title: Bad Girls Club (season 9)

text: The ninth season of "Bad Girls Club" is titled Bad Girls Club: Mexico and premiered on July 9, 2012 and was filmed in Cabo San Lucas in early 2012. This is the fourth season to take place in a different location from Los Angeles, the first being season five (filmed in Miami), the second being season seven (filmed in New Orleans), and the third being season eight (filmed in Las Vegas).


title: Bad Girls Club (season 9)

text: The season began with seven original bad girls, of which one left voluntarily and two were removed by production. Three replacement bad girls were introduced in their absences later in the season.


title: John Kiffmeyer

text: John Kiffmeyer (born July 11, 1969), known professionally as Al Sobrante, is an American cinematographer and retired musician and songwriter. He is best known as the first drummer for the punk rock band Green Day. His stage name is a reference to his hometown, El Sobrante.


title: John Kiffmeyer

text: John Kiffmeyer was born in El Sobrante, California on July 11, 1969. His first exposure in the punk scene was as the drummer of the band Isocracy. The group was popular in the East Bay, and mainstays at the famed club, 924 Gilman Street. He chose his stage name Al Sobrante for an evident pun on his birthplace.


title: John Kiffmeyer

text: Kiffmeyer is most well known for his time in Green Day; after Isocracy broke up, he joined Mike Dirnt and Billie Joe Armstrong in 1987 to replace original drummer Raj Punjabi and join Sweet Children, which was later renamed Green Day. Because of his experience and knowledge of the underground community, Kiffmeyer was able to get the young band on its feet by placing calls to friends, among them prominent figure of the East Bay Larry Livermore. The first few performances took place at Contra Costa College, where Kiffmeyer was a journalism student. On the strength of an early performance, Livermore vowed to release a Green Day record on his Lookout! Records. The group's first full-length effort, 1990 album "39/Smooth", would feature a Kiffmeyer original, "I Was There", which documented the band at that place in time. Being a fan of Ozzy Osbourne, he inspired the mini-covers of some famous songs, such as "I Don't Know" by Osbourne and "Sweet Home Alabama" by Lynyrd Skynyrd during the bridge of "Disappearing Boy", a practice that is still carried out today.


title: John Kiffmeyer

text: In 1990, he attended college at Humboldt State University in Arcata, California. While Kiffmeyer was attending college, Green Day members Billie Joe Armstrong and Mike Dirnt accepted drummer Tré Cool into the band, which Kiffmeyer "graciously accepted". In 1991, he worked as executive producer for the Green Day album "Kerplunk", released that year. Kiffmeyer later joined the band The Ne'er Do Wells, leaving abruptly in 1994. Following a stint with punk band The Ritalins, he became manager of The Shruggs until their split. In 1998 he was the executive producer of "The Great Lost Trouble Makers Album" by The Troublemakers, a garage rock band from Sacramento, California.


title: John Kiffmeyer

text: He now lives in San Francisco, California and is married to experimental filmmaker and San Francisco State University professor Greta Snider. He works as a Director of Photography, specializing in green screen and producing mainly commercial work.


title: John Kiffmeyer

text: On April 16, 2015, Kiffmeyer joined Billie Joe Armstrong and Mike Dirnt on stage during a Green Day concert at The House of Blues in Cleveland, Ohio, where the trio performed as "Sweet Children" and played songs that they had not performed since the 1990s, including "Sweet Children", "Green Day", "I Was There", "Don't Leave Me" and "Dry Ice".


title: Shing-Tung Yau

text: Shing-Tung Yau (; ; born April 4, 1949) is a Chinese-American mathematician and the William Caspar Graustein Professor of Mathematics at Harvard University. In April 2022, Yau announced retirement from Harvard to become Chair Professor of mathematics at Tsinghua University.


title: Shing-Tung Yau

text: Yau was born in Shantou, China, moved to Hong Kong at a young age, and to the United States in 1969. He was awarded the Fields Medal in 1982, in recognition of his contributions to partial differential equations, the Calabi conjecture, the positive energy theorem, and the Monge–Ampère equation. Yau is considered one of the major contributors to the development of modern differential geometry and geometric analysis.


title: Shing-Tung Yau

text: The impact of Yau's work can be seen in the mathematical and physical fields of differential geometry, partial differential equations, convex geometry, algebraic geometry, enumerative geometry, mirror symmetry, general relativity, and string theory, while his work has also touched upon applied mathematics, engineering, and numerical analysis.


title: Shing-Tung Yau

text: Yau was born in Shantou, China in 1949 to Chinese Hakka parents. Professor Yau's ancestral hometown is Jiaoling county, China. His mother, Yeuk Lam Leung, was from Meixian District; his father, Chen Ying Chiu, was a Chinese scholar of philosophy, history, literature, and economics. He was the fifth of eight children, with Hakka ancestry.


title: Shing-Tung Yau

text: During the Communist takeover of mainland China, when he was only a few months old, his family moved to Hong Kong where he was forced to learn to speak the Cantonese language as well as speak Chinese Hakka. He was not able to revisit until 1979, at the invitation of Hua Luogeng, when mainland China entered the reform and opening era.. They had financial troubles from having lost all of their possessions, and his father and second-oldest sister died when he was thirteen. Yau began to read and appreciate his father's books, and became more devoted to schoolwork. After graduating from Pui Ching Middle School, he studied mathematics at the Chinese University of Hong Kong from 1966 to 1969, without receiving a degree due to graduating early. He left his textbooks with his younger brother, Stephen Shing-Toung Yau, who then decided to major in mathematics as well.


title: Shing-Tung Yau

text: Yau left for the Ph.D. program in mathematics at University of California, Berkeley in the fall of 1969. Over the winter break, he read the first issues of the Journal of Differential Geometry, and was deeply inspired by John Milnor's papers on geometric group theory. Subsequently he formulated a generalization of Preissman's theorem, and developed his ideas further with Blaine Lawson over the next semester. Using this work, he received his Ph.D. the following year, in 1971, under the supervision of Shiing-Shen Chern.


title: Shing-Tung Yau

text: He spent a year as a member of the Institute for Advanced Study at Princeton before joining Stony Brook University in 1972 as an assistant professor. In 1974, he became an associate professor at Stanford University. In 1976 he took a visiting faculty position with UCLA and married physicist Yu-Yun Kuo, who he knew from his time as a graduate student at Berkeley. From 1984 to 1987 he worked at University of California, San Diego. Since 1987, he has been at Harvard University. In April 2022, Yau announced a forthcoming move from Harvard to Tsinghua University.


title: Shing-Tung Yau

text: In 1978, Yau became "stateless" after the British Consulate revoked his Hong Kong residency due to his United States permanent residency status. Regarding his status when receiving his Fields Medal in 1982, Yau stated "I am proud to say that when I was awarded the Fields Medal in mathematics, I held no passport of any country and should certainly be considered Chinese." Yau remained "stateless" until 1990, when he obtained United States citizenship.


title: Shing-Tung Yau

text: With science journalist Steve Nadis, Yau has written a non-technical account of Calabi-Yau manifolds and string theory, a history of Harvard's mathematics department, and an autobiography.


title: Shing-Tung Yau

text: Yau has made major contributions to the development of modern differential geometry and geometric analysis. As said by William Thurston in 1981:


title: Shing-Tung Yau

text: His most widely celebrated results include the resolution (with Shiu-Yuen Cheng) of the boundary-value problem for the Monge-Ampère equation, the positive mass theorem in the mathematical analysis of general relativity (achieved with Richard Schoen), the resolution of the Calabi conjecture, the topological theory of minimal surfaces (with William Meeks), the Donaldson-Uhlenbeck-Yau theorem (done with Karen Uhlenbeck), and the Cheng−Yau and Li−Yau gradient estimates for partial differential equations (found with Shiu-Yuen Cheng and Peter Li). Many of Yau's results (in addition to those of others) were written into textbooks co-authored with Schoen.


title: Shing-Tung Yau

text: In addition to his research, Yau is the founder and director of several mathematical institutes, mostly in China. John Coates has commented that "no other mathematician of our times has come close" to Yau's success at fundraising for mathematical activities in China and Hong Kong. During a sabbatical year at National Tsinghua University in Taiwan, Yau was asked by Charles Kao to start a mathematical institute at the Chinese University of Hong Kong. After a few years of fundraising efforts, Yau established the multi-disciplinary Institute of Mathematical Sciences in 1993, with his frequent co-author Shiu-Yuen Cheng as associate director. In 1995, Yau assisted Yongxiang Lu with raising money from Ronnie Chan and Gerald Chan's Morningside Group for the new Morningside Center of Mathematics at the Chinese Academy of Sciences. Yau has also been involved with the Center of Mathematical Sciences at Zhejiang University, at Tsinghua University, at National Taiwan University, and in Sanya. More recently, in 2014, Yau raised money to establish the Center of Mathematical Sciences and Applications (of which he is the director), the Center for Green Buildings and Cities, and the Center for Immunological Research, all at Harvard University.


title: Shing-Tung Yau

text: Modeled on an earlier physics conference organized by Tsung-Dao Lee and Chen-Ning Yang, Yau proposed the International Congress of Chinese Mathematicians, which is now held every three years. The first congress was held at the Morningside Center from December 12 to 18, 1998. He co-organizes the annual "Journal of Differential Geometry" and "Current Developments in Mathematics" conferences. Yau is an editor-in-chief of the Journal of Differential Geometry, Asian Journal of Mathematics, and Advances in Theoretical and Mathematical Physics. As of 2021, he has advised over seventy Ph.D. students.


title: Shing-Tung Yau

text: In Hong Kong, with the support of Ronnie Chan, Yau set up the Hang Lung Award for high school students. He has also organized and participated in meetings for high school and college students, such as the panel discussions "Why Math? Ask Masters!" in Hangzhou, July 2004, and "The Wonder of Mathematics" in Hong Kong, December 2004. Yau also co-initiated a series of books on popular mathematics, "Mathematics and Mathematical People".


title: Shing-Tung Yau

text: In 2002 and 2003, Grigori Perelman posted preprints to the arXiv claiming to prove the Thurston geometrization conjecture and, as a special case, the renowned Poincaré conjecture. Although his work contained many new ideas and results, his proofs lacked detail on a number of technical arguments. Over the next few years, several mathematicians devoted their time to fill in details and provide expositions of Perelman's work to the mathematical community. A well-known August 2006 article in the "New Yorker" written by Sylvia Nasar and David Gruber about the situation brought some professional disputes involving Yau to public attention.


title: Shing-Tung Yau

text: Yau claimed that Nasar and Gruber's article was defamatory and contained several falsehoods, and that they did not give him the opportunity to represent his own side of the disputes. He considered filing a lawsuit against the magazine, claiming professional damage, but says he decided that it wasn't sufficiently clear what such an action would achieve. He established a public relations website, with letters responding to the "New Yorker" article from several mathematicians, including himself and two others quoted in the article.


title: Shing-Tung Yau

text: In his autobiography, Yau said that his statements in 2006 such as that Cao and Zhu gave "the first complete and detailed account of the proof of the Poincaré conjecture" should have been phrased more carefully. Although he does believe Cao and Zhu's work to be the first and most rigorously detailed account of Perelman's work, he says he should have clarified that they had "not surpassed Perelman's work in any way." He has also maintained the view that (as of 2019) the final parts of Perelman's proof should be better understood by the mathematical community, with the corresponding possibility that there remain some unnoticed errors.


title: Shing-Tung Yau

text: Yau has made a number of major research contributions, centered on differential geometry and its appearance in other fields of mathematics and science. In addition to his research, Yau has compiled influential sets of open problems in differential geometry, including both well-known old conjectures with new proposals and problems. Two of Yau's most widely cited problem lists from the 1980s have been updated with notes on progress as of 2014. Particularly well-known are a conjecture on existence of minimal hypersurfaces and on the spectral geometry of minimal hypersurfaces.


title: Shing-Tung Yau

text: In 1978, by studying the complex Monge–Ampère equation, Yau resolved the Calabi conjecture, which had been posed by Eugenio Calabi in 1954. As a special case, this showed that Kähler-Einstein metrics exist on any closed Kähler manifold whose first Chern class is nonpositive. Yau's method adapted earlier work of Calabi, Jürgen Moser, and Aleksei Pogorelov, developed for quasilinear elliptic partial differential equations and the real Monge–Ampère equation, to the setting of the complex Monge–Ampère equation.


title: Shing-Tung Yau

text: The understanding of the Calabi conjecture in the noncompact setting is less definitive. Gang Tian and Yau extended Yau's analysis of the complex Monge−Ampère equation to the noncompact setting, where the use of cutoff functions and corresponding integral estimates necessitated the conditional assumption of certain controlled geometry near infinity. This reduces the problem to the question of existence of Kähler metrics with such asymptotic properties; they obtained such metrics for certain smooth quasi-projective complex varieties. They later extended their work to allow orbifold singularities. With Brian Greene, Alfred Shapere, and Cumrun Vafa, Yau introduced an ansatz for a Kähler metric on the set of regular points of certain surjective holomorphic maps, with Ricci curvature approximately zero. They were able to apply the Tian−Yau existence theorem to construct a Kähler metric which is exactly Ricci-flat. The Greene−Shapere−Vafa−Yau ansatz and its natural generalization, now known as a "semi-flat metric", has become important in several analyses of problems in Kähler geometry.


title: Shing-Tung Yau

text: The positive energy theorem, obtained by Yau in collaboration with his former doctoral student Richard Schoen, can be described in physical terms:


title: Shing-Tung Yau

text: However, it is a precise theorem of differential geometry and geometric analysis, in which physical systems are modeled by Riemannian manifolds with nonnegativity of a certain generalized scalar curvature. As such, Schoen and Yau's approach originated in their study of Riemannian manifolds of positive scalar curvature, which is of interest in and of itself. The starting point of Schoen and Yau's analysis is their identification of a simple but novel way of inserting the Gauss–Codazzi equations into the second variation formula for the area of a stable minimal hypersurface of a three-dimensional Riemannian manifold. The Gauss–Bonnet theorem then highly constrains the possible topology of such a surface when the ambient manifold has positive scalar curvature.


title: Shing-Tung Yau

text: Schoen and Yau exploited this observation by finding novel constructions of stable minimal hypersurfaces with various controlled properties. Some of their existence results were developed simultaneously with similar results of Jonathan Sacks and Karen Uhlenbeck, using different techniques. Their fundamental result is on the existence of minimal immersions with prescribed topological behavior. As a consequence of their calculation with the Gauss–Bonnet theorem, they were able to conclude that certain topologically distinguished three-dimensional manifolds cannot have any Riemannian metric of nonnegative scalar curvature.


title: Shing-Tung Yau

text: Schoen and Yau then adapted their work to the setting of certain Riemannian asymptotically flat initial data sets in general relativity. They proved that negativity of the mass would allow one to invoke the Plateau problem to construct stable minimal surfaces which are geodesically complete. A noncompact analogue of their calculation with the Gauss–Bonnet theorem then provides a logical contradiction to the negativity of mass. As such, they were able to prove the positive mass theorem in the special case of their Riemannian initial data sets.


title: Shing-Tung Yau

text: Schoen and Yau extended this to the full Lorentzian formulation of the positive mass theorem by studying a partial differential equation proposed by Pong-Soo Jang. They proved that solutions to the Jang equation exist away from the apparent horizons of black holes, at which solutions can diverge to infinity. By relating the geometry of a Lorentzian initial data set to the geometry of the graph of such a solution to the Jang equation, interpreting the latter as a Riemannian initial data set, Schoen and Yau proved the full positive energy theorem. Furthermore, by reverse-engineering their analysis of the Jang equation, they were able to establish that any sufficient concentration of energy in general relativity must be accompanied by an apparent horizon.


title: Shing-Tung Yau

text: Due to the use of the Gauss–Bonnet theorem, these results were originally restricted to the case of three-dimensional Riemannian manifolds and four-dimensional Lorentzian manifolds. Schoen and Yau established an induction on dimension by constructing Riemannian metrics of positive scalar curvature on minimal hypersurfaces of Riemannian manifolds which have positive scalar curvature. Such minimal hypersurfaces, which were constructed by means of geometric measure theory by Frederick Almgren and Herbert Federer, are generally not smooth in large dimensions, so these methods only directly apply up for Riemannian manifolds of dimension less than eight. Without any dimensional restriction, Schoen and Yau proved the positive mass theorem in the class of locally conformally flat manifolds. In 2017, Schoen and Yau published a preprint claiming to resolve these difficulties, thereby proving the induction without dimensional restriction and verifying the Riemannian positive mass theorem in arbitrary dimension.


title: Shing-Tung Yau

text: Gerhard Huisken and Yau made a further study of the asymptotic region of Riemannian manifolds with strictly positive mass. Huisken had earlier initiated the study of volume-preserving mean curvature flow of hypersurfaces of Euclidean space. Huisken and Yau adapted his work to the Riemannian setting, proving a long-time existence and convergence theorem for the flow. As a corollary, they established a new geometric feature of positive-mass manifolds, which is that their asymptotic regions are foliated by surfaces of constant mean curvature.


title: Shing-Tung Yau

text: Traditionally, the maximum principle technique is only applied directly on compact spaces, as maxima are then guaranteed to exist. In 1967, Hideki Omori found a novel maximum principle which applies on noncompact Riemannian manifolds whose sectional curvatures are bounded below. It is trivial that "approximate" maxima exist; Omori additionally proved the existence of approximate maxima where the values of the gradient and second derivatives are suitably controlled. Yau partially extended Omori's result to require only a lower bound on Ricci curvature; the result is known as the Omori−Yau maximum principle. Such generality is useful due to the appearance of Ricci curvature in the Bochner formula, where a lower bound is also typically used in algebraic manipulations. In addition to giving a very simple proof of the principle itself, Shiu-Yuen Cheng and Yau were able to show that the Ricci curvature assumption in the Omori−Yau maximum principle can be replaced by the assumption of the existence of cutoff functions with certain controllable geometry.


title: Shing-Tung Yau

text: Yau was able to directly apply the Omori−Yau principle to generalize the classical Schwarz−Pick lemma of complex analysis. Lars Ahlfors, among others, had previously generalized the lemma to the setting of Riemann surfaces. With his methods, Yau was able to consider the setting of a mapping from a complete Kähler manifold (with a lower bound on Ricci curvature) to a Hermitian manifold with holomorphic bisectional curvature bounded above by a negative number.


title: Shing-Tung Yau

text: Cheng and Yau extensively used their variant of the Omori−Yau principle to find Kähler−Einstein metrics on noncompact Kähler manifolds, under an ansatz developed by Charles Fefferman. The estimates involved in the method of continuity were not as difficult as in Yau's earlier work on the Calabi conjecture, due to the fact that Cheng and Yau only considered Kähler−Einstein metrics with negative scalar curvature. The more subtle question, where Fefferman's earlier work became important, is to do with geodesic completeness. In particular, Cheng and Yau were able to find complete Kähler-Einstein metrics of negative scalar curvature on any bounded, smooth, and strictly pseudoconvex subset of complex Euclidean space. These can be thought of as complex geometric analogues of the Poincaré ball model of hyperbolic space.


title: Shing-Tung Yau

text: Yau's original application of the Omori−Yau maximum principle was to establish gradient estimates for a number of second-order elliptic partial differential equations. Given a function on a complete and smooth Riemannian manifold which satisfies various conditions relating the Laplacian to the function and gradient values, Yau applied the maximum principle to various complicated composite expressions to control the size of the gradient. Although the algebraic manipulations involved are complex, the conceptual form of Yau's proof is strikingly simple.


title: Shing-Tung Yau

text: Yau's novel gradient estimates have come to be called "differential Harnack inequalities" since they can be integrated along arbitrary paths in to recover inequalities which are of the form of the classical Harnack inequalities, directly comparing the values of a solution to a differential equation at two different input points. By making use of Calabi's study of the distance function on a Riemannian manifold, Yau and Shiu-Yuen Cheng gave a powerful localization of Yau's gradient estimates, using the same methods to simplify the proof of the Omori−Yau maximum principle. Such estimates are widely quoted in the particular case of harmonic functions on a Riemannian manifold, although Yau and Cheng−Yau's original results cover more general scenarios.


title: Shing-Tung Yau

text: In 1986, Yau and Peter Li made use of the same methods to study parabolic partial differential equations on Riemannian manifolds. Richard Hamilton generalized their results in certain geometric settings to matrix inequalities. Analogues of the Li−Yau and Hamilton−Li−Yau inequalities are of great importance in the theory of Ricci flow, where Hamilton proved a matrix differential Harnack inequality for the curvature operator of certain Ricci flows, and Grigori Perelman proved a differential Harnack inequality for the solutions of a backwards heat equation coupled with a Ricci flow.


title: Shing-Tung Yau

text: Cheng and Yau were able to use their differential Harnack estimates to show that, under certain geometric conditions, closed submanifolds of complete Riemannian or pseudo-Riemannian spaces are themselves complete. For instance, they showed that if is a spacelike hypersurface of Minkowski space which is topologically closed and has constant mean curvature, then the induced Riemannian metric on is complete. Analogously, they showed that if is an affine hypersphere of affine space which is topologically closed, then the induced affine metric on is complete. Such results are achieved by deriving a differential Harnack inequality for the (squared) distance function to a given point and integrating along intrinsically defined paths.


title: Shing-Tung Yau

text: In 1985, Simon Donaldson showed that, over a nonsingular projective variety of complex dimension two, a holomorphic vector bundle admits a hermitian Yang–Mills connection if and only if the bundle is stable. A result of Yau and Karen Uhlenbeck generalized Donaldson's result to allow a compact Kähler manifold of any dimension. The Uhlenbeck–Yau method relied upon elliptic partial differential equations while Donaldson's used parabolic partial differential equations, roughly in parallel to Eells and Sampson's epochal work on harmonic maps. The results of Donaldson and Uhlenbeck–Yau have since been extended by other authors. Uhlenbeck and Yau's article is important in giving a clear reason that stability of the holomorphic vector bundle can be related to the analytic methods used in constructing a hermitian Yang–Mills connection. The essential mechanism is that if an approximating sequence of hermitian connections fails to converge to the required Yang–Mills connection, then they can be rescaled to converge to a subsheaf which can be verified to be destabilizing by Chern–Weil theory.


title: Shing-Tung Yau

text: Like the Calabi–Yau theorem, the Donaldson–Uhlenbeck–Yau theorem is of interest in theoretical physics. In the interest of an appropriately general formulation of supersymmetry, Andrew Strominger included the hermitian Yang–Mills condition as part of his Strominger system, a proposal for the extension of the Calabi−Yau condition to non-Kähler manifolds. Ji-Xiang Fu and Yau introduced an ansatz for the solution of Strominger's system on certain three-dimensional complex manifolds, reducing the problem to a complex Monge−Ampère equation, which they solved.


title: Shing-Tung Yau

text: Yau's solution of the Calabi conjecture had given a reasonably complete answer to the question of how Kähler metrics on compact complex manifolds of nonpositive first Chern class can be deformed into Kähler–Einstein metrics. Akito Futaki showed that the existence of holomorphic vector fields can act as an obstruction to the direct extension of these results to the case when the complex manifold has positive first Chern class. A proposal of Calabi's suggested that Kähler–Einstein metrics exist on any compact Kähler manifolds with positive first Chern class which admit no holomorphic vector fields. During the 1980s, Yau and others came to understand that this criterion could not be sufficient. Inspired by the Donaldson−Uhlenbeck−Yau theorem, Yau proposed that the existence of Kähler–Einstein metrics must be linked to stability of the complex manifold in the sense of geometric invariant theory, with the idea of studying holomorphic vector fields along projective embeddings, rather than holomorphic vector fields on the manifold itself. Subsequent research of Gang Tian and Simon Donaldson refined this conjecture, which became known as the Yau–Tian–Donaldson conjecture relating Kähler–Einstein metrics and K-stability. In 2019, Xiuxiong Chen, Donaldson, and Song Sun were awarded the Oswald Veblen prize for resolution of the conjecture.


title: Shing-Tung Yau

text: In 1982, Li and Yau resolved the Willmore conjecture in the non-embedded case. More precisely, they established that, given any smooth immersion of a closed surface in the 3-sphere which fails to be an embedding, the Willmore energy is bounded below by 8π. This is complemented by a 2012 result of Fernando Marques and André Neves, which says that in the alternative case of a smooth embedding of the 2-dimensional torus , the Willmore energy is bounded below by 2π. Together, these results comprise the full Willmore conjecture, as originally formulated by Thomas Willmore in 1965. Although their assumptions and conclusions are quite similar, the methods of Li−Yau and Marques−Neves are distinct. Nonetheless, they both rely on structurally similar minimax schemes. Marques and Neves made novel use of the Almgren–Pitts min-max theory of the area functional from geometric measure theory; Li and Yau's approach depended on their new "conformal invariant", which is a min-max quantity based on the Dirichlet energy. The main work of their article is devoted to relating their conformal invariant to other geometric quantities.


title: Shing-Tung Yau

text: William Meeks and Yau produced some foundational results on minimal surfaces in three-dimensional manifolds, revisiting points left open by older work of Jesse Douglas and Charles Morrey. Following these foundations, Meeks, Leon Simon, and Yau gave a number of fundamental results on surfaces in three-dimensional Riemannian manifolds which minimize area within their homology class. They were able to give a number of striking applications. For example, they showed that if is an orientable 3-manifold such that every smooth embedding of a 2-sphere can be extended to a smooth embedding of the unit ball, then the same is true of any covering space of . Interestingly, Meeks-Simon-Yau's paper and Hamilton's foundational paper on Ricci flow, published in the same year, have a result in common, obtained by very distinct methods: any simply-connected compact 3-dimensional Riemannian manifold with positive Ricci curvature is diffeomorphic to the 3-sphere.


title: Shing-Tung Yau

text: In the geometry of submanifolds, both the extrinsic and intrinsic geometries are significant. These are reflected by the intrinsic Riemannian metric and the second fundamental form. Many geometers have considered the phenomena which arise from restricting these data to some form of constancy. This includes as special cases the problems of minimal surfaces, constant mean curvature, and submanifolds whose metric has constant scalar curvature.


title: Shing-Tung Yau

text: Outside of the setting of submanifold rigidity problems, Yau was able to adapt Jürgen Moser's method of proving Caccioppoli inequalities, thereby proving new rigidity results for functions on complete Riemannian manifolds. A particularly famous result of his says that a subharmonic function cannot be both positive and L integrable unless it is constant. Similarly, on a complete Kähler manifold, a holomorphic function cannot be L integrable unless it is constant.


title: Shing-Tung Yau

text: The Minkowski problem of classical differential geometry can be viewed as the problem of prescribing Gaussian curvature. In the 1950s, Louis Nirenberg and Aleksei Pogorelov resolved the problem for two-dimensional surfaces, making use of recent progress on the Monge–Ampère equation for two-dimensional domains. By the 1970s, higher-dimensional understanding of the Monge–Ampère equation was still lacking. In 1976, Shiu-Yuen Cheng and Yau resolved the Minkowski problem in general dimensions via the method of continuity, making use of fully geometric estimates instead of the theory of the Monge–Ampère equation.


title: Shing-Tung Yau

text: As a consequence of their resolution of the Minkowski problem, Cheng and Yau were able to make progress on the understanding of the Monge–Ampère equation. The key observation is that the Legendre transform of a solution of the Monge–Ampère equation has its graph's Gaussian curvature prescribed by a simple formula depending on the "right-hand side" of the Monge–Ampère equation. As a consequence, they were able to prove the general solvability of the Dirichlet problem for the Monge–Ampère equation, which at the time had been a major open question except for two-dimensional domains.


title: Shing-Tung Yau

text: Cheng and Yau's papers followed some ideas presented in 1971 by Pogorelov, although his publicly available works (at the time of Cheng and Yau's work) had lacked some significant detail. Pogorelov also published a more detailed version of his original ideas, and the resolutions of the problems are commonly attributed to both Cheng–Yau and Pogorelov. The approaches of Cheng−Yau and Pogorelov are no longer commonly seen in the literature on the Monge–Ampère equation, as other authors, notably Luis Caffarelli, Nirenberg, and Joel Spruck, have developed direct techniques which yield more powerful results, and which do not require the auxiliary use of the Minkowski problem.


title: Shing-Tung Yau

text: Affine spheres are naturally described by solutions of certain Monge–Ampère equations, so that their full understanding is significantly more complicated than that of Euclidean spheres, the latter not being based on partial differential equations. In the "parabolic" case, affine spheres were completely classified as paraboloids by successive work of Konrad Jörgens, Eugenio Calabi, and Pogorelov. The "elliptic" affine spheres were identified as ellipsoids by Calabi. The "hyperbolic" affine spheres exhibit more complicated phenomena. Cheng and Yau proved that they are asymptotic to convex cones, and conversely that every (uniformly) convex cone corresponds in such a way to some hyperbolic affine sphere. They were also able to provide new proofs of the previous classifications of Calabi and Jörgens–Calabi–Pogorelov.


title: Shing-Tung Yau

text: A Calabi–Yau manifold is a compact Kähler manifold which is Ricci-flat; as a special case of Yau's verification of the Calabi conjecture, such manifolds are known to exist. Mirror symmetry, which is a proposal developed by theoretical physicists dating from the late 1980s, postulates that Calabi−Yau manifolds of complex dimension three can be grouped into pairs which share certain characteristics, such as Euler and Hodge numbers. Based on this conjectural picture, the physicists Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parkes proposed a formula of enumerative geometry which encodes the number of rational curves of any fixed degree in a general quintic hypersurface of four-dimensional complex projective space. Bong Lian, Kefeng Liu, and Yau gave a rigorous proof that this formula holds. A year earlier, Alexander Givental had published a proof of the mirror formulas; according to Lian, Liu, and Yau, the details of his proof were only successfully filled in following their own publication. The proofs of Givental and Lian–Liu–Yau have some overlap but are distinct approaches to the problem, and each have since been given textbook expositions.


title: Shing-Tung Yau

text: The works of Givental and of Lian−Liu−Yau confirm a prediction made by the more fundamental mirror symmetry conjecture of how three-dimensional Calabi−Yau manifolds can be paired off. However, their works do not logically depend on the conjecture itself, and so have no immediate bearing on its validity. With Andrew Strominger and Eric Zaslow, Yau proposed a geometric picture of how mirror symmetry might be systematically understood and proved to be true. Their idea is that a Calabi−Yau manifold with complex dimension three should be foliated by "special Lagrangian" tori, which are certain types of three-dimensional minimal submanifolds of the six-dimensional Riemannian manifold underlying the Calabi−Yau structure. Mirror manifolds would then be characterized, in terms of this conjectural structure, by having "dual" foliations. The Strominger−Yau−Zaslow (SYZ) proposal has been modified and developed in various ways since 1996. The conceptual picture that it provides has had a significant influence in the study of mirror symmetry, and research on its various aspects is currently an active field. It can be contrasted with the alternative homological mirror symmetry proposal by Maxim Kontsevich. The viewpoint of the SYZ conjecture is on geometric phenomena in Calabi–Yau spaces, while Kontsevich's conjecture abstracts the problem to deal with purely algebraic structures and category theory.


title: Shing-Tung Yau

text: In one of Yau's earliest papers, written with Blaine Lawson, a number of fundamental results were found on the topology of closed Riemannian manifolds with nonpositive curvature. Their "flat torus theorem" characterizes the existence of a flat and totally geodesic immersed torus in terms of the algebra of the fundamental group. The "splitting theorem" says that the splitting of the fundamental group as a maximally noncommutative direct product implies the isometric splitting of the manifold itself. Similar results were obtained at the same time by Detlef Gromoll and Joseph Wolf. Their results have been extended to the broader context of isometric group actions on metric spaces of nonpositive curvature.


title: Shing-Tung Yau

text: Jeff Cheeger and Yau studied the heat kernel on a Riemannian manifold. They established the special case of Riemannian metrics for which geodesic spheres have constant mean curvature, which they proved to be characterized by radial symmetry of the heat kernel. Specializing to rotationally symmetric metrics, they used the exponential map to transplant the heat kernel to a geodesic ball on a general Riemannian manifold. Under the assumption that the symmetric "model" space under-estimates the Ricci curvature of the manifold itself, they carried out a direct calculation showing that the resulting function is a subsolution of the heat equation. As a consequence, they obtained a lower estimate of the heat kernel on a general Riemannian manifold in terms of lower bounds on its Ricci curvature. In the special case of nonnegative Ricci curvature, Peter Li and Yau were able to use their gradient estimates to amplify and improve the Cheeger−Yau estimate.


title: Shing-Tung Yau

text: A well-known result of Yau's, obtained independently by Calabi, shows that any noncompact Riemannian manifold of nonnegative Ricci curvature must have volume growth of at least a linear rate. A second proof, using the Bishop–Gromov inequality instead of function theory, was later found by Cheeger, Mikhael Gromov, and Michael Taylor.


title: Shing-Tung Yau

text: Given a smooth compact Riemannian manifold, with or without boundary, spectral geometry studies the eigenvalues of the Laplace–Beltrami operator, which in the case that the manifold has a boundary is coupled with a choice of boundary condition, usually Dirichlet or Neumann conditions. Paul Yang and Yau showed that in the case of a closed two-dimensional manifold, the first eigenvalue is bounded above by an explicit formula depending only on the genus and volume of the manifold. Earlier, Yau had modified Jeff Cheeger's analysis of the Cheeger constant so as to be able to estimate the first eigenvalue from below in terms of geometric data.


title: Shing-Tung Yau

text: In the 1910s, Hermann Weyl showed that, in the case of Dirichlet boundary conditions on a smooth and bounded open subset of the plane, the eigenvalues have an asymptotic behavior which is dictated entirely by the area contained in the region. His result is known as Weyl's law. In 1960, George Pólya conjectured that the Weyl law actually gives control of each individual eigenvalue, and not only of their asymptotic distribution. Li and Yau proved a weakened version of Pólya's conjecture, obtaining control of the "averages" of the eigenvalues by the expression in the Weyl law.


title: Shing-Tung Yau

text: In 1980, Li and Yau identified a number of new inequalities for Laplace–Beltrami eigenvalues, all based on the maximum principle and the differential Harnack estimates as pioneered five years earlier by Yau and Cheng−Yau. Their result on lower bounds based on geometric data is particularly well-known, and was the first of its kind to not require any conditional assumptions. Around the same time, a similar inequality was obtained by isoperimetric methods by Mikhael Gromov, although his result is weaker than Li and Yau's. In collaboration with Isadore Singer, Bun Wong, and Shing-Toung Yau, Yau used the Li–Yau methodology to establish a gradient estimate for the quotient of the first two eigenfunctions. Analogously to Yau's integration of gradient estimates to find Harnack inequalities, they were able to integrate their gradient estimate to obtain control of the "fundamental gap," which is the difference between the first two eigenvalues. The work of Singer–Wong–Yau–Yau initiated a series of works by various authors in which new estimates on the fundamental gap were found and improved.


title: Shing-Tung Yau

text: In 1982, Yau identified fourteen problems of interest in spectral geometry, including the above Pólya conjecture. A particular conjecture of Yau's, on the control of the size of level sets of eigenfunctions by the value of the corresponding eigenvalue, was resolved by Alexander Logunov and Eugenia Malinnikova, who were awarded the 2017 Clay Research Award in part for their work.


title: Shing-Tung Yau

text: Xianfeng Gu and Yau considered the numerical computation of conformal maps between two-dimensional manifolds (presented as discretized meshes), and in particular the computation of uniformizing maps as predicted by the uniformization theorem. In the case of genus-zero surfaces, a map is conformal if and only if it is harmonic, and so Gu and Yau are able to compute conformal maps by direct minimization of a discretized Dirichlet energy. In the case of higher genus, the uniformizing maps are computed from their gradients, as determined from the Hodge theory of closed and harmonic 1-forms. The main work is thus to identify numerically effective discretizations of the classical theory. Their approach is sufficiently flexible to deal with general surfaces with boundary. With Tony Chan, Paul Thompson, and Yalin Wang, Gu and Yau applied their work to the problem of matching two brain surfaces, which is an important issue in medical imaging. In the most-relevant genus-zero case, conformal maps are only well-defined up to the action of the Möbius group. By further optimizing a Dirichlet-type energy which measures the mismatch of brain landmarks such as the central sulcus, they obtained mappings which are well-defined by such neurological features.


title: Shing-Tung Yau

text: In the field of graph theory, Fan Chung and Yau extensively developed analogues of notions and results from Riemannian geometry. These results on differential Harnack inequalities, Sobolev inequalities, and heat kernel analysis, found partly in collaboration with Ronald Graham and Alexander Grigor'yan, were later written into textbook form as the last few chapters of her well-known book "Spectral Graph Theory". Later, they introduced a Green's function as defined for graphs, amounting to a pseudo-inverse of the graph Laplacian. Their work is naturally applicable to the study of hitting times for random walks and related topics.


title: Shing-Tung Yau

text: In the interest of finding general graph-theoretic contexts for their results, Chung and Yau introduced a notion of Ricci-flatness of a graph. A more flexible notion of Ricci curvature, dealing with Markov chains on metric spaces, was later introduced by Yann Ollivier. Yong Lin, Linyuan Lu, and Yau developed some of the basic theory of Ollivier's definition in the special context of graph theory, considering for instance the Ricci curvature of Erdös–Rényi random graphs. Lin and Yau also considered the "curvature–dimension inequalities" introduced earlier by Dominique Bakry and Michel Émery, relating it and Ollivier's curvature to Chung–Yau's notion of Ricci-flatness. They were further able to prove general lower bounds on Bakry–Émery and Ollivier's curvatures in the case of locally finite graphs.


title: Shing-Tung Yau

text: Yau has received honorary professorships from many Chinese universities, including Hunan Normal University, Peking University, Nankai University, and Tsinghua University. He has honorary degrees from many international universities, including Harvard University, Chinese University of Hong Kong, and University of Waterloo. He is a foreign member of the National Academies of Sciences of China, India, and Russia.


title: Shing-Tung Yau

text: Yau is the author of over five hundred articles. The following, among the most cited, are surveyed above:


title: Centrosome

text: In cell biology, the centrosome (Latin centrum 'center' + Greek sōma 'body') (archaically cytocentre) is an organelle that serves as the main microtubule organizing center (MTOC) of the animal cell, as well as a regulator of cell-cycle progression. The centrosome provides structure for the cell. The centrosome is thought to have evolved only in the metazoan lineage of eukaryotic cells. Fungi and plants lack centrosomes and therefore use other structures to organize their microtubules. Although the centrosome has a key role in efficient mitosis in animal cells, it is not essential in certain fly and flatworm species.


title: Centrosome

text: Centrosomes are composed of two centrioles arranged at right angles to each other, and surrounded by a dense, highly structured mass of protein termed the pericentriolar material (PCM). The PCM contains proteins responsible for microtubule nucleation and anchoring — including γ-tubulin, pericentrin and ninein. In general, each centriole of the centrosome is based on a nine-triplet microtubule assembled in a cartwheel structure, and contains centrin, cenexin and tektin.


title: Centrosome

text: In many cell types, the centrosome is replaced by a cilium during cellular differentiation. However, once the cell starts to divide, the cilium is replaced again by the centrosome.


title: Centrosome

text: The centrosome was discovered jointly by Walther Flemming in 1875 and Edouard Van Beneden in 1876, and later described and named in 1888 by Theodor Boveri.


title: Centrosome

text: Centrosomes are associated with the nuclear membrane during the prophase stage of the cell cycle. During mitosis, the nuclear membrane breaks down, and the centrosome-nucleated microtubules can interact with the chromosomes to build the mitotic spindle.


title: Centrosome

text: The mother centriole, the older of the two in the centriole pair, also has a central role in making cilia and flagella.


title: Centrosome

text: The centrosome is copied only once per cell cycle, so that each daughter cell inherits one centrosome, containing two structures called centrioles. The centrosome replicates during the S phase of the cell cycle. During the prophase in the process of cell division called mitosis, the centrosomes migrate to opposite poles of the cell. The mitotic spindle then forms between the two centrosomes. Upon division, each daughter cell receives one centrosome. Aberrant numbers of centrosomes in a cell have been associated with cancer. Doubling of a centrosome is similar to DNA replication in two respects: the semiconservative nature of the process and the action of CDK2 as a regulator of the process. But the processes are essentially different in that centrosome doubling does not occur by template reading and assembly. The mother centriole just aids in the accumulation of materials required for the assembly of the daughter centriole.


title: Centrosome

text: Centrioles, however, are not required for the progression of mitosis. When the centrioles are irradiated by a laser, mitosis proceeds normally with a morphologically normal spindle. Moreover, development of the fruit fly "Drosophila" is largely normal when centrioles are absent due to a mutation in a gene required for their duplication. In the absence of the centrioles, the microtubules of the spindle are focused by motors, allowing the formation of a bipolar spindle. Many cells can completely undergo interphase without centrioles.


title: Centrosome

text: Unlike centrioles, centrosomes are required for survival of the organism. Cells without centrosomes lack radial arrays of astral microtubules. They are also defective in spindle positioning and in the ability to establish a central localization site in cytokinesis. The function of centrosomes in this context is hypothesized to ensure the fidelity of cell division, because it greatly increases the efficacy. Some cell types arrest in the following cell cycle when centrosomes are absent. This is not a universal phenomenon.


title: Centrosome

text: When the nematode "C. elegans" egg is fertilized, the sperm delivers a pair of centrioles. These centrioles will form the centrosomes, which will direct the first cell division of the zygote, and this will determine its polarity. It's not yet clear whether the role of the centrosome in polarity determination is microtubule-dependent or independent.


title: Centrosome

text: In human reproduction, the sperm supplies the centriole that creates the centrosome and microtubule system of the zygote.


title: Centrosome

text: Theodor Boveri, in 1914, described centrosome aberrations in cancer cells. This initial observation was subsequently extended to many types of human tumors. Centrosome alterations in cancer can be divided in two subgroups — i.e., structural or numeric aberrations — yet both can be found simultaneously in a tumor.


title: Centrosome

text: Usually, structural aberrations appear due to uncontrolled expression of centrosome components, or due to post-translational modifications (such as phosphorylations) that are not adequate for the components. These modifications may produce variations in centrosome size (usually too large, due to an excess of pericentriolar material). In addition, because centrosomal proteins have a tendency to form aggregates, centrosome-related bodies (CRBs) are often observed in ectopic places. Both enlarged centrosomes and CRBs are similar to the centrosomal structures observed in tumors. Even more, these structures can be induced in culture cells by overexpression of specific centrosomal proteins, such as CNap-1 or Nlp. These structures may look very similar, yet detailed studies reveal that they may present very different properties, depending on their proteic composition. For instance, their capacity to incorporate γ-TuRC complexes (see also: γ-tubulin) can be very variable, and so their capacity to nucleate microtubules therefore affects the shape, polarity and motility of implicated tumor cells in different ways.


title: Centrosome

text: The presence of an inadequate number of centrosomes is very often linked to the appearance of genome instability and the loss of tissue differentiation. However, the method to count the centrosome number (with two centrioles to each centrosome) is often not very precise, because it is frequently assessed using fluorescence microscopy, which does not have high enough optical resolution to resolve centrioles that are very close to each other. Nevertheless, it is clear that the presence of an excess of centrosomes is a common event in human tumors. It has been observed that loss of the tumor-suppressor p53 produces superfluous centrosomes, as well as deregulating other proteins implicated in cancer formation in humans, such as BRCA1 and BRCA2. (For references, see .) An excess of centrosomes can be generated by very different mechanisms: specific reduplication of the centrosome, cytokinesis failure during cell division (generating an increase in chromosome number), cell fusion (such as in cases of infection by specific viruses) or "de novo" generation of centrosomes. At this point, there is insufficient information to know how prevalent these mechanisms are "in vivo", but it is possible that the increase in centrosome numbers due to a failure during cell division might be more frequent than appreciated, because many "primary" defects in one cell (deregulation of the cell cycle, defective DNA or chromatin metabolism, failure in the spindle checkpoint, etc.) would generate a failure in cell division, an increase in ploidy and an increase in centrosome numbers as a "secondary" effect.


title: Centrosome

text: The evolutionary history of the centrosome and the centriole has been traced for some of the signature genes — e.g., the centrins. Centrins participate in calcium signaling and are required for centriole duplication. There exist two main subfamilies of centrins, both of which are present in the early-branching eukaryote "Giardia intestinalis". Centrins have therefore been present in the common ancestor of eukaryotes. Conversely, they have no recognizable homologs in archea and bacteria and are thus part of the "eukaryotic signature genes". Although there are studies on the evolution of the centrins and centrioles, no studies have been published on the evolution of the pericentriolar material.


title: Centrosome

text: It is evident that some parts of the centrosome are highly diverged in the model species "Drosophila melanogaster" and "Caenorhabditis elegans". For example, both species have lost one of the centrin subfamilies that are usually associated with centriole duplication. "Drosophila melanogaster" mutants that lack centrosomes can even develop to morphologically normal adult flies, which then die shortly after birth because their sensory neurons lack cilia. Thus, these flies have evolved functionally redundant machinery, which is independent of the centrosomes.


title: Centrosome

text: Research in 2006 indicated that centrosomes from Atlantic surf clam eggs contain RNA sequences. The sequences identified were found in "few to no" other places in the cell, and do not appear in existing genome databases. One identified RNA sequence contains a putative RNA polymerase, leading to the hypothesis of an RNA-based genome within the centrosome. However, subsequent research has shown that centrosome do not contain their own DNA-based genomes. While it was confirmed that RNA molecules associate with centrosomes, the sequences have still been found within the nucleus. Furthermore, centrosomes can form "de novo" after having been removed (e.g., by laser irradiation) from normal cells.


title: Ross Douthat

text: Ross Gregory Douthat (born 1979) is an American political analyst, blogger, author and "New York Times" columnist. He was a senior editor of "The Atlantic". He has written on a variety of topics, including the state of Christianity in America and "sustainable decadence" in contemporary society.


title: Ross Douthat

text: Ross Gregory Douthat was born in 1979 in San Francisco, California, and grew up in New Haven, Connecticut. As an adolescent, Douthat converted to Pentecostalism and then, with the rest of his family, to Catholicism.


title: Ross Douthat

text: His mother is a writer. His great-grandfather was the poet and Governor Charles Wilbert Snow of Connecticut. His father, Charles Douthat, is a partner in a New Haven law firm and a poet. In 2007, Douthat married Abigail Tucker, a reporter for "The Baltimore Sun" and a writer for "Smithsonian". He and his family live in New Haven, Connecticut.


title: Ross Douthat

text: Douthat has written that he suffers from chronic Lyme disease, a diagnosis that is unrecognized by mainstream medicine. His symptoms began in 2015, soon after he and his family had moved to Connecticut. This is the subject of his book "The Deep Places".


title: Ross Douthat

text: Douthat attended Hamden Hall, a private high school in Hamden, Connecticut. Douthat graduated "magna cum laude" with a Bachelor of Arts from Harvard University in 2002, where he was also elected to Phi Beta Kappa. While there he contributed to "The Harvard Crimson" and edited "The Harvard Salient".


title: Ross Douthat

text: Douthat is a regular columnist for "The New York Times". In April 2009, he became the youngest regular op-ed writer in "The New York Times" after replacing Bill Kristol as a conservative voice on the "Times" editorial page.


title: Ross Douthat

text: Before joining "The New York Times", he was a senior editor at "The Atlantic". He has published books on the decline of religion in American society, the role of Harvard University in creating an American ruling class and other topics related to religion, politics and society. His book "Grand New Party" (2008), which he co-wrote with Reihan Salam, was described by "New York Times" commentator David Brooks as the "best single roadmap of where the Republican Party should and is likely to head." Douthat's "The Decadent Society: How We Became the Victims of Our Own Success" (2020) received positive reviews in "The New York Times" and "National Review". Douthat frequently appeared on the video debate site Bloggingheads.tv until 2012.


title: Ross Douthat

text: Douthat has written in support of banning abortion, arguing that science shows that a zygote (a fertilized egg) is a distinct human and that destroying it would be to kill a human.


title: Presta valve

text: The Presta valve (also French valve (FV) or Sclaverand valve) is a tire valve commonly found in high pressure road style and some mountain bicycle inner tubes. It comprises an outer valve stem and an inner valve body. A lock nut to secure the stem at the wheel rim and a valve cap may also be present.


title: Presta valve

text: The " Sclaverand valve" was invented by Frenchman Etienne Sclaverand and is often referred to as the "French valve". Today it is also known as "Presta valve". "Presta" or "presto" stands in the Romance languages for "fast, hurry, immediately".


title: Presta valve

text: The outer valve stem is manufactured in various lengths for different applications and has a narrower diameter () than Dunlop and Schrader valves (). The weakest point of a bicycle rim is usually the hole for the valve stem. The smaller hole for a Presta valve makes it possible to have extremely narrow wheels while maintaining sufficient strength in the wheel.


title: Presta valve

text: The air pressure in an inflated tire holds the inner valve body shut. A small screw and captive nut on the top of the valve body permits the valve to be screwed shut and ensure that it remains tightly closed.


title: Presta valve

text: The nut must be unscrewed to permit airflow in either direction. The screw remains captive on the valve body even when unscrewed fully; it is tightened again after the tire is inflated and the pump removed. The valve cap protects the valve body, keeps dirt and mud out of the mechanism, and also prevents the valve from damaging the tube when it is rolled for storage, but is not necessary to prevent pressure loss.


title: Presta valve

text: The holes in rims sized for Presta valves can be enlarged to accommodate the wider Schrader valves, which can structurally weaken the rim. Conversely, when a Presta valve is fitted into the larger Schrader rim hole, grommets or reducers are sometimes used to take up the extra space.


title: Presta valve

text: The standard Presta valve has an external thread. An adapter can be fitted onto this external thread to permit the Presta valve to be connected to a pump with a Schrader chuck. The same adapter, because of a coincidence of thread sizes, may be able to convert a Schrader pump into one that can connect to flexible adapters of either kind.


title: Presta valve

text: Presta valves with removable cores may be used with a tubeless setup to add sealant through the valve. Sealant may also be added by pouring it directly into the tire.


title: Presta valve

text: Valve extenders can be used to lengthen shorter Presta valves to accommodate deeper and thicker rims, such as those on aerodynamic race wheels. There are two variants of valve extenders depending on whether the Presta core is removable.


title: Presta valve

text: The valve threads for Presta valves follow the ISO 4570 standard. The external threads at the tip of both "threaded" and "unthreaded" Presta valves are 5V2 (#12-24TPI), which measures out to 5.2×1.058 mm, the same thread size as the tip of a Dunlop valve. The external threads on the main body of "threaded" Presta valves are 6V1, which measures 6×0.80 mm.


title: Contents of the Voyager Golden Record

text: The Voyager Golden Record contains 116 images and a variety of sounds. The items for the record, which is carried on both the "Voyager 1" and "Voyager 2" spacecraft, were selected for NASA by a committee chaired by Carl Sagan of Cornell University. Included are natural sounds (including some made by animals), musical selections from different cultures and eras, spoken greetings in 59 languages, human sounds like footsteps and laughter, and printed messages from President Jimmy Carter and U.N. Secretary-General Kurt Waldheim.


title: Contents of the Voyager Golden Record

text: The first audio section contains a spoken greeting in English from then-Secretary-General of the United Nations Kurt Waldheim.


title: Contents of the Voyager Golden Record

text: The second audio section ("Greetings in 55 Languages") contains spoken greetings in 55 languages. The original plan was to use greetings made by United Nations delegates, but various problems with these recordings led to new recordings being made at Cornell University by people from the foreign-language departments. The number of native speakers of these 55 languages combined (excluding L2 speakers) is over 4.7 billion people, comprising over 65% of the world population. It includes four Chinese varieties (marked with **), 12 South Asian languages (marked #) and five ancient languages (marked §), listed here in alphabetical order:


title: Contents of the Voyager Golden Record

text: Later audio sections contain the spoken greetings by the United Nations delegates in the remaining four languages, including Esperanto and !Kung. The whale sounds were provided by Roger Payne.


title: Contents of the Voyager Golden Record

text: Included within the "Sounds of Earth" audio portion of the Golden Record is a track containing the inspirational message "per aspera ad astra" in Morse code. Translated from Latin, it means 'through hardships to the stars.'


title: Contents of the Voyager Golden Record

text: The life signs included on the record were an hour-long recording of the heartbeat and brainwaves of Ann Druyan, who would later marry Carl Sagan. The hour-long recording was compressed into the span of a minute to be able to fit into the essay. In the epilogue of the 1997 book "Billions and Billions", she describes the experience:


title: Contents of the Voyager Golden Record

text: On February 12, 2010, an interview with Ann Druyan was aired on NPR during which the above was explained in more detail.


title: Contents of the Voyager Golden Record

text: Following the section on the sounds of Earth, there is an eclectic 90-minute selection of music from many cultures, including Eastern and Western classics. The selections include:


title: Contents of the Voyager Golden Record

text: It has been claimed that Sagan had originally asked for permission to include "Here Comes the Sun" from the Beatles' album "Abbey Road"; but while the Beatles favored it, EMI opposed it and the song was not included. However, this has been refuted by Timothy Ferris, who worked on the selection with Sagan; he said the song was never even considered for inclusion.


title: Contents of the Voyager Golden Record

text: Along with the audio, the record contains a collection of 116 pictures (one of which is for calibration) detailing but not limited to human life on Earth and the planet itself. Many pictures are annotated with one or many indications of scales of time, size or mass. Some images also contain indications of chemical composition. All measures used on the pictures are first defined in the first few images using physical references.


title: Contents of the Voyager Golden Record

text: Following is a list of all the images contained in the Voyager Golden Record together with a description of the nature of the image and what annotations were included in them, and when copyright permits, the actual image.


title: Contents of the Voyager Golden Record

text: After NASA had received criticism over the nudity on the Pioneer plaque (line drawings of a naked man and woman), the agency chose not to allow Sagan and his colleagues to include George Hester's photograph of a nude man and woman on the record. Instead, only a silhouette of the couple was included.


title: Contents of the Voyager Golden Record

text: An official statement by President Jimmy Carter was included as images (positions 117, 118). It reads, in part:This Voyager spacecraft was constructed by the United States of America. We are a community of 240 million human beings among the more than 4 billion who inhabit the planet Earth. We human beings are still divided into nation states, but these states are rapidly becoming a global civilization.


title: Contents of the Voyager Golden Record

text: We cast this message into the cosmos ... It is likely to survive a billion years into our future, when our civilization is profoundly altered and the surface of the Earth may be vastly changed. Of the 200 billion stars in the Milky Way galaxy, some – perhaps many – may have inhabited planets and space faring civilizations. If one such civilization intercepts Voyager and can understand these recorded contents, here is our message: This is a present from a small distant world, a token of our sounds, our science, our images, our music, our thoughts, and our feelings. We are attempting to survive our time so we may live into yours. We hope some day, having solved the problems we face, to join a community of galactic civilizations. This record represents our hope and our determination and our goodwill in a vast and awesome universe.


title: Cheburashka

text: Cheburashka (), also known as Topple in earlier English translations, is a fictional character created by Soviet writer Eduard Uspensky in his 1965 children's book "Gena the Crocodile and His Friends". The character subsequently appeared as the protagonist in a series of stop-motion animated films by Roman Kachanov (Soyuzmultfilm studio), the first of which was made in 1969, with songs composed by Vladimir Shainsky.


title: Cheburashka

text: Cheburashka is an iconic Russian classic cartoon character who later became a popular character in Russian jokes (along with his friend, Gena the Crocodile). According to the creator of the character, Eduard Uspensky, Cheburashka is an "animal unknown to science", with large monkey-like ears and a body resembling that of a cub, who lives in a tropical forest. He accidentally gets into a crate of oranges, eats his fill, and falls asleep. The crate is eventually delivered to a grocery store in an unnamed Russian city (hinted to be Moscow), where the rest of the main story unfolds.


title: Cheburashka

text: The puzzled store manager finds the creature in the crate when he opens it, and takes him out and sits him on the table. The creature's paws are numb after staying in the crate for so long, and he tumbles down (, a Russian colloquialism meaning "tumbled") from the table, onto the chair, and then onto the floor. This inspires the store manager to name him Cheburashka. Words with this root were archaic in Russian; Uspensky gave them a new lease on life. ("The Explanatory Dictionary of the Live Great Russian language" of Vladimir Dahl gives the meaning of "cheburashka" as another name for the roly-poly toy.)


title: Cheburashka

text: Cheburashka is male, has a bear-like body, and is about the size of a 5-year-old child. He is a toddling creature with huge round ears on the side of his head that droop when he is discouraged. He has feet without legs, big black eyes, a snub nose. His voice is high-pitched and childlike. Cheburashka is an optimist as he only sees the best in people and is chirpy even in the gloomiest situation. Sergei Kapkov, animation historian and managing editor of Soyuzmultfilm, has said that Cheburashka "is absolutely useless and hopeless. He is like a stranger who doesn't understand a thing but just has one global idea, and that is to make friends and have others ... make friends with each other."


title: Cheburashka

text: After being turned down by the zoo as an "animal unknown to science," Cheburashka gets hired as a window display for a discount store selling factory seconds because he resembles one, residing in a phone booth. In the tale, he befriends an anthropomorphic crocodile named Gena, who wears a hat, a bow tie, and a coat, and plays the accordion. Gena works in a zoo as a zoo animal. Gena's favorite songs are "Such a Pity that One's Birthday Happens Only Once a Year" and "The Blue Train Car", both of which are extremely popular with children.


title: Cheburashka

text: Cheburashka and Gena have their adventures made more difficult by a character named "Старуха Шапокляк" (Old Lady Shapoklyak). She is a mischievous but charming old lady. Shapoklyak is tall and thin, wears a hat, a dark-coloured dress, and bloomers, and carries around a pet rat, Lariska, in her purse to help her play pranks on people, though near the end of some stories she turns around and helps the protagonists. The chorus of her theme song contains her motto, "One won't ever get famous for good deeds."


title: Cheburashka

text: The rights to the Cheburashka character and image have been heavily debated in court. In 1994, Eduard Uspensky (the writer) copyrighted the character's name and image and proceeded to sell the rights to various countries. Leonid Shvartsman, the art director of the animated films, has tried to prove in court that he was the creator of Cheburashka's visual appearance and that this copyright should be separate from the rights for the literary character. On 13 March 2007, Shvartsman and his lawyer lost a 4.7 million ruble lawsuit against BRK Cosmetics and Eduard Uspensky. Shvartsman alleged that Uspensky sold the rights to the Cheburashka image (which was allegedly not his to sell) to BRK Cosmetics, which used it on packets of toothpaste. The defence argued that the artist who drew the character for the packets had never seen the animated films and, despite the fact that the character on the packets was an exact copy of the one in the animated films, had created the character himself after the impressions left from reading Uspensky's books. Vladimir Entin, defender of Shvartsman's interests, suspected that the jury had to have been bribed in order to hand such an unlikely verdict, but admits that there is no proof.


title: Cheburashka

text: Cheburashka is now a staple of Russian cartoons, and there are several licensed products on the market, such as children's joke books and stuffed toys. He is also one of the few Russian animation characters to be the subject of numerous Russian jokes and riddles.


title: Cheburashka

text: The word "Cheburashka" is also used in a figurative sense to name objects that somehow resemble the creature (such as an An-72 aircraft which, when seen from the front, resembles the character's head) or are just as pleasing as it is (e.g. a colloquial name for a small bottle of lemonadefrom the brand name "Cheburashka").


title: Cheburashka

text: Cheburashka was also chosen as the official mascot with the main mascots for the Russian Olympic Team in the following games:


title: Cheburashka

text: "Cheburashka" also became known in some countries outside the former Soviet Union (and of the Soviet Bloc). He became very popular in Japan after an animated film series about him was shown in 15 cinemas all over Japan and was watched by about 700,000 between summer 2001 and spring 2002. In 2008, the Cheburashka films (as part of the "Ghibli Museum Library") were made available to Japanese cinemas on the same date as Hayao Miyazaki's "Ponyo on the Cliff by the Sea". An English-dubbed edition of at least one of the animated films was released in 1987, titled "The Adventures of Charlie and Cubby."


title: Cheburashka

text: In the 1970s a series of children's television shows, radio shows, records and magazines were produced in Sweden with the characters Drutten and crocodile Gena. These two characters were based on a couple of Cheburashka and Gena dolls bought on a trip to the Soviet Union, so they were visually identical to Cheburashka and Gena. ("Drutten" means "one who tumbles down", as one meaning of the Swedish colloquial verb "drutta" is "to fall or tumble down".)


title: Cheburashka

text: But that is where the similarity ends. The two characters sang and told different stories from those in the USSR, lived on a bookshelf rather than in a city and are hand puppets operated in live action rather than stop motion. Only occasionally Swedish public service TV would broadcast a segment of the Russian original, dubbed in Swedish. So, while many Swedes may visually recognize Cheburashka, they will generally not associate these characters with the ones Russian children know.


title: Cheburashka

text: Cheburashka dolls and other collectibles are produced in Russia, Japan and China. United States National Champion figure skater Johnny Weir is known to be an avid collector of Russian Cheburashka items.


title: Cheburashka

text: The white and red Olympic mascots were made in three sizes – 14 cm, 18 cm and 27 cm – and wear a sponsor's jersey with the "Bosco Sport" logo on the chest.


title: Cheburashka

text: T-shirts with Cheburashka are common, including several versions with the character drawn as Alberto Korda's Che Guevara photograph, labeled "Che Burashka".


title: Cheburashka

text: Estonian musician Tommy Cash (rapper) has compared himself to the beloved character, stating "I got huge ears, big eyes, call me Cheburashka".


title: Cheburashka

text: Ivan Maximov had said in a 2004 interview that Pilot Studio had been planning to make a "Cheburashka" feature film and that the scenario had been written out and possibly some footage shot, but that it had been frozen for lack of funds. Cheburashka's popularity in Japan is such that on 4 April 2006, TV Tokyo broadband issued a press announcement that it (in partnership with Frontier Works) has acquired the rights to remake the Cheburashka shorts as a feature film. It is unclear if this was the project that Pilot Studio had been forced to abandon. It was announced that the film, like the original shorts, will be based on puppet animation enhanced with modern stop-motion technology and computer graphics effects (similar to the plans for the Pilot Studio film), and would be shot simultaneously in English and Russian.


title: Cheburashka

text: In March 2009 it was announced that the new Cheburashka animation would consist of a new animated series, called "Cheburashka arere?", which ran for 26 3-minute episodes. "Cheburashka arere?" premiered on the "Nori-Suta 100%" television program on 7 October 2009.


title: Cheburashka

text: The new film, only titled "Cheburashka" is produced by both Ffango Entertoyment of South Korea and Frontier Works of Japan. Directed by Makoto Nakamura and written by both Mikhail Aldashin and Michiru Shimada. The film opened in 8 December 2010 in Japan. The film's theme song is titled "Orange", performed by Kaela Kimura.


title: Cheburashka

text: A shot-for-shot remake of the shorts also titled "Cheburashka" was released on June 15, 2014 in Russia.


title: Cheburashka

text: In September 2021, a full-length film titled "Cheburashka" was announced with filming beginning in Sochi, and shooting locations also planned in Moscow, Kislovodsk and Pyatigorsk. Dmitry Dyachenko is set to direct, with Central Partnership and Yellow, Black and White producing. The film has a release date set for January 1, 2023.


title: Online streamer

text: An online streamer or live streamer is a person who broadcasts themselves online through a live stream to an audience.


title: Online streamer

text: Streaming arose in the early 2010s, originating on sites like YouTube where users could upload videos of themselves in the form of vlogs or Let's Plays. While not all content featured a live audience, users were still able to gain a sizable following and make a living off of their content. Other sites like Twitch increased this popularity. Due to the millions of dollars that streamers can make, streaming has become a much-yearned-for career option.


title: Online streamer

text: Let's Players have been the most popular streamers by far since the beginning of live streaming. Today, the majority of streamers make their living from doing Let's Plays, live speedruns, and walkthroughs of video games. The biggest video game streamers are PewDiePie and Ninja who make millions of dollars each year just from streaming.


title: Online streamer

text: While the majority of professional and part-time streamers play video games, many often do IRL (in real life) streams where they broadcast their daily life. At first, many streaming sites prohibited non-gaming live streams as they thought it would harm the quality of the content on their sites but the demand for non-gaming content grew. Topics include answering questions in front of a computer, streaming from their phone while walking outside, or even doing tutorials. IRL streams are alternatives to viewers who do not necessarily like to play video games.


title: Online streamer

text: Virtual avatars, commonly known as VTubers, are a branch of streaming in which virtual avatars, occasionally paired with voice changers, are used instead of the streamer's face. In 2020 alone, there were more than 10,000 active VTubers.


title: Online streamer

text: Pornographic streams are a way to directly communicate with porn stars. Camgirls and camboys broadcast while nude or performing sexual acts often on demand from viewers. Sites like Plexstorm have created a niche by streaming video gamers performing or showing sexual content including pornographic games.


title: Online streamer

text: In South Korea, a streamer is called a broadcast jockey or BJ. Broadcast jockeys have become popular over the years in Korea thanks in part to many of them being more relatable to viewers than some celebrities and becoming famous enough to appear on TV shows. While it is common for broadcast jockeys to become national stars, there has been a recent rise in the number of famous Korean idols and celebrities becoming broadcast jockeys either as a way to supplement their career or full-time as they make more money streaming than they would acting or singing. The number of famous stars becoming full-time broadcast jockeys has outpaced the number of part-timers as many prefer freedom over professional offers. Politicians have streaming channels. Korean sites include AfreecaTV, Naver TV, and KakaoTV in addition to worldwide streaming sites like Twitch, YouTube, and Bigo Live.


title: Online streamer

text: Mukbang originated in South Korea, as the live-streaming of eating a meal. Global sites like Twitch offer "Social Eating".


title: Online streamer

text: China has become the largest marketplace for live streaming. A large number of streamers make $10,000–$100,000 a month without having to be a big name on the Internet. This is due to the large population and the ubiquity of smartphones, where many Chinese citizens prefer to consume their entertainment. The live streaming market grew 180% in 2016 and has grown even more since then. Chinese streaming sites may be restricted to Chinese content and audiences due to the strict Internet rules in the country and the difficulty of cooperating with the Chinese Communist Party. Many Chinese streamers average 100,000 viewers per stream and earn $29,000 per month just by partnering with an agency.


title: Mecca Province

text: The Mecca Province ( '), also known as the Mecca Region, is one of the 13 provinces of Saudi Arabia. It is the third-largest province by area at and the most populous with a population of 8,557,766 as of 2017, of which 4,041,189 were foreign nationals and 4,516,577 were Saudis. It is located in the historic Hejaz region, and has an extended coastline on the Red Sea. Its capital is Mecca, the holiest city in Islam, and its largest city is Jeddah, which is Saudi Arabia's main port city. The province accounts for 26.29% of the population of Saudi Arabia and is named after the holy city of Mecca.


title: Mecca Province

text: Historically, the area was inhabited by the Quraysh, the Banu Kinanah and the Thaqif, among other tribes. Part of the Hejaz region, the province has seen several exchanges of power between many Islamic realms within a short period of time. The province gains its significance as it contains the city of Mecca, the birthplace of Muhammad, and several other historic Islamic sites, such as the village of Hudaybiyyah, where the Treaty of Hudaybiyyah is said to have been agreed upon. More recently, the province was modernized under the Ottoman Empire and the Kingdom of Saudi Arabia after the oil boom.


title: Mecca Province

text: Most of the population is concentrated in three cities: Jeddah, Mecca and Ta'if. Jeddah is the largest city in the province and the second-largest in Saudi Arabia with an estimated population of 2,867,446 as of 2020. Mecca is the second-largest city in the province and third-largest in the kingdom at 1,323,624. After the city of Ta'if at third place, Rabigh, Shafa, Turbah and Jumum are other populous cities and towns in the region. The region receives Muslim pilgrims of the Umrah and the Hajj around the year and its population increases by up to 2 million during the Hajj. It has approximately of coastline on the Red Sea and hosts oil refineries in Rabigh, port and oil export facilities in Jeddah, the King Abdullah University of Science and Technology and the King Abdullah Economic City. The province also hosts part of the Haramain high-speed railway line, which is Saudi Arabia's first and only high-speed railway line.


title: Mecca Province

text: The province is divided into 11 governorates, of which 5 have been classified Category A and the rest, Category B, with Mecca serving as the administrative headquarters and capital of the province. It is governed by an Emir, translated as Governor from Arabic, who is assisted by the Deputy Governor, both appointed by the King of Saudi Arabia. The current emir is Khalid bin Faisal Al Saud, who has held the position for a second term since 2015.


title: Mecca Province

text: Ancient Mecca was an oasis on the old caravan trade route that linked the Mediterranean world with South Arabia, East Africa, and South Asia. The town was located about midway between Maʾrib in the south and Petra in the north, and it gradually developed by Roman and Byzantine times into an important trade and religious centre. Ptolemy's inclusion of Macoraba, a city of the Arabian interior, in his "Guide to Geography" was long held to show that Mecca was known to the Hellenistic world. Since the late 20th century, however, some scholarship has called the identification of Macoraba with Mecca into question.


title: Mecca Province

text: According to Islamic tradition, Abraham and Ishmael, his son by Hagar, built the Kaʿbah as the house of God. The central point of pilgrimage in Mecca before the advent of Islam in the 7th century, the cube-shaped stone building has been destroyed and rebuilt several times. During pre-Islamic times the region was ruled by a series of Yemeni tribes. Under the Quraysh it became a type of city-state, with strong commercial links to the rest of Arabia, Ethiopia, and Europe. Mecca became a place for trade, for pilgrimage, and for tribal gatherings. The city of Jeddah is believed to have been a fishing hamlet occupied by early Yemeni tribes. The region has held significant religious importance greatly increased with the expeditions of Muhammad in the early 7th century. As the ancient caravan route fell into decline, Mecca lost its commercial significance and has since lived mainly on the proceeds from the annual pilgrimages and the gifts of Muslim rulers.


title: Mecca Province

text: The city of Mecca was sacked by the Umayyad general al-Ḥajjāj ibn Yūsuf, and thereafter the city, and at the time, the region, acknowledged the power of the Umayyad caliphate at Damascus and, following the eclipse of that dynasty, of the ʿAbbāsid caliphate of Baghdad. The city suffered great indignity at the hands of the Shīʿite Qarmatians in 930 when that sect's leader Ṭāhir Sulaymān pillaged Mecca and carried off the Black Stone from the Kaʿbah. Beginning in the mid-10th century, the rulers of the city were chosen from the sharifs, or descendants of Muhammad, who retained a stronghold on the surrounding region while often paying homage to stronger political entities. The ability of the sharifs, originally moderate Shīʿites, to adapt to the changing political and religious climate ensured their preeminence in local affairs for the next 1,000 years. In 1269, the region came under the control of the Egyptian Mamlūk sultans. In 1517, dominion over the area passed to the Ottoman Empire, with its capital in Constantinople (now Istanbul). With the Ottoman collapse after World War I, control of Mecca was contested between the sharifs and the House of Saʿūd of central Arabia, adherents to an austere, puritanical form of Islam known as Wahhābism. King Ibn Saʿūd conquered the region in 1925, and the region of Mecca became a province of the Kingdom of Saudi Arabia and the city became the capital of the province.


title: Mecca Province

text: The region underwent extensive economic development as Saudi Arabia's petroleum resources were exploited after World War II, and the number of yearly pilgrims to Mecca has increased significantly.


title: Mecca Province

text: Most of the central and eastern portions of the province are desert, with the Hejaz mountains, which vary in elevation from 600 meters to 2000 meters, separating the relatively flat Nafud desert and coastal plains. Agriculture takes place in the region's many wadis and oases, with the most commonly-grown crops being dates and barley, alongside other vegetables and fruits. The city of Ta'if is famous for its cultivation of the Rosa × damascena flower, simplified as Damask rose and locally known as Ta'if rose.


title: Mecca Province

text: The province has an extended coastline that is approximately 700 kilometers (430 mi) long, with many cities spread out across the coastline. Several archipelagos can be found across the coast of the province, along with some coral reefs, such as the Great Coral Reef, located approximately 15 km (9 mi) northwest of Jeddah and the Five Coral Reef, located 25 km (16 mi). The coastline faces Sudan to the west and Eritrea and Ethiopia to the south. The province is bordered by the Madinah Province to the north, the Riyadh Province to the east, and the Al Baha and 'Asir provinces to the south.


title: Mecca Province

text: The Mecca Region hosts two of Saudi Arabia's 15 designated protected areas managed by the Saudi Wildlife Authority: the Mahazat as-Sayd Protected Area and the Saja Umm Ar-Rimth Natural Reserve, located on the eastern extremes of the province. Other minor sanctuaries in the province include the Saiysad Natural Reserve in the city of Ta'if and the Eastern Forest near Jeddah. The Hejaz mountains run through the center of the province, separating the Nafud desert from the western coastal plains, which run parallel to the coast of the province on the Red Sea.


title: Mecca Province

text: According to the Population Characteristics Surveys conducted by the General Authority of Statistics, the Mecca Province had a population of 8,557,766 as of December 2017, of which 4,516,577 were Saudis and 4,041,189 were foreign nationals. Divided by gender, 4,864,584 were males and 3,693,182 were females. The Mecca Province is the most populous province of Saudi Arabia and it has a population even larger than that of the Riyadh Region. With an estimated population of 4,076,000 as of 2019, Jeddah is the most populous city in the province and the second-most populous city in the country. The governorate with the largest population is the Jeddah Governorate. The sex ratio was approximately 132 males per 100 females.


title: Mecca Province

text: Censuses in Saudi Arabia do not collect or report data concerning religion. Sunni Islam of the Hanbali school of Islamic jurisprudence is the predominant religion overall in the country, with smaller numbers of Hanafis, Shafi‘is and Malikis. Muslims are estimated to live within the province, with even smaller numbers of Hindus, Christians and other religious groups, most of whom are expatriates from India and the Philippines, who mostly reside in Jeddah.


title: Mecca Province

text: The official language of Saudi Arabia is Arabic. The main regional dialect of the Mecca Province spoken by Saudis is Hejazi Arabic, with a minority of Najdi Arabic speakers in the eastern parts of the region. Saudi Sign Language is the principal language of the deaf community. The large expatriate communities also speak their own languages, the most numerous of which are some of the Indian languages, Filipino/Tagalog, Bengali and Urdu.


title: Mecca Province

text: From 1,823,598 Saudi male residents above the age of 10, 87.57%, representing 1,596,946 persons had some form of formal education, while 226,652 were illiterate. As for females, from the 1,765,666 residents above the age of 10, 77.28% or 1,364,529 persons were formally educated, while 401,137 were illiterate.


title: Mecca Province

text: Of the province's Saudi residents who were above the age of 15, 1.15% reported some form of disability in 2016, with visual impairment being the most common form of disability, followed by reduced mobility, while 107,770 persons reported severe or extreme disability.


title: Mecca Province

text: The position of Governor "(Emir)" of the Makkah Province has been held by the following individuals since 1925:


title: Mecca Province

text: The Mecca region has 11 governorates, of which 5, Jeddah, Rabigh, Ta'if, Qunfudhah, and Laith, have been classified Category A, while the rest are Category B. The City of Mecca () constitutes Mecca and the area surrounding the city and is the administrative center and capital of the province.


title: Golf club

text: A golf club is a club used to hit a golf ball in a game of golf. Each club is composed of a shaft with a grip and a club head. Woods are mainly used for long-distance fairway or tee shots; irons, the most versatile class, are used for a variety of shots; hybrids that combine design elements of woods and irons are becoming increasingly popular; putters are used mainly on the green to roll the ball into the hole. A set of clubs is limited by the rules of golf to a maximum of 14 golf clubs, and while there are traditional combinations sold at retail as matched sets, players are free to use any combination of legal clubs.


title: Golf club

text: The most significant difference between clubs of the same type is "loft", or the angle between the club's face and the vertical plane. It is loft that is the primary determinant of the ascending trajectory of the golf ball, with the tangential angle of the club head's swing arc at impact being a secondary and relatively minor consideration (though these small changes in swing angle can nevertheless have a significant influence on launch angle when using low-lofted clubs). The impact of the club compresses the ball, while grooves on the club face give the ball backspin. Together, the compression and backspin create lift. The majority of woods and irons are labeled with a number; higher numbers usually indicate shorter shafts and higher lofts, which give the ball a higher and shorter trajectory.


title: Golf club

text: "Woods" are long-distance clubs, meant to drive the ball a great distance down the fairway towards the hole. They generally have a large head and a long shaft for maximum club speed. Historically, woods were made from persimmon wood, although some manufacturers—notably Ping—developed laminated woods. In 1979, TaylorMade Golf introduced the first wood made of steel. Even more recently, manufacturers have started using materials such as carbon fiber, titanium, or scandium. Even though most ‘woods’ are made from different metals, they are still called ‘woods’ to denote the general shape and their intended use on the golf course. Most woods made today have a graphite shaft and a mostly-hollow titanium, composite, or steel head, of relatively light weight allowing faster club-head speeds. Woods are the longest clubs and the most powerful of all the golf clubs. There are typically three to four woods in a set which are used from the tee box and, if on a long hole, possibly for the second or even third shot. The biggest wood, known as the "driver" or "one wood", is often made of hollow titanium with feather-light shafts. The length of the woods has been increasing in recent decades, and a typical driver with a graphite shaft is now long. The woods may also have very large heads, up to in volume (the maximum allowed by the USGA in sanctioned events; drivers with even larger club-head volumes are available for long-drive competitions and informal games). The shafts range from senior to extra-stiff depending upon each player’s preference.


title: Golf club

text: "Irons" are clubs with a solid, all-metal head featuring a flat angled face, and a shorter shaft and more upright lie angle than a wood, for ease of access. Irons are designed for a variety of shots from all over the course, from the tee box on short or dog-legged holes, to the fairway or rough on approach to the green, to tricky situations like punching through or lobbing over trees, getting out of hazards, or hitting from tight lies requiring a compact swing. Most of the irons have a number from 1 to 9 (the numbers in most common use are from 3 to 9), corresponding to their relative loft angle within a matched set. Irons are typically grouped according to their intended distance (which also roughly corresponds to their shaft length and thus their difficulty to hit the ball); in the numbered irons, there are long irons (2–4), medium irons (5–7), and short irons (8–9), with progressively higher loft angles, shorter shafts, and heavier club heads.


title: Golf club

text: As with woods, ’irons’ get their name because they were originally made from forged iron. Modern irons are investment-cast out of steel alloys, which allows for better-engineered ‘cavity-back’ designs that have lower centers of mass and higher moments of inertia, making the club easier to hit and giving better distance than older forged ’muscle-back’ designs. Forged irons with less perimeter weighting are still seen, especially in sets targeting low-handicap and scratch golfers, because this less forgiving design allows a skilled golfer to intentionally hit a curved shot (a ’fade’ or ’draw’), to follow the contour of the fairway or ’bend’ a shot around an obstacle.


title: Golf club

text: "Wedges" are a subclass of irons with greater loft than the numbered irons (generally starting at 47°–48° of loft, above the 9-irons of 44°–45°), and other features such as high-mass club heads and wide soles that allow for easier use in tricky lies. Wedges are used for a variety of short-distance, high-altitude, high-accuracy ’utility’ shots, such as hitting the ball onto the green ("approach" shots), placing the ball accurately on the fairway for a better shot at the green ("lay-up" shots), or hitting the ball out of hazards or rough onto the green (chipping). There are five main types of wedges, with lofts ranging from 45° to 64°: pitching wedge (PW, 48–50°), gap wedge (GW, also "approach", "attack", "utility", or "dual" wedge, typically 52–54°), sand wedge (SW, 55–56°), lob wedge (LW, 58°–60°), and ultra lob wedge (sometimes called the "flop wedge" or FW, 64°–68°).


title: Golf club

text: "Hybrids" are a cross between a wood and an iron, giving these clubs the wood's long distance and higher launch, with the iron's familiar swing. The club head of a hybrid has a wood-inspired, slightly convex face, and is typically hollow like modern metal woods to allow for high impulse on impact and faster swing speeds. The head is usually smaller than true woods, however, not extending as far back from the face, and the lie and shaft length are similar to an iron giving similar swing mechanics. These clubs generally replace low-numbered irons in a standard set (between 2 and 5, most commonly 3–4), which are typically the hardest clubs in a player's bag to hit well. By doing so they also generally make higher-lofted woods redundant as well. However, some manufacturers produce "iron replacement" sets that use hybrid designs to replace an entire set of traditional irons, from 3 to pitching wedge. Sets designed for less muscular players commonly feature a combination of high-lofted woods (up to 7-wood) and hybrids to replace the 5, 6 and 7-irons, allowing these players to achieve greater carry distances with slower swings.


title: Golf club

text: "Putters" are a special class of clubs with a loft not exceeding ten degrees, designed primarily to roll the ball along the grass, generally from a point on the putting green toward the hole. Contrary to popular belief, putters do have a loft (often 5° from truly perpendicular at impact) that helps to lift the ball from any indentation it has made. Newer putters also include grooves on the face to promote roll rather than a skid off the impact. This increases rolling distance and reduces bouncing over the turf. Putters are the only class of club allowed to have certain features, such as two striking faces, non-circular grip cross-sections, bent shafts or hosels, and appendages designed primarily to aid players' aim.


title: Golf club

text: Present in some golfers' bags is the "chipper", a club designed to feel like a putter but with a more lofted face, used with a putting motion to lift the ball out of the higher grass of the rough and fringe and drop it on the green, where it will then roll like a putt. This club replaces the use of a high-lofted iron to make the same shot, and allows the player to make the shot from a stance and with a motion nearly identical to a putt, which is more difficult with a lofted iron due to a difference in lie angle.