Stability and Accuracy of Semi-discretized Finite Difference Methods

The relationship between the accuracy and stability of semi-discretizedfinite-difference schemes for the advection equation u_t = u_xis analysed. Given the scheme of accuracy p we establish that,subject to stability, p min {r+s+R+S, 2(r+R+1), 2(s+S)}. This is done by using the theory of order stars. Furthermore,we find stable methods which attain this bound for various choicesof r, s, R and S.     

The triviality of continuous multipliers for the real line

It is proved without resort to calculus methods that every continuous group multiplier for R can be reduced to the identity by a continuous remultiplication. The method introduced may generalize to infinitedimensional Abelian groups such as occur in analyzing the projective representations of the Bondi-Metzner-Sachs (BMS) group.     

Unsteady incompressible flow of magnetized aluminium oxide and titanium oxide nanoparticles with blood base fluid

In this investigation, a mixed convective nanoparticles fluid flow over an inclined plate is deliberated. The effects of slip boundary wall and magnetic field are also considered. The dimensionless governing system for the considered problem is attained by implementing recent definitions of fractional derivatives (FD). The generalized solution is obtained through the Laplace Transformation Scheme (LTS) for the momentum and thermal expressions. To improve the novelty and to demonstrate some more physical perception of the stated research work, some remarkable special cases of velocity distribution through CF and AB-fractional derivative concept are addressed, whose daily life implication is well known in the existing literature. Moreover, to evaluate the physical interest of the stated problem, the outcomes of the obtained system graphical illustrations are made by utilizing MATHEMATICA. As a result, we concluded that the aluminium oxide $A{l}_2{O}_3$ nanoparticles show more decaying behavior as compared to titanium oxide $Ti{O}_2$ nanoparticles for temperature and velocity profile. Furthermore, both fields i.e., momentum and thermal distributions are increased with the help of rising estimations parameter. Current results report novel applications in enhancement of heat transfer, thermal engineering, chemical processes, engineering and electronics devices, solar systems, extrusion processes, fission reactions etc.     

Numerical Investigations into the Stokes Phenomenon. II

The Stokes phenomenon associated with the differential equationsW " = WZ (z²–a²) and W" = w(z² –a²)(x²–b²)isconsidered. As an application to the method introduced in paper I, somenumerical and analytical results concerning the Stokes constantsof these equations are presented.     

An efficient access to both enantiomers of pipecolic acid

An efficient and convenient synthesis of both enantiomers of pipecolic acid has been developed using the intramolecular cyclization of 2-amino-6-bromohexanoic acid under mild conditions.     

Chemoenzymatic synthesis of enantiomerically enriched 2-oxobicyclo[m.1.0]alkan-3-yl acetate derivatives

Racemic α′-acetoxy α,β-unsaturated cyclopentanone and cyclohexanone have been resolved into the corresponding enantiomerically enriched α′-hydroxylated and acetoxylated compounds with 96–97% ee via PLE hydrolysis. Stereoselectivity in the palladium(II)-catalyzed reaction between the enantiomerically enriched α′-acetoxylated compounds and diazomethane has been investigated. In the α′-acetoxylated cyclopentenone, preferential cyclopropanation occurs in the anti-form, whereas α′-acetoxylated cyclohexenone affords both syn- and anti-products (syn:anti, 61:36%). The relative configuration of the products was determined by NOE experiments.     

Characteristic sequences for DNA primary sequence

A DNA sequence can be identified with a word over an alphabet N = [A, C, G, T]. Characteristic sequences of a DNA sequence are given in term of classifications of bases of nucleic acids. Using the characteristic sequences, we construct a set of 2 x 2 matrices to represent DNA primary sequences, which are based on counting of the frequency of occurrence of all (0,1) triplets of characteristic sequences. Furthermore, the leading eigenvalues of these matrices are computed and considered as invariants for the DNA primary sequences. Similarity and dissimilarity analysis based on the characteristic sequences are given for eight exon-1 genes of beta-globin about eight species.     

An ore-type condition for the existence ofk-factors in graphs

Letk be a positive integer, and letG be a graph of ordern withn 4k – 5,kn even and minimum degree at leastk. We prove that if the degree sum of each pair of nonadjacent vertices is at leastn, thenG has ak-factor.     

Instabilities of certain empty Robertson-Walker space-times

Results are established concerning perturbations of each empty Robertson-Walker space-time (M, g) with a nonvanishing cosmological constant. The perturbed space-times have the general form ( ) with an extension ofM, and lying in an open neighborhood of g in a type ofW ^m topology. These results indicate that large classes of such perturbations give rise to space-times which suffer from one of two types of incompleteness.     

Asymptotic behavior for a nematic liquid crystal model with different kinematic transport properties

We study the asymptotic behavior of global classical solutions to hydrodynamical systems modeling the nematic liquid crystal flows under kinematic transports for molecules of different shapes. The coupling system consists of Navier–Stokes equations and kinematic transport equations for the molecular orientations. We prove the convergence of global solutions to single steady states as time tends to infinity as well as estimates on the convergence rate both in 2D for arbitrary regular initial data and in 3D for certain particular cases.