2008–09 Paris Saint-Germain F.C. (Ladies) season: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Yobot
m WP:CHECKWIKI error fixes / special characters in sortkey fixed using AWB (9427)
en>Cydebot
m Robot - Speedily moving category Paris Saint-Germain F.C. (Ladies) seasons to Category:Paris Saint-Germain Féminines seasons per CFDS.
 
Line 1: Line 1:
In [[fluid dynamics]] and [[invariant theory]], a '''Reynolds operator''' is a mathematical operator given by averaging something over a group action, that satisfies a set of properties called Reynolds rules. In fluid dynamics Reynolds operators are often encountered in models of [[turbulence|turbulent flows]], particularly the [[Reynolds-averaged Navier–Stokes equations]], where the average is typically taken over the fluid flow under the group of time translations. In invariant theory the average is often taken over a compact group or reductive algebraic group acting on a commutative algebra, such as a ring of polynomials.  Reynolds operators were introduced into fluid dynamics by {{harvs|txt|authorlink=Osbourne Reynolds|first=Osbourne|last= Reynolds|year=1895}} and named by {{harvs|txt|authorlink=Kampé de Fériet|last= Kampé de Fériet|first= J. |year1=1934|year2=1935|year3=1949}}.
This will provide the cellulose for roughage, which takes care of proper movement of bowels. Not that your hair will instantly fall out if you get it wrong. Acne skin care is an important problem for many folks. If you'd like to add a little fragrance feel free to add a drop or two of your favorite essential oil to the powder and you're set. Products from reputed brand don't have any adverse effect on your skin or hair. <br><br>


==Definition==
As a result they will be able to provide you with better ideas with regards to the general decor and placement of various items within the bathroom. Remember that only if correct beauty products are utilized in the right proportion, only then these products can make any women’s beauty glow. You most likely know lots of far more buddies and family members that have eczema, other skin sensitivities and allergies now than if you were younger. Technological advances within this category have given women more control over treating their skin while saving them time and money. There are some of the best skin care products that are available in the market and are required for their efficiency in smoothening the skin. <br><br>You can find some types of skin care products for daily skin care. In fact, there are many beautifying essentials right in your own home. The Loreal Professional skin treatment can provide great help in all weather conditions. Just enter the terms "salon equipment" or "salon supplies" or "discount salons equipment" in the search bar of any search engine like Google. If you are not using a natural product already try an all-natural alternative. <br><br>Moisturizing also has the added bonus of locking in the moisture that can be lost without its use, so do not skimp on this beauty care product. Mineral oil and petrolatum are very common hair care product ingredients because they are cheap and appear to do the trick. Every natural hair diva knows that tangling is a definitely no-no for healthy natural hair.  If you have any issues about where and how to use [http://list.ly/ldhardas L.D. Hardas], you can get in touch with us at our own website. Get a chance to buy ponds age miracle and send it back to the Philippines by visiting an online gift shop in the Philippines. It regulates body temperature and prevents germs from getting into the body. <br><br>The third appears in the form of patches on the skin and looks like a flaky red coin. If that is the subject and you do not want to travel, but you still claim to buy your beauty supplies and products, you need to recall that beauty supply stores come in a number of various formats. Another important aspect to consider when searching for beauty products is the genuineness of the product itself. Aveda hair products are completely produced by using herbal essences, oils and extracts but not any synthetic chemicals. Removes all impurities from the nh  with skin, increases blood circulation so  and helps k to keep the skin free of rashes, problems pimples and acne.
Reynolds operators are used in fluid dynamics, functional analysis, and invariant theory, and the notation and definitions in these areas differ slightly.  A Reynolds operator acting on φ is sometimes denoted by ''R''(''φ''), ''P''(''φ''), ''ρ''(''φ''), 〈''φ''〉, or {{overline|φ}}. Reynolds operators are usually linear operators acting on some algebra of functions, satisfying the identity
 
: ''R''(''R''(''φ'')''ψ'') = ''R''(''φ'')''R''(''ψ'')  for all ''φ'', ''ψ''
 
and sometimes some other conditions, such as commuting with various group actions.
 
===Invariant theory===
In invariant theory a Reynolds operator ''R'' is usually a linear operator satisfying
 
: ''R''(''R''(''φ'')''ψ'') = ''R''(''φ'')''R''(''ψ'')  for all ''φ'', ''ψ''
 
and
 
:''R''(1) = 1.
 
Together these conditions imply that ''R'' is idempotent: ''R''<sup>2</sup> = ''R''. The Reynolds operator will also usually commute with some group action, and project onto the invariant elements of this group action.
 
===Functional analysis===
In functional analysis a Reynolds operator is a linear operator ''R'' acting on some algebra of functions ''φ'', satisfying the '''Reynolds identity'''
: ''R''(''φψ'') = ''R''(''φ'')''R''(''ψ'') + ''R''((''φ'' − ''R''(''φ''))(''ψ'' − ''R''(''ψ''))) for all ''φ'', ''ψ''
 
The operator ''R'' is called an '''averaging operator''' if it is linear and satisfies
 
: ''R''(''R''(''φ'')''ψ'') = ''R''(''φ'')''R''(''ψ'') for all ''φ'', ''ψ''.
 
If ''R''(''R''(''φ'')) = ''R''(''φ'') for all φ then ''R'' is an averaging operator if and only if it is a Reynolds operator. Sometimes the ''R''(''R''(''φ'')) = ''R''(''φ'') condition is added to the definition of Reynolds operators.
 
=== Fluid dynamics ===
Let <math>\phi</math> and <math>\psi</math> be two random variables, and <math>a</math> be an arbitrary constant.  Then the properties satisfied by Reynolds operators, for an operator <math>\langle \rangle,</math> include linearity and the averaging property:
 
:<math>
\langle \phi + \psi \rangle = \langle \phi \rangle + \langle \psi \rangle, \,
</math>
 
:<math>
\langle a \phi \rangle = a \langle \phi \rangle, \,
</math>
 
:<math>
\langle \langle \phi \rangle \psi \rangle = \langle \phi \rangle \langle \psi \rangle, \,
</math> which implies <math>
\langle \langle \phi \rangle \rangle = \langle \phi \rangle. \,
</math>
In addition the Reynolds operator is often assumed to commute with space and time translations:
:<math>
\left\langle \frac{ \partial \phi }{ \partial t } \right\rangle = \frac{ \partial \langle \phi \rangle }{ \partial t }, \qquad
\left\langle \frac{ \partial \phi }{ \partial x } \right\rangle = \frac{ \partial \langle \phi \rangle }{ \partial x },
</math>
 
:<math>
\left\langle \int \phi( \boldsymbol{x}, t ) \, d \boldsymbol{x} \, dt \right\rangle = \int \langle \phi(\boldsymbol{x},t) \rangle \, d \boldsymbol{x} \, dt.
</math>
 
Any operator satisfying these properties is a Reynolds operator.<ref name="Sagaut_2006">{{cite book
|author=Sagaut, Pierre
|title=Large Eddy Simulation for Incompressible Flows
|publisher=Springer
|year=2006
|edition=Third Edition
|isbn=3-540-26344-6 }}</ref>
 
==Examples==
Reynolds operators  are often given by projecting onto an invariant subspace of a group action.  
 
*The "Reynolds operator" considered by {{harvtxt|Reynolds|1895}} was essentially the projection of a fluid flow to the "average" fluid flow, which can be thought of as projection to time-invariant flows. Here the group action is given by the action of the group of time-translations.
 
*Suppose that ''G'' is a [[reductive algebraic group]] or a [[compact space|compact]] group, and ''V'' is a finite-dimensional representation of ''G''. Then ''G'' also acts on the symmetric algebra ''SV'' of polynomials.  The Reynolds operator ''R'' is the ''G''-invariant projection from ''SV'' to the subring ''SV''<sup>''G''</sup> of elements fixed by ''G''.
 
== References ==
{{reflist}}
*{{Citation | last1=Kampé de Fériet | first1=J. |journal=La Science Aérienne |volume=3|pages=9–34 |year=1934}}
*{{Citation | last1=Kampé de Fériet | first1=J. |journal=La Science Aérienne |volume=4|pages=12–52 |year=1935}}
*{{Citation | last1=Kampé de Fériet | first1=J. | title=Sur un problème d'algèbre abstraite posé par la définition de la moyenne dans la théorie de la turbulence | mr=0032718 | year=1949 | journal=Annales de la Societé Scientifique de Bruxelles. Série I. Sciences Mathématiques, Astronomiques et Physiques | issn=0037-959X | volume=63 | pages=165–180}}
*{{citation|last=Reynolds|first=O. |title=On the dynamical theory of incompressible viscous fluids and the determination of the criterion|journal=[[Philosophical Transactions of the Royal Society A]] |volume=186|year=1895|pages=123–164|jstor=90643}}
*{{Citation | last1=Rota | first1=Gian-Carlo | author1-link=Gian-Carlo Rota | title=Gian-Carlo Rota on analysis and probability | publisher=Birkhäuser Boston | location=Boston, MA | series=Contemporary Mathematicians | isbn=978-0-8176-4275-4 | mr=1944526 | year=2003}} Reprints several of Rota's papers on Reynolds operators, with commentary.
*{{Citation | last1=Rota | first1=Gian-Carlo | author1-link=Gian-Carlo Rota | title=Proc. Sympos. Appl. Math., Vol. XVI | publisher=Amer. Math. Soc. | location=Providence, R.I. | mr=0161140 | year=1964 | chapter=Reynolds operators | pages=70–83}}
*{{Citation | last1=Sturmfels | first1=Bernd | author1-link=Bernd Sturmfels | title=Algorithms in invariant theory | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Texts and Monographs in Symbolic Computation | isbn=978-3-211-82445-0 | mr=1255980 | year=1993}}
 
[[Category:Invariant theory]]
[[Category:Fluid dynamics]]
[[Category:Turbulence]]

Latest revision as of 22:27, 29 July 2014

This will provide the cellulose for roughage, which takes care of proper movement of bowels. Not that your hair will instantly fall out if you get it wrong. Acne skin care is an important problem for many folks. If you'd like to add a little fragrance feel free to add a drop or two of your favorite essential oil to the powder and you're set. Products from reputed brand don't have any adverse effect on your skin or hair.

As a result they will be able to provide you with better ideas with regards to the general decor and placement of various items within the bathroom. Remember that only if correct beauty products are utilized in the right proportion, only then these products can make any women’s beauty glow. You most likely know lots of far more buddies and family members that have eczema, other skin sensitivities and allergies now than if you were younger. Technological advances within this category have given women more control over treating their skin while saving them time and money. There are some of the best skin care products that are available in the market and are required for their efficiency in smoothening the skin.

You can find some types of skin care products for daily skin care. In fact, there are many beautifying essentials right in your own home. The Loreal Professional skin treatment can provide great help in all weather conditions. Just enter the terms "salon equipment" or "salon supplies" or "discount salons equipment" in the search bar of any search engine like Google. If you are not using a natural product already try an all-natural alternative.

Moisturizing also has the added bonus of locking in the moisture that can be lost without its use, so do not skimp on this beauty care product. Mineral oil and petrolatum are very common hair care product ingredients because they are cheap and appear to do the trick. Every natural hair diva knows that tangling is a definitely no-no for healthy natural hair. If you have any issues about where and how to use L.D. Hardas, you can get in touch with us at our own website. Get a chance to buy ponds age miracle and send it back to the Philippines by visiting an online gift shop in the Philippines. It regulates body temperature and prevents germs from getting into the body.

The third appears in the form of patches on the skin and looks like a flaky red coin. If that is the subject and you do not want to travel, but you still claim to buy your beauty supplies and products, you need to recall that beauty supply stores come in a number of various formats. Another important aspect to consider when searching for beauty products is the genuineness of the product itself. Aveda hair products are completely produced by using herbal essences, oils and extracts but not any synthetic chemicals. Removes all impurities from the nh with skin, increases blood circulation so and helps k to keep the skin free of rashes, problems pimples and acne.

Retrieved from "https://en.formulasearchengine.com/index.php?title=2008–09_Paris_Saint-Germain_F.C._(Ladies)_season&oldid=267499"