scholarly journals A new series of moduli components of rank-2 semistable sheaves on $ {\mathbb{P}}^{3}$ with singularities of mixed dimension

2020 ◽  
Vol 211 (7) ◽  
pp. 967-986
Author(s):  
A. N. Ivanov
Keyword(s):  
Rank 2 ◽  
Mixed Dimension

scholarly journals Semistable rank 2 sheaves with singularities of mixed dimension on P3

2018 ◽  
Vol 129 ◽  
pp. 90-98 ◽  
Author(s):  
Aleksei N. Ivanov ◽  
Alexander S. Tikhomirov
Keyword(s):  
Rank 2 ◽  
Mixed Dimension

The motion of the particles volume corresponding to invariant solution of rank 2 submodel of hydrodynamic type

2016 ◽  
Vol 11 (2) ◽  
pp. 205-209
Author(s):  
D.T. Siraeva
Keyword(s):  
Equation Of State ◽  
Invariant Solution ◽  
Hydrodynamic Type ◽  
Lagrangian Coordinates ◽  
Hydrodynamic Equations ◽  
Rank 2 ◽  
Invariant Submodel ◽  
Entropy Functions

Invariant submodel of rank 2 on the subalgebra consisting of the sum of transfers for hydrodynamic equations with the equation of state in the form of pressure as the sum of density and entropy functions, is presented. In terms of the Lagrangian coordinates from condition of nonhyperbolic submodel solutions depending on the four essential constants are obtained. For simplicity, we consider the solution depending on two constants. The trajectory of particles motion, the motion of parallelepiped of the same particles are studied using the Maple.

Powerfully nilpotent groups of rank 2 or small order

2020 ◽  
Vol 23 (4) ◽  
pp. 641-658
Author(s):  
Gunnar Traustason ◽  
James Williams
Keyword(s):  
Detailed Analysis ◽  
Special Kind ◽  
Nilpotent Groups ◽  
Nilpotency Class ◽  
Central Series ◽  
Rank 2 ◽  
Full Classification

AbstractIn this paper, we continue the study of powerfully nilpotent groups. These are powerful p-groups possessing a central series of a special kind. To each such group, one can attach a powerful nilpotency class that leads naturally to the notion of a powerful coclass and classification in terms of an ancestry tree. In this paper, we will give a full classification of powerfully nilpotent groups of rank 2. The classification will then be used to arrive at a precise formula for the number of powerfully nilpotent groups of rank 2 and order {p^{n}}. We will also give a detailed analysis of the ancestry tree for these groups. The second part of the paper is then devoted to a full classification of powerfully nilpotent groups of order up to {p^{6}}.

scholarly journals Towards the classification of rank-r $$ \mathcal{N} $$ = 2 SCFTs. Part I. Twisted partition function and central charge formulae

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Mario Martone
Keyword(s):  
Partition Function ◽  
Central Charge ◽  
Singular Locus ◽  
Companion Paper ◽  
Coulomb Branch ◽  
Energy Limit ◽  
Superconformal Field Theories ◽  
Rank 2 ◽  
Explicit Formulae

Abstract We derive explicit formulae to compute the a and c central charges of four dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also discover general properties of the low-energy limit behavior of the flavor symmetry of $$ \mathcal{N} $$ N = 2 SCFTs which culminate with our $$ \mathcal{N} $$ N = 2 UV-IR simple flavor condition. This is done by determining precisely the relation between the integrand of the partition function of the topologically twisted version of the 4d $$ \mathcal{N} $$ N = 2 SCFTs and the singular locus of their Coulomb branches. The techniques developed here are extensively applied to many rank-2 SCFTs, including new ones, in a companion paper.This manuscript is dedicated to the memory of Rayshard Brooks, George Floyd, Breonna Taylor and the countless black lives taken by US police forces and still awaiting justice. Our hearts are with our colleagues of color who suffer daily the consequences of this racist world.

scholarly journals THE HYPERELLIPTIC THETA MAP AND OSCULATING PROJECTIONS

2020 ◽  
pp. 1-23
Author(s):  
MICHELE BOLOGNESI ◽  
NÉSTOR FERNÁNDEZ VARGAS
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Hyperelliptic Curve ◽  
Geometric Description ◽  
Birational Model ◽  
Rank 2 ◽  
Semistable Vector Bundles ◽  
Ramification Locus

Abstract Let C be a hyperelliptic curve of genus $g \geq 3$ . In this paper, we give a new geometric description of the theta map for moduli spaces of rank 2 semistable vector bundles on C with trivial determinant. In order to do this, we describe a fibration of (a birational model of) the moduli space, whose fibers are GIT quotients $(\mathbb {P}^1)^{2g}//\text {PGL(2)}$ . Then, we identify the restriction of the theta map to these GIT quotients with some explicit degree 2 osculating projection. As a corollary of this construction, we obtain a birational inclusion of a fibration in Kummer $(g-1)$ -varieties over $\mathbb {P}^g$ inside the ramification locus of the theta map.

scholarly journals An open-label study to evaluate biomarkers and safety in systemic sclerosis patients treated with paquinimod

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Roger Hesselstrand ◽  
Jörg H. W. Distler ◽  
Gabriela Riemekasten ◽  
Dirk M. Wuttge ◽  
Marie Törngren ◽  
...  
Keyword(s):  
Systemic Sclerosis ◽  
Type I ◽  
Type I Ifn ◽  
Open Label ◽  
Reactive Protein ◽  
Before And After ◽  
Modified Rodnan Skin Score ◽  
Skin Biopsies ◽  
Rank 2

Abstract Objectives To evaluate the changes in disease-related biomarkers and safety of paquinimod, an oral immunomodulatory compound, in patients with systemic sclerosis (SSc). Methods In this open-label, single-arm, multicenter study, SSc patients with a rapidly progressive disease received paquinimod for 8 weeks. Blood and skin biopsies were collected at baseline, during treatment, and at follow-up for the analyses of type I interferon (IFN) activity, chemokine (C-C motif) ligand 2 (CCL2), and the number of myofibroblasts. The safety of paquinimod was evaluated throughout the study. Results Nine SSc patients were enrolled and completed the study treatment with paquinimod at 3 mg/day for 8 weeks. After the treatment, a reduction of type I IFN activity in the plasma from one patient with elevated baseline IFN activity was recorded. A trend towards reduced IFN activity in the skin after treatment was also observed in patients. The serum level of CCL2 was reduced in 7 of 9 patients after paquinimod treatment. There was a median reduction of 10% of the number of myofibroblasts in skin biopsies at week 8 compared to baseline. No change in modified Rodnan skin score and quality of life was detected in the study. Reported adverse events (AEs) were mild to moderate and expected with the most common being arthralgia (n = 3) and headache (n = 3), and C-reactive protein (CRP) increase. Conclusions Analysis of biomarkers before and after treatment suggest reduced type I IFN activity and reduced number of myofibroblasts in lesional skin. Paquinimod was overall well tolerated with mild to moderate and expected AEs. Trial registration ClinicalTrials.gov, NCT01487551. Registered on 7 September 2011

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