Equivariant acyclic maps

In this paper we apply a recently developed new version of the Bredon-Illman cohomology theory to obtain an equivariant analogue of a result of Kan and Thurston, which implies that a connected CW-complex has the homotopy type of a space obtained by applying the plus construction of Quillen to certain Eilenberg-MacLane spaces.

     

Semidiscrete finite element Galerkin approximations to the equations of motion arising in the Oldroyd model

In this paper, a semidiscrete finite element Galerkin methodfor the equations of motion arising in the 2D Oldroyd modelof viscoelastic fluids with zero forcing function is analysed.Some new a priori bounds for the exact solutions are derivedunder realistically assumed conditions on the data. Moreover,the long-time behaviour of the solution is established. By introducinga Stokes–Volterra projection, optimal error bounds forthe velocity in the L(L²) as well as in the L(H¹)-norms andfor the pressure in the L(L²)-norm are derived which are validuniformly in time t > 0.     

Finite element Galerkin approximations to a class of nonlinear and nonlocal parabolic problems

In this article, a finite element Galerkin method is applied to a general class of nonlinear and nonlocal parabolic problems. Based on an exponential weight function, new a priori bounds which are valid for uniform in time are derived. As a result, existence of an attractor is proved for the problem with nonhomogeneous right hand side which is independent of time. In particular, when the forcing function is zero or decays exponentially, it is shown that solution has exponential decay property which improves even earlier results in one dimensional problems. For the semidiscrete method, global existence of a unique discrete solution is derived and it is shown that the discrete problem has an attractor. Moreover, optimal error estimates are derived in both and ‐norms with later estimate is a new result in this context. For completely discrete scheme, backward Euler method with its linearized version is discussed and existence of a unique discrete solution is established. Further, optimal estimates in ‐norm are proved for fully discrete schemes. Finally, several numerical experiments are conducted to confirm our theoretical findings. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1232–1264, 2016     

A second-order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation

A second-order splitting method is applied to a KdV-like Rosenau equation in one space variable. Then an orthogonal cubic spline collocation procedure is employed to approximate the resulting system. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index 1. Error estimates in L² and L^∞ norms have been obtained for the semidiscrete approximations. For the temporal discretization, the time integrator RADAU5 is used for the resulting system. Some numerical experiments have been conducted to validate the theoretical results and to confirm the qualitative behaviors of the Rosenau equation. Finally, orthogonal cubic spline collocation method is directly applied to BBM (Benjamin–Bona–Mahony) and BBMB (Benjamin–Bona–Mahony–Burgers) equations and the well-known decay estimates are demonstrated for the computed solution. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 695–716, 1998     

Size tunable synthesis of cysteine-capped CdS nanoparticles by gamma-irradiation

Highly water soluble and biocompatible L-cysteine-capped CdS nanoparticles having narrow size distribution were synthesized for the first time by gamma-irradiation technique without using any additional stabilizer. FTIR study shows that CdS nanoparticles are capped through mercapto-group of cysteine amino acid while its free amino and carboxylate groups make it amenable to bio-conjugation. Size and luminescence of the nanoparticles can be well controlled by varying the parameters like radiation dose, pH and concentration of cysteine. The observed results suggest that pH 7 can be optimum for the synthesis of L-cysteine-capped CdS nanoparticles. CdS nanoparticles synthesized with molar ratio of Cd(2+):cysteine, 1:60 at pH 7 were found to be most luminescent. All nanoparticles formed lie in the size quantization regime and exhibit good crystallinity. Remarkable improvement in stability and luminescence was achieved on changing pH of as-prepared nanoparticles from 7 to 11.     

Novel oxidation of tetrasubstituted furans by pyridinium chlorochromate

A novel oxidation of tetrasubstituted furans with pyridinium chlorochromate has been studied and this has led to a convenient synthesis of 4-acetoxy-3-acetyl- or methoxycarbonyl-4-substituted phenylbut-3-en-2-one.     

A note on equivariant Euler characteristic

We give a new equivariant cohomological characterization of the equivariant Euler characteristic of aG-simplicial set as defined by Brown. This implies in particular that the equivariant Euler characteristic is aG-homotopy invariant.     

A qualocation method for Burgers’ equation

In this paper, a qualocation method for the one-dimensional Burgers’ equation is proposed. A semidiscrete scheme along with optimal error estimates is discussed. Results of a numerical experiment performed support the theoretical results.     

A Novel Strategy for N-Alkylation of Primary Amines

N-alkyiation of primary amines has been carried out with alkylbromide using commercial Me₂SO and K₂CO₃ as a base. This process offers a method of selection for obtaining either mono or dialkyl amines.     

Finite element approximation to global stabilization of the Burgers’ equation by Neumann boundary feedback control law

In this article, we discuss global stabilization results for the Burgers’ equation using nonlinear Neumann boundary feedback control law. As a result of the nonlinear feedback control, a typical nonlinear problem is derived. Then, based on C ⁰-conforming finite element method, global stabilization results for the semidiscrete solution are analyzed. Further, introducing an auxiliary projection, optimal error estimates in \(L^{\infty }(L^{2})\), \(L^{\infty }(H^{1})\) and \(L^{\infty }(L^{\infty })\)-norms for the state variable are obtained. Moreover, superconvergence results are established for the first time for the feedback control laws, which preserve exponential stabilization property. Finally, some numerical experiments are conducted to confirm our theoretical findings.