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A black hole is a region of spacetime wherein gravity is so strong that no matter or electromagnetic energy can escape it. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary of no escape is called the event horizon. A black hole has a great effect on the fate and circumstances of an object crossing it, but it has no locally detectable features according to general relativity. In many ways, a black hole acts like an ideal black body, as it reflects no light. Quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is of the order of billionths of a kelvin for stellar black holes, making it essentially impossible to observe directly.
Frequency, most often measured in hertz, is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as temporal frequency for clarity and to distinguish it from spatial frequency. Ordinary frequency is related to angular frequency by a factor of 2π. The period is the interval of time between events, so the period is the reciprocal of the frequency: T = 1/f.
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically independent, or stochastically independent if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds. Similarly, two random variables are independent if the realization of one does not affect the probability distribution of the other.
A supernova is a powerful and luminous explosion of a star. A supernova occurs during the last evolutionary stages of a massive star, or when a white dwarf is triggered into runaway nuclear fusion. The original object, called the progenitor, either collapses to a neutron star or black hole, or is completely destroyed to form a diffuse nebula. The peak optical luminosity of a supernova can be comparable to that of an entire galaxy before fading over several weeks or months.
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive where and when events occur.
In probability theory, the Borel–Cantelli lemma is a theorem about sequences of events. In general, it is a result in measure theory. It is named after Émile Borel and Francesco Paolo Cantelli, who gave statement to the lemma in the first decades of the 20th century. A related result, sometimes called the second Borel–Cantelli lemma, is a partial converse of the first Borel–Cantelli lemma. The lemma states that, under certain conditions, an event will have probability of either zero or one. Accordingly, it is the best-known of a class of similar theorems, known as zero-one laws. Other examples include Kolmogorov's zero–one law and the Hewitt–Savage zero–one law.
Eventing is an equestrian event where a single horse and rider combine and compete against other competitors across the three disciplines of dressage, cross-country, and show jumping. This event has its roots in a comprehensive cavalry test that required mastery of several types of riding. The competition may be run as a one-day event (ODE), where all three events are completed in one day or a three-day event (3DE), which is more commonly now run over four days, with dressage on the first two days, followed by cross-country the next day and then show jumping in reverse order on the final day. Eventing was previously known as Combined Training, and the name persists in many smaller organizations. The term "Combined Training" is sometimes confused with the term "Combined Test", which refers to a combination of just two of the phases, most commonly dressage and show jumping.
Bayesian inference is a method of statistical inference in which Bayes' theorem is used to calculate a probability of a hypothesis, given prior evidence, and update it as more information becomes available. Fundamentally, Bayesian inference uses a prior distribution to estimate posterior probabilities. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability".
The Schwarzschild radius or the gravitational radius is a physical parameter in the Schwarzschild solution to Einstein's field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole. It is a characteristic radius associated with any quantity of mass. The Schwarzschild radius was named after the German astronomer Karl Schwarzschild, who calculated this exact solution for the theory of general relativity in 1916.
Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them, or a difference in gravitational potential between their locations. When unspecified, "time dilation" usually refers to the effect due to velocity.
A heptathlon is a track and field combined events contest made up of seven events. The name derives from the Greek ἑπτά and ἄθλος. A competitor in a heptathlon is referred to as a heptathlete.
In relativity, proper time along a timelike world line is defined as the time as measured by a clock following that line. The proper time interval between two events on a world line is the change in proper time, which is independent of coordinates, and is a Lorentz scalar. The interval is the quantity of interest, since proper time itself is fixed only up to an arbitrary additive constant, namely the setting of the clock at some event along the world line.
Andreas Dittmer is a German sprint canoeist. The dominant sprint canoeist of his generation in 1000 m races, he has won three Olympic and eight world championship gold medals.
The Early Cretaceous or the Lower Cretaceous is the earlier or lower of the two major divisions of the Cretaceous. It is usually considered to stretch from 145 Ma to 100.5 Ma.
The Kaplan–Meier estimator, also known as the product limit estimator, is a non-parametric statistic used to estimate the survival function from lifetime data. In medical research, it is often used to measure the fraction of patients living for a certain amount of time after treatment. In other fields, Kaplan–Meier estimators may be used to measure the length of time people remain unemployed after a job loss, the time-to-failure of machine parts, or how long fleshy fruits remain on plants before they are removed by frugivores. The estimator is named after Edward L. Kaplan and Paul Meier, who each submitted similar manuscripts to the Journal of the American Statistical Association. The journal editor, John Tukey, convinced them to combine their work into one paper, which has been cited more than 34,000 times since its publication in 1958.
Canoeing has been featured as competition sports in the Summer Olympic Games since the 1936 Games in Berlin, and they were also demonstration sports at the 1924 Games in Paris. There are two disciplines of canoeing in Olympic competition: slalom and sprint.
The 2010 ICF Canoe Sprint World Championships were held 19–22 August 2010 in Poznań, Poland, on Lake Malta. This was the third time that the Polish city hosted the championships, having done so previously in 1990 and 2001. Paracanoe and the women's C-1 200 m events that were exhibition events at the previous world championships in Dartmouth, Nova Scotia, Canada, became official events at these championships.
The Paleocene, or Palaeocene, is a geological epoch that lasted from about 66 to 56 million years ago (mya). It is the first epoch of the Paleogene Period in the modern Cenozoic Era. The name is a combination of the Ancient Greek παλαιός palaiós meaning "old" and the Eocene Epoch, translating to "the old part of the Eocene".
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) is already known to have occurred. This particular method relies on event A occurring with some sort of relationship with another event B. In this situation, the event A can be analyzed by a conditional probability with respect to B. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B) or occasionally PB(A). This can also be understood as the fraction of probability B that intersects with A, or the ratio of the probabilities of both events happening to the "given" one happening (how many times A occurs rather than not assuming B has occurred): .
The Cretaceous–Paleogene (K–Pg) extinction event, also known as the K–T extinction, was the mass extinction of three-quarters of the plant and animal species on Earth approximately 66 million years ago. The event caused the extinction of all non-avian dinosaurs. Most other tetrapods weighing more than 25 kg (55 lb) also became extinct, with the exception of some ectothermic species such as sea turtles and crocodilians. It marked the end of the Cretaceous period, and with it the Mesozoic era, while heralding the beginning of the current era, the Cenozoic. In the geologic record, the K–Pg event is marked by a thin layer of sediment called the K–Pg boundary, Fatkito boundary or K–T boundary, which can be found throughout the world in marine and terrestrial rocks. The boundary clay shows unusually high levels of the metal iridium, which is more common in asteroids than in the Earth's crust.
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