THE AUTOMORPHIC COHOMOLOGY AND THE RESIDUAL SPECTRUM OF HERMITIAN GROUPS OF RANK ONE

2010 ◽  
Vol 21 (02) ◽  
pp. 255-278 ◽  
Author(s):  
HARALD GROBNER
Keyword(s):  
Congruence Subgroups ◽  
Residual Spectrum ◽  
Rank One ◽  
Cuspidal Cohomology

Let G/ℚ be an inner form of Sp4/ℚ which does not split over ℝ. Consequently, it is not quasi-split. In this paper we determine completely the automorphic cohomology of G. That is, we describe the Eisenstein and the cuspidal cohomology of congruence subgroups Γ of G with respect to arbitrary coefficient systems. In particular we establish precise nonvanishing results for cuspidal cohomology. In addition, we calculate the residual spectrum [Formula: see text] of G.

scholarly journals Computations of cuspidal cohomology of congruence subgroups of SL(3, Z)

1984 ◽  
Vol 19 (3) ◽  
pp. 412-436 ◽  
Author(s):  
Avner Ash ◽  
Daniel Grayson ◽  
Philip Green
Keyword(s):  
Congruence Subgroups ◽  
Cuspidal Cohomology

Performance Improvement of Digital Hearing Aid Systems

2015 ◽  
Vol 1 ◽  
pp. 27
Author(s):  
Isiaka Ajewale Alimi
Keyword(s):  
Noise Reduction ◽  
Hearing Aids ◽  
Digital Signal Processor ◽  
Speech Intelligibility ◽  
Communication Systems ◽  
Hearing Aid ◽  
Spectral Subtraction ◽  
Residual Spectrum ◽  
Digital Hearing Aids ◽  
Digital Hearing Aid

Digital hearing aids addresses the issues of noise and speech intelligibility that is associated with the analogue types. One of the main functions of the digital signal processor (DSP) of digital hearing aid systems is noise reduction which can be achieved by speech enhancement algorithms which in turn improve system performance and flexibility. However, studies have shown that the quality of experience (QoE) with some of the current hearing aids is not up to expectation in a noisy environment due to interfering sound, background noise and reverberation. It is also suggested that noise reduction features of the DSP can be further improved accordingly. Recently, we proposed an adaptive spectral subtraction algorithm to enhance the performance of communication systems and address the issue of associated musical noise generated by the conventional spectral subtraction algorithm. The effectiveness of the algorithm has been confirmed by different objective and subjective evaluations. In this study, an adaptive spectral subtraction algorithm is implemented using the noise-estimation algorithm for highly non-stationary noisy environments instead of the voice activity detection (VAD) employed in our previous work due to its effectiveness. Also, signal to residual spectrum ratio (SR) is implemented in order to control the amplification distortion for speech intelligibility improvement. The results show that the proposed scheme gives comparatively better performance and can be easily employed in digital hearing aid system for improving speech quality and intelligibility.

Derivation of the Wave and Scattering Operators for an Interaction of Rank One

1970 ◽  
Vol 11 (8) ◽  
pp. 2415-2424 ◽  
Author(s):  
M. Anthea Grubb ◽  
D. B. Pearson
Keyword(s):  
Rank One ◽  
Scattering Operators

scholarly journals Ramification Theory for Extensions of Degree p. II

1972 ◽  
Vol 46 ◽  
pp. 97-109
Author(s):  
Susan Williamson
Keyword(s):  
Valuation Ring ◽  
Quotient Field ◽  
Root Of Unity ◽  
Ramification Index ◽  
Ramification Theory ◽  
Rank One ◽  
The Absolute

Let k denote the quotient field of a complete discrete rank one valuation ring R of unequal characteristic and let p denote the characteristic of R̅; assume that R contains a primitive pth root of unity, so that the absolute ramification index e of R is a multiple of p — 1, and each Gallois extension K ⊃ k of degree p may be obtained by the adjunction of a pth root.

scholarly journals Algorithms and Applications to Weighted Rank-one Binary Matrix Factorization

2020 ◽  
Vol 11 (2) ◽  
pp. 1-33
Author(s):  
Haibing Lu ◽  
Xi Chen ◽  
Junmin Shi ◽  
Jaideep Vaidya ◽  
Vijayalakshmi Atluri ◽  
...  
Keyword(s):  
Matrix Factorization ◽  
Binary Matrix ◽  
Rank One ◽  
Binary Matrix Factorization ◽  
Weighted Rank

scholarly journals Dimension of the Exceptional Set in the Aronszajn–Donoghue Theorem for Finite Rank Perturbations

2020 ◽  
Author(s):  
Constanze Liaw ◽  
Sergei Treil ◽  
Alexander Volberg
Keyword(s):  
Finite Rank ◽  
Measure Zero ◽  
Adjoint Operator ◽  
Cyclic Vector ◽  
Spectral Measures ◽  
Hermitian Matrices ◽  
Exceptional Set ◽  
Direct Sum ◽  
Rank One Perturbation ◽  
Rank One

Abstract The classical Aronszajn–Donoghue theorem states that for a rank-one perturbation of a self-adjoint operator (by a cyclic vector) the singular parts of the spectral measures of the original and perturbed operators are mutually singular. As simple direct sum type examples show, this result does not hold for finite rank perturbations. However, the set of exceptional perturbations is pretty small. Namely, for a family of rank $d$ perturbations $A_{\boldsymbol{\alpha }}:= A + {\textbf{B}} {\boldsymbol{\alpha }} {\textbf{B}}^*$, ${\textbf{B}}:{\mathbb C}^d\to{{\mathcal{H}}}$, with ${\operatorname{Ran}}{\textbf{B}}$ being cyclic for $A$, parametrized by $d\times d$ Hermitian matrices ${\boldsymbol{\alpha }}$, the singular parts of the spectral measures of $A$ and $A_{\boldsymbol{\alpha }}$ are mutually singular for all ${\boldsymbol{\alpha }}$ except for a small exceptional set $E$. It was shown earlier by the 1st two authors, see [4], that $E$ is a subset of measure zero of the space $\textbf{H}(d)$ of $d\times d$ Hermitian matrices. In this paper, we show that the set $E$ has small Hausdorff dimension, $\dim E \le \dim \textbf{H}(d)-1 = d^2-1$.

scholarly journals Sharp Rank-One Convexity Conditions in Planar Isotropic Elasticity for the Additive Volumetric-Isochoric Split

2021 ◽  
Vol 143 (2) ◽  
pp. 301-335
Author(s):  
Jendrik Voss ◽  
Ionel-Dumitrel Ghiba ◽  
Robert J. Martin ◽  
Patrizio Neff
Keyword(s):  
Differential Inequalities ◽  
Two Dimensional ◽  
Ellipticity Condition ◽  
One Dimensional ◽  
Suitable Sense ◽  
Precise Analysis ◽  
Rank One ◽  
Isotropic Elasticity ◽  
Convexity Conditions

AbstractWe consider the volumetric-isochoric split in planar isotropic hyperelasticity and give a precise analysis of rank-one convexity criteria for this case, showing that the Legendre-Hadamard ellipticity condition separates and simplifies in a suitable sense. Starting from the classical two-dimensional criterion by Knowles and Sternberg, we can reduce the conditions for rank-one convexity to a family of one-dimensional coupled differential inequalities. In particular, this allows us to derive a simple rank-one convexity classification for generalized Hadamard energies of the type $W(F)=\frac{\mu }{2} \hspace{0.07em} \frac{\lVert F \rVert ^{2}}{\det F}+f(\det F)$ W ( F ) = μ 2 ∥ F ∥ 2 det F + f ( det F ) ; such an energy is rank-one convex if and only if the function $f$ f is convex.

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