The degenerate residual spectrum of quasi-split forms of $Spin_8$ associated to the Heisenberg parabolic subgroup

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.

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A decomposition formula for representations

Nagoya Mathematical Journal ◽

10.1017/s0027763000002543 ◽

1987 ◽

Vol 107 ◽

pp. 63-68 ◽

Cited By ~ 2

Author(s):

George Kempf

Keyword(s):

Irreducible Representation ◽

General Formula ◽

Parabolic Subgroup ◽

Characteristic Zero ◽

Maximal Torus ◽

Reductive Group ◽

Irreducible Representations ◽

Levi Subgroup ◽

Know How ◽

Decomposition Formula

Let H be the Levi subgroup of a parabolic subgroup of a split reductive group G. In characteristic zero, an irreducible representation V of G decomposes when restricted to H into a sum V = ⊕mαWα where the Wα’s are distinct irreducible representations of H. We will give a formula for the multiplicities mα. When H is the maximal torus, this formula is Weyl’s character formula. In theory one may deduce the general formula from Weyl’s result but I do not know how to do this.

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PREGARSIDE MONOIDS AND GROUPS, PARABOLICITY, AMALGAMATION, AND FC PROPERTY

International Journal of Algebra and Computation ◽

10.1142/s021819671350029x ◽

2013 ◽

Vol 23 (06) ◽

pp. 1431-1467

Author(s):

EDDY GODELLE ◽

LUIS PARIS

Keyword(s):

Parabolic Subgroup ◽

Parabolic Subgroups ◽

Basic Study ◽

The Family ◽

Definition Of ◽

Amalgamated Product

We define the notion of preGarside group slightly lightening the definition of Garside group so that all Artin–Tits groups are preGarside groups. This paper intends to give a first basic study on these groups. Firstly, we introduce the notion of parabolic subgroup, we prove that any preGarside group has a (partial) complemented presentation, and we characterize the parabolic subgroups in terms of these presentations. Afterwards we prove that the amalgamated product of two preGarside groups along a common parabolic subgroup is again a preGarside group. This enables us to define the family of preGarside groups of FC type as the smallest family of preGarside groups that contains the Garside groups and that is closed by amalgamation along parabolic subgroups. Finally, we make an algebraic and combinatorial study on FC type preGarside groups and their parabolic subgroups.

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Tangent bundle of hypersurfaces in G/P

Journal of K-theory K-theory and its Applications to Algebra Geometry and Topology ◽

10.1017/is008002001jkt052 ◽

2008 ◽

Vol 4 (1) ◽

pp. 91-100

Author(s):

Indranil Biswas ◽

Georg Schumacher

Keyword(s):

Line Bundle ◽

Algebraic Group ◽

Parabolic Subgroup ◽

Tangent Bundle ◽

Linear Algebraic Group ◽

Closed Field ◽

Algebraically Closed Field ◽

Smooth Hypersurface ◽

Canonical Line Bundle

AbstractLet G be a simple linear algebraic group defined over an algebraically closed field k of characteristic p ≥ 0, and let P be a maximal proper parabolic subgroup of G. If p > 0, then we will assume that dimG/P ≤ p. Let ι : H ↪ G/P be a reduced smooth hypersurface in G/P of degree d. We will assume that the pullback homomorphism is an isomorphism (this assumption is automatically satisfied when dimH ≥ 3). We prove that the tangent bundle of H is stable if the two conditions τ(G/P) ≠ d and hold; here n = dimH, and τ(G/P) ∈ is the index of G/P which is defined by the identity = where L is the ample generator of Pic(G/P) and is the anti–canonical line bundle of G/P. If d = τ(G/P), then the tangent bundle TH is proved to be semistable. If p > 0, and then TH is strongly stable. If p > 0, and d = τ(G/P), then TH is strongly semistable.

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