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Bessel
Bessel may refer to: Mathematics and science * Bessel beam * Bessel ellipsoid * Bessel function in mathematics * Bessel's inequality in mathematics * Bessel's correction in statistics * Bessel filter, a linear filter often used in audio crossover systems * Bessel transform, also known as Fourier-Bessel transform or Hankel transform * Bessel window, in signal processing * Besselian date, see Epoch (astronomy)#Besselian years Places * Bessel Fjord, NE Greenland * Bessel Fjord, NW Greenland * Bessel (crater), a small lunar crater People Surname * Friedrich Wilhelm Bessel (1784–1846), German mathematician, astronomer, and systematizer of the Bessel functions * Johann Franz Bessel (1672–1749), German Benedictine abbot and historian * Vasily Bessel (1843–1907), Russian music publisher Given name * Bessel Kok (born 1941), Dutch businessman and chess organiser * Bessel van der Kolk (born 1943), Dutch psychiatrist Other uses * 1552 Bessel, an asteroid * MV ''Bessel'', a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bessel Function
Bessel functions, named after Friedrich Bessel who was the first to systematically study them in 1824, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary complex number \alpha, which represents the ''order'' of the Bessel function. Although \alpha and -\alpha produce the same differential equation, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of \alpha. The most important cases are when \alpha is an integer or half-integer. Bessel functions for integer \alpha are also known as cylinder functions or the cylindrical harmonics because they appear in the solution to Laplace's equation in cylindrical coordinates. Spherical Bessel functions with half-integer \alpha are obtained when solving the Helmholtz equation in spherical coordinates. Applications Bessel's equation arises when finding separa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friedrich Wilhelm Bessel
Friedrich Wilhelm Bessel (; 22 July 1784 – 17 March 1846) was a German astronomer, mathematician, physicist, and geodesist. He was the first astronomer who determined reliable values for the distance from the Sun to another star by the method of parallax. Certain important mathematical functions were first studied systematically by Bessel and were named Bessel functions in his honour. Life and family Bessel was born in Minden, Westphalia, then capital of the Prussian administrative region Minden-Ravensberg, as second son of a civil servant into a large family. At the age of 14 he left the school, because he did not like the education in Latin language, and apprenticed in the import-export concern Kulenkamp at Bremen. The business's reliance on cargo ships led him to turn his mathematical skills to problems in navigation. This in turn led to an interest in astronomy as a way of determining longitude. Bessel came to the attention of Heinrich Wilhelm Olbers, a practising phy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bessel Filter
In electronics and signal processing, a Bessel filter is a type of analog linear filter with a maximally flat Group delay and phase delay, group delay (i.e., maximally linear phase response), which preserves the wave shape of filtered signals in the passband. Bessel filters are often used in audio crossover systems. The filter's name is a reference to German mathematician Friedrich Bessel (1784–1846), who developed the mathematical theory on which the filter is based. The filters are also called Bessel–Thomson filters in recognition of W. E. Thomson, who worked out how to apply Bessel functions to filter design in 1949. The Bessel filter is very similar to the Gaussian filter, and tends towards the same shape as filter order increases. While the time-domain step response of the Gaussian filter has zero overshoot (signal), overshoot, the Bessel filter has a small amount of overshoot, but still much less than other common frequency-domain filters, such as Butterworth filters. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1552 Bessel
1552 Bessel, provisional designation , is a stony Eoan asteroid from the outer regions of the asteroid belt, approximately 18 kilometers in diameter. It was discovered on 24 February 1938, by Finnish astronomer Yrjö Väisälä at Turku Observatory in Southwest Finland, and named after German astronomer Friedrich Bessel. Orbit and classification ''Bessel'' is a stony asteroid and a member of the Eos family that orbits the Sun in the outer main-belt at a distance of 2.7–3.3 AU once every 5 years and 3 months (1,909 days). Its orbit has an eccentricity of 0.10 and an inclination of 10 ° with respect to the ecliptic. First observed as at Heidelberg in 1933, the body's observation arc begins at Turku, 5 days prior to its official discovery observation. Naming This minor planet was named after German astronomer Friedrich Wilhelm Bessel (1789–1846), who measured the first stellar parallax in 1838. His measured parallax of 0.314 arcseconds for 61 Cygni gave a distance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bessel Beam
Bessel may refer to: Mathematics and science * Bessel beam * Bessel ellipsoid * Bessel function in mathematics * Bessel's inequality in mathematics * Bessel's correction In statistics, Bessel's correction is the use of ''n'' − 1 instead of ''n'' in the formula for the sample variance and sample standard deviation, where ''n'' is the number of observations in a sample. This method corrects the bias in ... in statistics * Bessel filter, a linear filter often used in audio crossover systems * Bessel transform, also known as Fourier-Bessel transform or Hankel transform * Bessel window, in signal processing * Besselian date, see Epoch (astronomy)#Besselian years Places * Bessel Fjord, NE Greenland * Bessel Fjord, NW Greenland * Bessel (crater), a small lunar crater People Surname * Friedrich Wilhelm Bessel (1784–1846), German mathematician, astronomer, and systematizer of the Bessel functions * Johann Franz Bessel (1672–1749), German Benedictine abbot an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bessel (crater)
Bessel is a small lunar impact crater that is located in the southern half of the Mare Serenitatis. The crater was named after the German astronomer Friedrich Wilhelm Bessel in 1935. Despite its small size, this is the largest crater to lie entirely within the mare. It lies to the north-northeast of the crater Menelaus. This crater is circular and bowl-shaped with a rim that has a higher albedo than the floor or the surrounding mare. The outer rim is not significantly worn, and there are no features of note on the interior, apart from some slumping of material from the inner walls to the floor. Bessel is not of sufficient size to have developed the terrace structures of larger craters. A large ray crosses the mare from north to south, passing Bessel's western side. This ray is enigmatic due to its unclear origin. It appears to originate at the rim of Menelaus crater, yet it aligns with the trajectory of a Tycho ray, suggesting Tycho as a possible source. However, the Tycho r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hankel Transform
In mathematics, the Hankel transform expresses any given function ''f''(''r'') as the weighted sum of an infinite number of Bessel functions of the first kind . The Bessel functions in the sum are all of the same order ν, but differ in a scaling factor ''k'' along the ''r'' axis. The necessary coefficient of each Bessel function in the sum, as a function of the scaling factor ''k'' constitutes the transformed function. The Hankel transform is an integral transform and was first developed by the mathematician Hermann Hankel. It is also known as the Fourier–Bessel transform. Just as the Fourier transform for an infinite interval is related to the Fourier series over a finite interval, so the Hankel transform over an infinite interval is related to the Fourier–Bessel series over a finite interval. Definition The Hankel transform of order \nu of a function ''f''(''r'') is given by : F_\nu(k) = \int_0^\infty f(r) J_\nu(kr) \,r\,\mathrmr, where J_\nu is the Bessel function of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bessel's Correction
In statistics, Bessel's correction is the use of ''n'' − 1 instead of ''n'' in the formula for the sample variance and sample standard deviation, where ''n'' is the number of observations in a sample. This method corrects the bias in the estimation of the population variance. It also partially corrects the bias in the estimation of the population standard deviation. However, the correction often increases the mean squared error in these estimations. This technique is named after Friedrich Bessel. Formulation In estimating the population variance from a sample when the population mean is unknown, the uncorrected sample variance is the ''mean'' of the squares of deviations of sample values from the sample mean (i.e., using a multiplicative factor 1/''n''). In this case, the sample variance is a biased estimator of the population variance. Multiplying the uncorrected sample variance by the factor : \frac n gives an ''unbiased'' estimator of the population varia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epoch (astronomy)
In astronomy, an epoch or reference epoch is a instant, moment in time used as a reference point for some time-varying astronomical quantity. It is useful for the celestial coordinates or orbital elements of a Astronomical object, celestial body, as they are subject to Perturbation (astronomy), perturbations and vary with time. These time-varying astronomical quantities might include, for example, the mean longitude or mean anomaly of a body, the node of its orbit relative to a reference plane, the direction of the apogee or Perihelion and aphelion, aphelion of its orbit, or the size of the major axis of its orbit. The main use of astronomical quantities specified in this way is to calculate other relevant parameters of motion, in order to predict future positions and velocities. The applied tools of the disciplines of celestial mechanics or its subfield orbital mechanics (for predicting orbital paths and positions for bodies in motion under the gravitational effects of other bodi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bessel Ellipsoid
The Bessel ellipsoid (or Bessel 1841) is an important reference ellipsoid of geodesy. It is currently used by several countries for their national geodetic surveys, but will be replaced in the next decades by modern ellipsoids of satellite geodesy. The Bessel ellipsoid was derived in 1841 by Friedrich Wilhelm Bessel, based on several arc measurements and other data of continental geodetic networks of Europe, Russia and the British Survey of India. It is based on 10 meridian arcs and 38 precise measurements of the astronomic latitude and longitude (see also astro geodesy). The dimensions of the Earth ellipsoid axes were defined by logarithms in keeping with former calculation methods. The Bessel and GPS ellipsoids The Bessel ellipsoid fits especially well to the geoid curvature of Europe and Eurasia. Therefore, it is optimal for National survey networks in these regions, although its axes are about 700 m shorter than that of the mean Earth ellipsoid derived by satellites ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bessel Van Der Kolk
Bessel van der Kolk (; born July 1943) is a Boston-based Dutch-American psychiatrist, author, researcher and educator. Since the 1970s his research has been in the area of post-traumatic stress. He is the author of four books, including ''The New York Times'' best seller, '' The Body Keeps the Score'', which was translated into 43 languages. Scientists have criticized the book for promoting pseudoscientific claims about trauma, memory, the brain, and development. Van der Kolk served as president of the International Society for Traumatic Stress Studies and is a former co-director of the National Child Traumatic Stress Network. He is a professor of psychiatry at Boston University School of Medicine and president of the Trauma Research Foundation in Brookline, Massachusetts. Early life and education Van der Kolk was born in the Netherlands in July 1943. The Hague was occupied by the Nazis at the time and his father was sent to a work-camp. He was the middle child of five. His mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MV Bessel
''Bessel'' was a cargo ship that was built in 1925 as ''Sorrento'' by AG Weser, Bremen for German owners. She was sold in 1926 and renamed ''Bessel''. She was seized by the Allies in Vigo, Spain, in May 1945, passed to the Ministry of War Transport (MoWT) and renamed ''Empire Coniston''. In 1946, she was lent to the Danish Government and was allocated to them in 1947. She was sold into Danish merchant service and renamed ''Birgitte Skou''. In 1959, she was sold to Italy and renamed ''N Martini''. She was renamed ''Nicolo Martini'' in 1961, serving until 1972 when she ran aground at Portoscuso, Sardinia. Although refloated she was declared a total loss and was scrapped in 1973. Description The ship was built in 1925 as yard number 395 by AG Weser, Bremen. The ship was long, with a beam of . She had a depth of . The ship had a GRT of 1,878 and a NRT of 915. The ship was propelled by two 4-stroke Single Cycle Single Acting diesel engines, which had 6 cylinders of diameter by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
