scholarly journals Representation Stability of Power Sets and Square Free Polynomials

2015 ◽  
Vol 67 (5) ◽  
pp. 1024-1045
Author(s):  
Samia Ashraf ◽  
Haniya Azam ◽  
Barbu Berceanu
Keyword(s):  
Symmetric Group ◽  
Braid Group ◽  
Point Of View ◽  
Pure Braid Group ◽  
Representation Stability ◽  
Stability Point ◽  
Power Set ◽  
The Stability

AbstractThe symmetric group 𝓢n acts on the power set 𝓟(n) and also on the set of square free polynomials in n variables. These two related representations are analyzed from the stability point of view. An application is given for the action of the symmetric group on the cohomology of the pure braid group.

A toral configuration space and regular semisimple conjugacy classes

1995 ◽  
Vol 118 (1) ◽  
pp. 105-113 ◽  
Author(s):  
G. I. Lehrer
Keyword(s):  
Topological Space ◽  
Symmetric Group ◽  
Configuration Space ◽  
Braid Group ◽  
Cohomology Ring ◽  
General Setting ◽  
De Rham Cohomology ◽  
Pure Braid Group ◽  
De Rham ◽  
Image Position

For any topological space X and integer n ≥ 1, denote by Cn(X) the configuration spaceThe symmetric group Sn acts by permuting coordinates on Cn(X) and we are concerned in this note with the induced graded representation of Sn on the cohomology space H*(Cn(X)) = ⊕iHi (Cn(X), ℂ), where Hi denotes (singular or de Rham) cohomology. When X = ℂ, Cn(X) is a K(π, 1) space, where π is the n-string pure braid group (cf. [3]). The corresponding representation of Sn in this case was determined in [5], using the fact that Cn(C) is a hyperplane complement and a presentation of its cohomology ring appears in [1] and in a more general setting, in [8] (see also [2]).

scholarly journals GEOMETRIC PRESENTATIONS FOR THE PURE BRAID GROUP

2009 ◽  
Vol 18 (01) ◽  
pp. 1-20 ◽  
Author(s):  
DAN MARGALIT ◽  
JON McCAMMOND
Keyword(s):  
Finite Number ◽  
Braid Group ◽  
Mapping Class Groups ◽  
Point Of View ◽  
Mapping Class ◽  
Class Groups ◽  
Pure Braid Group ◽  
Dehn Twists ◽  
Finite Presentations

We give several new positive finite presentations for the pure braid group that are easy to remember and simple in form. All of our presentations involve a metric on the punctured disc so that the punctures are arranged "convexly", which is why we describe them as geometric presentations. Motivated by a presentation for the full braid group that we call the "rotation presentation", we introduce presentations for the pure braid group that we call the "twist presentation" and the "swing presentation". From the point of view of mapping class groups, the swing presentation can be interpreted as stating that the pure braid group is generated by a finite number of Dehn twists and that the only relations needed are the disjointness relation and the lantern relation.

scholarly journals New Generation Stability Norms – How to Approach the Task

2018 ◽  
Vol 25 (s1) ◽  
pp. 56-62
Author(s):  
Lech Kobyliński
Keyword(s):  
Current Approach ◽  
Point Of View ◽  
Wave Crest ◽  
International Stability ◽  
Intact Stability ◽  
Stability Point ◽  
Weak Points ◽  
The Stability ◽  
New Generation ◽  
Dead Ship Condition

Abstract International stability norms included in the Code of Intact Stability 2008 adopted by IMO on 4 December 2008 constitutes the latest set of international requirements on intact stability of ships. However the requirements included in the Code, part of them compulsory (Included in the Part A of the Code), other only recommended (included in the Part B of the Code) are considered as not totally sufficient to assure safety of ships. Because of that, IMO decided that there would be the necessity to develop so called new generation stability criteria covering certain identified hazards, such as parametric resonance, loss of stability in the wave crest broaching, dead ship condition and excessive accelerations when rolling. Those criteria, or rather stability norms, are under development since 2008. The present approach, the work on which is well advanced, is however, not fully satisfactory and several important problems were discovered. This approach may need to be reconsidered or supplemented. The author in the paper presented discusses the weak points of the current approach and proposes possible different approach in order to make future ships safer from the stability point of view.

Nonlinear transient response of rough symmetric two lobe hole entry hybrid journal bearing system

2016 ◽  
Vol 23 (2) ◽  
pp. 190-219 ◽  
Author(s):  
Satish C Sharma ◽  
Prashant B Kushare
Keyword(s):  
Surface Roughness ◽  
Transient Response ◽  
Journal Bearing ◽  
Equations Of Motion ◽  
Point Of View ◽  
Stability Point ◽  
Nonlinear Transient ◽  
The Stability ◽  
Bearing System ◽  
Nonlinear Transient Response

The present paper describes the effect of surface roughness orientation pattern on the nonlinear transient response of symmetric two lobe capillary compensated hole entry hybrid journal bearing. Nonlinear equations of motion have been solved with the Runge-Kutta method. The stability of the journal bearing system has been studied by obtaining the journal center motion trajectories. The results of the study reveal that the surface roughness pattern significantly changes the stability of capillary compensated two lobe hole entry hybrid journal bearing. Hence, from the bearing stability point of view, a proper selection of the surface roughness pattern and bearing geometry is essential.

scholarly journals Bioactive textiles obtained by applying cinnamon essential oil-based emulsions

2020 ◽  
Author(s):  
Laura Chirila ◽  
Alina Popescu ◽  
Sabina Olaru ◽  
Angela Danila ◽  
Rodica Roxana Constantinescu ◽  
...  
Keyword(s):  
Essential Oil ◽  
Ostwald Ripening ◽  
Volume Fraction ◽  
Stability Index ◽  
Point Of View ◽  
Textile Materials ◽  
Stability Point ◽  
Experimental Variant ◽  
Cinnamon Essential Oil ◽  
The Stability

In order to obtain biomaterials with potential use in the treatment of inflammatory skin conditions, this experimental study approached the immobilization on knitted fabric, made of 100% organic cotton, of oil-in-water emulsions type, based on xanthan-propolis-cinnamon essential oil, in certain formulations. For this purpose, seven experimental variants of emulsions were prepared and characterized, by specific methods, from physical-chemical and stability point of view. The functionalized textile materials were also characterized from morphological and antibacterial activity view point. The stability index, determined after 10 days, indicated that the emulsions are stable, without showing the presence of one of the flocculation, creaming / sedimentation, coalescence or Ostwald ripening phenomena. The lowest value of the turbidity was obtained for the experimental variant containing the lowest amount of essential oil and propolis. For the same variant, the highest value of viscosity was obtained, in which 0,363 mL water /mL emulsion and 0,5 mL xanthan/mL emulsion volume fraction was used. The textile materials treated with the synthesized emulsions based on xanthan-propolis-cinnamon essential oil shows antibacterial effect against S. aureus and E. coli test strains

scholarly journals Agricultural unmanned ground vehicles: A review from the stability point of view

2020 ◽  
Vol 51 (5) ◽  
Author(s):  
Hugo Rafacho Fernandes ◽  
Edna Carolina Moriones Polania ◽  
Angel Pontin Garcia ◽  
Oscar Barrero ◽  
Daniel Albiero
Keyword(s):  
Point Of View ◽  
Unmanned Ground Vehicles ◽  
Ground Vehicles ◽  
Stability Point ◽  
The Stability

scholarly journals The reason analysis of the overburden rock dumps deformation

2021 ◽  
Vol 315 ◽  
pp. 01001
Author(s):  
Elena Ananenko ◽  
Svetlana Bakhaeva
Keyword(s):  
Preventive Measures ◽  
Point Of View ◽  
Overburden Rock ◽  
Stress Strain ◽  
Stability Point ◽  
The Stability ◽  
Strain Status

Due to the deficiency of areas for dump facilities, mining enterprises form dumps of a large height, or locate them in places unfavorable from the stability point of view. In this regard, cases of the dump areas landslides have become more frequent. Herein there are examples of the actual deformations, causes of their occurrence, as well as preventive measures. Experience of the field surveying observations and analysis of the dump landslide causes confirm that accidents could be prevented by timely substantiating of safety criteria for the stress strain status of the dumps and creating methodology for surveying monitoring, depending on a type of the overburden rock.

scholarly journals Oily water emulsification as the method of its pre-treatment for utilization via co-combustion

2019 ◽  
Vol 137 ◽  
pp. 01048
Author(s):  
Aleksandra Dzido ◽  
Piotr Krawczyk ◽  
Michalina Kurkus-Gruszecka ◽  
Krzysztof Badyda
Keyword(s):  
Natural Gas ◽  
Textile Industry ◽  
Direct Injection ◽  
Point Of View ◽  
Main Process ◽  
Stability Point ◽  
Additional Water ◽  
Oily Water ◽  
Pre Treatment ◽  
The Stability

Oily water can be the side product of many processes, like crude oil processing and transportation leakages, industries such as steel industry, machine industry, petroleum refinery, petrochemical industry, textile industry, metal industry, pyrolysis etc. It seems to be the difficult to dispose waste. Although several treatment methods have been developed, many times additional water disposal installation is required. When the main process consumes natural gas, to simplify oily water utilization, the method of its direct injection to the natural gas burner is suggested by the paper authors. To provide the proper combustion and the mixture homogenization, emulsification was proposed. The aim of the research was to find the optimal recipe from the stability point of view, taking into account technical and economic conditions. The article covers the variety of surfactants examination for the water-hydrocarbons mixture emulsification, including the surfactants concentration optimization.

Sign in / Sign up

Export Citation Format

Share Document