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sapphire oscillator in order to generate a single wavelength at 780 nm. The model offers a simple mechanism to investigate the impact of the variations of the input parameters (maximum amplification coefficient, pumping rate, loss coefficient, and pumping density) on the output pulse characteristics (delay time, pulse width, pulse build up time, duration and peaks maxima of the Nd3+ -YAG pumping laser). Moreover, this model allows studying the gain-switched Ti:sapphire output characteristics as being pumped by the second harmonic wavelength (532nm). Numerical results showed that the maxima of the output photon density, pulse width, delay time, and pulse duration are very much dependent on the power variations of the pumping source.
We have developed an analytic expression for the volume of intersection of any cylinder with any sphere in the usual threedimensional space, and give examples of its usefulness for physics. Produced from surface collisions either elastic collision , or inelastic collision, for the incoming energies greater than the binding energy of the nucleons in the nucleus, the reaction occurs and thus the effective size (what the target nucleus see from the nuclear material in the projectle, and What the projectle see from the nuclear material in the target nucleus) is formed and so for the different collisions parameters .
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