. We prove that the tangent bundle T (G/P) is stable.     

Polynomial solutions of certain differential equations arising in physics

Conditions for the existence of polynomial solutions of certain second‐order differential equations have recently been investigated by several authors. In this paper, a new algorithmic procedure is given to determine necessary and sufficient conditions for a differential equation with polynomial coefficients containing parameters to admit polynomial solutions and to compute these solutions. The effectiveness of this approach is illustrated by applying it to determine new solutions of several differential equations of current interest. A comparative analysis is given to demonstrate the advantage of this algorithmic procedure over existing software. Copyright © 2012 John Wiley & Sons, Ltd.     

Chiral induction in a ribose-decorated metallostar through intrinsic and interionic diastereomeric interactions

A ribose-functionalized bpy ligand has been prepared and shown to give modest diastereomeric excesses of Lambda-[FeL(3)](2+) complexes; interconversion of Delta and Lambda cations is relatively fast, and in CHCl(3), the favored complexes with Delta- or Lambda-TRISPHAT counterions are homochiral, (Delta(+)Delta(-)) or (Lambda(+)Lambda(-)). In the case of the Delta-TRISPHAT salt, a single diastereomer is observed (de > or = 96%).     

Synthesis,spectral studies,thermal behavior,and antibacterial activity of Ni(Ⅱ),Cu(Ⅱ),and Zn(Ⅱ) complexes with an ONO tridentate Schiff base

Three new transition metal complexes have been synthesized with a Schiff base,3-(2-hydroxy-5-chlorophenylimino)-l,3- diphenylpropen-1-one.In all complexes Schiff base is completely deprotonated and coordinated to metal as tridentate ligand via phenolic and enolic oxygens and imine nitrogen.Thermal decomposition of the complexes has been studied by thermogravimetry. The in vitro antibacterial activity of Schiff bases and their complexes has been evaluated and compared with the standard drugs.     

A new practical method for the synthesis of unsymmetrical ureas via high-pressure-promoted condensation of 2,2,2-trichloroethyl carbamates (Troc-carbamates) with amines

A new practical method for the synthesis of unsymmetrical ureas was achieved by condensation between 2,2,2-trichloroethyl carbamates (Troc-carbamates) and primary or secondary amines under high-pressure conditions.     

Analytic solutions of initial-boundary-value problems of transient conduction using symmetries

Lie symmetry method is applied to find analytic solutions of initial-boundary-value problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a manner highlighting the systematic procedure of extending the symmetry method for a PDE to investigate BVPs of the PDE. A comparative analysis of numerical and closed form solutions is carried out for a physical problem of heat conduction in a semi-infinite solid bar made of AISI 304 stainless steel.     

Effect of dielectric properties of metals on terahertz transmission subwavelength hole arrays

We study the influence of dielectric function of metals on the transmission properties of terahertz pulses through periodically patterned subwavelength holes. Because of a drastic increase in the value of dielectric constants, most metals become highly conductive at terahertz frequencies. Extraordinary terahertz transmission is observed in subwavelength hole arrays made from both good and poor electrical conductors. The measured transmittance of terahertz pulses is found to be enhanced with increasing ratio of the real to the imaginary dielectric constant of the constituent metals, for which the dielectric function follows the Drude model.     

Effect of metal permittivity on resonant properties of terahertz metamaterials

We investigate the effect of metal permittivity on resonant transmission of metamaterials by terahertz time-domain spectroscopy. Our experimental results on double split-ring resonators made from different metals confirm the recent numerical simulations [Phys. Rev. E 65, 036622 (2002)] that metamaterials exhibit permittivity-dependent resonant properties. In the terahertz regime, the measured inductive-capacitive resonance is found to strengthen with a higher ratio of the real to the imaginary parts of metal permittivity, and this remains consistent at various metal thicknesses. Furthermore, we found that metamaterials made even from a generally poor metal become highly resonant owing to a drastic increase in the value of the permittivity at terahertz frequencies.     

Near-wall velocity distributions within a straight conical diffuser

The measured mean velocity profiles at the various stations along a conical diffuser (8° total divergence angle) were found to consist of log regions, half-power law regions and linear regions. The describing coefficients for the inner half-power law region (which followed a rather narrow log region) differed from the standard values due to the axi-symmetric geometry and lack of moving equilibrium of the flow as it attempted to adjust to a varying adverse pressure gradient. However, these coefficients (like those for the linear region) correlated with the local wall shear stress and the kinematic pressure gradient.List of symbols A, B coefficients in logarithmic law velocity distribution (Eq. (1)) - C, D coefficients in half-power law velocity distribution (Eq. (5)) - D_i inside diameter of feed pipe (10.16 cm) - d _p outer diameter of Preston tube - E, F coefficients in linear law velocity distribution (Eq. (10)) - P _s local static pressure - R local radius of diffuser, (D _i /2) + x _w sin 4° - Re Reynolds number, D _i U _b /v - U local mean velocity in the x _w direction - U _b cross-sectional average mean velocity (x-direction) in feed pipe - U _c mean velocity at the diffuser centerline - u ^* local friction velocity - u ⁺ dimensionless local mean velocity, U/u ^* - axial distance along diffuser centerline (measured from inlet to diffuser) Fig. (2) - _w distance along diffuser wall (measured from inlet to difusser (Fig. 2) - y _w distance from wall in direction orthogonal to wall (Fig. 2) - y ⁺ dimensionless position, y _w u ^*/v - kinematic (axial static) pressure gradient, (1/g9) dP _s/dx - ^* displacement thickness (Eq. (4)) - dimensionless pressure gradient parameter, x v/(u*) ³ - Von Karman constant (0.41) - density - kinematic viscosity - shear stress