Polyphase matrix for rational decimation/interpolation systems

1993 ◽  
Author(s):  
Thomas J. Frederick ◽  
Nurgun Erdol
Keyword(s):  
Polyphase Matrix ◽  
Interpolation Systems

scholarly journals Fuzzy Interpolation Systems and Applications

10.5772/68051 ◽  
2017 ◽  
Author(s):  
Longzhi Yang ◽  
Zheming Zuo ◽  
Fei Chao ◽  
Yanpeng Qu
Keyword(s):  
Fuzzy Interpolation ◽  
Interpolation Systems

scholarly journals Symmetry Feature and Construction for the 3-Band Tight Framelets with Prescribed Properties

2012 ◽  
Vol 2012 ◽  
pp. 1-20
Author(s):  
Jianjun Sun ◽  
Bin Huang ◽  
Xiaodong Chen ◽  
Lihong Cui
Keyword(s):  
Wavelet Frames ◽  
Symmetric Extension ◽  
The Matrix ◽  
Polyphase Matrix ◽  
Necessary Constraints ◽  
Sobolev Exponent

A construction approach for the 3-band tight wavelet frames by factorization of paraunitary matrix is developed. Several necessary constraints on the filter lengths and symmetric features of wavelet frames are investigated starting at the constructed paraunitary matrix. The matrix is a symmetric extension of the polyphase matrix corresponding to 3-band tight wavelet frames. Further, the parameterizations of 3-band tight wavelet frames with3N+1filter lengths are established. Examples of framelets with symmetry/antisymmetry and Sobolev exponent are computed by appropriately choosing the parameters in the scheme.

scholarly journals A note on optimal Hermite interpolation in Sobolev spaces

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Guiqiao Xu ◽  
Xiaochen Yu
Keyword(s):  
Weight Function ◽  
Sobolev Spaces ◽  
Lagrange Interpolation ◽  
Hermite Interpolation ◽  
Weighted Spaces ◽  
Interpolation Algorithms ◽  
Interpolation Systems

AbstractThis paper investigates the optimal Hermite interpolation of Sobolev spaces $W_{\infty }^{n}[a,b]$ W ∞ n [ a , b ] , $n\in \mathbb{N}$ n ∈ N in space $L_{\infty }[a,b]$ L ∞ [ a , b ] and weighted spaces $L_{p,\omega }[a,b]$ L p , ω [ a , b ] , $1\le p< \infty $ 1 ≤ p < ∞ with ω a continuous-integrable weight function in $(a,b)$ ( a , b ) when the amount of Hermite data is n. We proved that the Lagrange interpolation algorithms based on the zeros of polynomial of degree n with the leading coefficient 1 of the least deviation from zero in $L_{\infty }$ L ∞ (or $L_{p,\omega }[a,b]$ L p , ω [ a , b ] , $1\le p<\infty $ 1 ≤ p < ∞ ) are optimal for $W_{\infty }^{n}[a,b]$ W ∞ n [ a , b ] in $L_{\infty }[a,b]$ L ∞ [ a , b ] (or $L_{p,\omega }[a,b]$ L p , ω [ a , b ] , $1\le p<\infty $ 1 ≤ p < ∞ ). We also give the optimal Hermite interpolation algorithms when we assume the endpoints are included in the interpolation systems.

scholarly journals Polyphase matrix characterization of framelets on local fields of positive characteristic

2017 ◽  
Vol 9 (1) ◽  
pp. 248-259
Author(s):  
F. A. Shah ◽  
M. Y. Bhat
Keyword(s):  
Positive Characteristic ◽  
Local Fields ◽  
Extension Principle ◽  
Wavelet Frames ◽  
Unitary Extension ◽  
Polyphase Matrix

AbstractAn important tool for the construction of framelets on local fields of positive characteristic using unitary extension principle was presented by Shah and Debnath [Tight wavelet frames on local fields, Analysis, 33 (2013), 293-307]. In this article, we continue the study of framelets on local fields and present a polyphase matrix characterization of framelets generated by the extension principle.

Microstructures reveal brittle and viscous flow during exhumation of the high-temperature lower oceanic crust from Site U1473A, Atlantis Bank, Southwest Indian Ridge (IODP Expedition 360)

2021 ◽  
Author(s):  
Rhander Taufner ◽  
Gustavo Viegas ◽  
Frederico Faleiros ◽  
Paulo Castellan ◽  
Raylline Silva
Keyword(s):  
Strain Localization ◽  
Shear Zones ◽  
Thermodynamic Modelling ◽  
Oriented Growth ◽  
Rock Interaction ◽  
Fine Grained ◽  
Atlantis Bank ◽  
Polyphase Matrix ◽  
Indian Ridge ◽  
Detachment Faulting

&lt;p&gt;Detachment faulting has been hypothesized as the main process of tectonic spreading in mid-ocean ridges. The ongoing faulting leads to exhumation of oceanic core complexes (OCC) through large-scale normal faults, exposing heterogeneous sectors of the mylonitic lower crust, locally interlayered with pristine upper-mantle rocks. However, the mechanisms involved in this process &amp;#8211; and the interplay between magmatism, deformation and fluid-rock interaction &amp;#8211; are still debatable. To address these issues, we performed a quantitative microstructural analysis and thermodynamic modelling on mafic shear zones that occur in the lower section (&amp;#8805; 600 meters below sea-floor) of Site U1473A (Atlantis Bank OCC, SW Indian Ridge), the target of IODP Expedition 360, to constrain deformation conditions and strain localization mechanisms during detachment faulting. The gabbroic shear zones consist of large (up to 5 mm in size) porphyroclasts of clinopyroxene, orthopyroxene, plagioclase and olivine embedded in a fine-grained (&amp;#8804; 30 &amp;#181;m), polyphase matrix composed of plagioclase, clinopyroxene, orthopyroxene, amphibole, ilmenite, magnetite and olivine. Plagioclase-rich layers (~ 80 &amp;#181;m) are in abrupt contact with the fine-grained mixture, which define the mylonitic foliation. The porphyroclasts have undulose extinction, subgrains and are surrounded by fine-grained recrystallized grains (core-mantle structure) showing internal lattice distortion. Microfractures are common in orthopyroxene porphyroclasts. Amphibole replaces clinopyroxene and orthopyroxene porphyroclasts at their margins and fills cleavage planes. The plagioclase-rich layers show undulose extinction and subgrain boundaries in the larger grains within the layers. Mechanical twin lamellae occur in some grains regardless of grain size. Plagioclase grains show a weak shape preferred orientation with their long axes parallel to the main planar fabric of the shear zone. The grains in the polyphase matrix are mostly strain free. EBSD data in clinopyroxene clasts indicate activation of (010)[001] slip system and twinning along (001)[100]. Plagioclase-rich layers deforms by slip along the (010)[100] system. The polyphase matrix has a very weak but non-random CPO pattern. #Mg and Al content in the recrystallized clinopyroxene and orthopyroxene grains are lower compared to the porphyroclasts. Plagioclase has similar An content in both porphyroclasts and recrystallized grains. Amphibole has low concentrations of Cl and high content of F. The content of #Mg, Al and Si is similar in amphibole grains replacing pyroxene and in the polyphase matrix. Thermodynamic modelling indicates that the gabbroic shear zones formed at 820-870 &amp;#176;C and 2.0-2.8 kbar. Our results suggest that deformation in the porphyroclasts was accommodated by combined mechanical fragmentation and intracrystalline plasticity, which resulted in fractured grains of orthopyroxene, and clasts rimmed by recrystallized neoblasts. Plagioclase-rich layers formed mainly through dislocation creep. Phase mixing and weak CPO in the polyphase matrix point to oriented-growth during diffusion-assisted grain boundary sliding, mainly in the presence of melt, as evidenced by amphibole formed at the expense of pyroxene. Magmatic fluids are the possible source of reactant amphibole. Such mechanisms effectively resulted in strain localization in fine-grained, polyphase shear zones that contributed to the weakening of the ocean crust during detachment faulting and subsequent exhumation of the Atlantis Bank OCC.&lt;/p&gt;

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