Finitely generated moduleIn mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated module over a ring R may also be called a finite R-module, finite over R, or a module of finite type. Related concepts include finitely cogenerated modules, finitely presented modules, finitely related modules and coherent modules all of which are defined below. Over a Noetherian ring the concepts of finitely generated, finitely presented and coherent modules coincide.
Hermite polynomialsIn mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets for wavelet transform analysis probability, such as the Edgeworth series, as well as in connection with Brownian motion; combinatorics, as an example of an Appell sequence, obeying the umbral calculus; numerical analysis as Gaussian quadrature; physics, where they give rise to the eigenstates of the quantum harmonic oscillator; and they also occur in some cases of the heat equation (when the term is present); systems theory in connection with nonlinear operations on Gaussian noise.
Ed Roberts (computer engineer)Henry Edward Roberts (September 13, 1941 – April 1, 2010) was an American engineer, entrepreneur and medical doctor who invented the first commercially successful personal computer in 1974. He is most often known as "the father of the personal computer." He founded Micro Instrumentation and Telemetry Systems (MITS) in 1970 to sell electronics kits to model rocketry hobbyists, but the first successful product was an electronic calculator kit that was featured on the cover of the November 1971 issue of Popular Electronics.
Perlin noisePerlin noise is a type of gradient noise developed by Ken Perlin in 1983. It has many uses, including but not limited to: procedurally generating terrain, applying pseudo-random changes to a variable, and assisting in the creation of s. It is most commonly implemented in two, three, or four dimensions, but can be defined for any number of dimensions. Ken Perlin developed Perlin noise in 1983 as a result of his frustration with the "machine-like" look of (CGI) at the time.
Mathematics in the medieval Islamic worldMathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta). Important progress was made, such as full development of the decimal place-value system to include decimal fractions, the first systematised study of algebra, and advances in geometry and trigonometry. Arabic works played an important role in the transmission of mathematics to Europe during the 10th—12th centuries.
Ohio ScientificOhio Scientific, Inc. (OSI, originally Ohio Scientific Instruments, Inc.), was a privately owned American computer company based in Ohio that built and marketed computer systems, expansions, and software from 1975 to 1986. Their best-known products were the Challenger series of microcomputers and Superboard single-board computers. The company was the first to market microcomputers with hard disk drives in 1977. The company was incorporated as Ohio Scientific Instruments in Hiram, Ohio, by husband and wife Mike and Charity Cheiky and business associate Dale A.
Associate degreeAn associate degree or associate's degree is an undergraduate degree awarded after a course of post-secondary study lasting two to three years. It is a level of academic qualification above a high school diploma and below a bachelor's degree. The first associate degrees were awarded in the UK (where they are no longer awarded) in 1873 before spreading to the US in 1898. In the United States, the associate degree may allow transfer into the third year of a bachelor's degree.
Associative algebraIn mathematics, an associative algebra A is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field K. The addition and multiplication operations together give A the structure of a ring; the addition and scalar multiplication operations together give A the structure of a vector space over K. In this article we will also use the term [[algebra over a field|K-algebra]] to mean an associative algebra over the field K.
Diethylene glycolDiethylene glycol (DEG) is an organic compound with the formula (HOCH2CH2)2O. It is a colorless, practically odorless, and hygroscopic liquid with a sweetish taste. It is a four carbon dimer of ethylene glycol. It is miscible in water, alcohol, ether, acetone, and ethylene glycol. DEG is a widely used solvent. It can be a contaminant in consumer products; this has resulted in numerous epidemics of poisoning since the early 20th century. DEG is produced by the partial hydrolysis of ethylene oxide.
Bernoulli polynomialsIn mathematics, the Bernoulli polynomials, named after Jacob Bernoulli, combine the Bernoulli numbers and binomial coefficients. They are used for series expansion of functions, and with the Euler–MacLaurin formula. These polynomials occur in the study of many special functions and, in particular, the Riemann zeta function and the Hurwitz zeta function. They are an Appell sequence (i.e. a Sheffer sequence for the ordinary derivative operator). For the Bernoulli polynomials, the number of crossings of the x-axis in the unit interval does not go up with the degree.
Micro Instrumentation and Telemetry SystemsMicro Instrumentation and Telemetry Systems (MITS) was an American electronics company founded in Albuquerque, New Mexico that began manufacturing electronic calculators in 1971 and personal computers in 1975. Ed Roberts and Forrest Mims founded MITS in December 1969 to produce miniaturized telemetry modules for model rockets such as a roll rate sensor. In 1971, Roberts redirected the company into the electronic calculator market and the MITS 816 desktop calculator kit was featured on the November 1971 cover of Popular Electronics.
Lie algebraIn mathematics, a Lie algebra (pronounced liː ) is a vector space together with an operation called the Lie bracket, an alternating bilinear map , that satisfies the Jacobi identity. Otherwise said, a Lie algebra is an algebra over a field where the multiplication operation is now called Lie bracket and has two additional properties: it is alternating and satisfies the Jacobi identity. The Lie bracket of two vectors and is denoted . The Lie bracket does not need to be associative, meaning that the Lie algebra can be non associative.
