A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.     

A New Asymmetric Long-Range Model and Algebraic Bethe Ansatz

A new integrable long-range model is derived from a new asymmetric R-matrix recently discussed by Bibikov in relation to a XXZ spin chain in an external magnetic field. The algebraic Bethe Ansatz is used to derive the eigenvalues and equations for the eigen momenta both for the usual and long-range model.     

Host–guest inter­action in a thio­urea–dimethyl oxalate (2/1) complex at 300 and 100 K

The title complex, 2CH₄N₂S·C₄H₆O₄, is a host–guest system. The asymmetric unit consists of one complete thio­urea mol­ecule and one‐half of a dimethyl oxalate mol­ecule lying on an inversion centre. The host thio­urea mol­ecules are connected to form zigzag chains by N—H⋯S hydrogen bonds. The guest dimethyl oxalate mol­ecules provide O‐atom acceptors for N—H⋯O hydrogen bonds, thus inter­connecting the chains of thio­urea mol­ecules to form completely connected sheets. The reduction in temperature from 300 to 100 K leaves the structure unchanged and still isostructural with that previously determined for the analogous thio­urea–diethyl oxalate (2/1) complex. It does, however, induce closer packing of the mol­ecules, general shrinkage of the unit cell and shortening of the hydrogen bonds, these last two to the extent of 1–2%.     

Working group report: Collider Physics

This is summary of the activities of the working group on collider physics in the IXth Workshop on High Energy Physics Phenomenology (WHEPP-9) held at the Institute of Physics, Bhubaneswar, India in January 2006. Some of the work subsequently done on these problems by the subgroups formed during the workshop is included in this report.     

Numerical Modeling of Solitons in a Low Birefringent Optical Fiber

A numerical investigation, based on the split-step Fourier transform algorithm of all optical switching of solitons in a low birefringent optical fiber is presented. The numerical algorithm is described in detail. This revised version was published online in August 2006 with corrections to the Cover Date.     

Steady state analysis of an M/G/1 queue with two phase service and Bernoulli vacation schedule under multiple vacation policy

This paper examines the steady state behaviour of a batch arrival queue with two phases of heterogeneous service along and Bernoulli schedule vacation under multiple vacation policy, where after two successive phases service or first vacation the server may go for further vacations until it finds a new batch of customer in the system. We carry out an extensive stationary analysis of the system, including existence of stationary regime, queue size distribution of idle period process, embedded Markov chain steady state distribution of stationary queue size, busy period distribution along with some system characteristics.     

Nonstatic perfect fluid sphere in higher-dimensional space-time

It is shown that in the case of a spherical nonstatic fluid distribution undergoing shear-free motion the field equations in higher dimensional space-time can be reduced to a single second-order differential equation involving an arbitrary function of the radial co-ordinate. This result extends to higher dimensions a similar one obtained by Wyman and Faulkes earlier for 4D space-time. Solving this differential equation a number of new solutions is found, and the dynamical behaviour of one of the models is briefly discussed. The ansatz is later generalised to include the electromagnetic field as well.     

A RANDOM FIXED POINT ITERATION FOR THREE RANDOM OPERATORS ON UNIFORMLY CONVEX BANACH SPACES

In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extersion of a known theorem in the corresponding non-random case.