On composition of some general fractional integral operators

In the present paper we derive three interesting expressions for the composition of two most general fractional integral oprators whose kernels involve the product of a general class of polynomials and a multivariableH-function. By suitably specializing the coefficients and the parameters in these functions we can get a large number of (new and known) interesting expressions for the composition of fractional integral operators involving classical orthogonal polynomials and simpler special functions (involving one or more variables) which occur rather frequently in problems of mathematical physics. We have mentioned here two special cases of the first composition formula. The first involves product of a general class of polynomials and the Fox’sH-functions and is of interest in itself. The findings of Buschman [1] and Erdélyi [4] follow as simple special cases of this composition formula. The second special case involves product of the Jacobi polynomials, the Hermite polynomials and the product of two multivariableH-functions. The present study unifies and extends a large number of results lying scattered in the lierature. Its findings are general and deep.     

A finite range failure model

In the present article the characterstics of a finite range failure time distribution, that includes the rectangular distribution as a particular case, are studied. When shape parameter surpass unity then the distribution is IFR otherwise it always remains IFRA. A graphic shape of the distribution is also formed for certain admissible values of the constants.     

Vapour and plasma ignition thresholds for visible pulsed-laser ablation of metallic targets

The coupling of visible nanosecond laser pulses to metallic targets irradiated in vacuum is studied. The expressions of the vapour and plasma ignition times are obtained. Two cases for vapour breakdown in the plasma ignition process are considered. The first case is that 40 generations of new electrons are born in vapour generation time before plasma formation as assumed in the literature. The second case is that 10 generations of new electrons are born in vapour generation time. Molybdenum (Mo), niobium (Nb) and aluminium (Al) targets are considered for illustrations of our results. The expression of the plasma ignition time for the Al target is substantially different from that reported in the literature. The vapour and plasma ignition threshold laser intensities are calculated and compared with those reported in the literature. Reasons for disagreement are discussed. The plasma ignition threshold estimated in the second case is noted to be in good agreement with the reported experimental result.     

Simultaneous Approximation for Generalized Baskakov-Durrmeyer-Type Operators

The present paper deals with the study of a Durrmeyer-type integral modification of certain modified Baskakov operators. Here we study simultaneous approximation properties for these operators by using the iterative combinations. We obtain an asymptotic formula and an error estimation in terms of higher order modulus of continuity for these operators.      

Design and operation characteristics of a high power transverse flow pulser sustained cw CO2 laser

A transverse flow, transverse discharge cw CO₂ laser in which de discharge is sustained by employing high repetition rate high voltage pulses has been developed. Pulser sustained discharge through electrodes of innovative design provided uniform excitation at electrical input power densities more than 10 W/cc. Laser output power more than 2.5 kW was obtained in a laser gas mixture consisting of 0.5 mbar of CO₂, 16 mbar of N₂ and 38.5 mbar of He. Design details and operational characteristics of this laser are presented.     

Conductivity and dielectric properties of sol–gel derived porous zirconia

The 8-mol percentage Y₂O₃-stabilized Porous Zirconia was prepared using sol–gel method. Zirconium oxalate gel was prepared by the addition of appropriate amount of oxalic acid solution into the 1 M aqueous solution of zirconium-oxy chloride. A cubic phase zirconia powder was obtained by calcination and milling of the zirconium oxalate gel. Crystallization temperature was found about 450 °C from the Differential thermal analysis. The phase analysis by X-ray diffraction shows the presence of cubic phase. Pellets sintered at 1,350 °C were highly porous, and the electrical conductivity was found with lower value due to the porosity, and the hardness was about 8.0 GPa. Paper presented at the Third International Conference on Ionic Devices (ICID 2006), Chennai, Tamilnadu, India, Dec. 7–9, 2006.     

Simultaneous approximation for the Bézier variant of Baskakov-Beta operators

In the present paper, we study the rate of convergence in simultaneous approximation for the Bézier variant of the Baskakov-Beta operators by using the decomposition technique of functions of bounded variation.     

HPTLC Determination of Swertiamarin and Amarogentin in Swertia Species from the Western Himalayas

JPC – Journal of Planar Chromatography – Modern TLC - A high-performance thin-layer chromatographic (HPTLC) method has been established for simple and rapid quantification of two...     

“Optimization of aircraft maintenance/support infrastructure using genetic algorithms—level of repair analysis”

Level of repair analysis (LORA) is an approach used during the design stage of complex equipment for analysis of the cost effectiveness of competing maintenance strategies. LORA is carried as a part of the life cycle cost and cost of ownership analysis and plays a significant role in minimizing the life cycle cost and cost of ownership of the capital equipment. Since many purchasing decisions of complex equipment are based on cost of ownership, it has become essential to carry out LORA to compete in the market. In this paper, we develop a mathematical model for LORA and propose a solution methodology based on genetic algorithms. The concept is illustrated using a hypothetical aircraft engine.     

Stability and throughput analysis of unslotted CDMA‐ALOHA with finite number of users and code sharing

We consider a system comprising a finite number of nodes, with infinite packet buffers, that use unslotted ALOHA with Code Division Multiple Access (CDMA) to share a channel for transmitting packetised data. We propose a simple model for packet transmission and retransmission at each node, and show that saturation throughput in this model yields a sufficient condition for the stability of the packet buffers; we interpret this as the capacity of the access method. We calculate and compare the capacities of CDMA‐ALOHA (with and without code sharing) and TDMA‐ALOHA; we also consider carrier sensing and collision detection versions of these protocols. In each case, saturation throughput can be obtained via analysis of a continuous time Markov chain. Our results show how saturation throughput degrades with code‐sharing. Finally, we also present some simulation results for mean packet delay. Our work is motivated by optical CDMA in which “chips” can be optically generated, and hence the achievable chip rate can exceed the achievable TDMA bit rate which is limited by electronics. Code sharing may be useful in the optical CDMA context as it reduces the number of optical correlators at the receivers. Our throughput results help to quantify by how much the CDMA chip rate should exceed the TDMA bit rate so that CDMA‐ALOHA yields better capacity than TDMA‐ALOHA. This revised version was published online in June 2006 with corrections to the Cover Date.