Abstract It is well-known that a B type Kadomtsev–Petviashvili (BKP) tau-function the square root of certain (KP) tau-function, provided one puts even KP times equal to zero. In this paper we compute for all polynomial BKP its corresponding ‘square’. We also give, in case, representation theoretical proof recent result by Alexandrov, viz Korteweg–de Vries (KdV) becomes when divides KdV 2.

Abstract. In this paper we classify a linear family of Lie brackets on the space of rectangular matrices Mat(n×m, K) and we give an analogue of the Ado’s Theorem. We give also a similar classification on the algebra of the square matrices Mat(n, K) and as a consequence, we prove that we can’t built a faithful representation of the (2n + 1)-dimensional Heisenberg Lie algebra Hn in a vector space...

A square complex matrix A is called if it can be written in the form EP   1 0 U A U  with U being fixed unitary and 1 A being arbitrary matrix in . We give necessary and sufficient conditions for the existence of the solution to the system of complex matrix equation r r   r EP , AX B XC D   and present an expression of the solution to the system when the solvability conditions are satisf...

Abstract. In this paper we classify a linear family of Lie brackets on the space of rectangular matrices Mat(n×m, K) and we give an analogue of the Ado’s Theorem. We give also a similar classification on the algebra of the square matrices Mat(n, K) and as a consequence, we prove that we can’t built a faithful representation of the (2n + 1)-dimensional Heisenberg Lie algebra Hn in a vector space...

We present a group-theoretical derivation of the continuous wavelet transform (CWT) on the 2-sphere S2, based on the construction of coherent states associated to square integrable group representations. The parameter space X is the product of SO(3) x J&, embedded into the Lorentz group S00(3, 1) via the Iwasawa decomposition, and X Y SO,(3,1)/C. The space L2(S2, a!~) carries a unitary irreduci...

It is obvious to anyone familiar with the rules of the game of chess that a king on an empty board can reach every square. It is true, but not obvious, that a knight can reach every square. Why is the first fact obvious but the second fact not? This paper presents an analytic theory of a class of obviousness judgments of this type. Whether or not the specifics of this analysis are correct, it s...

The two-dimensional surface of an integer quantum hall multilayer is mapped onto a Heisenberg spin chain with ferromagnetic coupling. Using this mapping it is shown nonperturbatively that the surface states constitute a very anisotropic metal in the infinite size limit. For multilayers of finite size, two diffusive mesoscopic regimes are identified and the conductance fluctuations are calculate...

Motion blur can significantly degrade the quality of an image. The images become blurred due to camera movements, object movements or displacements of pixels. Deblurring of an image is done by processing an image through curvelet transform and removal of noise by median filter. Experimental results show that proposed deblurring technique and accuracy measurement using peak signal to noise ratio...

Two formulas for Macdonald functions (which are a widely known in mathematics and applications particular case of cylinder functions) obtained by using some integral bilinear functionals defined on pair representation spaces or square these