|
Yegor Zolotarev
Yegor (Egor) Ivanovich Zolotaryov () (31 March 1847, Saint Petersburg – 19 July 1878, Saint Petersburg) was a Russian mathematician. Biography Yegor was born as a son of Agafya Izotovna Zolotaryova and the merchant Ivan Vasilevich Zolotaryov in Saint Petersburg, Imperial Russia. In 1857 he began to study at the fifth St Petersburg gymnasium, a school which centred on mathematics and natural science. He finished it with the silver medal in 1863. In the same year he was allowed to be an auditor at the physico-mathematical faculty of St Petersburg university. He had not been able to become a student before 1864 because he was too young. Among his academic teachers were Somov, Chebyshev and Aleksandr Korkin, with whom he would have a tight scientific friendship. In November 1867 he defended his Kandidat thesis ''“About the Integration of Gyroscope Equations”'', after 10 months there followed his thesis pro venia legendi ''About one question on Minima''. With this work ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heidelberg
Heidelberg (; ; ) is the List of cities in Baden-Württemberg by population, fifth-largest city in the States of Germany, German state of Baden-Württemberg, and with a population of about 163,000, of which roughly a quarter consists of students, it is List of cities in Germany by population, Germany's 51st-largest city. Located about south of Frankfurt, Heidelberg is part of the densely populated Rhine-Neckar, Rhine-Neckar Metropolitan Region which has its centre in Mannheim. Heidelberg is located on the Neckar River, at the point where it leaves its narrow valley between the Oden Forest and the Kleiner Odenwald, Little Oden Forest, and enters the wide Upper Rhine Plain. The old town lies in the valley, the end of which is flanked by the Königstuhl (Odenwald), Königstuhl in the south and the Heiligenberg (Heidelberg), Heiligenberg in the north. The majority of the population lives in the districts west of the mountains in the Upper Rhine Plain, into which the city has expan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19th-century Mathematicians From The Russian Empire
The 19th century began on 1 January 1801 (represented by the Roman numerals MDCCCI), and ended on 31 December 1900 (MCM). It was the 9th century of the 2nd millennium. It was characterized by vast social upheaval. Slavery was abolished in much of Europe and the Americas. The First Industrial Revolution, though it began in the late 18th century, expanded beyond its British homeland for the first time during the 19th century, particularly remaking the economies and societies of the Low Countries, France, the Rhineland, Northern Italy, and the Northeastern United States. A few decades later, the Second Industrial Revolution led to ever more massive urbanization and much higher levels of productivity, profit, and prosperity, a pattern that continued into the 20th century. The Catholic Church, in response to the growing influence and power of modernism, secularism and materialism, formed the First Vatican Council in the late 19th century to deal with such problems and confirm cer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1878 Deaths
Events January * January 5 – Russo-Turkish War: Battle of Shipka Pass IV – Russian and Bulgarian forces defeat the Ottoman Empire. * January 9 – Umberto I becomes King of Italy. * January 17 – Russo-Turkish War: Battle of Philippopolis – Russian troops defeat the Ottoman Empire. * January 23 – Benjamin Disraeli orders the British fleet to the Dardanelles. * January 24 – Russian revolutionary Vera Zasulich shoots at Fyodor Trepov, Governor of Saint Petersburg. * January 28 – In the United States: ** The world's First Telephone Exchange begins commercial operation in New Haven, Connecticut. ** ''The Yale News'' becomes the first daily college newspaper in the U.S. * January 31 – Turkey agrees to an armistice at Adrianople. February * February 2 – Greece declares war on the Ottoman Empire. * February 7 – Pope Pius IX dies, after a 31½ year pontificate (the longest definitely confirmed). * February 8 &nd ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1847 Births
Events January–March * January 4 – Samuel Colt sells his first revolver pistol to the U.S. government. * January 13 – The Treaty of Cahuenga ends fighting in the Mexican–American War in California. * January 16 – John C. Frémont is appointed Governor of the new California Territory. * January 17 – St. Anthony Hall fraternity is founded at Columbia University, New York City. * January 30 – Yerba Buena, California, is renamed San Francisco. * February 5 – A rescue effort, called the First Relief, leaves Johnson's Ranch to save the ill-fated Donner Party of California-bound migrants who became snowbound in the Sierra Nevada earlier this winter. Some have resorted to survival by cannibalism. * February 22 – Mexican–American War: Battle of Buena Vista – 5,000 American troops under General Zachary Taylor use their superiority in artillery to drive off 15,000 Mexican troops under Antonio López de Santa Anna, defeating the Mexicans the next day. * Febr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Filter
An elliptic filter (also known as a Cauer filter, named after Wilhelm Cauer, or as a Zolotarev filter, after Yegor Zolotarev) is a filter (signal processing), signal processing filter with equalized ripple (filters), ripple (equiripple) behavior in both the passband and the stopband. The amount of ripple in each band is independently adjustable, and no other filter of equal order can have a faster transition in Gain (electronics), gain between the passband and the stopband, for the given values of ripple (whether the ripple is equalized or not). Alternatively, one may give up the ability to adjust independently the passband and stopband ripple, and instead design a filter which is maximally insensitive to component variations. As the ripple in the stopband approaches zero, the filter becomes a type I Chebyshev filter. As the ripple in the passband approaches zero, the filter becomes a type II Chebyshev filter and finally, as both ripple values approach zero, the filter becomes a B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zolotarev Polynomials
In mathematics, Zolotarev polynomials are polynomials used in approximation theory. They are sometimes used as an alternative to the Chebyshev polynomials where accuracy of approximation near the origin is of less importance. Zolotarev polynomials differ from the Chebyshev polynomials in that two of the coefficients are fixed in advance rather than allowed to take on any value. The Chebyshev polynomials of the first kind are a special case of Zolotarev polynomials. These polynomials were introduced by Russian mathematician Yegor Ivanovich Zolotarev in 1868. Definition and properties Zolotarev polynomials of degree n in x are of the form : Z_n(x,\sigma) = x^n -\sigma x^ + \cdots + a_k x^k + \cdots + a_0 \ , where \sigma is a prescribed value for a_ and the a_k \in \mathbb R are otherwise chosen such that the deviation of Z_n(x) from zero is minimum in the interval 1,1/math>. A subset of Zolotarev polynomials can be expressed in terms of Chebyshev polynomials of the first kin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zolotarev's Lemma
In number theory, Zolotarev's lemma states that the Legendre symbol :\left(\frac\right) for an integer ''a'' modulo an odd prime number ''p'', where ''p'' does not divide ''a'', can be computed as the sign of a permutation: :\left(\frac\right) = \varepsilon(\pi_a) where ε denotes the signature of a permutation and π''a'' is the permutation of the nonzero residue classes mod ''p'' induced by multiplication by ''a''. For example, take ''a'' = 2 and ''p'' = 7. The nonzero squares mod 7 are 1, 2, and 4, so (2, 7) = 1 and (6, 7) = −1. Multiplication by 2 on the nonzero numbers mod 7 has the cycle decomposition (1,2,4)(3,6,5), so the sign of this permutation is 1, which is (2, 7). Multiplication by 6 on the nonzero numbers mod 7 has cycle decomposition (1,6)(2,5)(3,4), whose sign is −1, which is (6, 7). Proof In general, for any finite group ''G'' of order ''n'', it is straightforward to determine the signature of the permutation π''g'' made by left-multiplication by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nouvelles Annales De Mathématiques
The ''Nouvelles Annales de Mathématiques'' (subtitled ''Journal des candidats aux écoles polytechnique et normale'') was a French scientific journal in mathematics. It was established in 1842 by Olry Terquem and Camille-Christophe Gerono, and continued publication until 1927, with later editors including Charles-Ange Laisant and Raoul Bricard. , retrieved 2014-07-14. Initially published by Carilian-Goeury, it was taken over after several years by a different publisher, Bachelier. Although competing in subject matter with Joseph Lio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stable Distributions
In probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. Of the four parameters defining the family, most attention has been focused on the stability parameter, \alpha (see panel). Stable distributions have 0 < \alpha \leq 2, with the upper bound corresponding to the , and to the |
Blood Poisoning
Blood is a body fluid in the circulatory system of humans and other vertebrates that delivers necessary substances such as nutrients and oxygen to the cells, and transports metabolic waste products away from those same cells. Blood is composed of blood cells suspended in blood plasma. Plasma, which constitutes 55% of blood fluid, is mostly water (92% by volume), and contains proteins, glucose, mineral ions, and hormones. The blood cells are mainly red blood cells (erythrocytes), white blood cells (leukocytes), and (in mammals) platelets (thrombocytes). The most abundant cells are red blood cells. These contain hemoglobin, which facilitates oxygen transport by reversibly binding to it, increasing its solubility. Jawed vertebrates have an adaptive immune system, based largely on white blood cells. White blood cells help to resist infections and parasites. Platelets are important in the clotting of blood. Blood is circulated around the body through blood vessels by the pumpin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tsarskoe Selo
Tsarskoye Selo (, , ) was the town containing a former residence of the Russian imperial family and visiting nobility, located south from the center of Saint Petersburg. The residence now forms part of the town of Pushkin. Tsarskoye Selo forms one of the World Heritage Site Saint Petersburg and Related Groups of Monuments. The town bore the name Tsarskoye Selo until 1918. The new Bolshevik government of Soviet Russia renamed it as Detskoye Selo (), which it held from 1918–1937. At that time, it was renamed under Stalin's government as Pushkin () after the famous Russian poet and writer. It is still known by that name. History The area of Tsarskoye Selo, once part of Swedish Ingria, first became a Russian royal/imperial residence in the early 18th century as an estate of the Empress-consort Catherine (later Empress-regnant as Catherine I, ), for whom the Catherine Palace is named. When Peter the Great took possession of the mouth of the Neva, a Finnish village, Saari-mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
