Vol. 1 No. 1 (2008)
Published:
2008-07-11
Articles
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Articles
Interaction of Non-Abelian Tensor Gauge Fields
AbstractRecently we introduced an extended vector bundle $X$ on which non-Abelian tensor gauge fields realize a connection. Our aim here is to introduce interaction of non-Abelian tensor gauge fields with fermions and bosons. We have found that there exist two series of gauge invariant forms describing this interaction. The linear sum of these forms comprises the general gauge invariant Lagrangian. Studying the corresponding Euler-Lagrange equations we found that a particular linear combination of these forms exhibits enhanced symmetry which guarantees the conservation of the corresponding high-rank currents. A possible mechanism of symmetry breaking and mass generation of tensor gauge bosons is suggested.
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Articles
Boundedness of Maximal and Singular Operators in Morrey Spaces with Variable Exponent
AbstractIn this paper the boundedness of Hardy-Littlewood maximal and singular operators in variable exponent Morrey spaces $M^{p(\cdot)}_{q(\cdot)}(X)$ defined on spaces of homogeneous type is established provided that $p$ and $q$ satisfy Dini-Lipschitz (log-H\"older continuity) condition.References -
Articles
Transmutations for Strings
AbstractWe investigate the existence and representation of transmutations, also known as transformation operators, for strings. Using measure theory and functional analytic methods we prove their existence and study their representation. We show that in general they are not close to unity since their representation does not involve a Volterra operator but rather the eigenvalue parameter. We also obtain conditions under which the transmutation is either a bounded or a compact operator. Explicit examples show that they cannot be reduced to Volterra type operators.
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Articles
Frequency detection using Pade approximation
AbstractThe current paper describes an application of Pade approximation to obtain a frequency detection method similar to (and, in a sense, more general than) linear prediction. While generally not applicable for spectrum estimation, the described method is in many cases more precise in finding the frequencies of a harmonic signal. A great number of numerical tests were performed for comparing frequency detection performance of the method under consideration and of linear prediction. Their methodology and results are summarized in the article.
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Articles
The Convergence Acceleration of Two-Dimensional Fourier Interpolation
AbstractHereby, the convergence acceleration of two-dimensional trigonometric interpolation for a smooth functions on a uniform mesh is considered. Together with theoretical estimates some numerical results are presented and discussed that reveal the potential of this method for application in image processing. Experiments show that suggested algorithm allows acceleration of conventional Fourier interpolation even for sparse meshes that can lead to an efficient image compression/decompression algorithms and also to applications in image zooming procedures.
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