Within the premise of canonical quantisation, we re-examine the quantum structure of bosonic tensionless string theory. In the classical theory, the worldsheet metric degenerates and the Bondi-Metnzer-Sachs (BMS) algebra arises as the residual symmetries on fixing the tensionless equivalent of the conformal gauge. In the quantum regime, we find, on careful examination, that there are multiple ways to impose constraints to restrict the physical Hilbert space, which in turn lead to three distinct choices of tensionless vacua. We analyse these vacua in detail, commenting on various aspects like the central charges and the spectrum around each of them.

Performance of four mesoscale models namely, the MM5, ETA, RSM and WRF, run at NCMRWF for short range weather forecasting has been examined during monsoon-2006. Evaluation is carried out based upon comparisons between observations and day-1 and day-3 forecasts of wind, temperature, specific humidity, geopotential height, rainfall, systematic errors, root mean square errors and specific events like the monsoon depressions.It is very difficult to address the question of which model performs best over the Indian region? An honest answer is 'none'. Perhaps an ensemble approach would be the best. However, if we must make a final verdict, it can be stated that in general, (i) the WRF is able to produce best All India rainfall prediction compared to observations in the day-1 forecast and, the MM5 is able to produce best All India rainfall forecasts in day-3, but ETA and RSM are able to depict the best distribution of rainfall maxima along the west coast of India, (ii) the MM5 is able to produce least RMSE of wind and geopotential fields at most of the time, and (iii) the RSM is able to produce least errors in the day-1 forecasts of the tracks, while the ETA model produces least errors in the day-3 forecasts.

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In the first part of the paper, following the works of Pehlivan et al. (2004), we study the set of allA-statistical cluster points of sequences inm-dimensional spaces and make certain investigations on the set of allA-statistical cluster points of sequences inm-dimensional spaces. In the second part of the paper, we apply this notion to study an asymptotic behaviour of optimal paths and optimal controls in the problem of optimal control in discrete time and prove a general version of turnpike theorem in line of the work of Mamedov and Pehlivan (2000). However, all results of this section are presented in terms of a more general notion ofℐ-cluster points.

We show that a one-to-one bounded linear operator T from a separable Banach space E to a Banach space X is a G δ -embedding if and only if every T -null tree in S E has a branch which is a boundedly complete basic sequence. We then consider the notions of regulators and skipped blocking decompositions of Banach spaces and show, in a fairly general set up, that the existence of a regulator is equivalent to that of special skipped blocking decomposition. As applications, the following results are obtained.(a) A separable Banach space E has separable dual if and only if every w * -null tree in S E * has a branch which is a boundedly complete basic sequence. (b) A Banach space E with separable dual has the point of continuity property if and only if every w-null tree in S E has a branch which is a boundedly complete basic sequence. We also give examples to show that the tree hypothesis in both the cases above cannot be replaced in general with the assumption that every normalized w * -null (w-null in (b)) sequence has a subsequence which is a boundedly complete basic sequence.

Medium range weather forecasts are being generated in real time using Global Data Assimilation Forecasting System (GDAFS) at NCMRWF since 1994. The system has been continuously upgraded in terms of data usage, assimilation and forecasting system. Recently this system was upgraded to a horizontal resolution of T574 (about 22 km) with 64 levels in vertical. The assimilation scheme of this upgraded system is based on the latest Grid Statistical Interpolation (GSI) scheme and it has the provision to use most of available meteorological and oceanographic satellite datasets besides conventional meteorological observations. The new system has an improved procedure for relocating tropical cyclone to its observed position with the correct intensity. All these modifications have resulted in improvement of skill of medium range forecasts by about 1 day.

We show that a separable Banach space with property (M * ) has a Szlenk index equal to ω0, and a norm with an optimal modulus of asymptotic uniform smoothness. From this we derive a condition on the Szlenk functions of the space and its dual which characterizes embeddability into c0 or an psum of finite dimensional spaces. We also prove that two Lipschitz-isomorphic Orlicz sequence spaces contain the same p-spaces.