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1 dzień temu · In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1 / 2.Many consider it to be the most important unsolved problem in pure mathematics. It is of great interest in number theory because it implies results about the distribution of prime numbers.
4 godz. temu · Definition and basic operations Various complex numbers depicted in the complex plane. A complex number is an expression of the form a + bi, where a and b are real numbers, and i is an abstract symbol, the so-called imaginary unit, whose meaning will be explained further below.For example, 2 + 3i is a complex number. For a complex number a + bi, the real number a is called its real part, and ...
1 dzień temu · In mathematics and computer algebra, automatic differentiation (auto-differentiation, autodiff, or AD), also called algorithmic differentiation, computational differentiation, is a set of techniques to evaluate the partial derivative of a function specified by a computer program.. Automatic differentiation exploits the fact that every computer calculation, no matter how complicated, executes a ...
1 dzień temu · Cayley Q8 graph showing the six cycles of multiplication by i, j and k. (If the image is opened in the Wikimedia Commons by clicking twice on it, cycles can be highlighted by hovering over or clicking on them.). In mathematics, the quaternion number system extends the complex numbers.Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to ...
1 dzień temu · In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform on the interval [0, 1]. Copulas are used to describe/model the dependence (inter-correlation) between random variables. Their name, introduced by applied mathematician Abe Sklar in 1959, comes from the Latin for "link" or ...
4 godz. temu · The number π (/ p aɪ /; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159.The number π appears in many formulae across mathematics and physics.It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as are commonly used to ...
1 dzień temu · Type I Chebyshev filters are the most common types of Chebyshev filters. The gain (or amplitude) response, , as a function of angular frequency of the th-order low-pass filter is equal to the absolute value of the transfer function evaluated at : where is the ripple factor, is the cutoff frequency and is a Chebyshev polynomial of the th order.
