scholarly journals Duality of capacities and Sobolev extendability in the plane

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Yi Ru-Ya Zhang
Keyword(s):  
Planar Domain ◽  
Alternative Proof ◽  
Necessary Condition ◽  
Extension Domain

AbstractWe reveal relations between the duality of capacities and the duality between Sobolev extendability of Jordan domains in the plane, and explain how to read the curve conditions involved in the Sobolev extendability of Jordan domains via the duality of capacities. Finally as an application, we give an alternative proof of the necessary condition for a Jordan planar domain to be $$W^{1,\,q}$$ W 1 , q -extension domain when $$2<q<\infty$$ 2 < q < ∞ .

The Infancy of Solar-Type Stars and its Relevance for the Origin of Life

1997 ◽  
Vol 161 ◽  
pp. 267-282 ◽  
Author(s):  
Thierry Montmerle
Keyword(s):  
Main Sequence ◽  
Solar Nebula ◽  
Circumstellar Disks ◽  
T Tauri Stars ◽  
Necessary Condition ◽  
Sequence Evolution ◽  
T Tauri ◽  
Solar Type ◽  
Optical Domain ◽  
The Origin Of Life

AbstractFor life to develop, planets are a necessary condition. Likewise, for planets to form, stars must be surrounded by circumstellar disks, at least some time during their pre-main sequence evolution. Much progress has been made recently in the study of young solar-like stars. In the optical domain, these stars are known as «T Tauri stars». A significant number show IR excess, and other phenomena indirectly suggesting the presence of circumstellar disks. The current wisdom is that there is an evolutionary sequence from protostars to T Tauri stars. This sequence is characterized by the initial presence of disks, with lifetimes ~ 1-10 Myr after the intial collapse of a dense envelope having given birth to a star. While they are present, about 30% of the disks have masses larger than the minimum solar nebula. Their disappearance may correspond to the growth of dust grains, followed by planetesimal and planet formation, but this is not yet demonstrated.

Universal ESEM

1993 ◽  
Vol 51 ◽  
pp. 786-787
Author(s):  
G.D. Danilatos
Keyword(s):  
Electron Microscope ◽  
Scanning Electron Microscope ◽  
High Vacuum ◽  
Natural Extension ◽  
Necessary Condition ◽  
Environmental Scanning ◽  
Detection Systems ◽  
Small Gain ◽  
Detection Medium ◽  
Scanning Electron

The environmental scanning electron microscope (ESEM) has evolved as the natural extension of the scanning electron microscope (SEM), both historically and technologically. ESEM allows the introduction of a gaseous environment in the specimen chamber, whereas SEM operates in vacuum. One of the detection systems in ESEM, namely, the gaseous detection device (GDD) is based on the presence of gas as a detection medium. This might be interpreted as a necessary condition for the ESEM to remain operational and, hence, one might have to change instruments for operation at low or high vacuum. Initially, we may maintain the presence of a conventional secondary electron (E-T) detector in a "stand-by" position to switch on when the vacuum becomes satisfactory for its operation. However, the "rough" or "low vacuum" range of pressure may still be considered as inaccessible by both the GDD and the E-T detector, because the former has presumably very small gain and the latter still breaks down.

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

Analysis of interconnections between technical systems on hierarchically connected technological levels of steel sheet production by hot rolling

2020 ◽  
Vol 76 (8) ◽  
pp. 847-855
Author(s):  
E. N. Shiryaeva ◽  
M. A. Polyakov ◽  
D. V. Terent'ev
Keyword(s):  
Hot Rolling ◽  
Systems Analysis ◽  
Rolling Mill ◽  
Steel Sheet ◽  
Technological System ◽  
Necessary Condition ◽  
Rolled Sheet ◽  
Technological Systems ◽  
Hot Rolling Mill ◽  
Technical Systems

Complexity of modern metallurgical plants, presence of great number of horizontal and vertical interactions between their various structural subdivisions makes it necessary to apply a systems analysis to elaborate effective measures for stable development of a plant operation. Among such measures, digitalization of a plant is widespread at present. To implement the digitalization it is necessary to have clear vision about links at all the levels of the technological system of a plant. A terminology quoted, accepted in the existing regulatory documents for defining of conceptions, comprising the technological system. It was shown, that the following four hierarchical levels of technological systems are distinguished: technological systems of operations, technological systems of processes, technological systems of production subdivisions and technological systems of plants. A hierarchical scheme of technological systems of hot-rolled sheet production at an integrated steel plant presented. Existing horizontal and vertical links between the basic plant’s shops shown. Peculiarities of flows of material, energy and information at the operation “rolling” of the technological system “hot rolling of a steel sheet” considered. As a technical system of the technological process of the hot rolling, the hot rolling mill was chosen. A structural diagram of the hot rolling mill was elaborated, the mill being consisted of reheating furnaces, roughing and finishing stand groups, with an intermediate roll-table between them, and down-coilers section. Since the rolling stands are the basic structural elements of the hot rolling mill, structural diagrams of a roughing and a finishing stands were elaborated. Results of the systems analysis of the technological and technical systems, hierarchically linked in the process of steel sheet hot rolling, can be applied for perfection of organization structure of the whole plant, as well as for elaboration mathematical models of a system separate elements functioning, which is a necessary condition for a plant digitalization.

Review of methods of slag removal from melt surface in hot metal and steel ladles

2020 ◽  
Vol 76 (12) ◽  
pp. 1243-1252
Author(s):  
B. A. Sivak ◽  
A. V. Protasov ◽  
L. A. Smirnov
Keyword(s):  
Settling Tank ◽  
Necessary Condition ◽  
Hot Metal ◽  
Slag Removal ◽  
Production Scale ◽  
Technical Parameters ◽  
Ecological Requirements ◽  
The Usa ◽  
Work Done ◽  
Technological Methods

The removal of slag from melt surface of hot metal and steel ladles is a necessary condition to provide a deep desulphurization and dephosphorization of hot metal and steel in the process of their processing. A review of methods of slag skimming presented, mainly based on slag mechanical shoveling and its removal out of ladles by vacuum sucking. It was shown, that manipulators design for the slag skimming working instrument moving depends on the production scale, mass of the processed heats, amount and properties of the slag to be removed, production process intensity and ecological requirements. Peculiarities of designs and technical parameters of machines for slag skimming presented, designed by Irkutsk plant of heavy machinery, Scientific and Production Enterprise n.a. M.I. Platov, VNIIMETMASH, Kuznetsk and Novolipetsk steel plants. Technological methods of control of slag composition and physical properties considered, first of all of viscosity and fluidity, which have significant effect on selection of a method of slag skimming. Advantages and drawbacks of actions, aimed at more complete slag removal from metal surface by a scraper noted including bath blowing off by an inert gas, liquid slag tapping into am intermediate settling tank following its removal into a slag bowl. In case of satisfactory fluidity it is possible to slag removal by vacuum sucking, which at the same time promoted the melt degassing. Work done in this area abroad noted. Methods of vacuum slag removal developed in the USA and Japan described.

What Is an Institution?

2007 ◽  
pp. 5-27 ◽  
Author(s):  
J. Searle
Keyword(s):  
Physical Structure ◽  
Necessary Condition ◽  
Collective Intentionality ◽  
Institutional Facts ◽  
Institutional Fact ◽  
The Status ◽  
The Creation ◽  
State Of Affairs ◽  
In Virtue Of ◽  
Typical Point

The author claims that an institution is any collectively accepted system of rules (procedures, practices) that enable us to create institutional facts. These rules typically have the form of X counts as Y in C, where an object, person, or state of affairs X is assigned a special status, the Y status, such that the new status enables the person or object to perform functions that it could not perform solely in virtue of its physical structure, but requires as a necessary condition the assignment of the status. The creation of an institutional fact is, thus, the collective assignment of a status function. The typical point of the creation of institutional facts by assigning status functions is to create deontic powers. So typically when we assign a status function Y to some object or person X we have created a situation in which we accept that a person S who stands in the appropriate relation to X is such that (S has power (S does A)). The whole analysis then gives us a systematic set of relationships between collective intentionality, the assignment of function, the assignment of status functions, constitutive rules, institutional facts, and deontic powers.

Eurasian Economic union: Prospects and challenges for Development

2015 ◽  
pp. 87-108 ◽  
Author(s):  
A. Knobel
Keyword(s):  
Oil And Gas ◽  
Economic Effects ◽  
Necessary Condition ◽  
Gas Transfer ◽  
Eurasian Economic Union ◽  
Economic Union ◽  
Food Imports ◽  
Cis Countries ◽  
Integration Problems ◽  
Integration Challenge

The paper is devoted to the analysis of development prospects and problems of Eurasian Economic Union (EAEU) of Russia, Kazakhstan, Belarus and Armenia. It considers integration problems inside EAEU, interactions of EAEU with other CIS countries and with countries from the rest of the world. The paper shows that the major integration challenge inside EAEU is the domination of the redistributive motive over the creative one. It estimates the value of the oil and gas transfer from Russia to other EAEU members and the influence of the Russian tax maneuver on this transfer. The paper shows the need in redistribution mechanism inside EAEU as a necessary condition for getting the potential positive economic effects of free trade with other countries. It also assesses the risks for EAEU due to Russian embargo for food imports from countries of the sanctions list and possible application of tariff in the trade with Ukraine.

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