Symplectic Banach–Mazur distances between subsets of ℂn

2020 ◽  
pp. 1-56
Author(s):  
Michael Usher
Keyword(s):  
Finite Dimension ◽  
Convex Bodies ◽  
The Other ◽  
Symplectic Homology ◽  
Hamiltonian Flows ◽  
Dimension Formula ◽  
Isometric Embeddings ◽  
Cotangent Bundles ◽  
Definition Of ◽  
General Method

Following proposals of Ostrover and Polterovich, we introduce and study “coarse” and “fine” versions of a symplectic Banach–Mazur distance on certain open subsets of [Formula: see text] and other open Liouville domains. The coarse version declares two such domains to be close to each other if each domain admits a Liouville embedding into a slight dilate of the other; the fine version, which is similar to the distance on subsets of cotangent bundles of surfaces recently studied by Stojisavljević and Zhang, imposes an additional requirement on the images of these embeddings that is motivated by the definition of the classical Banach–Mazur distance on convex bodies. Our first main result is that the coarse and fine distances are quite different from each other, in that there are sequences that converge coarsely to an ellipsoid but diverge to infinity with respect to the fine distance. Our other main result is that, with respect to the fine distance, the space of star-shaped domains in [Formula: see text] admits quasi-isometric embeddings of [Formula: see text] for every finite dimension [Formula: see text]. Our constructions are obtained from a general method of constructing [Formula: see text]-dimensional Liouville domains whose boundaries have Reeb dynamics determined by certain autonomous Hamiltonian flows on a given [Formula: see text]-dimensional Liouville domain. The bounds underlying our main results are proven using filtered equivariant symplectic homology via methods from [J. Gutt and M. Usher, Symplectically knotted codimension-zero embeddings between domains in [Formula: see text], Duke Math. J. 168 (2019) 2299–2363].

scholarly journals Convertible mesh dome

2019 ◽  
Vol 135 ◽  
pp. 03031
Author(s):  
Aleksandr Ibragimov ◽  
Ljubov’ Gnedina
Keyword(s):  
Computer Calculation ◽  
Complete Separation ◽  
Fundamental Difference ◽  
The Other ◽  
Shell Surface ◽  
Positive Side ◽  
Definition Of ◽  
New Location ◽  
General Method ◽  
Theory Of Shells

The developed design of the mesh shell has the ability to fold by decreasing its dimension in one direction and increasing in the other. The fundamental difference of this design is the feasibility of folding the dome exactly wholly without the need for a complete separation of the shell into separate elements. The positive side of using such a design is expressed in the manufacture of elements, acceleration of installation and the mobility property, in which the dome can be folded and moved to a new location. The above described step-by-step description of actions in the general method of constructing the shell surface allows one to model the skeleton of a folded mesh dome. Recommendations for calculating design include a description of the methods used to perform calculations manually, the derivation of arguments in favor of computer calculation, the instructions for creating a model, the definition of rigidity and types of finite elements, as well as accounting for nonlinearity in the design of the dome in the software LIRA-CAD. The specification of the calculation scheme and the calculation itself are carried out using the general theory of shells.

Immunoferritin localization of intracellular antigens in positively stained frozen sections

1978 ◽  
Vol 36 (2) ◽  
pp. 168-169
Author(s):  
K. T. Tokuyasu
Keyword(s):  
Surface Tension ◽  
Water Surface ◽  
Thin Layers ◽  
The Other ◽  
Positive Staining ◽  
Frozen Sections ◽  
The Past ◽  
Ultrathin Frozen Sections ◽  
Definition Of

During the past investigations of immunoferritin localization of intracellular antigens in ultrathin frozen sections, we found that the degree of negative staining required to delineate u1trastructural details was often too dense for the recognition of ferritin particles. The quality of positive staining of ultrathin frozen sections, on the other hand, has generally been far inferior to that attainable in conventional plastic embedded sections, particularly in the definition of membranes. As we discussed before, a main cause of this difficulty seemed to be the vulnerability of frozen sections to the damaging effects of air-water surface tension at the time of drying of the sections.Indeed, we found that the quality of positive staining is greatly improved when positively stained frozen sections are protected against the effects of surface tension by embedding them in thin layers of mechanically stable materials at the time of drying (unpublished).

scholarly journals Language Family Engineering with Product Lines of Multi-level Models

2021 ◽  
Author(s):  
Juan de Lara ◽  
Esther Guerra
Keyword(s):  
Software Engineering ◽  
Arbitrary Number ◽  
Formal Theory ◽  
The Other ◽  
Language Family ◽  
Top Down ◽  
Product Lines ◽  
Modelling Languages ◽  
Multi Level ◽  
Definition Of

AbstractModelling is an essential activity in software engineering. It typically involves two meta-levels: one includes meta-models that describe modelling languages, and the other contains models built by instantiating those meta-models. Multi-level modelling generalizes this approach by allowing models to span an arbitrary number of meta-levels. A scenario that profits from multi-level modelling is the definition of language families that can be specialized (e.g., for different domains) by successive refinements at subsequent meta-levels, hence promoting language reuse. This enables an open set of variability options given by all possible specializations of the language family. However, multi-level modelling lacks the ability to express closed variability regarding the availability of language primitives or the possibility to opt between alternative primitive realizations. This limits the reuse opportunities of a language family. To improve this situation, we propose a novel combination of product lines with multi-level modelling to cover both open and closed variability. Our proposal is backed by a formal theory that guarantees correctness, enables top-down and bottom-up language variability design, and is implemented atop the MetaDepth multi-level modelling tool.

Identity, Community and Belonging in gcc States

2018 ◽  
Vol 6 (4) ◽  
pp. 401-428
Author(s):  
Miriam R. Lowi
Keyword(s):  
Religious Affiliation ◽  
Protective Role ◽  
The Other ◽  
National Project ◽  
Scholarly Literature ◽  
National Community ◽  
The Difference ◽  
Definition Of

Studies of identity and belonging in Gulf monarchies tend to privilege tribal or religious affiliation, if not the protective role of the ruler as paterfamilias. I focus instead on the ubiquitous foreigner and explore ways in which s/he contributes to the definition of national community in contemporary gcc states. Building upon and moving beyond the scholarly literature on imported labor in the Gulf, I suggest that the different ‘categories’ of foreigners impact identity and the consolidation of a community of privilege, in keeping with the national project of ruling families. Furthermore, I argue that the ‘European,’ the non-gcc Arab, and the predominantly Asian (and increasingly African) laborer play similar, but also distinct roles in the delineation of national community: while they are differentially incorporated in ways that protect the ‘nation’ and appease the citizen-subject, varying degrees of marginality reflect Gulf society’s perceptions or aspirations of the difference between itself and ‘the other(s).’

scholarly journals Note on osmotic pressure

1914 ◽  
Vol 90 (615) ◽  
pp. 41-45
Keyword(s):  
Osmotic Pressure ◽  
Vapour Pressure ◽  
Numerical Data ◽  
The Other ◽  
Present Moment ◽  
Capillary Surface ◽  
Pure Solvent ◽  
Definition Of ◽  
Complete Account ◽  
Strict Definition

The vapour pressure theory regards osmotic pressure as the pressure required to produce equilibrium between the pure solvent and the solution. Pressure applied to a solution increases its internal vapour pressure. If the compressed solution be on one aide of a semi-permeable partition and the pure solvent on the other, there is osmotic equilibrium when the com-pression of the solution brings its vapour pressure to equality with that of the solvent. So long ago as 1894 Ramsay* found that with a partition of palladium, permeable to hydrogen but not to nitrogen, the hydrogen pressures on each side tended to equality, notwithstanding the presence of nitrogen under pressure on one side, which it might have been supposed would have resisted tin- transpiration of the hydrogen. The bearing of this experiment on the problem of osmotic pressure was recognised by van’t Hoff, who observes that "it is very instructive as regards the means by which osmotic pressure is produced." But it was not till 1908 that the vapour pressure theory of osmotic pressure was developed on a finu foundation by Calendar. He demonstrated, by the method of the "vapour sieve" piston, the proposition that “any two solutions in equilibrium through any kind of membrane or capillary surface must have the same vapour pressures in respect of each of their constituents which is capable of diffusing through their surface of separation"—a generalisation of great importance for the theory of solutions. Findlay, in his admirable monograph, gives a very complete account of the contending theories of osmotic pressure, a review of which leaves no doubt that at the present moment the vapour pressure theory stands without a serious rival Some confusion of ideas still arises from the want of adherence to a strict definition of osmotic pressure to which numerical data from experimental measurements should he reduced. Tire following definitions appear to be tire outcome of tire vapour pressure theory :— Definition I.—The vapour pressure of a solution is the pressure of the vapour with which it is in equilibrium when under pressure of its own vapour only.

Mastication of Rubber. II. Interpolymerization of Natural Rubber and Neoprene on Cold Milling

1956 ◽  
Vol 29 (2) ◽  
pp. 427-437
Author(s):  
D. J. Angier ◽  
W. F. Watson
Keyword(s):  
Free Radicals ◽  
Natural Rubber ◽  
Small Molecules ◽  
The Other ◽  
Polymer Molecules ◽  
Commercially Important ◽  
The Individual ◽  
Cold Mill ◽  
General Method ◽  
Butadiene Styrene

Abstract The softening of elastomers on cold milling results from scission of the polymer molecules by the applied shearing forces. The ruptured chains are free radicals, which can undergo mutual combination, interaction with oxygen and various additives, and branching (grafting) on to other polymer molecules. A general method of producing graft and block interpolymers between elstomers is therefore indicated, namely, to cold-mill the polymers together in the absence of small molecules which can terminate the polymeric radicals in order that the radicals may cross-terminate or graft onto the polymer molecules of the other type. A survey of several pairs of the commercially important elastomers, natural rubber, butadiene-styrene, Neoprene, and butadiene-acrylonitrile, has shown that cold milling does effect interlinking. Detailed results for the rubber-Neoprene system are reported in this communication. Experimental verification of polymer interlinking was obtained from the solubility properties of the milled elastomers. Cold milling of Neoprene under nitrogen produces gel, whereas of natural rubber does not, but the milling of mixtures gives gels containing natural rubber. Also, the solubilities and precipitation of the milled mixtures cannot be accounted for by these properties of the individual polymers. Finally, Neoprene-natural rubber mixtures, after and not before cold-milling, can be cross-linked by magnesium oxide, with rubber bound into the vulcanizate.

Two Commentaries on Euclid's Definition of Proportional Magnitudes

1994 ◽  
Vol 4 (1) ◽  
pp. 181-198 ◽  
Author(s):  
Bijan Vahabzadeh
Keyword(s):  
18Th Century ◽  
The Other ◽  
Identical Manner ◽  
Definition Of

Euclid's definition of proportional magnitudes in the Fifth Book of the Elements gave rise to many commentaries. We examine closely two of these commentaries, one by al-Jayyānī (11th century) and the other by Saunderson (18th century). Both al-Jayyānī and Saunderson attempted to defend Euclid's definition by making explicit what Euclid had only implied. We show that the two authors explain Euclid's position in a virtually identical manner.

Correction to a definition of negation

1984 ◽  
Vol 49 (1) ◽  
pp. 47-50 ◽  
Author(s):  
Frederic B. Fitch
Keyword(s):  
Fixed Point ◽  
Personal Communication ◽  
The Other ◽  
Transfinite Induction ◽  
Original Form ◽  
Basic Logic ◽  
Double Negation ◽  
Original Letter ◽  
The Law ◽  
Definition Of

In [3] a definition of negation was presented for the system K′ of extended basic logic [1], but it has since been shown by Peter Päppinghaus (personal communication) that this definition fails to give rise to the law of double negation as I claimed it did. The purpose of this note is to revise this defective definition in such a way that it clearly does give rise to the law of double negation, as well as to the other negation rules of K′.Although Päppinghaus's original letter to me was dated September 19, 1972, the matter has remained unresolved all this time. Only recently have I seen that there is a simple way to correct the definition. I am of course very grateful to Päppinghaus for pointing out my error in claiming to be able to derive the rule of double negation from the original form of the definition.The corrected definition will, as before, use fixed-point operators to give the effect of the required kind of transfinite induction, but this time a double transfinite induction will be used, somewhat like the double transfinite induction used in [5] to define simultaneously the theorems and antitheorems of system CΓ.

Jainism in Danger? Temple entry and the rhetoric of religion and reform in post-colonial India

2020 ◽  
pp. 1-37
Author(s):  
MANISHA SETHI
Keyword(s):  
Twentieth Century ◽  
The State ◽  
The Other ◽  
Post Colonial ◽  
Colonial India ◽  
The Public ◽  
Public Debates ◽  
Definition Of ◽  
Open The Doors ◽  
The Relationship

Abstract A bitter debate broke out in the Digambar Jain community in the middle of the twentieth century following the passage of the Bombay Harijan Temple Entry Act in 1947, which continued until well after the promulgation of the Untouchability (Offences) Act 1955. These laws included Jains in the definition of ‘Hindu’, and thus threw open the doors of Jain temples to formerly Untouchable castes. In the eyes of its Jain opponents, this was a frontal and terrible assault on the integrity and sanctity of the Jain dharma. Those who called themselves reformists, on the other hand, insisted on the closeness between Jainism and Hinduism. Temple entry laws and the public debates over caste became occasions for the Jains not only to examine their distance—or closeness—to Hinduism, but also the relationship between their community and the state, which came to be imagined as predominantly Hindu. This article, by focusing on the Jains and this forgotten episode, hopes to illuminate the civilizational categories underlying state practices and the fraught relationship between nationalism and minorities.

Devotio and human sacrifice in archaic Italy and Rome

2021 ◽  
Vol 60 (3-4) ◽  
pp. 363-398
Keyword(s):  
Crucial Role ◽  
The Other ◽  
Human Sacrifice ◽  
Roman Religion ◽  
Other Hand ◽  
Mona Island ◽  
Narrow Definition ◽  
Definition Of ◽  
Father And Son ◽  
Very High

Abstract The Roman father and son of the same name, P. Decius Mus, became paragon heroes by deliberately giving their lives in battle that Rome might win over a fierce enemy. Both engaged in a special ritual called devotio (from which our word “devotion” derives) to offer themselves to the gods of the Underworld, with whom regular people have very little interaction and to whom they rarely sacrifice. While the Mus family is the most famous for this act, it turns out the willingness to sacrifice oneself for Rome frequently occurs within stories of great patriots, including the story of Horatius Cocles, Mettius Curtius, Atilius Regulus, and even the traitors Coriolanus and Tarpeia. Romans regarded self-sacrifice as a very high, noble endeavor, whereas they loathed and persecuted practitioners of human sacrifice. It is therefore quite amazing to read that the Romans thrice engaged in state-sponsored human sacrifice, a fact they rarely mention and generally forget. The most famous enemy practitioners of human sacrifice were the Druids, whom the Romans massacred on Mona Island on Midsummer Night's Eve, but the Carthaginians, the Germans, the Celts, and the Thracians all infamously practiced human sacrifice. To Romans, the act of human sacrifice falls just short of cannibalism in the spectrum of forbidden practices, and was an accusation occasionally thrown against an enemy to claim they are totally barbaric. On the other hand, Romans recognized their own who committed acts of self-sacrifice for the good of the society, as heroes. There can be no better patriot than he who gives his life to save his country. Often the stories of their heroism have been exaggerated or sanitized. These acts of heroism often turn out to be acts of human sacrifice, supposedly a crime. It turns out that Romans have a strong legacy of practicing human sacrifice that lasts into the historic era, despite their alleged opposition to it. Numerous sources relate one story each. Collecting them all makes it impossible to deny the longevity of human sacrifice in Rome, although most Romans under the emperors were probably unaware of it. The paradox of condemning but still practicing human sacrifice demonstrates the nature of Roman religion, where do ut des plays a crucial role in standard sacrifice as well as in unpleasant acts like human sacrifice. Devotio was an inverted form of sacrifice, precisely because it was an offering to the gods of the Underworld, rather than to Jupiter or the Parcae. Romans may have forsaken devotio, but they continued to practice human sacrifice far longer than most of us have suspected, if one widens the current narrow definition of human sacrifice to include events where a life is taken in order to bring about a better future for the commonwealth, appease the gods, or ensure a Roman victory in battle.

Sign in / Sign up

Export Citation Format

Share Document