In this paper, we propose a novel method to test if a non-uniform filter bank can achieve perfect reconstruction via a tree structure. The set of decimators is first sorted in an ascending order. A non-uniform filter bank can achieve perfect reconstruction via a tree structure if and only if some or all of the channels corresponding to the maximum decimation ratio can be grouped into one channe...

We present here an exact formulation for the three-dimensional (3-D) boundary-value problem of plane wave scattering by a two-dimensionally (2-D) periodic impedance surface in a uniform medium. The scattering characteristics of such a structure are rigorously analyzed in terms of the complete set of both TEand TM-polarized plane waves in the uniform medium. Extensive numerical results are given...

In this paper, we propose a novel method to test if a non-uniform filter bank can achieve perfect reconstruction via a tree structure. The set of decimators is first sorted in an ascending order. A non-uniform filter bank can achieve perfect reconstruction via a tree structure if and only if some or all of the channels corresponding to the maximum decimation ratio can be grouped into one channe...

Hierarchically porous silica monoliths with well-defined interconnected macropores and uniform spherical mesopores were spontaneously prepared by combining polymerization-induced phase separation with an epoxide-mediated sol-gel route without any complicated aging and drying and high-temperature heat treatment. The precise control of pore structures can be realized by using propylene oxide (PO)...

The aim of this paper is to set up appropriate uniform convergence spaces in which to reformulate and enrich the Order Completion Method [25] for nonlinear PDEs. In this regard, we consider an appropriate space ML (X) of normal lower semi-continuous functions. The space ML (X) appears in the ring theory of C (X) and its various extensions [15], as well as in the theory of nonlinear, PDEs [25] a...

The symmetry of the cholesteric uniform lying helix (ULH) structure, where the helix axis is aligned in a single direction parallel to the device substrates, is not compatible with a uniform surface alignment and an unwinding of the helical structure is expected at the interface. Fluorescence confocal polarizing microscopy experiments are performed on the interface between a bulk ULH and a unif...