HMS Ark Royal was an aircraft carrier of the Royal Navy that served during the Second World War. Designed in 1934 to fit the restrictions of the Washington Naval Treaty, Ark Royal was built by Cammell Laird at Birkenhead and completed in November 1938, her design differed from previous aircraft carriers. Ark Royal was the first ship on which the hangars and flight deck were an integral part of the hull, instead of an add-on or part of the superstructure. Designed to carry a large number of aircraft, she had two hangar deck levels, she served during a period. Ark Royal served in some of the most active naval theatres of the Second World War, she was involved in the first aerial and U-boat kills of the war, operations off Norway, the search for the German battleship Bismarck, the Malta Convoys. Ark Royal survived several near misses and gained a reputation as a'lucky ship', she sank the following day. Her sinking was the subject of several inquiries, they found that several design flaws contributed to the loss, which were rectified in new British carriers.

The wreck was discovered in December 2002 by an American underwater survey company using sonar mounted on an autonomous underwater vehicle, under contract from the BBC for the filming of a documentary about the ship, at a depth of about 1,000 metres and 30 nautical miles from Gibraltar. In 1923, the Admiralty prepared a 10-year building programme which included an aircraft carrier and 300 aircraft for the Fleet Air Arm; the economic downturn following the First World War caused it to be postponed. In 1930, the Director of Naval Construction, Sir Arthur Johns, began to update the plans for the carrier by incorporating developed technology, his aim was to increase the number of aircraft carried by shortening the landing and take-off distances of aircraft using arrestor gear and compressed steam catapults which would make more deck space available for storage and aircraft preparation. Along with the inclusion of two hangar decks, this allowed Ark Royal to carry up to 72 aircraft, although the development of larger and heavier aircraft during the carrier's construction meant that the actual number carried was between 50 and 60.

Ark Royal featured an enclosed hangar design where the flight deck was the'strength deck' and was built with.75in thick Ducol steel plating. The two hangar decks were thus enclosed within the hull girder, which gave splinter protection to the hangars; the machinery spaces were protected by 4.5-inch belt armour. Three lifts moved aircraft between the flight deck. Another feature was the height of the flight deck. At 800 feet, the flight deck was 118 feet longer than the keel. Due to the twin hangar decks, the flight deck rose to 66 feet above the waterline; the Washington and London Naval treaties had restricted warship tonnage for a number of nations after the end of the great war and were both to expire by the end of 1936. With a potential naval arms race developing between Britain and Italy, the British government sought a second treaty, which included limiting the maximum displacement of an aircraft carrier to 22,000 long tons. Ark Royal would have to fit this anticipated limit. Installation of an armoured flight deck was not possible, as the weight would have placed Ark Royal above the proposed limit, while reducing her endurance and stability.

The ship was designed with a three layer side protection system based upon a void-liquid-void scheme similar to that used on the King George V-class battleships, was designed to protect against torpedoes with up to a 750-pound warhead. The ship was fitted with six boilers; the turbines were connected via three driveshafts to three propellers 16 feet in diameter, to produce a maximum theoretical speed of 30 knots. Speed was important, as with catapults and arrestor gear, Ark Royal would have to turn into the wind to launch and recover aircraft. To avoid endangering other ships with the frequent course changes associated with flight operations, Ark Royal would have to break away from accompanying ships, catch up on completion. Additionally, as the carrier was not armed for ship-to-ship combat, speed was her main protection against enemy warships; the deteriorating international situation by 1933, typified by Germany's rearmament and the expansion of Japan and Italy, convinced the British to announce funds for the carrier's construction in the 1934 budget proposals.

The plans were finished by November 1934 and were tendered in February 1935 to Cammell Laird and Company Ltd. which calculated the cost of the hull at £1,496,250 and the main machinery at £500,000. The overall cost was estimated to be over £3 million, making Ark Royal the most expensive ship ordered by the Royal Navy. Construction began on Job No. 1012 when Ark Royal's keel was laid down on 16 September 1935. Ark Royal spent nearly two years in the builder's yard before being launched on 13 April 1937 by Lady Maud Hoare, wife of Sir Sam

In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as countable additivity. The difference between a probability measure and the more general notion of measure is that a probability measure must assign value 1 to the entire probability space. Intuitively, the additivity property says that the probability assigned to the union of two disjoint events by the measure should be the sum of the probabilities of the events, e.g. the value assigned to "1 or 2" in a throw of a die should be the sum of the values assigned to "1" and "2". Probability measures have applications in diverse fields, from physics to biology; the requirements for a function μ to be a probability measure on a probability space are that: μ must return results in the unit interval, returning 0 for the empty set and 1 for the entire space.μ must satisfy the countable additivity property that for all countable collections of pairwise disjoint sets: μ = ∑ i ∈ I μ.

For example, given three elements 1, 2 and 3 with probabilities 1/4, 1/4 and 1/2, the value assigned to is 1/4 + 1/2 = 3/4, as in the diagram on the right. The conditional probability based on the intersection of events defined as: μ = μ μ. satisfies the probability measure requirements so long as μ is not zero. Probability measures are distinct from the more general notion of fuzzy measures in which there is no requirement that the fuzzy values sum up to 1, the additive property is replaced by an order relation based on set inclusion. Market measures which assign probabilities to financial market spaces based on actual market movements are examples of probability measures which are of interest in mathematical finance, e.g. in the pricing of financial derivatives. For instance, a risk-neutral measure is a probability measure which assumes that the current value of assets is the expected value of the future payoff taken with respect to that same risk neutral measure, discounted at the risk-free rate.

If there is a unique probability measure that must be used to price assets in a market the market is called a complete market. Not all measures that intuitively represent chance or likelihood are probability measures. For instance, although the fundamental concept of a system in statistical mechanics is a measure space, such measures are not always probability measures. In general, in statistical physics, if we consider sentences of the form "the probability of a system S assuming state A is p" the geometry of the system does not always lead to the definition of a probability measure under congruence, although it may do so in the case of systems with just one degree of freedom. Probability measures are used in mathematical biology. For instance, in comparative sequence analysis a probability measure may be defined for the likelihood that a variant may be permissible for an amino acid in a sequence. Borel measure Fuzzy measure Haar measure Martingale measure Lebesgue measure Billingsley, Patrick.

Probability and Measure. John Wiley. ISBN 0-471-00710-2. Ash, Robert B.. Probability & Measure Theory. Academic Press. ISBN 0-12-065202-1. Media related to Probability measure at Wikimedia Commons

Carolina Cruz-Neira is a Spanish-Venezuelan-American computer engineer, designer, a pioneer of virtual reality. She is known for inventing the CAVE automatic virtual environment, she worked at Iowa State University, University of Louisiana at Lafayette, University of Arkansas at Little Rock, she is an Agere Chair Professor at University of Central Florida. Cruz-Neira graduated cum laude with a degree in systems engineering from the Universidad Metropolitana in Caracas, Venezuela in 1987, she earned a master's degree in electrical engineering and computer science from the University of Illinois, Chicago in 1991, her PhD in 1995, working under computer graphics researcher Thomas DeFanti. The first CAVE was invented by Carolina Cruz-Neira, Daniel J. Sandin, Thomas A. DeFanti in 1992. For her PhD dissertation, Cruz-Neira designed and developed the CAVE Automatic Virtual Environment, its specifications, implementation, she designed and implemented the CAVELib software API, now a commercial product.

She was the architect of the Open Source API VR Juggler, an open source virtual reality applications development framework. The CAVE is an immersive system that became the standard for rear projection-based Virtual Reality systems; the normal full system consists of projections screens along the front and floor axes, a tracking system for the "user". Although they used the recursive acronym Cave Automatic Virtual Environment for the CAVE system, the name refers to Plato's "Republic" and "The Allegory of the Cave" where he explored the concepts of reality and human perception. There have been a couple offshoots of the CAVE technology, including ImmersaDesk, Infinity Wall and Oblong Industries' G-speak system; the ImmersaDesk is a semi-immersive system, resembling a drafting table, while the Infinity Wall is designed to cater to an entire room of people, such as a conference room. Extending this concept, G-speak supports gestural input from multiple-users and multiple-devices on and expandable array of monitors.

Cruz-Neira was the Stanley Chair professor in Interdisciplinary Engineering, a co-founder of the Virtual Reality Applications Center at Iowa State University. In 2002, Dr. Cruz-Neira co-founded and co-directed the Human-Computer Interaction graduate program at ISU, she joined the University of Louisiana at Lafayette in 2005, in 2006, was the first CEO and Chief Scientist of LITE, a Louisiana State initiative to support economic development immersive technologies. From 2009 to 2014 she was the W. Hansen Hall and Mary Officer Hall/BORSF Endowed Super Chair in Telecommunications in Computer Engineering at the University of Louisiana at Lafayette. In 2014, she was named an Arkansas Research Scholar by the Arkansas Research Alliance and moved to Little Rock to lead the Emerging Analytics Center at the University of Arkansas at Little Rock. In 2019, Cruz-Neira joined the University of Central Florida, as an Agere Chair Professor in the Computer Science Department. In 2017, Cruz-Neira was included in episode 8 "the player", in a ten part, Dutch documentary series, The Mind of the Universe by Robbert Dijkgraaf and VPRO broadcast.

In January, she was invited by Dell to participate in the “VR for Good” panel at the 2018 Consumer Electronics Show to demonstrate how innovators are using virtual reality to make a positive impact on society. Since June 2019, she has served as Chief Editor of VR and Industry for Frontiers in Virtual Reality Journal. 2007 – awarded the IEEE VGTC Virtual Reality Technical Achievement Award, in recognition of the development of the CAVE. 2009 – International Digital Media and Arts Association awarded her the Distinguished Career Award 2014 – Arkansas Research Alliance Scholar 2016 – Polygon website's Top 25 VR Innovators award 2016 – University Herald website's named her as one of the three greatest female innovators in virtual reality 2018 – In February 2018 Dr. Cruz-Neira was elected to the National Academy of Engineering. 2018 – Association for Computer Machinery, named Computer Pioneer. Video: The Mind of The Universe, episode 8 on YouTube