Extrinsic eigenvalues upper bounds for submanifolds in weighted manifolds

Annals of Global Analysis and Geometry - We prove Reilly-type upper bounds for divergence-type operators of the second order as well as for Steklov problems on submanifolds of Riemannian manifolds...     

Slant Lightlike Submanifolds of Indefinite Cosymplectic Manifolds

In this paper, we introduce the notion of a slant lightlike submanifold of an indefinite Cosymplectic manifold. We provide a nontrivial example and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold. Also, we give an example of a minimal slant lightlike submanifold of R⁹₂{R^{9}_{2}} and prove some characterization Theorems.     

Nonconforming h-p spectral element methods for elliptic problems

In this paper we show that we can use a modified version of the h-p spectral element method proposed in [6,7,13,14] to solve elliptic problems with general boundary conditions to exponential accuracy on polygonal domains using nonconforming spectral element functions. A geometrical mesh is used in a neighbourhood of the corners. With this mesh we seek a solution which minimizes the sum of a weighted squared norm of the residuals in the partial differential equation and the squared norm of the residuals in the boundary conditions in fractional Sobolev spaces and enforce continuity by adding a term which measures the jump in the function and its derivatives at inter-element boundaries, in fractional Sobolev norms, to the functional being minimized. In the neighbourhood of the corners, modified polar coordinates are used and a global coordinate system elsewhere. A stability estimate is derived for the functional which is minimized based on the regularity estimate in [2]. We examine how to parallelize the method and show that the set of common boundary values consists of the values of the function at the corners of the polygonal domain. The method is faster than that proposed in [6,7,14] and the h-p finite element method and stronger error estimates are obtained.     

Multiple attractors and crisis route to chaos in a model food-chain

An attempt has been made to identify the mechanism, which is responsible for the existence of chaos in narrow parameter range in a realistic ecological model food-chain. Analytical and numerical studies of a three species food-chain model similar to a situation likely to be seen in terrestrial ecosystems has been carried out. The study of the model food chain suggests that the existence of chaos in narrow parameter ranges is caused by the crisis-induced sudden death of chaotic attractors. Varying one of the critical parameters in its range while keeping all the others constant, one can monitor the changes in the dynamical behaviour of the system, thereby fixing the regimes in which the system exhibits chaotic dynamics. The computed bifurcation diagrams and basin boundary calculations indicate that crisis is the underlying factor which generates chaotic dynamics in this model food-chain. We investigate sudden qualitative changes in chaotic dynamical behaviour, which occur at a parameter value a₁=1.7804 at which the chaotic attractor destroyed by boundary crisis with an unstable periodic orbit created by the saddle-node bifurcation. Multiple attractors with riddled basins and fractal boundaries are also observed. If ecological systems of interacting species do indeed exhibit multiple attractors etc., the long term dynamics of such systems may undergo vast qualitative changes following epidemics or environmental catastrophes due to the system being pushed into the basin of a new attractor by the perturbation. Coupled with stochasticity, such complex behaviours may render such systems practically unpredictable.     

Generalised BRST symmetry and gaugeon formalism for perturbative quantum gravity: Novel observation

In this paper the novel features of Yokoyama gaugeon formalism are stressed out for the theory of perturbative quantum gravity in the Einstein curved spacetime. The quantum gauge transformations for the theory of perturbative gravity are demonstrated in the framework of gaugeon formalism. These quantum gauge transformations lead to renormalised gauge parameter. Further, we analyse the BRST symmetric gaugeon formalism which embeds more acceptable Kugo–Ojima subsidiary condition. Further, the BRST symmetry is made finite and field-dependent. Remarkably, the Jacobian of path integral under finite and field-dependent BRST symmetry amounts to the exact gaugeon action in the effective theory of perturbative quantum gravity.     

Surface spin-glass-like behavior of monodispersed superparamagnetic Mn0.5Zn0.5Fe2O4 magnetic fluid

Zero field cooled dc-magnetization measurements of monodispersed Mn_0.5Zn_0.5Fe₂O₄ nanoparticles dispersed in kerosene exhibit two transitions at low temperatures. These transitions correspond to (i) the superparamagnetic to blocked superparamagnetic and (ii) the blocked superparamagnetic to surface spin-glass like/quantum superparamagnetic state upon lowering the temperature. The existence of a disorder surface is confirmed by recording small-angle neutron scattering data below and above the Curie temperature. Magnetic relaxation analysis shows a plateau at low temperature (below 5 K) with a slight minimum at 3 K, which is a characteristic of the surface spin-glass-like state. This is analyzed considering the energy distribution n(E)∼1/E. The existence of surface disorder dominates at low temperature and mimics the transition from superparamagnetic to quantum superparamagnetic states.     

Lp-Norm inequality of the product of pseudo-differential operators involving Hankel transformation

Lp-norm type inequalities for pseudo-differential operators L(x,D) and H(x,D) are derived for 1 ≤ p < ∞. Product of pseudo-differential operators associated with Bessel operator Sμ are defined and its Lp-norm type inequalities are obtained.     

On compact anisotropic Weingarten hypersurfaces in Euclidean space

Let $$Omega subset mathbb {R}^n$$ be a bounded mean convex domain. If $$alpha <0$$ , we prove the existence and uniqueness of classical solutions of the Dirichlet problem in $$Omega $$ for the $$alpha $$ -singular minimal surface equation with arbitrary continuous boundary data.     

Multiplicative Lie algebras and Schur multiplier

In this paper, we attempt to study the structure of multiplicative Lie algebras, the theory of extensions, the second cohomology groups of multiplicative Lie algebras, and in turn the Schur multipliers. The Schur–Hopf formula is established for multiplicative Lie algebras. We also introduce the group of nontrivial relations satisfied by the Lie product in a multiplicative Lie algebra, and study it as a functor arising from the presentations of multiplicative Lie algebras. Some applications in K-theory are also discussed.     

The gas‐phase elimination kinetics of ethyl 2‐furoate and ethyl 2‐thiophenecarboxylate

The gas‐phase elimination kinetics of ethyl 2‐furoate and 2‐ethyl 2‐thiophenecarboxylate was carried out in a static reaction system over the temperature range of 623.15–683.15 K (350–410°C) and pressure range of 30–113 Torr. The reactions proved to be homogeneous, unimolecular, and obey a first‐order rate law. The rate coefficients are expressed by the following Arrhenius equations: ethyl 2‐furoate, log k₁ (s^?1) = (11.51 ± 0.17)–(185.6 ± 2.2) kJ mol^?1 (2.303 RT)^?1; ethyl 2‐thiophenecarboxylate, log k₁ (s^?1) = (11.59 ± 0.19)–(183.8 ± 2.4) kJ mol^?1 (2.303 RT)^?1. The elimination products are ethylene and the corresponding heteroaromatic 2‐carboxylic acid. However, as the reaction temperature increases, the intermediate heteroaromatic carboxylic acid products slowly decarboxylate to give the corresponding heteroaromatic furan and thiophene, respectively. The mechanisms of these reactions are suggested and described. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 41: 145–152, 2009