We consider the polarization of unstable type-IIB D0-branes in the presence of a background five-form field strength. This phenomenon is studied from the point of view of the leading terms in the non-abelian Born Infeld action of the unstable D0-branes. The equations have SO(4) invariant solutions describing a non-commutative 3-sphere, which becomes a classical 3-sphere in the large-N limit. We discuss the interpretation of these solutions as spherical D3-branes. The tachyon plays a tantalizingly geometrical role in relating the fuzzy S 3 geometry to that of a fuzzy S 4 .

The possible applications of double phase conjugation effect (DPC) such as optical computing, image processing and so on attracted investigators last few years. The realization of DPC was successfully fulfilled in photorefractive crystalls [1]. Meanwhile DPC in nonlocal responce media is seemed to be desirable due to considerable nonlinearities of some of such media. In addition these media are more available. However, when reflected waves were otained in experiments they were not phase conjugated [2]. In this work we treat conditions of phase conjugated wave generation in nonlocal responce medium.

By accounting for both the speckle nature of the coherent noise and the depletion of the pump beam in a semilinear oscillator, we show that the buildup of phase conjugation from the noise level is characterized by a buildup time. The dependence of the buildup time on the noise level is in good agreement with experimental results.

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It is demonstrated that the self-starting generation for a phase-conjugate semilinear mirror is preceded by the silent zone, which is necessary for preparing a phase-conjugate generation structure in a multimode nonlinear resonator. The threshold for self-starting and the response delay are calculated. The experiment with a strontium barium niobate crystal demonstrates the reasonable quantitative agreement with the theory.