Appearance
🎉 your ETH🥳
"The C([0,1],\mathbb{R}^3)),}} and outputs a real scalar. This is an example of a non-linear functional. The \mathbb{R}.}} In mathematics, the term functional (as a noun) has at least three meanings. * In modern linear algebra, it refers to a linear mapping from a vector space V into its field of scalars, i.e., it refers to an element of the dual space V^*. * In mathematical analysis, more generally and historically, it refers to a mapping from a space X into the real numbers, or sometimes into the complex numbers, for the purpose of establishing a calculus-like structure on X. Depending on the author, such mappings may or may not be assumed to be linear, or to be defined on the whole space X. * In computer science, it is synonymous with higher-order functions, i.e. functions that take functions as arguments or return them. This article is mainly concerned with the second concept, which arose in the early 18th century as part of the calculus of variations. The first concept, which is more modern and abstract, is discussed in detail in a separate article, under the name linear form. The third concept is detailed in the article on higher- order functions. Commonly, the space X is a space of functions. In this case, the functional is a "function of a function", and some older authors actually define the term "functional" to mean "function of a function". However, the fact that X is a space of functions is not mathematically essential, so this older definition is no longer prevalent. The term originates from the calculus of variations, where one searches for a function that minimizes (or maximizes) a given functional. A particularly important application in physics is search for a state of a system that minimizes (or maximizes) the action, or in other words the time integral of the Lagrangian. Details =Duality= The mapping :x_0\mapsto f(x_0) is a function, where is an argument of a function . At the same time, the mapping of a function to the value of the function at a point :f\mapsto f(x_0) is a functional; here, is a parameter. Provided that is a linear function from a vector space to the underlying scalar field, the above linear maps are dual to each other, and in functional analysis both are called linear functionals. =Definite integral= Integrals such as :f\mapsto I[f]=\int_{\Omega} H(f(x),f'(x),\ldots)\;\mu(\mbox{d}x) form a special class of functionals. They map a function f into a real number, provided that H is real-valued. Examples include * the area underneath the graph of a positive function f ::f\mapsto\int_{x_0}^{x_1}f(x)\;\mathrm{d}x * Lp norm of a function on a set E ::f\mapsto \left(\int_Ef^p \; \mathrm{d}x\right)^{1/p} * the arclength of a curve in 2-dimensional Euclidean space ::f \mapsto \int_{x_0}^{x_1} \sqrt{ 1+f'(x)^2 } \; \mathrm{d}x = Inner product spaces = Given an inner product space X, and a fixed vector \vec{x} \in X, the map defined by \vec{y} \mapsto \vec{x} \cdot \vec{y} is a linear functional on X. The set of vectors \vec{y} such that \vec{x}\cdot \vec{y} is zero is a vector subspace of X, called the null space or kernel of the functional, or the orthogonal complement of \vec{x}, denoted \\{ \vec{x} \\}^\perp. For example, taking the inner product with a fixed function g \in L^2([-\pi,\pi]) defines a (linear) functional on the Hilbert space L^2([-\pi,\pi]) of square integrable functions on [-\pi,\pi]: f \mapsto \langle f,g \rangle = \int_{[-\pi,\pi]} \bar{f} g =Locality= If a functional's value can be computed for small segments of the input curve and then summed to find the total value, the functional is called local. Otherwise it is called non-local. For example: :F(y) = \int_{x_0}^{x_1}y(x)\;\mathrm{d}x is local while :F(y) = \frac{\int_{x_0}^{x_1}y(x)\;\mathrm{d}x}{\int_{x_0}^{x_1} (1+ [y(x)]^2)\;\mathrm{d}x} is non-local. This occurs commonly when integrals occur separately in the numerator and denominator of an equation such as in calculations of center of mass. Equation solving The traditional usage also applies when one talks about a functional equation, meaning an equation between functionals: an equation between functionals can be read as an 'equation to solve', with solutions being themselves functions. In such equations there may be several sets of variable unknowns, like when it is said that an additive function is one satisfying the functional equation :f(x + y) = f(x) + f(y) . Derivative and integration Functional derivatives are used in Lagrangian mechanics. They are derivatives of functionals: i.e. they carry information on how a functional changes when the input function changes by a small amount. Richard Feynman used functional integrals as the central idea in his sum over the histories formulation of quantum mechanics. This usage implies an integral taken over some function space. See also * Linear form * Optimization (mathematics) * Tensor References Types of functions "
"Gordon Lyon (also known by his pseudonym Fyodor Vaskovich) is a network security expert. Lyon created Nmap, and has written numerous books, web sites, and technical papers about network security. He is a founding member of the Honeynet Project and was Vice President of Computer Professionals for Social Responsibility. Personal life Lyon has been active in the network security community since the mid-1990s. His handle, Fyodor, was taken from Russian author Fyodor Dostoyevsky. Most of his programming is done in the C, C++, and Perl programming languages. Opposition to grayware In December 2011 Lyon published his strong dislike of the way Download.com started bundling grayware with their installation managers and concerns over the bundled software, causing many people to spread the post on social networks, and a few dozen media reports. The main problem is the confusion between Download.com-offered content and software offered by original authors; the accusations included deception as well as copyright and trademark violation. Lyon lost control of the Nmap Sourceforge page in 2015, with Sourceforge taking over the project's page and offering adware wrapped download bundles. Currently (2019) the original Sourceforge page does no longer contain any files but the Sourceforge "mirror" page used to hijack the Nmap account redirects to the official https://nmap.org/ site now. Web sites Lyon maintains several network security web sites: *Nmap.Org - Host of the Nmap security scanner and its documentation *SecTools.Org - The top 100 network security tools (ranked by thousands of Nmap users) *SecLists.Org - Archive of the most common security mailing lists *Insecure.Org - His main site, offering security news/updates, exploit world archive, and other misc. security resources Published books Lyon has written and co-authored several books: *Know Your Enemy: Revealing the Security Tools, Tactics, and Motives of the Blackhat Community (Addison-Wesley, 2002, ), co-authored with other members of the Honeynet Project. A 2nd edition is now available (), as are sample chapters. *Stealing the Network: How to Own a Continent (Syngress, 2004, ). Hacker fiction, but tries to stay realistic. Co-authored with Kevin Mitnick and other hackers. Gordon's chapter is freely available online. *Nmap Network Scanning (Nmap Project, 2008, ) Interviews Public interviews with Lyon/Vaskovich have been posted by SecurityFocus, Slashdot, Zone-H, TuxJournal, Safemode, and Google. Many of these provide more personal details than his official bio page does. Conferences Lyon attends and speaks at many security conferences. He has presented at DEFCON, CanSecWest, FOSDEM, IT Security World, Security Masters' Dojo, ShmooCon, IT-Defense, SFOBug, and others. See also * W00w00 References External links *Home page Living people Writers about computer security American computer programmers Free software programmers American technology writers Writers from California Year of birth missing (living people) "
"Van Cleef & Arpels-designed crown of Empress Farah Pahlavi of Iran. She wore the crown in 1967 coronation ceremony. Van Cleef & Arpels is a French luxury jewelry, watch, and perfume company. It was founded in 1896 by Alfred Van Cleef and his father-in-law Salomon Arpels in Paris. Their pieces often feature flowers, animals, and fairies, and have been worn by style icons such as Farah Pahlavi,The Queen of Culture, The official website of Queen Farah the Duchess of Windsor, Grace Kelly, Elizabeth Taylor, Eva Perón. and Queen Nazli of Egypt. History Alfred Van Cleef and his father-in-law, Salomon Arpels, founded the company in 1896. In 1906, following Arpels’s death, Alfred and two of his brothers-in-law, Charles and Julien, acquired space for Van Cleef & Arpels at 22 Place Vendôme, across from the Hôtel Ritz, where Van Cleef & Arpels opened its first boutique shop.vancleefarpels.com The third Arpels brother, Louis, soon joined the company. Van Cleef & Arpels opened boutiques in holiday resorts such as Deauville, Vichy, Le Touquet, Nice, and Monte-Carlo. In 1925, a Van Cleef & Arpels bracelet with red and white roses fashioned from rubies and diamonds won the grand prize at the International Exposition of Modern Industrial and Decorative Arts. Alfred and Esther’s daughter, Renée (born Rachel) Puissant, assumed the company’s artistic direction in 1926. Puissant worked closely with draftsman René Sim Lacaze for the next twenty years. Van Cleef & Arpels were the first French jewelers to open boutiques in Japan and China. Compagnie Financière Richemont S.A. acquired the firm in 1999. In 1966, Van Cleef & Arpels was charged with the task of making the crown of Empress Farah Pahlavi for her upcoming coronation in 1967. A team was sent to Iran to choose the major gems to use for the crown. After 11 months of work, the company presented the empress with a crown made of emerald velvet set with 36 emeralds, 36 rubies, 105 pearls and 1,469 diamonds. Van Cleef & Arpels was charged with the task of making the crown of Queen Nazli of Egypt in the 1930s Boutiques Van Cleef & Arpels has stores in the Middle East and South East Asia, with its products offered in standalone boutiques, boutiques within major department stores, and in independent stores. Standalone boutiques are located in Geneva, Zurich, Munich, London, Milan, Shanghai, and Paris, where the company has multiple locations, including its flagship store at Place Vendôme. In the United States, the company operates standalone boutiques in Boston, New York City, Beverly Hills, Chicago, Houston and Las Vegas. It also maintains stores in Naples, Palm Beach, as well as a location in Aspen. The Chicago boutique opened in 2001 at 636 North Michigan Avenue and moved to a larger location within the Drake Hotel in November 2011 while the New York City flagship store was redesigned in 2013. The brand expanded to Australia in 2016, opening a boutique at Collins Street, Melbourne. The following year, another boutique opened at Castlereagh Street, Sydney. A second Melbourne boutique is set to open in Chadstone Shopping Centre in 2018. The Mystery Setting On 2 December 1933, Van Cleef and Arpels received French Patent No. 764,966 for a proprietary gem setting style it calls Serti Mysterieux, or "Mystery Setting", a technique employing a setting where the prongs are invisible. Each stone is faceted onto gold rails less than two-tenths of a millimeter thick. The technique can require 300 hours of work per piece or more, and only a few are produced each year. Chaumet received an English patent for a similar technique in 1904 as did Cartier in 1933, however neither used the process as extensively. Value In 2010/2011, the company's estimated sales were €450 million in total sales and €45 million in watches. A 1936 Van Cleef & Arpels custom jewelry piece with a "Mystery Setting" sold for $326,500 during an auction at Christie's New York in 2009. Gallery Image:montre cadenas wiki.jpg Cadenas (Padlock) wristwatch (1936) Image:CollierZip wiki.jpg Zip necklace (1950) Image:Sautoir Alhambra wiki.jpg Alhambra necklace (1968) Image:Jardin lenotre necklace wiki.jpg Necklace from the Jardins (Gardens) collection (2008) Image:Minaudiere wiki.jpgMinaudière Bibliography References External links * Official Website * Poetry For The Wrist: The Van Cleef & Arpels Heure d’ici & Heure d’ailleurs Retail companies of France Jewellery retailers of France Watch manufacturing companies of France Luxury brands French jewellers Comité Colbert members "