Related:
Abel's identity,
Artificial membrane,
Asymptotic analysis,
Bessel–Clifford function,
Bessel filter,
Bessel polynomials,
Complex number,
Complex plane,
Conduction (heat),
Confluent hypergeometric function,
Cylindrical coordinates,
Daniel Bernoulli,
Differential equation,
Dirac delta function,
Drum,
Electromagnetic radiation,
Encyclopaedia of Mathematics,
Entire function,
Eta (letter),
Euler–Mascheroni constant,
Exponential decay,
Exponential growth,
FM synthesis,
Factorial,
Fourier–Bessel series,
Fourier series,
Fourier transform,
Frequency,
Frequency modulation,
Friedrich Bessel,
G. N. Watson,
Gamma function,
Half-integer,
Handbook of Mathematical Functions,
Hankel transform,
Helmholtz equation,
Hermann Hankel,
Hermitian,
Holomorphic function,
Hypergeometric series,
Imaginary unit,
Integer,
International Standard Book Number,
Jacobi–Anger expansion,
Kaiser window,
Kelvin functions,
Kronecker delta,
Laguerre polynomials,
Laplace's equation,
Laplace transform,
Laurent series,
Linearly independent,
Lommel function,
Lommel polynomial,
Mathematician,
Mathematics,
Membranophone,
Methods of contour integration,
Mie scattering,
Multiplication theorem,
Neumann polynomial,
P. A. Hansen,
Peter Debye,
Plane wave,
Propagator,
Recurrence relation,
Root of a function,
Schrödinger equation,
Sign convention,
Sinc function,
Spherical coordinates,
Struve function,
Taylor series,
Trigonometric function,
Wave propagation,
Waveguide,
Wronskian,
In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y(x) of Bessel's differential equation:
In mathematics, Abel's identity (also called Abel's differential equation identity) is an equation that expresses the Wronskian of two homogeneous solutions of a second-order linear ordinary differential equation in terms of a coefficient of the original differential equation. The relation can be generalised to nth-order linear ordinary differential equations. The identity is named after the Norwegian mathematician Niels Henrik Abel.
Artificial membrane also known as synthetic membrane is a syntheticly created membrane which is usually intended for separation purposes in laboratory or in industry. Synthetic membranes have been successfully used for small and large-scale industrial processes since the middle of twentieth century.[1] A wide variety of synthetic membranes is known.[2] They can be produced from organic materials such as polymers and liquids, as well as inorganic materials. The most of commercially utilized synthetic membranes in separation industry are made of polymeric structures. They can be classified based on their surface chemistry, bulk structure, morphology, and production method. The chemical and physical properties of synthetic membranes and separated particles as well as a choice of driving force define a particular membrane separation process. The most commonly used driving forces of a membrane process in industry are pressure and concentration gradients. The respective membrane process is therefore known as filtration. Synthetic membranes utilized in a separation process can be of different geometry and the respective flow configuration. They can be also categorized based on their application and separation regime.[2] The most known synthetic membranes separation processes include water purification, reverse osmosis, dehydrogenation of natural gas, removal of cell particles by microfiltration and ultrafiltration, removal of microorganisms from dairy products, and dialysis.
In computer science and applied mathematics, particularly the analysis of algorithms, asymptotic analysis is a method of describing limiting behavior. Examples include the performance of algorithms when applied to very large input data, or the behavior of physical systems when they are very large.In mathematical analysis, the Bessel–Clifford function, named after Friedrich Bessel and William Kingdon Clifford, is an entire function of two complex variables that can be used to provide an alternative development of the theory of Bessel functions. If
In electronics and signal processing, a Bessel filter is a type of linear filter with a maximally flat group delay (maximally linear phase response). Bessel filters are often used in audio crossover systems. Analog Bessel filters are characterized by almost constant group delay across the entire passband, thus preserving the wave shape of filtered signals in the passband.In mathematics, the Bessel polynomials are an orthogonal sequence of polynomials. There are a number of different but closely related definitions. The definition favored by mathematicians is given by the series (Krall & Fink, 1948)A complex number, in mathematics, is a number comprising a real number and an imaginary number. It can be written in the form a + bi, where a and b are real numbers, and i is the standard imaginary unit with the property i 2 = −1.[1] The complex numbers contain the ordinary real numbers, but extend them by adding in extra numbers and correspondingly expanding the understanding of addition and multiplication. This is in order to form a closed field, where any polynomial equation has a root, including examples such as x2 = −1.