Fashion in France is an important aspect in the spectrum of culture and social life, as well as being an important aspect of the economy. Fashion design and production is from prominence in France from the 15th century. From the 17th century, it exploded into a rich industry both for export; the Royal Minister of Finances, Jean-Baptiste Colbert, expressed it as "Fashion is to France what the gold mines of Peru are to Spain...". During the 19th century, fashion transitioned into many styles; the modern term of haute couture originated for fashion in good taste. The term prêt-à-porter was born in the 1960s, reacting against the traditional notions of fashion and garment-making process, satisfying the needs of pop culture and mass media. Paris holds the name of global fashion capital; the city is home to many prime designers, including Chanel, Louis Vuitton, Balmain, Pierre Cardin, Yves Saint Laurent, Roger Vivier, Thierry Mugler, Jean Paul Gaultier, Hermès, Chloé, Céline. With the decentralization of the fashion industry, many cities including: Lyon, Bordeaux, Toulouse and Strasbourg have their own luxury districts and avenues.

In recent times, these have become significant producers. Île-de-France, Manosque, La Gacilly, Vichy lead the cosmetic industry, house well-known international beauty houses such as L'Oreal, Lancôme, Clarins, Yves Rocher, L'Occitane, etc. The cities of Nice, Cannes and St. Tropez among others in the French riviera are well known as places of pleasure, annually hosting many media celebrities and personalities and billionaires; the clothing of France is famous throughout the world. The association of France with fashion and style is credited as beginning during the reign of Louis XIV when the luxury goods industries in France came under royal control and the French royal court became, the arbiter of taste and style in Europe; the rise in prominence of French fashion was linked to the creation of the fashion press in the early 1670s, which transformed the fashion industry by marketing designs to a broad public outside the French court and by popularizing notions such as the fashion "season" and changing styles.

The prints were 14.25 X 9.5 and depicted a man or woman of quality wearing the latest fashions. They were shown head to toe, but with no individuality or defined facial features. Sometimes the figure would be depicted from behind in order to showcase a different side of the clothing. Although the individual in the prints was crudely sketched, the garment itself was impeccably drawn and detailed. Accessories to the garment received nuanced attention. Louis XIV, although hailed as a patron of fashion, did not have a large role in its spread and proliferation—which was due to the fashion prints; the fashion prints were ubiquitous, but Louis XIV neither sponsored nor hindered their production and proliferation, stayed out of it unless the prints of himself were treasonous, satirical, or caricatures. Over his lifetime, Louis commissioned numerous works of art to portray himself, among them over 300 formal portraits; the earliest portrayals of Louis followed the pictorial conventions of the day in depicting the child king as the majestically royal incarnation of France.

This idealisation of the monarch continued in works, which avoided depictions of the effect of the smallpox that Louis contracted in 1647. In the 1660s, Louis began to be shown as a Roman emperor, the god Apollo, or Alexander the Great, as can be seen in many works of Charles Le Brun, such as sculpture and the decor of major monuments; the depiction of the King in this manner focused on allegorical or mythological attributes, instead of attempting to produce a true likeness. As Louis aged, so too did the manner in which he was depicted. Nonetheless, there was still a disparity between realistic representation and the demands of royal propaganda. There is no better illustration of this than in Hyacinthe Rigaud's frequently-reproduced Portrait of Louis XIV of 1701, in which a 63-year-old Louis appears to stand on a set of unnaturally young legs. In 1680, Louis began to be portrayed directly rather than in a mythological setting; this began the "fashion portraits", which were prints that depicted the King wearing the notable fashions of the season.

These prints were largely unofficial, which meant printers were unaffiliated with the Crown. They went unchallenged by authorities, however, as long as they portrayed the King in a positive light; those who did with the use of caricature faced imprisonment. Rigaud's portrait exemplified the height of royal portraiture in Louis's reign. Although Rigaud crafted a credible likeness of Louis, the portrait was neither meant as an exercise in realism nor to explore Louis's personal character. Rigaud was concerned with detail and depicted the King's costume with great precision, down to his shoe buckle. However, Rigaud's intention was to glorify the monarchy. Rigaud's original, now housed in the Louvre, was meant as a gift to Louis's grandson, Philip V of Spain. However, Louis was so pleased with the work that he kept the original and commissioned a copy to be sent to his grandson; that became the first of many copies, both in full and half-length formats, to be made by Rigaud with the help of his assistants.

The portrait became a model for French royal and imperial portraiture down to the time of Charles X over a century later. In his work, Rigaud proclaims Louis's exalted royal status throug

The Compton wavelength is a quantum mechanical property of a particle. It was introduced by Arthur Compton in his explanation of the scattering of photons by electrons; the Compton wavelength of a particle is equal to the wavelength of a photon whose energy is the same as the mass of that particle. The standard Compton wavelength, λ, of a particle is given by λ = h m c, where h is the Planck constant, m is the particle's mass, c is the speed of light; the significance of this formula is shown in the derivation of the Compton shift formula. The CODATA 2014 value for the Compton wavelength of the electron is 2.4263102367×10−12 m. Other particles have different Compton wavelengths; when the Compton wavelength is divided by 2π, one obtains the "reduced" Compton wavelength ƛ, i.e. the Compton wavelength for 1 radian instead of 2π radians: where ħ is the "reduced" Planck constant. The inverse reduced Compton wavelength is a natural representation for mass on the quantum scale, as such, it appears in many of the fundamental equations of quantum mechanics.

The reduced Compton wavelength appears in the relativistic Klein–Gordon equation for a free particle: ∇ 2 ψ − 1 c 2 ∂ 2 ∂ t 2 ψ = 2 ψ. It appears in the Dirac equation: − i γ μ ∂ μ ψ + ψ = 0; the reduced Compton wavelength appears in Schrödinger's equation, although its presence is obscured in traditional representations of the equation. The following is the traditional representation of Schrödinger's equation for an electron in a hydrogen-like atom: i ℏ ∂ ∂ t ψ = − ℏ 2 2 m ∇ 2 ψ − 1 4 π ϵ 0 Z e 2 r ψ. Dividing through by ℏ c, rewriting in terms of the fine structure constant, one obtains: i c ∂ ∂ t ψ = − 1 2 ∇ 2 ψ − α Z r ψ; the reduced Compton wavelength is a natural representation of mass on the quantum scale. Equations that pertain to inertial mass like Klein-Gordon and Schrödinger's, use the reduced Compton wavelength; the non-reduced Compton wavelength is a natural representation for mass, converted into energy. Equations that pertain to the conversion of mass into energy, or to the wavelengths of photons interacting with mass, use the non-reduced Compton wavelength.

A particle of mass m has a rest energy of E = mc2. The non-reduced Compton wavelength for this particle is the wavelength of a photon of the same energy. For photons of frequency f, energy is given by E = h f = h c λ = m c 2, which yields the non-reduced or standard Compton wavelength formula if solved for λ; the Compton wavelength expresses a fundamental limitation on measuring the position of a particle, taking into account quantum mechanics and special relativity. This limitation depends on the mass m of the particle. To see how, note that we can measure the position of a particle by bouncing light off it – but measuring the position requires light of short wavelength. Light with a short wavelength consists of photons of high energy. If the energy of these photons exceeds mc2, when one hits the particle whose position is being measured the collision may yield enough energy to create a new particle of the same type; this renders moot the question of the original particle's location. This argument shows that the reduced Compton wavelength is the cutoff below which quantum field theory – which can describe particle creation and annihilation – becomes important.

The above argument can be made a bit more precise. Suppose we wish to measure the position of a particle to within an accuracy Δx; the uncertainty relation for position and momentum says that Δ x Δ p ≥ ℏ 2, so the uncertainty in the particle's momentum satisfies

The Cascade Conference is a Michigan high school athletic conference, in the Jackson County area. It was formed prior to the 1954 school year; the conference includes Class B and C schools from the Jackson County area, as well as schools from the surrounding area. The following institutions are full members of the Cascade Conference for the 2018/19 academic year: The Cascade Conference has five former members; the Cascades Conference was formed in 1954 with eight schools from the Jackson County League. The original members were: Brooklyn, East Jackson, Grass Lake, Jackson Vandercook Lake, Michigan Center, Napoleon and Springport high schools. With the growth of suburbs, some Cascades Conference schools grew more than others; this led to the creation of the Blue divisions. Between 1983 and 1996, four schools were listed as Cascades-Red Members: Jackson Lumen Christi, Jackson Northwest, Parma Jackson County Western and Brooklyn Columbia Central. In 1996, Jackson Northwest and Jackson Lumen Christi left the Cascades Red for the Capital-Circuit Conference.

Brooklyn Columbia Central left the Cascades Red after 1995 and competed as an independent for two years, before joining the Lenawee County Conference at the start of the 1997 school year. Parma Jackson County Western left the Cascades Red after the 1995 school year and joined the Twin Valley Conference. Members