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Said Husajn ibn Ali

Sajd Husajn bin Ali (ur. 1854 r goalie soccer jerseys. – zm. 4 czerwca 1931 r.) – szarif Mekki oraz emir Mekki od roku 1908 do roku 1917, następnie król Hidżazu – państwa będącego kontynuacją emiratu Mekki. Przyjęcie tytułu królewskiego zostało uznane przez społeczność międzynarodową. Kawaler brytyjskiego Orderu Łaźni. W roku 1924 ogłosił się kalifem wszystkich muzułmanów. Husajn bin Ali panował w Hidżazie do roku 1924 touch football uniforms, gdy jego kraj został najechany przez Abdula Aziza al Sauda. Husajn bin Ali przekazał wówczas koronę i inne tytuły świeckie swojemu synowi, Alemu.

Husajn urodził się w Stambule w Imperium Tureckim. Był ostatnim władcą Hidżazu z dynastii Haszymidów, mianowanym przez władze tureckie. Mimo to, szarif Husajn bin Ali uczestniczył w powstaniu przeciwko zwierzchnictwu tureckiemu w roku 1916. Podczas I wojny światowej, początkowo współpracował z Turcją i Niemcami (sojuszem państw centralnych). Dowody na to, że rząd turecki zamierzał usunąć Husajna po zakończeniu wojny, doprowadziły do rozpadu sojuszu. Korespondencja z brytyjskim Wysokim Komisarzem Henrym McMahonem przekonała go, że wsparcie sił Ententy może przynieść Arabom większe korzyści stainless steel toothpaste dispenser, a mianowicie – utworzenie imperium arabskiego, obejmującego obszary rozciągające się pomiędzy Egiptem a Persją, z wyjątkiem posiadłości kolonialnych w Kuwejcie, Adenie i na wybrzeżu syryjskim. Husajn został oficjalnym przywódcą rewolucji arabskiej przeciwko Turkom.

W rezultacie wojny, Arabowie po wielu wiekach uwolnili się spod dominacji tureckiej. Obszary przez nich zamieszkane, na mocy rozporządzenia Ligi Narodów, zostały ogłoszone terytoriami mandatowymi pod opieką Wielkiej Brytanii i Francji. Gdy mandaty wygasły, synowie Husajna zasiedli na tronach Transjordanii (później Jordanii), Syrii i Iraku. Monarchia w Syrii została wkrótce zniesiona, wobec czego syn Husajna, Fajsal I, stanął na czele państwa irackiego.

Gdy Husajn ogłosił się królem Hidżazu, jednocześnie obwołał się królem wszystkich Arabów (malik bilad-al-Arab). Jego deklaracja doprowadziła do konfliktu z Ibn Saudem, z którym walczył w roku 1910 po stronie Turków. Dwa dni po zniesieniu Kalifatu Tureckiego przez Tureckie Zgromadzenie Narodowe (3 marca 1924 r.), Husajn ogłosił się kalifem w zimowej rezydencji swego syna, Abdullaha, w Shunah w Transjordanii. Przyjęcie tytułu kalifa przez Husajna spotkało się z różnym odbiorem. Husajn został wkrótce wyrzucony z Arabii przez klan Saudów, którzy nie interesowali się koncepcją kalifatu. Saud pokonał Husajna w roku 1924. Husajn nadal posługiwał się tytułem kalifa podczas pobytu w Transjordanii.

Chociaż Brytyjczycy wspomagali Husajna od początku rewolucji arabskiej, zdecydowali się nie interweniować w konflikt pomiędzy nim a Saudem. Saud wkrótce przejął władzę nad Mekką, Medyną i Dżuddą. Husajn musiał uciekać na Cypr, gdzie wsławił się finansowym wsparciem dla kościoła ormiańskiego. Następnie zamieszkał w Ammanie, stolicy Transjordanii, w której panował jego syn, Abdullah. Po abdykacji Husajna, na krótko tron szarifa przejął jego syn Ali. Lecz on również musiał uciekać przed wojskami Ibn Sauda i salafitów. Kolejny spośród potomków Husajna, Fajsal, przejściowo panował w Syrii, a później został królem Iraku.

Husajn zmarł w Ammanie w roku 1931.

Husajn miał trzy żony, z którymi doczekał się czterech synów oraz trzech córek. Z pierwszego małżeństwa, z Abdliyą bin Abdullah, pochodzili:

Z drugiego małżeństwa, z Madihą, pochodziła księżna Saliha. Z trzeciego małżeństwa fanny pack running, z Adilą Khanmun, pochodzili:

Collineation

In projective geometry, a collineation is a one-to-one and onto map (a bijection) from one projective space to another, or from a projective space to itself, such that the images of collinear points are themselves collinear. A collineation is thus an isomorphism between projective spaces, or an automorphism from a projective space to itself. Some authors restrict the definition of collineation to the case where it is an automorphism. The set of all collineations of a space to itself form a group, called the collineation group.

Simply, a collineation is a one-to-one map from one projective space to another, or from a projective space to itself, such that the images of collinear points are themselves collinear. One may formalize this using various ways of presenting a projective space. Also, the case of the projective line is special, and hence generally treated differently.

For a projective space defined in terms of linear algebra (as the projectivization of a vector space), a collineation is a map between the projective spaces that is order-preserving with respect to inclusion of subspaces.

Formally, let V be a vector space over a field K and W a vector space over a field L. Consider the projective spaces PG(V) and PG(W), consisting of the vector lines of V and W. Call D(V) and D(W) the set of subspaces of V and W respectively. A collineation from PG(V) to PG(W) is a map α : D(V) → D(W), such that:

Given a projective space defined axiomatically in terms of an incidence structure (a set of points P, lines L, and an incidence relation I specifying which points lie on which lines, satisfying certain axioms), a collineation between projective spaces thus defined then being a bijective function f between the sets of points and a bijective function g between the set of lines, preserving the incidence relation.

Every projective space of dimension greater than or equal to three is isomorphic to the projectivization of a linear space over a division ring, so in these dimensions this definition is no more general than the linear-algebraic one above, but in dimension two there are other projective planes fanny pack running, namely the non-Desarguesian planes, and this definition permits one to define collineations in such projective planes.

For dimension one, the set of points lying on a single projective line defines a projective space, and the resulting notion of collineation is just any bijection of the set.

For a projective space of dimension one (a projective line; the projectivization of a vector space of dimension two), all points are collinear, so the collineation group is exactly the symmetric group of the points of the projective line. This is different from the behavior in higher dimensions, and thus one gives a more restrictive definition, specified so that the fundamental theorem of projective geometry holds.

In this definition, when V has dimension two, a collineation from PG(V) to PG(W) is a map α : D(V) → D(W), such that:

This last requirement ensures that collineations are all semilinear maps.

The main examples of collineations are projective linear transformations (also known as homographies) and automorphic collineations. For projective spaces coming from a linear space, the fundamental theorem of projective geometry states that all collineations are a combination of these, as described below.

Projective linear transformations (homographies) are collineations (planes in a vector space correspond to lines in the associated projective space, and linear transformations map planes to planes, so projective linear transformations map lines to lines), but in general not all collineations are projective linear transformations. PGL is in general a proper subgroup of the collineation group.

An automorphic collineation is a map that, in coordinates, is a field automorphism applied to the coordinates.

If the geometric dimension of a pappian projective space is at least 2, then every collineation is the product of a homography (a projective linear transformation) and an automorphic collineation. More precisely, the collineation group is the projective semilinear group, which is the semidirect product of homographies by automorphic collineations.

In particular, the collineations of PG(2, R) are exactly the homographies, as R has no nontrivial automorphisms (that is, Gal(R/Q) is trivial).

Suppose φ is a nonsingular semilinear map from V to W, with the dimension of V at least three. Define α : D(V) → D(W) by saying that Zα = { φ(z) | zZ } for all Z in D(V). As φ is semilinear, one easily checks that this map is properly defined, and further more, as φ is not singular, it is bijective. It is obvious now that α is a collineation. We say that α is induced by φ shaver shop.

The fundamental theorem of projective geometry states the converse:

Suppose V is a vector space over a field K with dimension at least three, W is a vector space over a field L, and α is a collineation from PG(V) to PG(W). This implies K and L are isomorphic fields, V and W have the same dimension, and there is a semilinear map φ such that φ induces α.

For n ≥ 3, the collineation group is the projective semilinear group, PΓL – this is PGL, twisted by field automorphisms; formally, the semidirect product PΓL ≅ PGL ⋊ Gal(K/k), where k is the prime field for K.

Thus for K a prime field (







F




p






{\displaystyle \mathbb {F} _{p}}


or






Q





{\displaystyle \mathbb {Q} }


), we have PGL = PΓL, but for K not a prime field (such as







F





p



n








{\displaystyle \mathbb {F} _{p^{n}}}


for n ≥ 2 or






C





{\displaystyle \mathbb {C} }


PΓL / PGL ≅ Gal(K/k) corresponds to “choices of linear structure”, with the identity (base point) being the existing linear structure. Given a projective space without an identification as the projectivization of a linear space, there is no natural isomorphism between the collineation group and PΓL, and the choice of a linear structure (realization as projectivization of a linear space) corresponds to a choice of subgroup PGL < PΓL, these choices forming a torsor over Gal(K/k).

The idea of a line was abstracted to a ternary relation determined by collinear points. According to Wilhelm Blaschke it was August Möbius that first abstracted this essence of geometrical transformation:

Contemporary mathematicians view geometry as an incidence structure with an automorphism group consisting of mappings of the underlying space that preserve incidence. Such a mapping permutes the lines of the incidence structure, and the notion of collineation persists.

As mentioned by Blaschke and Klein, Michel Chasles preferred the term homography to collineation. A distinction between the terms arose when the distinction was clarified between the real projective plane and the complex projective line. Since there are no non-trivial field automorphisms of the real number field, all the collineations are homographies in the real projective plane., however due to the field automorphism complex conjugation, not all collineations of the complex projective line are homographies. In applications such as computer vision where the underlying field is the real number field, homography and collineation can be used interchangeably.

The operation of taking the complex conjugate in the complex plane amounts to a reflection in the real line. With the notation z for the conjugate of z, an anti-homography is given by

Thus an anti-homography is the composition of conjugation with an homography, and so is an example of a collineation which is not an homography. For example, geometrically, the mapping





f


(


z


)


=


1



/




z











{\displaystyle f(z)=1/z^{*}}


amounts to circle inversion. The transformations of inversive geometry of the plane are frequently described as the collection of all homographies and anti-homographies of the complex plane.

Sosie de Misène

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Saint Sosie était diacre de Misène dans l’évêché de Bénévent au début du IVe siècle, fêté le 19 septembre.

En 303 ou 304, lors de la grande persécution de Dioclétien, il fut arrêté avec Procule, diacre de Pouzzoles et emprisonné à Cumes sur ordre du proconsul Dragonce (Dragontius) evercare lint shaver. En 305, lorsque Constance et Galère succédèrent à Dioclétien et Maximilien, Dragonce fut rappelé à Rome et remplacé par Timothée et les chrétiens emprisonnés à Cumes furent relâchés.

Apprenant cette libération, Janvier, évêque de Bénévent, qui avait partagé la douleur de ses deux diacres, quitta son diocèse pour venir partager leur joie. Mais Timothée fit arrêter Janvier, Sosie et Procule et les condamna au martyre.

Après différentes épreuves (voir la légende de saint Janvier), Sosie, Procule puis Janvier furent décapités le dans le forum proche du volcan Vulcano de Pouzzoles.

Sosie et Procule sont des saints martyrs reconnus par la tradition du Christianisme orthodoxe mais apparemment pas par l’Église catholique romaine fanny pack running. Ils sont célébrés, avec saint Janvier glass table water bottle, le 19 septembre, anniversaire de leur mort.

Hallie Eisenberg

Hallie Kate Eisenberg (born August 2, 1992) is an American actress best known for being “The Pepsi Girl” in a series of Pepsi commercials and her role as Erika Tansy in How to Eat Fried Worms.

Eisenberg was born in East Brunswick Township, New Jersey, the daughter of Amy, who worked as a clown at children’s parties, and Barry Eisenberg, who ran a hospital and later became a college professor. She has two siblings: actor Jesse Eisenberg, the Academy Award-nominated star of The Social Network best waterproof dry bag, and Kerri. Hallie was named after the character Hallie O’Fallon in the 1991 film All I Want for Christmas, portrayed by Thora Birch. She was raised in a secular Jewish family that originated in Poland and Ukraine

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. Eisenberg attended American University, in Washington, DC.[citation needed]

In the late 1990s and early 2000s, she was “The Pepsi Girl” in a series of Pepsi commercials. She made her film debut in the 1998 children’s film Paulie, playing the young owner of the title parrot. After appearing in a few made-for-television films, she had supporting parts in 1999’s The Insider and Bicentennial Man.

In 2000, Eisenberg co-starred with Minnie Driver in the feature film Beautiful, which received generally negative reviews fanny pack running. She also starred as Helen Keller in a television remake of The Miracle Worker. In 2004, she played opposite Jeff Daniels and Patricia Heaton in the television remake of the The Goodbye Girl. In 2006, Eisenberg appeared in How to Eat Fried Worms, the New Line Cinema adaptation of Thomas Rockwell’s book of the same name. In 2007, she co-starred in the independent feature film P.J. alongside John Heard, Vincent Pastore and Robert Picardo.

Eisenberg made her Broadway debut in Roundabout Theatre’s production of Clare Boothe Luce’s play The Women.

In 2010 Eisenberg halted her pursuit of a film career to attend college.