scholarly journals On cohomology of the invariant part of an isolating block

1999 ◽  
Vol 14 (2) ◽  
pp. 257 ◽  
Author(s):  
Roman Srzednicki
Keyword(s):  
Isolating Block ◽  
Invariant Part

scholarly journals Mixed NNLO QCD×electroweak corrections of $$ \mathcal{O} $$(Nfαsα) to single-W/Z production at the LHC

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Stefan Dittmaier ◽  
Timo Schmidt ◽  
Jan Schwarz
Keyword(s):  
Z Bosons ◽  
Leading Order ◽  
Current Standard ◽  
Gauge Invariant ◽  
Mass Distributions ◽  
Self Energy ◽  
Electroweak Gauge Boson ◽  
First Results ◽  
Invariant Part ◽  
The Impact

Abstract First results on the radiative corrections of order $$ \mathcal{O} $$ O (Nfαsα) are presented for the off-shell production of W or Z bosons at the LHC, where Nf is the number of fermion flavours. These corrections comprise all diagrams at $$ \mathcal{O} $$ O (αsα) with closed fermion loops, form a gauge-invariant part of the next-to-next-to-leading-order corrections of mixed QCD×electroweak type, and are the ones that concern the issue of mass renormalization of the W and Z resonances. The occurring irreducible two-loop diagrams, which involve only self-energy insertions, are calculated with current standard techniques, and explicit analytical results on the electroweak gauge-boson self-energies at $$ \mathcal{O} $$ O (αsα) are given. Moreover, the generalization of the complex-mass scheme for a gauge-invariant treatment of the W/Z resonances is described for the order $$ \mathcal{O} $$ O (αsα). While the corrections, which are implemented in the Monte Carlo program Rady, are negligible for observables that are dominated by resonant W/Z bosons, they affect invariant-mass distributions at the level of up to 2% for invariant masses of ≳ 500 GeV and are, thus, phenomenologically relevant. The impact on transverse-momentum distributions is similar, taking into account that leading-order predictions to those distributions underestimate the spectrum.

Knowledge and innovation management system as an element of CALS-technologies

2020 ◽  
pp. 118-122
Author(s):  
K.I. Porsev ◽  
Keyword(s):  
Knowledge Management ◽  
Management System ◽  
Innovation Management ◽  
Information Support ◽  
Management Systems ◽  
Invariant Part ◽  
Constructing Knowledge

The article considers one of the promising directions of development of information support for enterprises based on the use of CALS-technologies in their activities. The need to improve the existing algorithms for constructing the invariant part of CALS-technologies that allow for multivariate accounting of aspects of innovation and enterprise knowledge management is determined. An algorithm for constructing knowledge and innovation management systems based on the invariant part of CALS-technologies is proposed.

A simple semi-relativistic hypercentral constituent quark model for light baryons

2016 ◽  
Vol 94 (2) ◽  
pp. 236-242 ◽  
Author(s):  
M. Aslanzadeh ◽  
A.A. Rajabi
Keyword(s):  
Constituent Quark ◽  
Exact Analytical Solution ◽  
Average Energy ◽  
Experimental Spectrum ◽  
Constituent Quark Model ◽  
Quadratic Term ◽  
Linear Potential ◽  
Baryon Spectrum ◽  
Relativistic Approach ◽  
Invariant Part

In this work, baryons as a three-body bound system have been investigated in a semi-relativistic approach. Our model, like all constituent quark models, contains a dominant SU(6)-invariant part accounting for the average multiplet energies, and a perturbative SU(6)-violating interaction for the splitting within the multiplets, a structure that is inspired by lattice QCD calculations. Introducing a spin-independent relativistic description for the SU(6)-invariant part of the spectrum, we presented the exact analytical solution of the three-particle Klein–Gordon equation, through which the average energy values of the nonstrange resonances are reproduced. To describe the hyperfine structure of the baryon, the splittings within the SU(6) multiplets are produced by the spin- and isospin-dependent SU(6)-violating interaction, which have been treated as perturbative terms. For the SU(6)-invariant potential, we have added a quadratic term to the popular “Coulombic-plus-linear” potential. The resulting description of the baryon spectrum is comparable with those obtained by other calculations and experimental spectrum.

INTERVAL METHODS FOR RIGOROUS INVESTIGATIONS OF PERIODIC ORBITS

2001 ◽  
Vol 11 (09) ◽  
pp. 2427-2450 ◽  
Author(s):  
ZBIGNIEW GALIAS
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Discrete Time ◽  
Interval Arithmetic ◽  
Basin Of Attraction ◽  
Interval Methods ◽  
Henon Map ◽  
Invariant Part ◽  
The Basin Of Attraction ◽  
Discrete Time Dynamical Systems

In this paper, we investigate the possibility of using interval arithmetic for rigorous investigations of periodic orbits in discrete-time dynamical systems with special emphasis on chaotic systems. We show that methods based on interval arithmetic when implemented properly are capable of finding all period-n cycles for considerable large n. We compare several interval methods for finding periodic orbits. We consider the interval Newton method and methods based on the Krawczyk operator and the Hansen–Sengupta operator. We also test the global versions of these three methods. We propose algorithms for computation of the invariant part and nonwandering part of a given set and for computation of the basin of attraction of stable periodic orbits, which allow reducing greatly the search space for periodic orbits. As examples we consider two-dimensional chaotic discrete-time dynamical systems, defined by the Hénon map and the Ikeda map, with the "standard" parameter values for which the chaotic behavior is observed. For both maps using the algorithms presented in this paper, we find very good approximation of the invariant part and the nonwandering part of the region enclosing the chaotic attractor observed numerically. For the Hénon map we find all cycles with period n ≤ 30 belonging to the trapping region. For the Ikeda map we find the basin of attraction of the stable fixed point and all periodic orbits with period n ≤ 15. For both systems using the number of short cycles, we estimate its topological entropy.

From structure topology to chemical composition. IX. Titanium silicates: revision of the crystal chemistry of lomonosovite and murmanite, Group-IV minerals

2008 ◽  
Vol 72 (6) ◽  
pp. 1207-1228 ◽  
Author(s):  
F. Cámara ◽  
E. Sokolova ◽  
F. C. Hawthorne ◽  
Y. Abdu
Keyword(s):  
Hydrogen Bonding ◽  
Crystal Structures ◽  
Structure Refinement ◽  
Group Iv ◽  
Oh Groups ◽  
Structure Topology ◽  
Intermediate Space ◽  
Titanium Silicates ◽  
Invariant Part ◽  
Cation Sites

AbstractThe crystal structures of lomonosovite, ideally Na10Ti4(Si2O7)2(PO4)2 O4, a = 5.4170(7) Å, b = 7.1190(9) Å, c = 14.487(2) Å, a = 99.957(3)°, β = 96.711(3)°, γ = 90.360(3)°, V= 546.28(4) Å3, Dcalc. = 3.175 g cm“3, and murmanite, ideally Na4Ti4(Si2O7)2O4(H2O)4, a = 5.3875(6) Å, b = 7.0579(7) Å, c = 12.176(1) Å, a = 93.511(2)°, 0 = 107.943(4)°, y = 90.093(2)°, V = 439.55(2) Å3, Dcalc. = 2.956 g.cm∼3, from the Lovozero alkaline massif, Kola Peninsula, Russia, have been refined in the space group P1̄ (Z = 1) to R values of 2.64 and 4.47%, respectively, using 4572 and 2222 observed |F°≥ 4σF| reflections collected with a single-crystal Bruker AXS SMART APEX diffractometer with a CCD detector and Mo-Kα. radiation. Electron microprobe analysis gave empirical formulae for lomonosovite (Na9.50Mn0.16Ca0.11)Σ9.77(Ti4+2.83Nb0.51Mn0.272+Zr0.11Mg0.11Fe2+0.10Fe3+0.06Ta0.01)Σ4.00(Si2.02O7)2(P0.98O4)2(O3.50F0.50)Σ4, Z = 1, calculated on the basis of 22(O+F) a.p.f.u., with H2O determined from structure refinement and Fe3+/(Fe2++Fe3+) ratios obtained by Mössbauer spectroscopy. The crystal structures of lomonosovite and murmanite are a combination of a titanium silicate (TS) block and an intermediate (I) block. The TS block consists of HOH sheets (H-heteropolyhedral, O-octahedral), and is characterized by a planar cell based on translation vectors, t1 and t2, with t1\ ∼5.5 and t2 ∼7 Å and ttA t2 close to 90°. The TS block exhibits linkage and stereochemistry typical for Group IV (Ti = 4 a.p.f.u.) of the Ti disilicate minerals: two H sheets connect to the O sheet such that two (Si2O7) groups link to Ti polyhedra of the O sheet adjacent along tx. In murmanite and lomonosovite, the invariant part of the TS block is of composition Na4Ti4(Si2O7)2O4. There is no evidence of vacancy-dominant cation sites or (OH) groups in the O sheet of lomonosovite or murmanite. In lomonosovite, the I block is a framework of Na polyhedra and P tetrahedra which gives 2[Na3 (PO)4] p.f.u. In murmanite, there are four (H2O) groups in the intermediate space between TS blocks. In lomonosovite, TS and I blocks alternate along c. In murmanite, TS blocks are connected via hydrogen bonding. The H atoms were located and details of the hydrogen bonding are discussed.

THE DOMINANT PART OF HIGHER ORDER CORRECTIONS FOR THE SUBPROCESS qg → γq

1990 ◽  
Vol 05 (12) ◽  
pp. 901-910 ◽  
Author(s):  
A. P. CONTOGOURIS ◽  
S. PAPADOPOULOS
Keyword(s):  
Structure Functions ◽  
Higher Order ◽  
Gauge Invariant ◽  
Invariant Part ◽  
Fragmentation Functions ◽  
Higher Order Corrections ◽  
Dominant Part ◽  
Gluon Bremsstrahlung

Earlier work has shown that in processes involving structure functions and/or fragmentation functions initiated by 2 → 2 parton subprocesses there is a gauge invariant part that dominates higher order corrections, and for the gluon Bremsstrahlung contributions to this part simple and general expressions were derived and applied to [Formula: see text]. Here we apply these expressions and determine the dominant part of qg → γq, thus complementing the work and demonstrating the efficiency of the approach.

scholarly journals NONCROSSING SETS AND A GRASSMANN ASSOCIAHEDRON

2017 ◽  
Vol 5 ◽  
Author(s):  
FRANCISCO SANTOS ◽  
CHRISTIAN STUMP ◽  
VOLKMAR WELKER
Keyword(s):  
Simplicial Complex ◽  
Natural Generalization ◽  
Adjacency Graph ◽  
Simplicial Polytope ◽  
Acyclic Orientation ◽  
Weak Separability ◽  
Initial Ideal ◽  
Alternative Approach ◽  
Invariant Part ◽  
Order Polytope

We study a natural generalization of the noncrossing relation between pairs of elements in$[n]$to$k$-tuples in$[n]$that was first considered by Petersenet al.[J. Algebra324(5) (2010), 951–969]. We give an alternative approach to their result that the flag simplicial complex on$\binom{[n]}{k}$induced by this relation is a regular, unimodular and flag triangulation of the order polytope of the poset given by the product$[k]\times [n-k]$of two chains (also called Gelfand–Tsetlin polytope), and that it is the join of a simplex and a sphere (that is, it is a Gorenstein triangulation). We then observe that this already implies the existence of a flag simplicial polytope generalizing the dual associahedron, whose Stanley–Reisner ideal is an initial ideal of the Grassmann–Plücker ideal, while previous constructions of such a polytope did not guarantee flagness nor reduced to the dual associahedron for$k=2$. On our way we provide general results about order polytopes and their triangulations. We call the simplicial complex thenoncrossing complex, and the polytope derived from it the dualGrassmann associahedron. We extend results of Petersenet al.[J. Algebra324(5) (2010), 951–969] showing that the noncrossing complex and the Grassmann associahedron naturally reflect the relations between Grassmannians with different parameters, in particular the isomorphism$G_{k,n}\cong G_{n-k,n}$. Moreover, our approach allows us to show that the adjacency graph of the noncrossing complex admits a natural acyclic orientation that allows us to define aGrassmann–Tamari orderon maximal noncrossing families. Finally, we look at the precise relation of the noncrossing complex and the weak separability complex of Leclerc and Zelevinsky [Amer. Math. Soc. Transl.181(2) (1998), 85–108]; see also Scott [J. Algebra290(1) (2005), 204–220] among others. We show that the weak separability complex is not only a subcomplex of the noncrossing complex as noted by Petersenet al.[J. Algebra324(5) (2010), 951–969] but actually its cyclically invariant part.

FOREGROUND ANALYSIS FROM THE 1-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) DATA

2005 ◽  
Vol 14 (07) ◽  
pp. 1273-1292 ◽  
Author(s):  
PAVEL D. NASELSKY ◽  
LUNG-YIH CHIANG ◽  
IGOR D. NOVIKOV ◽  
OLEG V. VERKHODANOV
Keyword(s):  
Detailed Analysis ◽  
Cross Correlation ◽  
Dust Emission ◽  
Wilkinson Microwave Anisotropy Probe ◽  
Spectral Indices ◽  
Frequency Independent ◽  
Invariant Part ◽  
Foreground Analysis ◽  
Wmap Data ◽  
Common Signal

We present a detailed analysis on the phases of the WMAP foregrounds (synchrotron, free–free and dust emission) of the WMAP K–W bands in order to estimate the significance of the variation of the spectral indices at different components. We first extract the spectral-index varying signals by assuming that the invariant part among different frequency bands have 100% cross-correlation of phases. We then use the minimization of variance, which is normally used for extracting the CMB signals, to extract the frequency independent signals. Such a common signal in each foreground component could play a significant role for any kind of component separation methods, because the methods cannot discriminate frequency independent foregrounds and CMB.

THE DOMINANT PART OF HIGHER ORDER CORRECTIONS IN PERTURBATIVE QCD

1990 ◽  
Vol 05 (10) ◽  
pp. 1951-1973 ◽  
Author(s):  
A.P. CONTOGOURIS ◽  
N. MEBARKI ◽  
S. PAPADOPOULOS
Keyword(s):  
Perturbative Qcd ◽  
Higher Order ◽  
Soft Gluon ◽  
Gauge Invariant ◽  
Invariant Part ◽  
Fragmentation Functions ◽  
Bremsstrahlung Contribution ◽  
Higher Order Corrections ◽  
Dominant Part ◽  
Gluon Bremsstrahlung

It is shown that in processes involving structure functions and/or fragmentation functions initiated by 2→2 parton subprocesses, there is a gauge invariant part that dominates higher order corrections over a sizeable kinematic domain. The gluon Bremsstrahlung contribution to this part arises from collinear and soft gluon configurations. This Bremsstrahlung contribution (and more generally the contribution to this part from 2→3 parton subprocesses) is shown to arise from expressions remarkably simple and general.

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