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The number e, also known as Euler's number, is a mathematical constant approximately equal to 2.71828, and can be characterized in many ways. It is the base of the natural logarithm. It is the limit of (1 + 1/n)n as n approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series
In probability theory, the expected value of a random variable , often denoted , , or , is a generalization of the weighted average, and is intuitively the arithmetic mean of a large number of independent realizations of . The expectation operator is also commonly stylized as or . The expected value is also known as the expectation, mathematical expectation, mean, average, or first moment. Expected value is a key concept in economics, finance, and many other subjects.
The exponential function is a mathematical function denoted by or . It can be defined in several equivalent ways. Its ubiquitous occurrence in pure and applied mathematics has led mathematician W. Rudin to opine that the exponential function is "the most important function in mathematics". Its value at 1, is a mathematical constant called Euler's number.
In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest. Formally, a kinetic energy is any term in a system's Lagrangian which includes a derivative with respect to time.
Maxwell's equations are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. They describe how electric and magnetic fields are generated by charges, currents, and changes of the fields. The equations are named after the physicist and mathematician James Clerk Maxwell, who, in 1861 and 1862, published an early form of the equations that included the Lorentz force law. Maxwell first used the equations to propose that light is an electromagnetic phenomenon. The modern form of the equations in their most common formulation is credited to Oliver Heaviside.
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events.
Colonel Thomas Edward Lawrence was a British archaeologist, army officer, diplomat, and writer, who became renowned for his role in the Arab Revolt (1916–1918) and the Sinai and Palestine Campaign (1915–1918) against the Ottoman Empire during the First World War. The breadth and variety of his activities and associations, and his ability to describe them vividly in writing, earned him international fame as Lawrence of Arabia, a title used for the 1962 film based on his wartime activities.
In probability theory and statistics, the exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts.
In mathematics, a Fourier transform (FT) is a mathematical transform that decomposes functions depending on space or time into functions depending on spatial or temporal frequency, such as the expression of a musical chord in terms of the volumes and frequencies of its constituent notes. The term Fourier transform refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time.
The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by , , or .
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject. The equation is named after Erwin Schrödinger, who postulated the equation in 1925, and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933.
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of the empirical Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. The ideal gas law is often written in an empirical form:
Electrical resistivity is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter ρ (rho). The SI unit of electrical resistivity is the ohm-meter (Ω⋅m). For example, if a 1 m3 solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is 1 Ω, then the resistivity of the material is 1 Ω⋅m.
E.T. the Extra-Terrestrial is a 1982 American science fiction film produced and directed by Steven Spielberg, and written by Melissa Mathison. It tells the story of Elliott, a boy who befriends an extraterrestrial, dubbed E.T., who is stranded on Earth. Along with his friends and family, Elliott must find a way to help E.T. return home while avoiding the government. The film stars Dee Wallace, Henry Thomas, Peter Coyote, Robert MacNaughton, and Drew Barrymore.
The second law of thermodynamics establishes the concept of entropy as a physical property of a thermodynamic system. Entropy change predicts the direction of spontaneous processes, and determines whether they are irreversible or impossible despite obeying the requirement of conservation of energy as expressed in the first law of thermodynamics. The second law may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease, as they always arrive at a state of thermodynamic equilibrium, where the entropy is highest at the given internal energy. If all processes in the system are reversible, the entropy is constant. An increase in entropy accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time.
Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is considered radioactive. Three of the most common types of decay are alpha decay, beta decay, and gamma decay, all of which involve emitting one or more particles. The weak force is the mechanism that is responsible for beta decay, while the other two are governed by the electromagnetic and strong forces.
In biochemistry, Michaelis–Menten kinetics is one of the best-known models of enzyme kinetics. It is named after German biochemist Leonor Michaelis and Canadian physician Maud Menten. The model takes the form of an equation describing the rate of enzymatic reactions, by relating reaction rate to , the concentration of a substrate S. Its formula is given by
In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them or to a difference in gravitational potential between their locations. When unspecified, "time dilation" usually refers to the effect due to velocity.
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by , is the factor by which the eigenvector is scaled.
In probability theory and statistics, the Poisson distribution, named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.
References
- Arias, E.T.; Slipinski, A.; Lawrence, J.F.; Elgueta, M. 2009: A review of the Chilean Egoliini (Coleoptera: Trogossitidae) with description of a new species of Necrobiopsis Crowson. Zootaxa, 2170: 37–45
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