A sufficient condition for a point to be of swallowtail type on the envelope of a one-parameter family of surfaces

1990 ◽  
Vol 48 (1) ◽  
pp. 72-76
Author(s):  
V. V. Mozharski�
Keyword(s):  
Parameter Family ◽  
Sufficient Condition

A Combinatorial Distinction Between Unit Circles and Straight Lines: How Many Coincidences Can they Have?

2009 ◽  
Vol 18 (5) ◽  
pp. 691-705 ◽  
Author(s):  
GYÖRGY ELEKES ◽  
MIKLÓS SIMONOVITS ◽  
ENDRE SZABÓ
Keyword(s):  
Parameter Family ◽  
Sufficient Condition ◽  
Simple Application ◽  
Quadratic Number ◽  
General Sufficient Condition ◽  
Family Of Curves ◽  
Unit Circles ◽  
Triple Points ◽  
Straight Lines ◽  
Special Case

We give a very general sufficient condition for a one-parameter family of curves not to have n members with ‘too many’ (i.e., a near-quadratic number of) triple points of intersections. As a special case, a combinatorial distinction between straight lines and unit circles will be shown. (Actually, this is more than just a simple application; originally this motivated our results.)

scholarly journals Orden de Lorenz en la familia de distribuciones gamma triparamétricas = Lorenz ordering of the three parameter gamma distributions

2012 ◽  
pp. 21
Author(s):  
Héctor Manuel Ramos Romero ◽  
Miguel Ángel Sordo Díaz
Keyword(s):  
Parameter Family ◽  
Sufficient Condition ◽  
Income Distributions ◽  
Gamma Distributions

<p>El orden de Lorenz es una herramienta adecuada para comparar la desigualdad de dos distribuciones de rentas. En este artículo obtenemos una condición suficiente para que dos distribuciones sean comparables en el orden de Lorenz y aplicamos el resultado para ordenar la familia de distribuciones Gamma triparamétricas.</p><p>Lorenz ordering is an useful tool for comparing inequality of income distributions. In this note, we give a sufficient condition for this order and then apply it to order the three parameter family of Gamma distributions.</p>

scholarly journals Orden de Lorenz en la familia de distribuciones gamma triparamétricas = Lorenz ordering of the three parameter gamma distributions

2012 ◽  
pp. 21
Author(s):  
Héctor Manuel Ramos Romero ◽  
Miguel Ángel Sordo Díaz
Keyword(s):  
Parameter Family ◽  
Sufficient Condition ◽  
Income Distributions ◽  
Gamma Distributions

<p>El orden de Lorenz es una herramienta adecuada para comparar la desigualdad de dos distribuciones de rentas. En este artículo obtenemos una condición suficiente para que dos distribuciones sean comparables en el orden de Lorenz y aplicamos el resultado para ordenar la familia de distribuciones Gamma triparamétricas.</p><p>Lorenz ordering is an useful tool for comparing inequality of income distributions. In this note, we give a sufficient condition for this order and then apply it to order the three parameter family of Gamma distributions.</p>

Maximisers for Strichartz inequalities on the torus

Nonlinearity ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 311-342
Author(s):  
Oreoluwa Adekoya ◽  
John P Albert
Keyword(s):  
Model Equation ◽  
Parameter Family ◽  
Sufficient Condition ◽  
Fourier Space ◽  
Optical Pulses ◽  
Space And Time ◽  
Stable Periodic ◽  
Range Of Values

Abstract We study the existence of maximisers for a one-parameter family of Strichartz inequalities on the torus. In general, maximising sequences can fail to be precompact in L 2 ( T ) , and maximisers can fail to exist. We provide a sufficient condition for precompactness of maximising sequences (after translation in Fourier space), and verify the existence of maximisers for a range of values of the parameter. Maximisers for the Strichartz inequalities correspond to stable, periodic (in space and time) solutions of a model equation for optical pulses in a dispersion-managed fiber.

The Current Situation in Chemical Stabilization of Biological Materials

1972 ◽  
Vol 30 ◽  
pp. 132-133
Author(s):  
John H. Luft
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Osmium Tetroxide ◽  
Molecular Level ◽  
Cross Linking ◽  
Chemical Stabilization ◽  
Specimen Preparation ◽  
Sufficient Condition ◽  
Radio Telescopes

With information processing devices such as radio telescopes, microscopes or hi-fi systems, the quality of the output often is limited by distortion or noise introduced at the input stage of the device. This analogy can be extended usefully to specimen preparation for the electron microscope; fixation, which initiates the processing sequence, is the single most important step and, unfortunately, is the least well understood. Although there is an abundance of fixation mixtures recommended in the light microscopy literature, osmium tetroxide and glutaraldehyde are favored for electron microscopy. These fixatives react vigorously with proteins at the molecular level. There is clear evidence for the cross-linking of proteins both by osmium tetroxide and glutaraldehyde and cross-linking may be a necessary if not sufficient condition to define fixatives as a class.

Sign in / Sign up

Export Citation Format

Share Document