On a Connectedness Theorem for a Birational Transformation at a Simple Point

1958 ◽  
Vol 80 (1) ◽  
pp. 3 ◽  
Author(s):  
J. P. Murre
Keyword(s):  
Simple Point ◽  
Birational Transformation

Continuity of homotopies

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Open Subset ◽  
Small Neighborhood ◽  
Unit Vector ◽  
Zariski Topology ◽  
Simple Point ◽  
Smooth Variety ◽  
Additional Material ◽  
Generic Type ◽  
Zariski Open Subset

This chapter includes some additional material on homotopies. In particular, for a smooth variety V, there exists an “inflation” homotopy, taking a simple point to the generic type of a small neighborhood of that point. This homotopy has an image that is properly a subset of unit vector V, and cannot be understood directly in terms of definable subsets of V. The image of this homotopy retraction has the merit of being contained in unit vector U for any dense Zariski open subset U of V. The chapter also proves the continuity of functions and homotopies using continuity criteria and constructs inflation homotopies before proving GAGA type results for connectedness. Additional results regarding the Zariski topology are given.

scholarly journals An efficient optimizer for simple point process models

2013 ◽  
Author(s):  
Ahmed Gamal-Eldin ◽  
Guillaume Charpiat ◽  
Xavier Descombes ◽  
Josiane Zerubia
Keyword(s):  
Point Process ◽  
Process Models ◽  
Simple Point ◽  
Point Process Models

A simple point vortex model for two‐dimensional decaying turbulence

1992 ◽  
Vol 4 (5) ◽  
pp. 1036-1039 ◽  
Author(s):  
R. Benzi ◽  
M. Colella ◽  
M. Briscolini ◽  
P. Santangelo
Keyword(s):  
Point Vortex ◽  
Two Dimensional ◽  
Simple Point ◽  
Vortex Model ◽  
Decaying Turbulence ◽  
Point Vortex Model

scholarly journals Experimental Validation of the Mean Pitch Theory

2021 ◽  
Vol 2090 (1) ◽  
pp. 012042
Author(s):  
T Meda ◽  
A Rogala
Keyword(s):  
Control Systems ◽  
Experimental Validation ◽  
Significant Loss ◽  
Simple Point ◽  
Fire Control ◽  
Mass Model ◽  
Body Model ◽  
Rigid Body Model ◽  
The Mean ◽  
In Fire

Abstract There are several types of exterior ballistic models used to calculate projectile’s flight trajectories. The most complex 6 degree of freedom rigid body model has many disadvantages to using it to create firing tables or rapid calculations in fire control systems. Some of ballistic phenomena can be simplified by empirical equations without significant loss of accuracy. This approach allowed to create standard NATO ballistic model for spin stabilized projectiles named Modified Point of Mass Model (PM Model). For fin (aerodynamically) stabilized projectiles like mortar projectiles simple Point of Mass Model is commonly used. The PM Model excludes many flight phenomena in calculations. In this paper authors show the mean pitch theory as an approximation of the natural fin stabilised projectile pitch during flight. The theory allows for simple improvement of accuracy of the trajectories calculation. In order to validate the theory data obtained from shooting of supersonic mortar projectiles were used. The comparison of accuracy between simple PM Model and PM Model including mean pitch theory were shown. Results were also compared with the angle of response theory.

Comparison of under-actuated and fully-actuated serial robotic arms: a case study

2021 ◽  
pp. 1-13
Author(s):  
Matteo Bottin ◽  
Giulio Rosati
Keyword(s):  
Degrees Of Freedom ◽  
Simple Point ◽  
Controllable System ◽  
Robotic Arms ◽  
Passive Joint ◽  
Final Configuration ◽  
Vibration Behavior ◽  
Rotational Joint ◽  
Point To Point

Abstract Under-actuated robots are very interesting in terms of cost and weight since they can result in a state-controllable system with a number of actuators lower than the number of joints. In this paper, a comparison between an under-actuated planar 3 degrees of freedom (DOF) robot and a comparable fully-actuated 2 degrees of freedom robot is presented, mainly focusing on the performances in terms of trajectories, actuator torques, and vibrations. The under-actuated system is composed of 2 active rotational joints followed by a passive rotational joint equipped with a torsional spring. The fully-actuated robot is inertial equivalent to the under-actuated manipulator: the last link is equal to the sum of the last two links of the under-actuated system. Due to the conditions on the inertia distribution and spring placement, in a simple point-to-point movement the last passive joint starts and ends in a zero-value configuration, so the 3 DOF robot is equivalent, in terms of initial and final configuration, to the 2 DOF fully-actuated robot, thus they can be compared. Results show how while the fully actuated robot is better in terms of reliable trajectory and actuator torques, the under-actuated robot wins in flexibility and vibration behavior.

scholarly journals Invariant Bipartite Random Graphs on Rd

2014 ◽  
Vol 51 (3) ◽  
pp. 769-779
Author(s):  
Fabio Lopes
Keyword(s):  
Point Processes ◽  
Random Number ◽  
Probability Distributions ◽  
Sufficient Conditions ◽  
Stable Marriage ◽  
Simple Point ◽  
Stable Marriage Problem ◽  
Blue Point ◽  
Translation Invariant ◽  
Positive Integers

Suppose that red and blue points occur in Rd according to two simple point processes with finite intensities λR and λB, respectively. Furthermore, let ν and μ be two probability distributions on the strictly positive integers with means ν̅ and μ̅, respectively. Assign independently a random number of stubs (half-edges) to each red (blue) point with law ν (μ). We are interested in translation-invariant schemes for matching stubs between points of different colors in order to obtain random bipartite graphs in which each point has a prescribed degree distribution with law ν or μ depending on its color. For a large class of point processes, we show that such translation-invariant schemes matching almost surely all stubs are possible if and only if λRν̅ = λBμ̅, including the case when ν̅ = μ̅ = ∞ so that both sides are infinite. Furthermore, we study a particular scheme based on the Gale-Shapley stable marriage problem. For this scheme, we give sufficient conditions on ν and μ for the presence and absence of infinite components. These results are two-color versions of those obtained by Deijfen, Holroyd and Häggström.

Negative-U Properties for Point Defects in Silicon

1980 ◽  
Vol 2 ◽  
Author(s):  
G. D. Watkins
Keyword(s):  
Experimental Evidence ◽  
Point Defects ◽  
Electron Irradiation ◽  
Correlation Energy ◽  
Energy Levels ◽  
Unusual Property ◽  
Simple Point ◽  
Normal Order ◽  
Defect Energy ◽  
Lattice Vacancy

ABSTRACTA defect has negative-U properties if it can trap two electrons (or holes) with the second bound more strongly than the first. It is as if there were a net attraction between the two carriers (negative Hubbard correlation energy U) at the defect, and the defect energy levels in the gap are therefore inverted from their normal order. Experimental evidence is presented that interstitial boron and the lattice vacancy, both common simple point defects produced by electron irradiation of silicon, have this unusual property. These defects represent the first and only concrete examples of negative-U centers in any material and serve as models for an understanding of the phenomenon.

An application of local uniformization to the theory of divisors

1951 ◽  
Vol 47 (2) ◽  
pp. 279-285
Author(s):  
D. G. Northcott
Keyword(s):  
Quotient Ring ◽  
Local Rings ◽  
Simple Point ◽  
Unique Factorization ◽  
The Third ◽  
Unique Factorization Domain ◽  
Irreducible Variety ◽  
Structure Theorems ◽  
Local Uniformization

If V is an irreducible variety and W is an irreducible simple subvariety of V, then one of the properties of the quotient ring of W in V is that it is a unique factorization domain. A proof of this theorem has been given by Zariski ((2), Theorem 5, p. 22), based on the structure theorems for complete local rings, and the fact that the local rings which arise geometrically are always analytically unramified. Here the theorem is deduced from certain properties of functions and their divisors which will be established by entirely different considerations. The terminology which will be employed is that proposed by A. Weil in his book(1), and we shall use, for instance, F-viii, Th. 3, Cor. 1, when referring to Corollary 1 of the third theorem in Chapter 8. Before proceeding to details it should be noted that Weil and Zariski differ in then-definitions, and that in particular the terms ‘variety’ and ‘simple point’ do not mean quite the same in the two theories. The effect of this is to make Zariski's result somewhat stronger than Theorem 3 of this paper.

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