Μ operatorIn computability theory, the μ-operator, minimization operator, or unbounded search operator searches for the least natural number with a given property. Adding the μ-operator to the primitive recursive functions makes it possible to define all computable functions. Suppose that R(y, x1, ..., xk) is a fixed (k+1)-ary relation on the natural numbers. The μ-operator "μy", in either the unbounded or bounded form, is a "number theoretic function" defined from the natural numbers to the natural numbers.
Timekeeping on MarsThough no standard exists, numerous calendars and other timekeeping approaches have been proposed for the planet Mars. The most commonly seen in the scientific literature denotes the time of year as the number of degrees on its orbit from the northward equinox, and increasingly there is use of numbering the Martian years beginning at the equinox that occurred April 11, 1955. Mars has an axial tilt and a rotation period similar to those of Earth. Thus, it experiences seasons of spring, summer, autumn and winter much like Earth.
General recursive functionIn mathematical logic and computer science, a general recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to natural numbers that is "computable" in an intuitive sense – as well as in a formal one. If the function is total, it is also called a total recursive function (sometimes shortened to recursive function). In computability theory, it is shown that the μ-recursive functions are precisely the functions that can be computed by Turing machines (this is one of the theorems that supports the Church–Turing thesis).
Viking 2The Viking 2 mission was part of the American Viking program to Mars, and consisted of an orbiter and a lander essentially identical to that of the Viking 1 mission. Viking 2 was operational on Mars for sols ( days; ). The Viking 2 lander operated on the surface for days, or sols, and was turned off on April 12, 1980, when its batteries failed. The orbiter worked until July 25, 1978, returning almost 16,000 images in 706 orbits around Mars. The craft was launched on September 9, 1975.
AinAin (æ̃, ɛ̃; En) is a French department in the Auvergne-Rhône-Alpes region, Eastern France. Named after the Ain river, it is bordered by the Saône and Rhône rivers. Ain is located on the country's eastern edge, on the Swiss border, where it neighbours the cantons of Geneva and Vaud. In 2019, it had a population of 652,432. Ain is composed of four geographically different areas (Bresse, Dombes, Bugey and Pays de Gex), each of which contribute to the diverse and dynamic economic development of the department.
MoonThe Moon is Earth's only natural satellite. Its diameter is about one-quarter of Earth's (comparable to the width of Australia), making it the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet. It is larger than all known dwarf planets in the Solar System. The Moon is a planetary-mass object with a differentiated rocky body, making it a satellite planet under the geophysical definitions of the term. It lacks any significant atmosphere, hydrosphere, or magnetic field.
History of paintingThe history of painting reaches back in time to artifacts and artwork created by pre-historic artists, and spans all cultures. It represents a continuous, though periodically disrupted, tradition from Antiquity. Across cultures, continents, and millennia, the history of painting consists of an ongoing river of creativity that continues into the 21st century. Until the early 20th century it relied primarily on representational, religious and classical motifs, after which time more purely abstract and conceptual approaches gained favor.
History of artThe history of art focuses on objects made by humans for any number of spiritual, narrative, philosophical, symbolic, conceptual, documentary, decorative, and even functional and other purposes, but with a primary emphasis on its aesthetic visual form. Visual art can be classified in diverse ways, such as separating fine arts from applied arts; inclusively focusing on human creativity; or focusing on different media such as architecture, sculpture, painting, film, photography, and graphic arts.
Ain (river)The Ain (æ̃, ɛ̃; En) is a river in eastern France. It gave its name to the Ain department. It is long. The river rises at an altitude of some 700 metres, near the village of La Favière, in the Jurassic limestone of the southern end of the Jura mountains and flows into the Rhône near Saint-Maurice-de-Gourdans, about 40 kilometres upstream of Lyon. Its source is in the old county of Franche-Comté. It flows south through the combined lengths of the two departments of: Jura (named after the mountains), and Ain (named after the river).
Stopping timeIn probability theory, in particular in the study of stochastic processes, a stopping time (also Markov time, Markov moment, optional stopping time or optional time) is a specific type of “random time”: a random variable whose value is interpreted as the time at which a given stochastic process exhibits a certain behavior of interest. A stopping time is often defined by a stopping rule, a mechanism for deciding whether to continue or stop a process on the basis of the present position and past events, and which will almost always lead to a decision to stop at some finite time.
Optimal stoppingIn mathematics, the theory of optimal stopping or early stopping is concerned with the problem of choosing a time to take a particular action, in order to maximise an expected reward or minimise an expected cost. Optimal stopping problems can be found in areas of statistics, economics, and mathematical finance (related to the pricing of American options). A key example of an optimal stopping problem is the secretary problem. Optimal stopping problems can often be written in the form of a Bellman equation, and are therefore often solved using dynamic programming.
Ample line bundleIn mathematics, a distinctive feature of algebraic geometry is that some line bundles on a projective variety can be considered "positive", while others are "negative" (or a mixture of the two). The most important notion of positivity is that of an ample line bundle, although there are several related classes of line bundles. Roughly speaking, positivity properties of a line bundle are related to having many global sections. Understanding the ample line bundles on a given variety X amounts to understanding the different ways of mapping X into projective space.
YY, or y, is the twenty-fifth and penultimate letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. According to some authorities, it is the sixth (or seventh if including W) vowel letter of the English alphabet. In the English writing system, it mostly represents a vowel and seldom a consonant, and in other orthographies it may represent a vowel or a consonant. Its name in English is wye (pronounced 'waɪ), plural wyes.
Nef line bundleIn algebraic geometry, a line bundle on a projective variety is nef if it has nonnegative degree on every curve in the variety. The classes of nef line bundles are described by a convex cone, and the possible contractions of the variety correspond to certain faces of the nef cone. In view of the correspondence between line bundles and divisors (built from codimension-1 subvarieties), there is an equivalent notion of a nef divisor. More generally, a line bundle L on a proper scheme X over a field k is said to be nef if it has nonnegative degree on every (closed irreducible) curve in X.
ZhengzhouZhengzhou (dʒɛŋ'dʒoʊ,_dʒʌŋ-, ; ), also spelt Zheng Zhou and alternatively romanized as Chengchow, is the capital and largest city of Henan Province in the central part of the People's Republic of China. Located in north-central Henan, it is one of the National Central Cities in China, the centre of Central Plains area, and serves as the political, economic, technological, and educational center of the province. The Zhengzhou metropolitan area (including Zhengzhou and Kaifeng) is the core area of the Central Plains Economic Zone.
Zhao (state)Zhao () was one of the seven major states during the Warring States period of ancient China. It emerged from the tripartite division of Jin, along with Han and Wei, in the 5th century BC. Zhao gained considerable strength from the military reforms initiated during the reign of King Wuling, but suffered a crushing defeat at the hands of Qin at the Battle of Changping. Its territory included areas in the modern provinces of Inner Mongolia, Hebei, Shanxi and Shaanxi.
