The first type of pseudo-splines were introduced in [12, 24] to construct tight framelets with desired approximation orders via the unitary extension principle of [22]. In the spirit of the first type of pseudo-splines, we introduce here a new type (the second type) of pseudo-splines to construct symmetric or antisymmetric tight framelets with desired approximation orders. Pseudo-splines provid...

Attention has been brought to the possibility that statistical fluctuation properties of several complex spectra, or, well-known number sequences may display strong signatures that the Hamiltonian yielding them as eigenvalues is PT-symmetric (Pseudo-Hermitian). We find that the random matrix theory of pseudo-Hermitian Hamiltonians gives rise to new universalities of levelspacing distributions o...

Abstract We study the statistical estimation problem of orthogonal group synchronization and rotation synchronization. The model is $Y_{ij} = Z_i^* Z_j^{*T} + \sigma W_{ij}\in{\mathbb{R}}^{d\times d}$ where $W_{ij}$ a Gaussian random matrix $Z_i^*$ either an or matrix, each $Y_{ij}$ observed independently with probability $p$. analyze iterative polar decomposition algorithm for $Z^*$ show it ha...

Abstract—Wireless Body Area Network (WBAN) is a short-range wireless communication around human body for various applications such as wearable devices, entertainment, military, and especially medical devices. WBAN attracts the attention of continuous health monitoring system including diagnostic procedure, early detection of abnormal conditions, and prevention of emergency situations. Compared ...

The asymmetric unit of the enanti-omerically pure title compound, C18H18N2O3S, comprises two independent mol-ecules (A and B) having almost identical conformations. When overlayed, the alignment-r.m.s. deviation value is 0.30 Å. The six-membered heterocycle has a twisted half-chair conformation in both mol-ecules. The O atom on the S atom of the ring is pseudo-axial on the thia-zine ring and tr...

It is shown that a N ×N real symmetric [complex hermitian] positive definite matrix V is congruent to a diagonal matrix modulo a pseudo-orthogonal [pseudo-unitary] matrix in SO(m,n) [ SU(m,n)], for any choice of partition N = m+n. It is further shown that the method of proof in this context can easily be adapted to obtain a rather simple proof of Williamson’s theorem which states that if N is e...

This paper is concerned with the numerical treatment of pseudo-diierential equations in I R 2 , employing wavelet Galerkin methods. We construct wavelet bases adapted to a given pseudo-diierential operator in the sense that functions on diierent reenement levels are orthogonal with respect to a certain bilinear form induced by the operator.