A Note on the Alos Decomposition Formula

2021 ◽  
Author(s):  
Frido Rolloos
Keyword(s):  
Decomposition Formula

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.

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.

A constitutive model for an internally balanced compressible elastic material

2016 ◽  
Vol 22 (3) ◽  
pp. 372-400 ◽  
Author(s):  
Ashraf Hadoush ◽  
Hasan Demirkoparan ◽  
Thomas J Pence
Keyword(s):  
Energy Density ◽  
Potential Energy ◽  
Constitutive Models ◽  
Field Equations ◽  
Multiplicative Decomposition ◽  
Finite Strain Plasticity ◽  
Decomposition Formula ◽  
New Feature ◽  
Internal Balance ◽  
Traction Boundary Conditions

Many large deformation constitutive models for the mechanical behavior of solid materials make use of the multiplicative decomposition [Formula: see text] as, for example, used by Kröner in the context of finite-strain plasticity. Then [Formula: see text] describes the elastic effect by letting the potential energy of the deformation depend upon [Formula: see text]. In this paper we allow the potential energy to depend upon both portions of the multiplicative decomposition. As in hyperelasticity, energy minimization with respect to displacement gives equilibrium field equations and traction boundary conditions. The new feature, minimization with respect to the decomposition itself, generates an additional mathematical requirement that is interpreted here in terms of a principle of internal mechanical balance. We specifically consider a Blatz–Ko-type solid suitably generalized to incorporate the notion of internal balance. Conventional results of hyperelasticity are retrieved for certain limiting forms of the energy density, whereas the general form of the energy density gives rise to an overall softening response, as is demonstrated in the context of pure pressure and uniaxial loading.

Edge geodetic self-decomposition in graphs

2020 ◽  
Vol 12 (05) ◽  
pp. 2050064
Author(s):  
J. John ◽  
D. Stalin
Keyword(s):  
Connected Graph ◽  
Edge Disjoint ◽  
General Properties ◽  
Decomposition Formula ◽  
Simple Connected Graph

Let [Formula: see text] be a simple connected graph of order [Formula: see text] and size [Formula: see text]. A decomposition of a graph [Formula: see text] is a collection of edge-disjoint subgraphs [Formula: see text] of [Formula: see text] such that every edge of [Formula: see text] belongs to exactly one [Formula: see text]. The decomposition [Formula: see text] of a connected graph [Formula: see text] is said to be an edge geodetic self-decomposition if [Formula: see text] for all [Formula: see text]. Some general properties satisfied by this concept are studied.

scholarly journals The Decomposition Formula of ⟨001⟩ Symmetrical Tilt Grain Boundaries

2015 ◽  
Vol 56 (12) ◽  
pp. 1945-1952 ◽  
Author(s):  
Kazutoshi Inoue ◽  
Mitsuhiro Saito ◽  
Zhongchang Wang ◽  
Motoko Kotani ◽  
Yuichi Ikuhara
Keyword(s):  
Grain Boundaries ◽  
Decomposition Formula ◽  
Symmetrical Tilt

scholarly journals On the Mechanics of Economic Convergence

2006 ◽  
Vol 7 (3) ◽  
pp. 317-337 ◽  
Author(s):  
Thomas M. Steger
Keyword(s):  
Steady State ◽  
Rate Of Convergence ◽  
Driving Forces ◽  
Relative Importance ◽  
Economic Convergence ◽  
Resource Reallocation ◽  
Numerical Techniques ◽  
Instantaneous Rate ◽  
Convergence Process ◽  
Decomposition Formula

Abstract The speed at which an economy converges to its steady state is investigated by using a general non-scale R&D-based growth model. To accomplish this task, an analytical decomposition formula for the instantaneous rate of convergence is developed. By applying this decomposition to the model under study, the driving forces behind the convergence process are identified. Two convergence mechanisms are distinguished: the accumulation-decumulation mechanism and the resource-reallocation mechanism. The relative importance of the different convergence mechanisms is assessed using numerical techniques. Moreover, it is shown that the specific shock being considered might be crucial for the instantaneous rate of convergence.

CONSTRUCTION OF SELF-DUAL RADICAL 2-CODES OF GIVEN DISTANCE

2012 ◽  
Vol 04 (04) ◽  
pp. 1250052
Author(s):  
CAROLIN HANNUSCH ◽  
PIROSKA LAKATOS
Keyword(s):  
Abelian Group ◽  
Group Algebra ◽  
Abelian Groups ◽  
Dual Code ◽  
Decomposition Formula ◽  
Construction Of Self ◽  
Characteristic 2

We prove that for arbitrary n ∈ ℕ and [Formula: see text] and for a field K of characteristic 2 there exists an abelian group G of order 2n such that one of the powers of the radical of the group algebra K[G] is a (2n, 2n-1, 2d)-self-dual code. These codes are constructed for abelian groups G with decomposition [Formula: see text] where a1 ≥ 3 and si ≥ 0(1 ≤ i ≤ 3).

scholarly journals Process Dimension of Classical and Non-Commutative Processes

2012 ◽  
Vol 19 (01) ◽  
pp. 1250007
Author(s):  
Wolfgang Löhr ◽  
Arleta Szkoła ◽  
Nihat Ay
Keyword(s):  
Stochastic Process ◽  
Ergodic Decomposition ◽  
Statistical Complexity ◽  
Lower Semi ◽  
Decomposition Formula ◽  
Close Relationship ◽  
Natural Characteristic ◽  
Causal States ◽  
Definition Of ◽  
Process Dimension

We treat observable operator models (OOM) and their non-commutative generalisation, which we call NC-OOMs. A natural characteristic of a stochastic process in the context of classical OOM theory is the process dimension. We investigate its properties within the more general formulation, which allows one to consider process dimension as a measure of complexity of non-commutative processes: We prove lower semi-continuity, and derive an ergodic decomposition formula. Further, we obtain results on the close relationship between the canonical OOM and the concept of causal states which underlies the definition of statistical complexity. In particular, the topological statistical complexity, i.e. the logarithm of the number of causal states, turns out to be an upper bound to the logarithm of process dimension.

scholarly journals Decomposition of degenerate Gromov–Witten invariants

2020 ◽  
Vol 156 (10) ◽  
pp. 2020-2075
Author(s):  
Dan Abramovich ◽  
Qile Chen ◽  
Mark Gross ◽  
Bernd Siebert
Keyword(s):  
Moduli Stacks ◽  
Smooth Family ◽  
Decomposition Formula ◽  
Singular Fibre

We prove a decomposition formula of logarithmic Gromov–Witten invariants in a degeneration setting. A one-parameter log smooth family $X \longrightarrow B$ with singular fibre over $b_0\in B$ yields a family $\mathscr {M}(X/B,\beta ) \longrightarrow B$ of moduli stacks of stable logarithmic maps. We give a virtual decomposition of the fibre of this family over $b_0$ in terms of rigid tropical maps to the tropicalization of $X/B$. This generalizes one aspect of known results in the case that the fibre $X_{b_0}$ is a normal crossings union of two divisors. We exhibit our formulas in explicit examples.

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