scholarly journals Formalizing Calculus without Limit Theory in Coq

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1377
Author(s):  
Yaoshun Fu ◽  
Wensheng Yu

Formal verification of mathematical theory has received widespread concern and grown rapidly. The formalization of the fundamental theory will contribute to the development of large projects. In this paper, we present the formalization in Coq of calculus without limit theory. The theory aims to found a new form of calculus more easily but rigorously. This theory as an innovation differs from traditional calculus but is equivalent and more comprehensible. First, the definition of the difference-quotient control function is given intuitively from the physical facts. Further, conditions are added to it to get the derivative, and define the integral by the axiomatization. Then some important conclusions in calculus such as the Newton–Leibniz formula and the Taylor formula can be formally verified. This shows that this theory can be independent of limit theory, and any proof does not involve real number completeness. This work can help learners to study calculus and lay the foundation for many applications.

Author(s):  
Galen Strawson

This chapter examines the difference between John Locke's definition of a person [P], considered as a kind of thing, and his definition of a subject of experience of a certain sophisticated sort [S]. It first discusses the equation [P] = [S], where [S] is assumed to be a continuing thing that is able to survive radical change of substantial realization, as well as Locke's position about consciousness in relation to [P]'s identity or existence over time as [S]. It argues that Locke is not guilty of circularity because he is not proposing consciousness as the determinant of [S]'s identity over time, but only of [S]'s moral and legal responsibility over time. Finally, it suggests that the terms “Person” and “Personal identity” pull apart, in Locke's scheme of things, but in a perfectly coherent way.


2019 ◽  
Vol 3 ◽  
pp. 00013
Author(s):  
Danny Susanto

<p class="Abstract">The purpose of this study is to analyze the phenomenon known as&nbsp;<span style="font-size: 1rem;">“anglicism”: a loan made to the English language by another language.&nbsp;</span><span style="font-size: 1rem;">Anglicism arose either from the adoption of an English word as a&nbsp;</span><span style="font-size: 1rem;">result of a translation defect despite the existence of an equivalent&nbsp;</span><span style="font-size: 1rem;">term in the language of the speaker, or from a wrong translation, as a&nbsp;</span><span style="font-size: 1rem;">word-by-word translation. Said phenomenon is very common&nbsp;</span><span style="font-size: 1rem;">nowadays and most languages of the world including making use of&nbsp;</span><span style="font-size: 1rem;">some linguistic concepts such as anglicism, neologism, syntax,&nbsp;</span><span style="font-size: 1rem;">morphology etc, this article addresses various aspects related to&nbsp;</span><span style="font-size: 1rem;">Anglicisms in French through a bibliographic study: the definition of&nbsp;</span><span style="font-size: 1rem;">Anglicism, the origin of Anglicisms in French and the current situation,&nbsp;</span><span style="font-size: 1rem;">the areas most affected by Anglicism, the different categories of&nbsp;</span><span style="font-size: 1rem;">Anglicism, the difference between French Anglicism in France and&nbsp;</span><span style="font-size: 1rem;">French-speaking Canada, the attitude of French-speaking society&nbsp;</span><span style="font-size: 1rem;">towards to the Anglicisms and their efforts to stop this phenomenon.&nbsp;</span><span style="font-size: 1rem;">The study shows that the areas affected are, among others, trade,&nbsp;</span><span style="font-size: 1rem;">travel, parliamentary and judicial institutions, sports, rail, industrial&nbsp;</span><span style="font-size: 1rem;">production and most recently film, industrial production, sport, oil industry, information technology,&nbsp;</span><span style="font-size: 1rem;">science and technology. Various initiatives have been implemented either by public institutions or by&nbsp;</span><span style="font-size: 1rem;">individuals who share concerns about the increasingly felt threat of the omnipresence of Anglicism in&nbsp;</span><span style="font-size: 1rem;">everyday life.</span></p>


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).’


1987 ◽  
Vol 105 ◽  
Author(s):  
Hisham Z. Massoud

AbstractThe magnitude of the dipole moment at the Si-SiO2 interface resulting from partial charge transfer that takes place upon the formation of interface bonds has been calculated. The charge transfer occurs because of the difference in electronegativity between silicon atoms and SiO2 molecules which are present across the interface. Results obtained for (100) and (111) silicon substrates indicate that the magnitude of the interface dipole moment is dependent on substrate orientation and the interface chemistry. Dipole moments at the Si-SiO2 and gate-SiO2 interfaces should be included in the definition of the flatband voltage VFB of MOS structures. CV-based measurements of the metal-semiconductor workfunction difference φms on (100) and (111) silicon oxidized in dry oxygen and metallized with Al agree with the predictions of this model. Other types of interface dipoles and their processing dependence are briefly discussed.


Author(s):  
Elena A. Bragina

The article analyzes the conditions for the formation of the middle class in India. Shown is its important balancing role in the politics and economy of the country. The nature of the definition of &quot;middle class&quot;, its special significance in developing countries is considered. Due to the difference in the applied criterion - the initial unit of account (employee, family, population group), due to the weakness of statistical services, the results of sociological studies, statistical estimates of the size of the middle class are often approximate. The work shows that the official and infor-mal (shadow) parts of the middle class coexist in the economies of developing countries in parallel.  The pressure of the COVID-19 pandemic on the development of the Indian middle class is taken into account.  The article examines the national characteristics of the formation of the middle class inherent in India. Due to the unclear definition of the criteria, the inconsistency of its assessments, the insufficient level of work of statistical organizations, information on the size of the middle class is inaccurate (according to various estimates, about 210-360 million people). Attention is paid to the formation of the rural middle class in India, rural residents make up a significant part of it (estimated at 48-66%).The forecast of the recovery of the Indian middle class ispresented. It is assumed that its quantitative growth, which was observed before the pandemic, and a gradual increase in influence will continue and will allow in the future. The topic is relevant, in demand by the Russian reader.


1892 ◽  
Vol s2-33 (130) ◽  
pp. 313-324
Author(s):  
ASAJIRO OKA ◽  
ARTHUR WILLEY

Sarcodidemnoides misakiense, Oka and Willey. Generic Characters.--Colony (or cormus) forming very thick lobose masses, laterally compressed; sessile, but not encrusting. Excurrent orifices placed on the tips of the knoll-like prominences. Ascidiozooids very numerous, not arranged in systems; branchial sac with four rows of stigmata; canal system complicated, differentiated into peripheral and central portions. Specific Characters.--Atrial apertures of Ascidiozooids simple pores without teeth or languet; spicules fairly abundant, extremely delicate, confined to a thin layer near surface of test. Test gelatinous, containing numerous bladder-cells, crystals, fusiform cells, and pigment concretions. Stomach of Ascidiozooids vertically placed; surface of attachment of colony narrower than the free portion. Colour, brilliant red. Habitat.--Moroiso, Japan, between the tide-marks. N.B.--Since the above was written I have seen for the first time the exhaustive work of Fernand Lahille, entitled ‘Recherches sur les Tuniciers des côtes de France,' Toulouse, 1890. Lahille devotes considerable attention to what have been spoken of above as tentacle-like processes of the larva, figures them in many larvæ, and gives an excellent figure of the metamorphosing larva of Styela glomerata. He gives an opinion as to their significance which I cannot entirely endorse in the light of my own researches on the "Postembryonic development of Styela," commenced last August at Plymouth. However, I hope to return to this question on a future occasion. Lahille raises an objection to von Drasche's genus Didemnoides on the ground that the thickness of the cormus is not an anatomical character, and that the distinction between thick and thin colonies is a purely subjective one. There is no doubt some truth in this; but the difference between a compound Ascidian which possesses, say, a very few spicules, and one which possesses none at all, would appear to be no more fundamental than that between a colony whose mode of growth resulted in the production of a fleshy mass and one which grew in the form of a thin leathery crust. As stated above, von Drasche intends by Didemnoides a fleshy form of Leptoclinum, the test containing spicules, and the Ascidiozooids having four rows of stigmata in the branchial sac. Lahille, on the contrary,applies the name Didemnoides to those Didemnidse which are characterised by the absence of spicules, and the possession of three rows of stigmata in the branchial sac. The compound Ascidian which we have described above has spicules in the test, and four rows of stigmata in the branchial sac. But as it would be too absurd to call the new form "Sarcoleptoclinum," we shall persist in regarding the genus Didemnoides from the point of view of von Drasche.--A. W.


Author(s):  
I Putu Juniartha ◽  
Made Antara ◽  
I Made Sudarma

The results of this study indicate: (1) Characteristics of waste in Pakraman Padangtegal Village consisted of 83.88% organic waste, 7.24% plastic waste, 4.42% paper waste, 2.22% bottle waste, glass waste at 1.28% and metal waste at 0.96%; (2) public perception in waste management in Pakraman Village, Padangtegal that most of the people in Pakraman Village, Padangtegal, already know about the definition of waste and the danger of waste if it is not managed properly. Besides that the community also knows the difference between organic and inorganic waste so that the process of sorting waste in the place provided can run well, and the community's perception of waste management services has gone well with the transportation of waste twice a day; (3) the participation of the Pakraman Padangtegal Village community in waste management has played a role in various stages of waste management, starting from the sorting, garbage collection and garbage disposal, which complies with waste regulations and maintains the quality of the environment in Padangtegal Pakraman Village. The participation of the tourism industry in the process of waste management in Pakraman Village, Padangtegal, can be seen as being involved in the process of sorting waste and paying monthly fees and waste fees. The community participation in the waste management process is to help the government to socialize the waste management process by carrying out waste collection activities every week and provide a place for the waste management process. Suggestions in this study are that waste managers will immediately add facilities and infrastructure for waste transportation and accelerate the expansion of waste management in the village of Pakraman Padangtegal.   Keywords: Waste Management System, Pakraman Village


2009 ◽  
Vol 20 (04) ◽  
pp. 527-538 ◽  
Author(s):  
ELENA RAMÍREZ BARRIOS ◽  
JUAN G. DÍAZ OCHOA

We present a novel optimization method for an Ising like system suspended in a lattice with nonstatic defects. Depending on the size of the experimental probe the system spontaneously defines a defect free lattice where the control function can be optimized using conventional methods as Metropolis heuristics. We illustrate this method in a lattice with variable defects and show how the magnetization of the system depends on the spontaneous definition of the defect-free lattice. This approximation should be useful as a basis for the definition of systems of agents with imperfect coordination.


2007 ◽  
Vol 79 (1) ◽  
pp. 81-86 ◽  
Author(s):  
Srecko F. Oman ◽  
M. Filomena Camões ◽  
Kipton J. Powell ◽  
Raj Rajagopalan ◽  
Petra Spitzer

The measured cell potentials for suspension potentiometric cells have been interpreted and explained by a detailed analysis of the schemes for these cells ["Guidelines for potentiometric measurements in suspensions. Part A. The suspension effect (IUPAC Technical Report", Pure Appl. Chem.79, 67 (2007)]. Some former disagreements amongst investigations have been clarified. A new unambiguous operational definition of the suspension effect (SE) is presented. It is defined as the difference in cell potential for two suspension potentiometric cells, one with both electrodes in the separated equilibrium solution (eqs) and the other with both electrodes in the sediment or suspension. This potential difference is the sum of the change in the indicator electrode (IE) potential and the change in the liquid junction potential of the reference electrode (RE), when the electrodes are used for measurement, once in the sediment of the suspension and then in its eqs.


2012 ◽  
Vol 4 (2) ◽  
pp. 196-211
Author(s):  
Nikola Dedić

This text attempts to mark the difference between traditional, modern, monodisciplinary and contemporary interdisciplinary approaches within the analysis of reception of media and artistic contents. Monodisciplinary approaches are connected with the classical basis of humanistic and social sciences which are related to the definition of culture based on opposition between mass and elite culture (art). Avant-garde and linguistic turn within social sciences in the 60s realized re-evaluation of the notion of culture-culture is not seen anymore as a sum of elite products of human spirit but rather as a production of cultural meaning, i.e. as a discourse. This turn enabled interdisciplinary turn within the sciences as aesthetics and art history and also enabled the emergence of contemporary interdisciplinary media theory.


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