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Inspired by the wavelet transform in quantum mechanics, we define the new Ridgelet transform for quantum optics by rewriting the classic Ridgelet transform via the two-mode coordinate representation in Fock space. Furthermore, we give the explicit form of the asymmetric operator's integral and derive two useful formulas for the normal ordering of the two-mode operator with the help of the technique of integration within an ordered product (IWOP) of operators. By choosing the two-variable Mexican hat's mother wavelet function, we analyse the Ridgelet transforms of the coherent state, special squeezed coherent state, intermediary entangled state on the basis of the theories we have mentioned.

We derive a useful formula for the normal ordering of two-mode operator by the technique of integration within an ordered product (IWOP) of operators. Furthermore, we also calculate the Radon transformations for the coherent state, special squeezed coherent state, intermediary entangled state in the view of the quantum mechanics. Based on the results above, the Mexican hat's mother wavelet function is selected to analyse Ridgelet transformations of these three quantum optical states.

Based on the results of constructing the wavelet transform in continuous variable quantum state and the classical continuous ridgelet transform, we construct the continuous complex ridgelet transform in the expression of quantum operators and representations. We study the theory of the complex ridgelet transform in quantum optic state via calculating the inner product and projection of quantum states.

In this paper, we treat the modified function projective lag synchronization between two non-identical multi-scroll chaotic systems with unknown disturbances. By utilizing the lyapunov stability theory, the fuzzy adaptive controller and parameter update law are derived to make the state of chaotic system achieve modified function projective lag synchronization. The controller can keep the systems stable even when the disturbance changes. Finally numerical simulations are performed to show the effectiveness of the proposed method.

Two new mother wavelets are constructed on the basis of the quantum mechanics of classical wavelet transform. Based on that, the wavelet transform of coherent state and particle number state is studied with the technique of integration within an ordered product, and the wavelet transform from coherent state to particle number state is obtained by numerical calculation.

One-dimensional pre-mixed model for a pulsed chemical oxygen-iodine laser is presented according to the reaction mechanism in chemical oxygen-iodine laser. The influences of gas temperature of 150-450 K and pressure of 660-2660 Pa on single pulse energy, pulse duration and peak power are studied. The internal reason of the influences of pressure and temperature on laser characteristics is analyzed. The results show that the higher laser peak power can be obtained in the case of gas temperature of 150 K and pressure of 1330 Pa than in the case of 400 K and 2660 Pa. Thus an efficient pulsed chemical oxygen-iodine laser is promising if the abundant atomic iodine is generated instantaneously. The approach to atomic iodine generation does not disturb the state of supersonic flow.

In non-commutative spaces the invariant eigen-operator method is used to derive and calculate Hamiltonian spectra for three kinds of three coupled harmonic oscillators: no coupling, coordinate coupling and momentum coupling. According to the comparison with the results in commutative space, it is shown that when the non-commutative parameter is zero the obtained energy levels are equal to the energy levels in commutative space. Finally the effect of the coupling coefficient on Hamiltonian spectrum in non-commutative space is discussed.

One-dimensional pre-mixed model for a pulsed chemical oxygen-iodine laser is presented according to the reaction mechanism in chemical oxygen-iodine laser. The dependence of species concentration and optical parameters on single pulse energy and pulse duration is studied. The dynamical process is analyzed while laser is running. Gain switching during lasing is discussed.These results can provide theoretical support for the optimization of pulsed chemical oxygen-iodine laser.