In this expression ↠and â denote the creation and annihilation operators of the one-mode radiation field of frequency Ω, ωA the separation between the atomic levels, Ĵz denotes a collective atomic operator which counts the difference of population between the two atomic levels, Ĵ+ a collective atomic operator which promotes atoms from the lower level to the upper level, Ĵ− = Ĵ † +, and μ stan...

We first give a geometrical description of the action of the parity operator (P̂ ) on non relativistic spin 12 Pauli spinors in terms of bundle theory. The relevant bundle, SU(2)⊙Z2 → O(3), is a non trivial extension of the universal covering group SU(2) → SO(3). P̂ is the non relativistic limit of the corresponding Dirac matrix operator P = iγ0 and obeys P̂ 2 = −1. Then, from the direct product o...

Optimum filters for an image restoration are formed by a degradation operator, a covariance operator of original images, and one of noise. However, in a practical image restoration problem, the degradation operator and the covariance operators are estimated on the basis of empirical knowledge. Thus, it appears that they differ from the true ones. When we restore a degraded image by an optimum f...

We continue the study of multidimensional operator multipliers initiated in [12]. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and...

The spectral representation for stochastic integration operators with respect to the Wiener process is proposed in form of a composition characteristics used mathematical description control systems. This can be defined relative various orthonormal bases. For given deterministic square-integrable kernels, characteristic operator determined as an infinite random matrix. main applications such su...

We first give a geometrical description of the action of the parity operator (ˆ P) on non relativistic spin 1 2 Pauli spinors in terms of bundle theory. The relevant bundle, SU (2) ⊙ Z 2 → O(3), is a non trivial extension of the universal covering group SU (2) → SO(3). ˆ P is the non relativistic limit of the corresponding Dirac matrix operator P = iγ 0 and obeysˆP 2 = −1. Then, from the direct...

The problem of finding a general, parallel, and hierarchical operator for picture processing is considered. An operator is defined which at different levels can detect and describe structure as opposed to uniformity within local regions, whatever structure and uniformity may imply at a particular level. The operator performs a mapping from one complex field to another. The important characteris...

In this paper, we recast the fermionic ghost sector of Witten’s open bosonic string field theory in the language of noncommutative field theory. In particular, following the methods of hep-th/0202087, we find that in Siegel gauge Witten’s star product roughly corresponds to a continuous tensor product of Clifford Algebras, and we formulate important operators of the theory in this language, not...

Consider an elliptic self-adjoint pseudodifferential operator A acting on m-columns of half-densities a closed manifold M, whose principal symbol is assumed to have simple eigenvalues. Relying basis projections commuting with A, we construct almost-unitary that diagonalizes modulo infinitely smoothing operator. We provide invariant algorithm for the computation its full symbol, as well explicit...