Poisson point processIn probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field.
Compound Poisson processA compound Poisson process is a continuous-time stochastic process with jumps. The jumps arrive randomly according to a Poisson process and the size of the jumps is also random, with a specified probability distribution. To be precise, a compound Poisson process, parameterised by a rate and jump size distribution G, is a process given by where, is the counting variable of a Poisson process with rate , and are independent and identically distributed random variables, with distribution function G, which are also independent of When are non-negative integer-valued random variables, then this compound Poisson process is known as a stuttering Poisson process.
Mortal sinA mortal sin (peccatum mortale), in Catholic theology, is a gravely sinful act which can lead to damnation if a person does not repent of the sin before death. It is alternatively called deadly, grave, and serious. A sin is considered to be "mortal" when its quality is such that it leads to a separation of that person from God's saving grace. Three conditions must together be met for a sin to be mortal: "Mortal sin is sin whose object is grave matter and which is also committed with full knowledge and deliberate consent.
Christian views on sinIn Christianity, 'sin' is an immoral act considered to be a transgression of divine law. The doctrine of sin is central to the Christian faith, since its basic message is about redemption in Christ. Hamartiology, a branch of Christian theology which is the study of sin, describes sin as an act of offence against God by despising his persons and Christian biblical law, and by injuring others. Christian hamartiology is closely related to concepts of natural law, moral theology and Christian ethics.
Eternal sinIn Christian hamartiology, eternal sin, the unforgivable sin, unpardonable sin, or ultimate sin is the sin which will not be forgiven by God. One eternal or unforgivable sin (blasphemy against the Holy Spirit), also known as the sin unto death, is specified in several passages of the Synoptic Gospels, including Mark 3:28–29, Matthew 12:31–32, and Luke 12:10, as well as other New Testament passages including Hebrews 6:4–6, Hebrews 10:26–31, and 1 John 5:16.
Cox processIn probability theory, a Cox process, also known as a doubly stochastic Poisson process is a point process which is a generalization of a Poisson process where the intensity that varies across the underlying mathematical space (often space or time) is itself a stochastic process. The process is named after the statistician David Cox, who first published the model in 1955.
11 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0.
Σ-algebraIn mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a nonempty collection Σ of subsets of X closed under complement, countable unions, and countable intersections. The ordered pair is called a measurable space. The σ-algebras are a subset of the set algebras; elements of the latter only need to be closed under the union or intersection of finitely many subsets, which is a weaker condition.
Σ-finite measureIn mathematics, a positive (or signed) measure μ defined on a σ-algebra Σ of subsets of a set X is called a finite measure if μ(X) is a finite real number (rather than ∞), and a set A in Σ is of finite measure if μ(A) < ∞. The measure μ is called σ-finite if X is a countable union of measurable sets each with finite measure. A set in a measure space is said to have σ-finite measure if it is a countable union of measurable sets with finite measure. A measure being σ-finite is a weaker condition than being finite, i.
22 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures. The digit used in the modern Western world to represent the number 2 traces its roots back to the Indic Brahmic script, where "2" was written as two horizontal lines. The modern Chinese and Japanese languages (and Korean Hanja) still use this method.
Po (river)The Po (poʊ , ˈpɔ) is the longest river in Italy. It flows eastward across northern Italy starting from the Cottian Alps. The river's length is either or , if the Maira, a right bank tributary, is included. The headwaters of the Po are a spring seeping from a stony hillside at Pian del Re, a flat place at the head of the Val Po under the northwest face of Monviso. The Po then extends along the 45th parallel north before ending at a delta projecting into the Adriatic Sea near Venice.
Po ValleyThe Po Valley, Po Plain, Plain of the Po, or Padan Plain (Pianura Padana pjaˈnuːra paˈdaːna, or Val Padana) is a major geographical feature of Northern Italy. It extends approximately in an east-west direction, with an area of including its Venetic extension not actually related to the Po river basin; it runs from the Western Alps to the Adriatic Sea. The flatlands of Veneto and Friuli are often considered apart since they do not drain into the Po, but they effectively combine into an unbroken plain, making it the largest in Southern Europe.
Spent nuclear fuelSpent nuclear fuel, occasionally called used nuclear fuel, is nuclear fuel that has been irradiated in a nuclear reactor (usually at a nuclear power plant). It is no longer useful in sustaining a nuclear reaction in an ordinary thermal reactor and, depending on its point along the nuclear fuel cycle, it will have different isotopic constituents than when it started. Nuclear fuel rods become progressively more radioactive (and less thermally useful) due to neutron activation as they are fissioned, or "burnt" in the reactor.
Stochastic processIn probability theory and related fields, a stochastic (stəˈkæstɪk) or random process is a mathematical object usually defined as a sequence of random variables, where the index of the sequence has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule.
FranceFrance (fʁɑ̃s), officially the French Republic (République française ʁepyblik fʁɑ̃sɛz), is a country located primarily in Western Europe. It also includes overseas regions and territories in the Americas and the Atlantic, Pacific and Indian Oceans, giving it one of the largest discontiguous exclusive economic zones in the world. Its metropolitan area extends from the Rhine to the Atlantic Ocean and from the Mediterranean Sea to the English Channel and the North Sea; overseas territories include French Guiana in South America, Saint Pierre and Miquelon in the North Atlantic, the French West Indies, and many islands in Oceania and the Indian Ocean.
Al-QaedaAl-Qaeda is a Sunni pan-Islamist militant organization led by Salafi jihadists who self-identify as a vanguard spearheading a global Islamist revolution to unite the Muslim world under a supra-national Islamic state known as the Caliphate. Its members are mostly composed of Arabs, but also include other peoples. Al-Qaeda has mounted attacks on civilian and military targets in various countries, including the 1998 United States embassy bombings and the September 11 attacks; it has been designated as a terrorist group by the United Nations Security Council, the North Atlantic Treaty Organization (NATO), the European Union, and various countries around the world.
Islamic StateThe Islamic State (IS), also known as the Islamic State of Iraq and the Levant (ISIL; ˈaɪsᵻl), Islamic State of Iraq and Syria (ISIS; ˈaɪsᵻs), and by its Arabic acronym Da'ish or Daesh (داعش, Dāʿish, ˈdaːʕɪʃ), is a transnational militant Islamist terrorist group and former unrecognized quasi-state that follows the Salafi jihadist branch of Sunni Islam. It was founded by Abu Musab al-Zarqawi in 1999 and gained global prominence in 2014, when it captured a large amount of Iraqi territory, and took advantage of the civil war in Syria to take control of chunks of territory in Eastern Syria.
44 (four) is a number, numeral and digit. It is the natural number following 3 and preceding 5. It is a square number, the smallest semiprime and composite number, and is considered unlucky in many East Asian cultures. Brahmic numerals represented 1, 2, and 3 with as many lines. 4 was simplified by joining its four lines into a cross that looks like the modern plus sign. The Shunga would add a horizontal line on top of the digit, and the Kshatrapa and Pallava evolved the digit to a point where the speed of writing was a secondary concern.
Homogeneous functionIn mathematics, a homogeneous function is a function of several variables such that, if all its arguments are multiplied by a scalar, then its value is multiplied by some power of this scalar, called the degree of homogeneity, or simply the degree; that is, if k is an integer, a function f of n variables is homogeneous of degree k if for every and For example, a homogeneous polynomial of degree k defines a homogeneous function of degree k.
Sigma-additive set functionIn mathematics, an additive set function is a function mapping sets to numbers, with the property that its value on a union of two disjoint sets equals the sum of its values on these sets, namely, If this additivity property holds for any two sets, then it also holds for any finite number of sets, namely, the function value on the union of k disjoint sets (where k is a finite number) equals the sum of its values on the sets. Therefore, an additive set function is also called a finitely additive set function (the terms are equivalent).
