scholarly journals Arrow diagrams on spherical curves and computations

2021 ◽  
Vol 30 (07) ◽  
Author(s):  
Noboru Ito ◽  
Masashi Takamura

We give a definition of an integer-valued function [Formula: see text] derived from arrow diagrams for the ambient isotopy classes of oriented spherical curves. Then, we introduce certain elements of the free [Formula: see text]-module generated by the arrow diagrams with at most [Formula: see text] arrows, called relators of Type ([Formula: see text]) (([Formula: see text]), ([Formula: see text]), ([Formula: see text]) or ([Formula: see text]), respectively), and introduce another function [Formula: see text] to obtain [Formula: see text]. One of the main results shows that if [Formula: see text] vanishes on finitely many relators of Type ([Formula: see text]) (([Formula: see text]), ([Formula: see text]), ([Formula: see text]) or ([Formula: see text]), respectively), then [Formula: see text] is invariant under the deformation of type RI (strong RI[Formula: see text]I, weak RI[Formula: see text]I, strong RI[Formula: see text]I[Formula: see text]I or weak RI[Formula: see text]I[Formula: see text]I, respectively). The other main result is that we obtain new functions of arrow diagrams with up to six arrows explicitly. This computation is done with the aid of computers.

Author(s):  
K. T. Tokuyasu

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the effects of surface tension by embedding them in thin layers of mechanically stable materials at the time of drying (unpublished).


Author(s):  
Juan de Lara ◽  
Esther Guerra

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.


2018 ◽  
Vol 6 (4) ◽  
pp. 401-428
Author(s):  
Miriam R. Lowi

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).’


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.


1994 ◽  
Vol 4 (1) ◽  
pp. 181-198 ◽  
Author(s):  
Bijan Vahabzadeh

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.


1984 ◽  
Vol 49 (1) ◽  
pp. 47-50 ◽  
Author(s):  
Frederic B. Fitch

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.


2020 ◽  
pp. 1-37
Author(s):  
MANISHA SETHI

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.


2021 ◽  
Vol 60 (3-4) ◽  
pp. 363-398

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.


2021 ◽  
Author(s):  
Christopher Herrmann ◽  

In today’s world of manufacturing, R&D, and testing across diverse industries, the definition of Metrology and calibration has taken on new meanings, whether it is right or wrong. With the evolving requirements for defining traceability, which is impacted through ISO/IEC 17025: 2017 as well as the NIST’s definition of Metrological Traceability, we must step back and truly understand what the differences are between these 2 terms. In this paper, we will evaluate the definitions of Metrology and calibration. We will also look at the importance of each and how one affects the other. While both terms are important, as liaisons within the Science of Measurement, we need to be able to articulate the differences between both terms to assist in bringing the representatives working in various industries to a clear understanding of how calibration is an action within the world of Metrology.


1902 ◽  
Vol 48 (202) ◽  
pp. 434-450 ◽  
Author(s):  
T. S. Clouston

Dr. Clouston said that when he suggested toxæmia to the secretary as a suitable subject for a discussion at this meeting he had not intended to be the first speaker, because his object was to bring out more fully the views of the younger members who had recently committed themselves so strongly to the toxæmic and bacterial etiology of insanity, and so to get light thrown on some of the difficulties which he and others had felt in applying this theory to many of their cases in practice. It was not that he did not believe in the toxic theory as explaining the onset of many cases, or that he under-rated its importance, but that he could not see how it applied so universally or generally as some of the modern pathological school were now inclined to insist on. He knew that it was difficult for those of the older psychological and clinical school to approach the subject with that full knowledge of recent bacteriological and pathological doctrine which the younger men possessed, or to breathe that all-pervading pathological atmosphere which they seemed to inhale. He desired to conduct this discussion in an absolutely non-controversial and purely scientific spirit. To do so he thought it best to put his facts, objections, and difficulties in a series of propositions which could be answered and explained by the other side. He thought it important to define toxæmia, but should be willing to accept Dr. Ford Robertson's definition of toxines, viz., “Substances which are taken up by the (cortical nerve) cell and then disorder its metabolism.” He took the following extracts from his address at the Cheltenham meeting of the British Association (1) as representing Dr. Ford Robertson's views and the general trend of much investigation and hypothesis on the Continent.


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