scholarly journals Alòs Type Decomposition Formula for Barndorff-Nielsen and Shephard Model

2021 ◽  
Vol 2 (2) ◽  
Author(s):  
Takuji Arai
Keyword(s):  
Decomposition Formula ◽  
Type Decomposition

scholarly journals G-marked moduli spaces

2018 ◽  
Vol 20 (06) ◽  
pp. 1750061 ◽  
Author(s):  
Binru Li
Keyword(s):  
Finite Group ◽  
Moduli Spaces ◽  
Effective Action ◽  
Canonical Representation ◽  
Hilbert Polynomial ◽  
Projective Varieties ◽  
Canonical Models ◽  
Decomposition Formula ◽  
Polynomial Formula ◽  
Type Decomposition

The aim of this paper is to investigate the closed subschemes of moduli spaces corresponding to projective varieties which admit an effective action by a given finite group [Formula: see text]. To achieve this, we introduce the moduli functor [Formula: see text] of [Formula: see text]-marked Gorenstein canonical models with Hilbert polynomial [Formula: see text], and prove the existence of [Formula: see text], the coarse moduli scheme for [Formula: see text]. Then we show that [Formula: see text] has a proper and finite morphism onto [Formula: see text] so that its image [Formula: see text] is a closed subscheme. In the end we obtain the canonical representation type decomposition [Formula: see text] of [Formula: see text] and use [Formula: see text] to study the structure of [Formula: see text].

scholarly journals The Weitzenböck Type Curvature Operator for Singular Distributions

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 365
Author(s):  
Paul Popescu ◽  
Vladimir Rovenski ◽  
Sergey Stepanov
Keyword(s):  
Riemannian Manifold ◽  
Vector Bundle ◽  
Tangent Bundle ◽  
Null Space ◽  
Curvature Operator ◽  
Vanishing Theorems ◽  
Lie Algebroid ◽  
Decomposition Formula ◽  
Adjoint Operators ◽  
Type Decomposition

We study geometry of a Riemannian manifold endowed with a singular (or regular) distribution, determined as an image of the tangent bundle under smooth endomorphisms. Following construction of an almost Lie algebroid on a vector bundle, we define the modified covariant and exterior derivatives and their L 2 adjoint operators on tensors. Then, we introduce the Weitzenböck type curvature operator on tensors, prove the Weitzenböck type decomposition formula, and derive the Bochner–Weitzenböck type formula. These allow us to obtain vanishing theorems about the null space of the Hodge type Laplacian. The assumptions used in the results are reasonable, as illustrated by examples with f-manifolds, including almost Hermitian and almost contact ones.

scholarly journals A decomposition formula for representations

1987 ◽  
Vol 107 ◽  
pp. 63-68 ◽  
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.

scholarly journals EMeth: An EM algorithm for cell type decomposition based on DNA methylation data

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hanyu Zhang ◽  
Ruoyi Cai ◽  
James Dai ◽  
Wei Sun
Keyword(s):  
Dna Methylation ◽  
Tumor Cells ◽  
T Regulatory Cells ◽  
Simulated Data ◽  
Cell Types ◽  
Computational Method ◽  
Methylation Data ◽  
Cell Type ◽  
A Cell ◽  
Type Decomposition

AbstractWe introduce a new computational method named EMeth to estimate cell type proportions using DNA methylation data. EMeth is a reference-based method that requires cell type-specific DNA methylation data from relevant cell types. EMeth improves on the existing reference-based methods by detecting the CpGs whose DNA methylation are inconsistent with the deconvolution model and reducing their contributions to cell type decomposition. Another novel feature of EMeth is that it allows a cell type with known proportions but unknown reference and estimates its methylation. This is motivated by the case of studying methylation in tumor cells while bulk tumor samples include tumor cells as well as other cell types such as infiltrating immune cells, and tumor cell proportion can be estimated by copy number data. We demonstrate that EMeth delivers more accurate estimates of cell type proportions than several other methods using simulated data and in silico mixtures. Applications in cancer studies show that the proportions of T regulatory cells estimated by DNA methylation have expected associations with mutation load and survival time, while the estimates from gene expression miss such associations.

PRIMARY PROCESS STUDIES BY MONOISOTOPIC PHOTOSENSITIZATION ON THE REACTIONS OF Hg 6(3P1) ATOMS WITH ALKYL CHLORIDES

1964 ◽  
Vol 42 (9) ◽  
pp. 2056-2064 ◽  
Author(s):  
J. K. S. Wan ◽  
O. P. Strausz ◽  
W. F. Allen ◽  
H. E. Gunning
Keyword(s):  
Mercury Vapor ◽  
Quantum Yields ◽  
Primary Process ◽  
Reaction Parameters ◽  
Specific Nature ◽  
Electrodeless Discharge ◽  
Discharge Source ◽  
Bond Scission ◽  
Decomposition Formula ◽  
Process Studies

The specific nature of the primary process in the reaction of 202Hg 6(3P1) atoms, photoexcited in natural mercury vapor by a cool 202Hg electrodeless discharge source, with CH3Cl has been examined in detail. Primary C–Cl bond scission occurs with unit efficiency. Quantum yields (φ) for the two primary modes of decomposition[Formula: see text]were found to have values of 0.71 (b) and 0.29 (a). The effect of various reaction parameters on the 202Hg enrichment in the calomel product has been investigated and the importance of isotopic mercury depletion in the reaction zone demonstrated by the use of intermittent illumination.A brief study of the reaction of ethyl, n-propyl, i-propyl, t-butyl, and n-amyl chlorides has revealed a relation between the molecular structure of the alleyl chloride and the efficiency of the monoisotopic route (a) to calomel formation. Thus, while the reactions of all the normal alkyl chlorides have φa values between 0.29 and 0.32, φa (isopropyl chloride) is only 0.22 and φa (t-butyl chloride) is 0.17.

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