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Toy Model for Large Non-Symmetric Random Matrices

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Acta Physica Polonica A
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2008
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vol. 114
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issue 3
555-559
EN
Non-symmetric rectangular correlation matrices occur in many problems in economics. We test the method of extracting statistically meaningful correlations between input and output variables of large dimensionality and build a toy model for artificially included correlations in large random time series.The results are then applied to analysis of polish macroeconomic data and can be used as an alternative to classical cointegration approach.
Acta Physica Polonica A
|
2008
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vol. 114
|
issue 6A
A-139-A-142
EN
The analytical expression for mutual capacitance of periodic strips is presented in this paper. This expression utilizing the spectral theory is obtained. It is studied how the metallization ratio affects a mutual capacitance of periodic strips. The mutual capacitance of periodic strips as a function of metallization ratio, for split electrodes, was shown in the paper. This approach should be applicable to modeling of the surface acoustic waves interdigital transducers.
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issue 2
386-388
EN
The analytic formula for the on-site Green function on the two-dimensional rectangular lattice is shown for arbitrary energy, both within the band (complex Green function) and outside the band (real Green function), expressed by means of elliptic integrals. The recursion formulae enabling calculation of the Green functions on other lattice sites are shown.
EN
Theoretical investigation of acoustic field in a tellurium two-coordinate deflector was carried out. We used angular spectrum method supported by consideration to boundary conditions in approximation of a given displacement to calculate spatial distribution of the acoustic field intensity. Volumetric illustration is presented for the acoustic beam launched from YZ face of the crystal. Cross-sections of the acoustic field generated from XZ face are also presented in the work. It is shown that the strong anisotropy of acoustic properties in the Te crystal leads to principally different structure of the two fields excited from the XZ and YZ crystal faces. The acoustic field excited from the XZ face may be considered as a simple beam with a relatively high divergence. On the other hand, the field generated from the YZ face looks like superposition of two beams with relatively low divergence. Ratio of intensities of the two beams generated by longitudinal piezotransducers is equal to the ratio predicted by analysis based by plane-wave theory.
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