The Lax conjecture is true

In 1958 Lax conjectured that hyperbolic polynomials in three variables are determinants of linear combinations of three symmetric matrices. This conjecture is equivalent to a recent observation of Helton and Vinnikov.

     

Thermal decomposition of potassium bis -oxalatodiaqua-indate(III) monohydrate

Indium (III) is precipitated with oxalic acid in the presence of potassium nitrate maintaining an overall concentration of 0·125 M in HNO₃. Chemical analysis of the complex salt obtained indicates the formula, K[In(C₂O₄)₂]·3H₂O. Thermal decomposition studies show that the compound decomposes first to the anhydrous potassium indium oxalate and then to the final mixture of the oxides through formation of potassium carbonate and indium (III) oxide as intermediates. Isothermal study, X-ray diffraction pattern and IR spectral data support the proposed thermal decomposition mechanism.     

C-Glycosides of dodecanoic acid: new capping/reducing agents for glyconanoparticle synthesis

A concise synthesis of 12-C-glycosylated dodecanoic acids employing an olefin cross-metathesis reaction is developed. Examination of these acids as capping agents for the synthesis of metal nanoparticles reveals that they do not cap the Co-metal nanoparticles synthesized in aqueous phase, but that two of them can reduce and cap the Ag nanoparticles in water without any aggregation.     

A carbohydrate-based approach for the total synthesis of strictifolione

A chiral pool approach starting with d-glucose, using the Yamaguchi protocol and a Z-selective HWE reaction followed by lactonization, has been applied to execute the total synthesis of strictifolione.     

Fixed Point Theorems on Chain Complete Partially Ordered Sets

In this paper, we extend the results of Tarski, Abian and Brown on the completeness of lattices by fixed point theorems, to partially ordered sets or (Po sets) with chain completeness property. We also sharpen some of the existing results on completeness of lattices and fixed-point theorems. We also provide counter examples to some of the claims of R. Taskovic to disprove his theorem.Milan R. Taskovic claims to have proved this theorem but his proof is based on a false argument. In fact most of the contentions of Milan R. Taskovic in [4] are factually incorrect. Actually, reviewer of Taskovics paper has pointed out some of his inaccurate observations. See Mathematical Reviews No. 90b:06007, 06A10.     

An expedient synthesis of tetrakis(cyclopropylmethyl)methane

Synthesis of tetrakis(cyclopropylmethyl)methane, a new symmetric product has been described using the radical mediated gem-diallylation of cyclopropylmethyl xanthate as a key step and its single crystal X-ray analysis established its C2-symmetry.     

Numerical computations of supersonic inlet flow

Air‐breathing propulsion systems for high‐speed space travel applications are studied. Ramjets and scramjets have been identified as potential candidates. The flow inlets of such systems are modelled with a simulation that can predict all complex inlet flow features, including shock due to forebody, multiple shock reflections, normal shock, shock–boundary layer interaction and associated separation for two‐dimensional and axisymmetric inlets. Computed values are in good agreement with experimental data. Copyright © 2001 John Wiley & Sons, Ltd.     

On MHD flow along an infinite flat wall with constant suction

Exact solutions of the Navier-Stokes equations are derived by a Laplace-transform technique for two-dimensional, incompressible flow of an electrically conducting fluid past an infinite porous plate under the action of a transverse magnetic field subject to the conditions: (i) the magnetic Prandtl number P_m is unity, and (ii) the Alfven velocity is less than the suction velocity. It is assumed that the flow is independent of the distance parallel to the plate and that the velocity component normal to the plate is constant. General formulae are derived for the velocity distribution and the magnetic field in terms of the given external velocity. The skin-friction is obtained and some special cases are considered.     

A note on Hydromagnetic oscillatory flow along an infinite flat plate with variable suction

The two-dimensional, incompressible flow past an infinite plate of a weakly conducting fluid in the presence of a transverse magnetic field is discussed when the suction velocity normal to the plate as well as the external flow velocity vary periodically with time. Expressions for the velocity and the skin-friction in the boundary layer have been obtained in a non-dimensional form.