Estimation of the convergence rate in a transfer theorem for centered random sums

Estimates of the convergence rate in a transfer theorem for random sums centered by constants are presented. The estimates are obtained as a consequence of the estimates of the stability of the distributions of the sums represented in the form of special mixtures to small variations in the mixing and miscible distributions.     

Existence Results for Semilinear Neutral Functional Differential Inclusions via Analytic Semigroups

In this paper we prove existence results for semilinear neutral functional differential inclusions with finite or infinite delay in Banach spaces. Our theory makes use of analytic semigroups and fractional powers of closed operators, integrated semigroups and cosine families.      

Stored energy release behaviour of disordered carbon

The use of graphite as a moderator in a low temperature thermal nuclear reactor is restricted due to accumulation of energy caused by displacement of atoms by neutrons and high energetic particles. Thermal transients may lead to a release of stored energy that may raise the temperature of the fuel clad above the design limit. Disordered carbon is thought to be an alternative choice for this purpose. Two types of disordered carbon composites, namely, CB (made up of 15 wt. % carbon black dispersed in carbonized phenolic resin) and PAN (made up of 20 vol. % chopped polyacrylonitrile carbon fibre dispersed in carbonized phenolic resin matrix) have been irradiated with 145 MeV Ne⁶⁺ ions at three fluence levels of 1.0×10¹³, 5.0×10¹³ and 1.5×10¹⁴ Ne⁶⁺/cm², respectively. The XRD patterns revealed that both the samples remained disordered even after irradiation. The maximum release of stored energy for CB was 212 J/g and that of PAN was 906 J/g. For CB, the release of stored energy was a first order reaction with activation energy of 2.79 eV and a frequency factor of 3.72×10²⁸ per second. 13% of the defects got annealed by heating up to 700 °C. PAN showed a third-order release rate with activation energy of 1.69 eV and a frequency factor of 1.77×10¹⁴ per second. 56% of the total defects got annealed by heating it up to 700 °C. CB seems to be the better choice than PAN as it showed less energy release with a slower rate. PACS 61.80.Jh; 61.80.-x; 61.43Er; 61.43.-j; 68.43.Vx     

Dynamic programming in cricket: optimizing batting order for a sticky wicket

In cricket, a rain-affected pitch can make batting more difficult than normal. Several other conditions such as poor light or an initially lively pitch, may also result in difficulties for the batsmen. In this note, we refer to all of them as ‘sticky wickets’. On sticky wickets, lower order batsmen are often sent into ‘hold the fort’ until conditions improve. In this paper, a stochastic dynamic programming model is used to examine the appropriateness of this policy. The model suggests that the tactic is often optimal when the sticky wicket persists until the end of the day's play, but not often when the sticky wicket is transitory. In some circumstances, it is worthwhile, on a normal wicket near the end of the day, to send in a lower order batsman to hold the fort (a night watchman): when the wicket is sticky, this tactic is even more worthwhile.     

ZnO:Mn as a member of II-VI:Mn family

ZnO:Mn thin films are grown by the metal organic chemical vapor deposition technique. Mn (x) varies in the 0<x<0.44 range. Vegard’s law has been verified for the lattice parameters. Electron paramagnetic resonance (EPR) measurements prove the substitutional incorporation of Mn²⁺ on zinc sites. The behavior of the EPR line width regarding temperature is discussed. All ZnO:Mn layers show antiferromagnetic interaction and a J₁/k_B=-15 K effective exchange constant. The optical band gap of ZnO:Mn increases with the manganese concentration. Raman spectroscopy reveals a Mn-related scattering band. PACS 71.55.Gs; 75.50.Pp; 61.10.Nz; 76.30.Fc; 75.30.Et; 78.40.-q     

A few points on omnidirectional band gaps in one-dimensional photonic crystals

The universal condition for the formation of omnidirectional band gaps (OBG) in photonic crystal (PC) was derived with consideration of permeability of the materials. And it was found that there are four kinds of PCs: one of them has no OBG, and one always possesses OBG. For the other two kinds of PCs, there are OBG for only TM or TE waves respectively. Moreover, in all PCs, the OBG can be broadened by decreasing the refractive index of the ambient medium or/and increasing the contrast between the wave impedances of the component materials of the PC. PACS 42.70.Qs; 71.20.Tx     

Preliminary design of high-power wave-guide/transmission system for multimegawatt CW requirements of 100 MeV proton LINAC

Development of a 100 MeV CW proton LINAC has been planned at CAT. This LINAC will be needing CW rf power in the frequency ranges of 350 MHz and 700 MHz for its RFQ and DTL/CCDTL/SFDTL structures respectively. The power to the accelerating structures will be produced by either 1 MW CW or 250 kW CW klystrons/inductive output tubes (HOM IOTs). The power needed by respective feed points in the structure is max. 250 kW which will be powered by splitting the power from 1 MW klystron/klystrode into four channels by using a wave-guide system. In case of using 250 kW tubes the power to the structures will be provided directly from each tube. Two types of wave-guide transmission system have been considered, viz, WR 2300 for 350 MHz rf needs and WR 1500 for 700 MHz rf needs. The typical wave-guide system has been designed using the 1 MW CW klystron followed by wave-guide filter, dual directional coupler, high-power circulator, three 3 dB magic TEE power dividers to split the main channel into four equal channels of 250 kW each. Each individual channel has dual directional couplers, flexible wave-guide sections and high power ceramic vacuum window. The circulator and each power divider is terminated into the isolated ports by high power CW loads. Out of the four channels three channels have phase shifters. Present paper describes the technological aspects and design specifications-considerations for these stringent requirements.