The 2013 Sydney to Hobart Yacht Race, sponsored by Rolex, is the 69th annual running of the "blue water classic" Sydney to Hobart Yacht Race. As in past editions of the race, it is hosted by the Cruising Yacht Club of Australia based in Sydney, New South Wales; as with previous Sydney to Hobart Yacht Races, the 2013 edition began on Sydney Harbour, at 1pm on Boxing Day, before heading south for 630 nautical miles through the Tasman Sea, past Bass Strait, into Storm Bay and up the River Derwent, to cross the finish line in Hobart, Tasmania. Line honours were claimed by Wild Oats XI in a time of 6 hours, 7 minutes and 27 seconds, it was the yacht's seventh win, equaling Morna/Kurrewa IV's 1960 record for most line honours victories
Functional analysis is a branch of mathematical analysis, the core of, formed by the study of vector spaces endowed with some kind of limit-related structure and the linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view turned out to be useful for the study of differential and integral equations; the usage of the word functional as a noun goes back to the calculus of variations, implying a function whose argument is a function. The term was first used in Hadamard's 1910 book on that subject. However, the general concept of a functional had been introduced in 1887 by the Italian mathematician and physicist Vito Volterra; the theory of nonlinear functionals was continued by students of Hadamard, in particular Fréchet and Lévy.
Hadamard founded the modern school of linear functional analysis further developed by Riesz and the group of Polish mathematicians around Stefan Banach. In modern introductory texts to functional analysis, the subject is seen as the study of vector spaces endowed with a topology, in particular infinite-dimensional spaces. In contrast, linear algebra deals with finite-dimensional spaces, does not use topology. An important part of functional analysis is the extension of the theory of measure and probability to infinite dimensional spaces known as infinite dimensional analysis; the basic and first class of spaces studied in functional analysis are complete normed vector spaces over the real or complex numbers. Such spaces are called Banach spaces. An important example is a Hilbert space; these spaces are of fundamental importance in many areas, including the mathematical formulation of quantum mechanics. More functional analysis includes the study of Fréchet spaces and other topological vector spaces not endowed with a norm.
An important object of study in functional analysis are the continuous linear operators defined on Banach and Hilbert spaces. These lead to the definition of C*-algebras and other operator algebras. Hilbert spaces can be classified: there is a unique Hilbert space up to isomorphism for every cardinality of the orthonormal basis. Finite-dimensional Hilbert spaces are understood in linear algebra, infinite-dimensional separable Hilbert spaces are isomorphic to ℓ 2. Separability being important for applications, functional analysis of Hilbert spaces mostly deals with this space. One of the open problems in functional analysis is to prove that every bounded linear operator on a Hilbert space has a proper invariant subspace. Many special cases of this invariant subspace problem have been proven. General Banach spaces are more complicated than Hilbert spaces, cannot be classified in such a simple manner as those. In particular, many Banach spaces lack a notion analogous to an orthonormal basis. Examples of Banach spaces are L p -spaces for any real number p ≥ 1.
Given a measure μ on set X L p, sometimes denoted L p or L p, has as its vectors equivalence classes of measurable functions whose absolute value's p -th power has finite integral, that is, functions f for which one has ∫ X | f | p d μ < + ∞. If μ is the counting measure the integral may be replaced by a sum; that is, we require ∑ x ∈ X | f | p < + ∞. It is not necessary to deal with equivalence classes, the space is denoted ℓ p, written more ℓ p in the case when X is the set of non-negative integers. In Banach spaces, a large part of the study involves the dual space: the space of all continuous linear maps from the space into its underlying field, so-called functionals. A Banach space can be canonically identified with a subspace of its bidual, the dual of its dual space; the corresponding map is an isometry but in general not onto. A general Banach space and its bidual need not be isometrically isomorphic in any way, contrary to the finite-dimensional situation; this is explained in the dual space article.
The notion of derivative can be extended to arbitrary functions be
Jonathan Don Farrar was the United States Ambassador to the Republic of Panama from 2012 to 2015. He was the Chief of Mission of the United States Interests Section in Havana, from July 2008-September 2011. Farrar joined the U. S. State Department in 1980 as an economic officer, is a career member of the Senior Foreign Service, he was born in Los Angeles, graduated from Covina High School, studied at California State Polytechnic University, Claremont Graduate University, the Industrial College of the Armed Forces. Farrar has three children. Farrar's career includes extensive experience in Latin America, his most recent overseas posting was as the Deputy Chief of Mission in Uruguay. Farrar served at the U. S. embassies in Mexico and Paraguay. Prior to assuming his position as USINT COM, Farrar served as the Principal Deputy Assistant Secretary of the State Department's Bureau of Democracy, Human Rights, Labor, was DRL's Acting Assistant Secretary from August 2007 to March 2008. In this capacity, Farrar oversaw DRL's human rights and democracy programs around the world, with a particular focus on Asia and the Western Hemisphere.
From 2004 to 2005, Farrar served as a Deputy Assistant Secretary in the State Department's Bureau of International Narcotics and Law Enforcement Affairs, with responsibility for INL's programs in the Western Hemisphere, Africa and Europe. Farrar has held a variety of domestic assignments in the State Department's Bureau of Western Hemisphere Affairs, including service as Deputy Director of the Office of Andean Affairs and as country desk officer for Argentina. Farrar served twice on the staff of the Under Secretary for Democracy and Global Affairs, most as chief of staff to the Under Secretary from 2002 to 2004. Appearances on C-SPAN
Eduardo'Edu' Ramos Gómez is a Spanish footballer who plays for Cádiz CF as a central midfielder. Born in Málaga, Ramos was a product of hometown Málaga CF's youth ranks, he made his first-team debut at only 17 on 4 October 2009, playing the entire second half of the 1–1 draw away against Xerez CD. He spent his first professional season, however exclusively with the B-side, only appearing two more times in the league. In December 2010, shortly after the arrival of manager Manuel Pellegrini, Ramos was deemed surplus to requirements, alongside five other players. On 5 January 2011, he was sent on loan to CD Leganés in the third division until the end of the campaign. On 11 July 2011, Ramos signed for Villarreal CF, with Málaga still having a buyback option for the player. After starting with the C-team, he was soon promoted to the reserves in the second level, making his debut – as a starter – on 3 February 2012 in a 0−0 home draw against FC Barcelona B. Ramos scored his first goal for Villarreal B on 3 March 2012.
He made his official debut for the main squad on 14 December of the following year, starting in a 1−2 loss at FC Barcelona. On 9 July 2014, Ramos moved to Albacete Balompié, newly promoted to the second tier. On 13 July 2016, after the club's relegation, he signed for Córdoba CF. On 30 August 2018, Ramos moved to fellow second division side Cádiz CF on a one-year contract, with Córdoba holding a buy-back clause. Ramos represented Spain's under-17 team in the 2009 FIFA World Cup played in Nigeria, helping the nation to the third place. On 17 August 2010, he was selected by the under-19s for the SBS International Cup in Japan. Spain U17 FIFA U-17 World Cup: Third place 2009 Edu Ramos at BDFutbol Edu Ramos at Futbolme Edu Ramos at Soccerway
Trouble's Door is the sixth studio album by Australian blues musician Ash Grunwald. It was released in May peaking at number 29 on the ARIA Charts. Upon release, Grunwald said the album involved "some of my most personal songwriting", laying the foundations for "his most internal album to date". At the APRA Music Awards of 2013 "Longtime" won "Blues & Roots Work of the Year" Andrew Nock from Music Feeds said "Across the record, Ash complements his voice with expert guitar playing that delves in influences of blues and roots and psychedelia, his use of different guitar effects are one of many elements that give each track their own signature feeling and sound, impressive considering he uses the same base instruments for each track." Adding "There is not a single dull moment on this record. As the mood shifts with each song, you are pulled into another experience, there are many to be had. A refreshing listen from start to finish."Tyler Quiring from Blues Rock Review said "There's a lot here to appeal to fans of many genres, as Grunwald makes himself and his music accessible and easy to appreciate.
His songwriting flawlessly interweaves clever lyrics through a metrical tapestry of tunes. As he effortlessly combines traditional and non-traditional instrumentation and musical methods, his true talent rises to the surface." Calling it "a tight and well-executed record.". NZ Herald said the album "...channel blues musicians of old, mixed in with a little Ben Harper and The Black Keys" but added "the lyrical material sometimes gets a little overbearing in its political protest, though he has all the right raw ingredients, these 12 songs don't reach the compelling genius of The Black Keys."