Some generalizations of Chirka's extension theorem

In this paper, we generalize Chirka's theorem on the extension of functions holomorphic in a neighbourhood of - where is the open unit disc in and is the graph of a continuous valued function on - to higher dimensions, for certain classes of graphs 1$">. In particular, we show that Chirka's extension theorem generalizes to configurations in 1$">, involving graphs of (non-holomorphic) polynomial maps with small coefficients.

     

Applications of SMP Bounds to Multi-class Traffic in High-speed Networks

In this paper, we consider the stochastic fluid-flow model of a single node in a high-speed telecommunication network handling multi-class traffic. The node has multiple buffers, one for each class of traffic. The contents of these buffers are multiplexed onto a single output channel using one of the service scheduling policies: the Timed Round Robin Policy or the Static Priority Service Policy. The Quality of Service requirements for each class are based on cell loss probabilities. Using effective bandwidth methodologies and the recently developed bounds for semi-Markov modulated traffic, we solve call admission control problems for the two service scheduling policies at this node. We compare the performance of the effective bandwidth methodologies and the SMP bounds technique. We also numerically compare the performance of the two service scheduling policies.     

A stochastic Lagrangian representation of the three‐dimensional incompressible Navier‐Stokes equations

In this paper we derive a probabilistic representation of the deterministic three‐dimensional Navier‐Stokes equations based on stochastic Lagrangian paths. The particle trajectories obey SDEs driven by a uniform Wiener process; the inviscid Weber formula for the Euler equations of ideal fluids is used to recover the velocity field. This method admits a self‐contained proof of local existence for the nonlinear stochastic system and can be extended to formulate stochastic representations of related hydrodynamic‐type equations, including viscous Burgers equations and Lagrangian‐averaged Navier‐Stokes alpha models. © 2007 Wiley Periodicals, Inc.     

Characteristic polynomials of linear polyacenes and their subspectrality

Coefficients of characteristic polynomials (CP) of linear polyacenes (LP) have been shown to be obtainable from Pascal’s triangle by using a graph factorisation and squaring technique. Strong subspectrality existing among the members of the linear polyacene series has been shown from the derivation of the CP’s. Thus it has been shown that the entire eigenspectrum of ann-ring LP is included in that of (2n + 1)-ring LP. Correspondence between the eigenspectra of linear chains and LP’s is brought out by a recently developed vertex-alternation and squaring algorithm.     

Strongly clean matrix rings over commutative local rings

We will completely characterize the commutative local rings for which M_n(R) is strongly clean, in terms of factorization in R[t]. We also obtain similar elementwise results which show additionally that for any monic polynomial f∈R[t], the strong cleanness of the companion matrix of f is equivalent to the strong cleanness of all matrices with characteristic polynomial f.     

Quantization of degenerate vacua and symmetry breaking in string theory

We consider the implications of the existence of continuous families of classically degenerate vacua in constructing quantum string theory in compact toroidal spacetimes. We show that in the presence of unbroken supersymmetry when quantum corrections do not lift the degeneracy, symmetries of particular compactifications can be broken by the presence of the neighbouring vacua. We explicitly demonstrate this in case of the heterotic string where the gauge group SO(32) or E₈×E₈ breaks down to U(1)¹⁶ due to neighbouring configurations of arbitrary Wilson lines.     

Isochronicity and limit cycle oscillation in chemical systems

Chemical oscillation is an interesting nonlinear dynamical phenomenon which arises due to complex stability condition of the steady state of a reaction far away from equilibrium which is usually characterised by a periodic attractor or a limit cycle around an interior stationary point. In this context Lienard equation is specifically used in the study of nonlinear dynamical properties of an open system which can be utilized to obtain the condition of limit cycle. In conjunction with the property of limit cycle oscillation, here we have shown the condition for isochronicity for different chemical oscillators with the help of renormalisation group method with multiple time scale analysis from a Lienard system. When two variable open system of equations are transformed into a Lienard system of equation the condition for limit cycle and isochronicity can be stated in a unified way. For any such nonlinear oscillator we have shown the route of a dynamical transformation of a limit cycle oscillation to a periodic orbit of centre type depending on the parameters of the system.     

Stereoselective synthesis of (+)-(1R,2S,5S,7R)-2-hydroxy-exo-brevicomin

A stereoselective approach for the synthesis of (+)-(1R,2S,5S,7R)-2-hydroxy-exo-brevicomin from l-ascorbic acid has been described. The key steps are highly stereoselective nucleophilic addition reaction on aldehyde 8 and also a single pot transformation of 15 to (+)-(1R,2S,5S,7R)-2-hydroxy-exo-brevicomin. The later tandem reaction which involves the hydrogenation of double bond, debenzylation, MOM deprotection and bicyclic ketal formation was carried under Pd/C, H₂ followed by acid treatment.