Computing local dimension of a semialgebraic set

1998 ◽  
Author(s):  
Nicolai Vorobjov
Keyword(s):  
Local Dimension ◽  
Semialgebraic Set

scholarly journals Newtonian Fractional-dimension Gravity and Rotationally Supported Galaxies

2021 ◽  
Author(s):  
Gabriele U Varieschi
Keyword(s):  
Fractional Dimension ◽  
Newtonian Gravity ◽  
Axially Symmetric ◽  
Local Dimension ◽  
Radial Acceleration ◽  
Modified Newtonian Dynamics ◽  
Newtonian Dynamics ◽  
The Subject ◽  
Symmetric Structures ◽  
Natural Scale

Abstract We continue our analysis of Newtonian Fractional-Dimension Gravity, an extension of the standard laws of Newtonian gravity to lower dimensional spaces including those with fractional (i.e., non-integer) dimension. We apply our model to three rotationally supported galaxies: NGC 7814 (Bulge-Dominated Spiral), NGC 6503 (Disk-Dominated Spiral), and NGC 3741 (Gas-Dominated Dwarf). As was done in the general cases of spherically-symmetric and axially-symmetric structures, which were studied in previous work on the subject, we examine a possible connection between our model and Modified Newtonian Dynamics, a leading alternative gravity model which explains the observed properties of these galaxies without requiring the Dark Matter hypothesis. In our model, the MOND acceleration constant a0 ≃ 1.2 × 10−10m s−2 can be related to a natural scale length l0, namely $a_{0} \approx GM/l_{0}^{2}$ for a galaxy of mass M. Also, the empirical Radial Acceleration Relation, connecting the observed radial acceleration gobs with the baryonic one gbar, can be explained in terms of a variable local dimension D. As an example of this methodology, we provide detailed rotation curve fits for the three galaxies mentioned above.

Security in local communities from the perspective of the Police

2020 ◽  
Vol 4 (37) ◽  
pp. 31-42
Author(s):  
Robert Gwardyński
Keyword(s):  
Public Safety ◽  
Major Element ◽  
Local Communities ◽  
The State ◽  
Security System ◽  
Local Dimension ◽  
State Security ◽  
Sense Of Security

The Police constitute a major element in the state security system. Their operation has both a national and local dimension. The Police have an impact on a local community’s security, ensuring the safety of people, their health, life, property, as well as maintaining public safety and order. This article aims to indicate the areas of the Police’s operation that result in an improvement of the residents’ safety and an increase in their sense of security.

scholarly journals A Numerical Local Dimension Test for Points on the Solution Set of a System of Polynomial Equations

2009 ◽  
Vol 47 (5) ◽  
pp. 3608-3623 ◽  
Author(s):  
Daniel J. Bates ◽  
Jonathan D. Hauenstein ◽  
Chris Peterson ◽  
Andrew J. Sommese
Keyword(s):  
Solution Set ◽  
Polynomial Equations ◽  
Local Dimension ◽  
System Of Polynomial Equations

ON THE IRREDUCIBLE COMPONENTS OF A SEMIALGEBRAIC SET

2012 ◽  
Vol 23 (04) ◽  
pp. 1250031 ◽  
Author(s):  
JOSÉ F. FERNANDO ◽  
J. M. GAMBOA
Keyword(s):  
Integral Domain ◽  
Hilbert Problem ◽  
Semialgebraic Sets ◽  
Semialgebraic Set ◽  
Irreducible Components ◽  
Real Geometry ◽  
Nash Manifold ◽  
Substitution Theorem ◽  
Satisfactory Theory ◽  
17Th Hilbert Problem

In this work we define a semialgebraic set S ⊂ ℝn to be irreducible if the noetherian ring [Formula: see text] of Nash functions on S is an integral domain. Keeping this notion we develop a satisfactory theory of irreducible components of semialgebraic sets, and we use it fruitfully to approach four classical problems in Real Geometry for the ring [Formula: see text]: Substitution Theorem, Positivstellensätze, 17th Hilbert Problem and real Nullstellensatz, whose solution was known just in case S = M is an affine Nash manifold. In fact, we give full characterizations of the families of semialgebraic sets for which these classical results are true.

scholarly journals The Fall of the Chorupnik Parish. A Contribution to the History of the Reformation in Poland

2019 ◽  
Vol 66 (2 SELECTED PAPERS IN ENGLISH) ◽  
pp. 31-42
Author(s):  
Bogumił Szady
Keyword(s):  
Catholic Church ◽  
Local Dimension ◽  
Economic Relations ◽  
Parish Church ◽  
Parish Priest ◽  
The Social ◽  
Counter Reformation ◽  
The Reformation ◽  
Polish Version ◽  
History Of

The Polish version of the article was published in “Roczniki Humanistyczne,” vol. 61 (2013), issue 2. The article addresses the question of the fall of the Latin parish in Chorupnik that belonged to the former diocese of Chełm. The parish church in Chorupnik was taken over by Protestants in the second half of the 16th century. Unsuccessful attempts at recovering its property were made by incorporating it into the neighbouring parish in Gorzków. The actions taken by the Gorzków parish priest and the bishop together with his chapter failed, too. A detailed study of such attempts to recover the property of one of the parishes that ceased to exist during the Reformation falls within the context of the relations between the nobility and the clergy in the period of Counter-Reformation. Studying the social, legal and economic relations in a local dimension is important for understanding the mechanisms of the mass transition of the nobility to reformed denominations, and then of their return to the Catholic Church.

Nasjonale partier og lokale lister i kommunestyrevalgene 2015 og 2019

2021 ◽  
pp. 63-85
Author(s):  
Dag Arne Christensen ◽  
Bjarte Folkestad ◽  
Jacob Aars
Keyword(s):  
Party System ◽  
Party Systems ◽  
The Other ◽  
Local Dimension ◽  
Municipal Council ◽  
Municipal Reform ◽  
Other Hand ◽  
Local Party

The term local party systems suggests that party systems not only vary between municipalities, but that the systems also have a local dimension. This chapter is concerned with the balance between national parties and the local lists in municipal council elections in Norway. We also examine whether municipal amalgamation reform has changed the balance between these types of parties. Our analyses show that the correspondence between the party system in the parliament (“Stortinget”) and in the municipal councils is strong in Norwegian municipalities. One consequence of the municipal reform is that constituencies have become larger (on average), and more representatives are being elected to the municipal councils. By comparing merged and non-merged municipalities over two elections, we find that the reform has contributed to greater party diversity in the municipal councils. This applies both to the supply of lists that stand for election and the number of lists that are represented in the municipal councils. The municipal reform, on the other hand, does not seem to have contributed to greater party diversity in the form of more or fewer local lists.

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