Blowing-Up and Whitney (a)-Regularity

1989 ◽  
Vol 32 (4) ◽  
pp. 482-485 ◽  
Author(s):  
Tzee-Char Kuo ◽  
David J. A. Trotman ◽  
Li Pei Xin
Keyword(s):  

AbstractWhen a pair of adjacent C1 strata (X, Y) is Whitney (a)- regular at a point , there is, up to homeomorphism, just one germ at 0 of intersections S ∩ X where S is a Lipschitz transversal to Y at 0 (S is the graph of a Lipschitz map from The proof uses a blowing-up construction and a strong form of Verdier's (w)-regularity.

Virittäjä ◽  
2020 ◽  
Vol 124 (1) ◽  
Author(s):  
Mikko Laasanen

Artikkeli käsittelee saussurelaista kielikäsitystä kohtaan esitettyä kritiikkiä. Artikkelin tavoitteena on puolustaa saussurelaista kielikäsitystä ja esittää Saussure moni-puolisempana ajattelijana kuin mitä Kurssin vahvasti strukturalisesta luennasta voisi päätellä. Artikkelissa tarkastellaan käsitystä kielestä järjestelmänä (Saussuren langue), kontekstivapaata merkitystä, kirjoitetun kielen vääristymää (written language bias), Roy Harrisin kielimyyttiä sekä kielen dynaamisuutta. Artikkelissa esitetään, että langue on sekä metodologinen että ontologinen käsite, joka viittaa sekä kielen järjestäytymättömiin sääntöihin että kielitieteilijän niistä luomaan järjestelmään. Kontekstivapaan merkityksen osalta korostetaan sitä, että jonkinlainen merkityksen pysyvyys on välttämätön osa kieltä kommunikaatiojärjestelmänä. Artikkelissa argumentoidaan kirjoitetun kielen vääristymän vahvaa muotoa vastaan, jonka mukaan esimerkiksi puheen analysoiminen diskreeteiksi yksiköiksi johtuu kirjoitetun kielen vaikutuksesta. Harrisin kielimyytin osalta esitetään, että kyse ei ole Saussuren näkemyksistä vaan Harrisin tulkinnoista. Artikkelissa esitetään myös, että dynaamisuus ei ole yhteensopimaton käsite saussurelaisen kielikäsityksen kanssa.   On the critique of the Saussurean concept of language: some perspectives and counter-arguments The article deals with the critique of the Saussurean concept of language. The purpose of the article is to defend the Saussurean concept of language and to present Saussure as a more versatile thinker than may be assumed from a purely structuralist reading of Course. The article discusses the concept of language as a system (Saussure’s langue), the notion of context-free meaning, the so-called written-language bias, Roy Harris’ language myth, and the notion of dynamicity in language in relation to the Saussurean concept of language. The article begins by arguing that langue is both a methodological and an ontological concept that refers both to the unorganised rules of language and to the system of language rules as organised by the linguist. Second, the author asserts that some kind of permanence of meaning is essential to the concept of language as a communication system. Third, an argument is presented against the strong form of written-language bias, according to which, for instance, the analysis and reduction of continuous speech into discrete units is based on the model of written language. Fourth, the author posits that the language myth, developed by Harris, is not based on Saussure’s views but on Harris’ interpretation of Saussure’s views. The article ends with the contention that the notion of dynamicity is not incompatible with the Saussurean concept of language.


Author(s):  
Dusa McDuff ◽  
Dietmar Salamon

This chapter examines various ways to construct symplectic manifolds and submanifolds. It begins by studying blowing up and down in both the complex and the symplectic contexts. The next section is devoted to a discussion of fibre connected sums and describes Gompf’s construction of symplectic four-manifolds with arbitrary fundamental group. The chapter also contains an exposition of Gromov’s telescope construction, which shows that for open manifolds the h-principle rules and the inclusion of the space of symplectic forms into the space of nondegenerate 2-forms is a homotopy equivalence. The final section outlines Donaldson’s construction of codimension two symplectic submanifolds and explains the associated decompositions of the ambient manifold.


Author(s):  
Ch. Konstadilaki-Savvapoulou ◽  
D. Janković

A strong form of continuity of functions between topological spaces is introduced and studied. It is shown that in many known results, especially closed graph theorems, functions under consideration areR-continuous. Several results in the literature concerning strong continuity properties are generalized and/or improved.


Author(s):  
Adrienne Stone ◽  
Lael K Weis

Abstract In The Principles of Constitutionalism, Nicholas Barber provides a sophisticated yet highly readable introduction to fundamental constitutional principles. At the same time, Barber seeks to reorient constitutional theory scholarship away from a mistaken ‘negative’ understanding of constitutionalism towards a ‘positive’ understanding. This essay examines that argument. We suggest that the idea of ‘positive constitutionalism’ has a weaker and a stronger sense. In its weak form, the argument calls for greater attention to what constitutions enable as well as what they restrict, and thus serves as a welcome reminder of the full potential of constitutional principles. However, it cannot be regarded as the correction of a widespread mistake. In its strong form, the argument calls for greater recognition that the state’s essential function lies in advancing the ‘well-being’ of its members. Although this amounts to a significant reorientation, it weakens the theory’s claim to universalism. These tensions indicate limitations to efforts to construct general theories of constitutionalism.


2021 ◽  
Vol 10 (1) ◽  
pp. 952-971
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Mokhtar Kirane ◽  
Berikbol T. Torebek

Abstract This paper is devoted to the study of initial-boundary value problems for time-fractional analogues of Korteweg-de Vries, Benjamin-Bona-Mahony, Burgers, Rosenau, Camassa-Holm, Degasperis-Procesi, Ostrovsky and time-fractional modified Korteweg-de Vries-Burgers equations on a bounded domain. Sufficient conditions for the blowing-up of solutions in finite time of aforementioned equations are presented. We also discuss the maximum principle and influence of gradient non-linearity on the global solvability of initial-boundary value problems for the time-fractional Burgers equation. The main tool of our study is the Pohozhaev nonlinear capacity method. We also provide some illustrative examples.


2021 ◽  
Vol 5 (1) ◽  
pp. 191-222
Author(s):  
Karima Kourtit

AbstractThe contemporary ‘digital age’ prompts the need for a re-assessment of urban planning principles and practices. Against the background of current data-rich urban planning, this study seeks to address the question whether an appropriate methodological underpinning can be provided for smart city governance based on a data-driven planning perspective. It posits that the current digital technology age has a drastic impact on city strategies and calls for a multi-faceted perspective on future urban development, termed here the ‘XXQ-principle’ (which seeks to attain the highest possible level of quality for urban life). Heterogeneity in urban objectives and data embodied in the XXQ-principle can be systematically addressed by a process of data decomposition (based on a ‘cascade principle’), so that first, higher-level urban policy domains are equipped with the necessary (‘big’) data provisions, followed by lower-ranking urban governance levels. The conceptual decomposition principle can then be translated into a comprehensive hierarchical model architecture for urban intelligence based on the ‘flying disc’ model, including key performance indicators (KPIs). This new model maps out the socio-economic arena of a complex urban system according to the above cascade system. The design of this urban system architecture and the complex mutual connections between its subsystems is based on the ‘blowing-up’ principle that originates from a methodological deconstruction-reconstruction paradigm in the social sciences. The paper advocates the systematic application of this principle to enhance the performance of smart cities, called the XXQ performance value. This study is not empirical, although it is inspired by a wealth of previous empirical research. It aims to advance conceptual and methodological thinking on principles of smart urban planning.


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