|
Paul Du Bois-Reymond
Paul David Gustav du Bois-Reymond (2 December 1831 – 7 April 1889) was a German mathematician who was born in Berlin and died in Freiburg. He was the brother of Emil du Bois-Reymond. His thesis was concerned with the mechanical equilibrium of fluids. He worked on the theory of functions and in mathematical physics. His interests included Sturm–Liouville theory, integral equations, variational calculus, and Fourier series. In this latter field, he was able in 1873 to construct a continuous function whose Fourier series is not convergent. His lemma defines a sufficient condition to guarantee that a function vanishes almost everywhere. In a paper of 1875, du Bois-Reymond employed for the first time the method of diagonalization, later associated with the name of Cantor. Du Bois-Reymond also established that a trigonometric series that converges to a continuous function at every point is the Fourier series of this function. He is also associated with the fundam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trigonometric Series
In mathematics, trigonometric series are a special class of orthogonal series of the form : A_0 + \sum_^\infty A_n \cos + B_n \sin, where x is the variable and \ and \ are coefficients. It is an infinite version of a trigonometric polynomial. A trigonometric series is called the Fourier series of the integrable function f if the coefficients have the form: :A_n=\frac1\pi \int^_0\! f(x) \cos \,dx :B_n=\frac\displaystyle\int^_0\! f(x) \sin \, dx Examples Every Fourier series gives an example of a trigonometric series. Let the function f(x) = x on \pi,\pi/math> be extended periodically (see sawtooth wave). Then its Fourier coefficients are: :\begin A_n &= \frac1\pi\int_^ x \cos \,dx = 0, \quad n \ge 0. \\ ptB_n &= \frac1\pi\int_^ x \sin \, dx \\ pt&= -\frac \cos + \frac1\sin \Bigg\vert_^\pi \\ mu&= \frac, \quad n \ge 1.\end Which gives an example of a trigonometric series: :2\sum_^\infty \frac \sin = 2\sin - \frac22\sin + \frac23\sin - \frac24\sin + \cdots However ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
German People Of French Descent
German(s) may refer to: * Germany, the country of the Germans and German things **Germania (Roman era) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizenship in Germany, see also German nationality law **Germanic peoples (Roman era) *German diaspora * German language * German cuisine, traditional foods of Germany People * German (given name) * German (surname) * Germán, a Spanish name Places * German (parish), Isle of Man * German, Albania, or Gërmej * German, Bulgaria * German, Iran * German, North Macedonia * German, New York, U.S. * Agios Germanos, Greece Other uses * German (mythology), a South Slavic mythological being * Germans (band), a Canadian rock band * "German" (song), a 2019 song by No Money Enterprise * ''The German'', a 2008 short film * "The Germans", an episode of ''Fawlty Towers'' * ''The German'', a nickname for Congolese rebel André Kisase Ngandu See also * Germanic (disambiguatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academic Staff Of Technische Universität Berlin
An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of tertiary education. The name traces back to Plato's school of philosophy, founded approximately 386 BC at Akademia, a sanctuary of Athena, the goddess of wisdom and Skills, skill, north of Ancient Athens, Athens, Greece. The Royal Spanish Academy defines academy as scientific, literary or artistic society established with public authority and as a teaching establishment, public or private, of a professional, artistic, technical or simply practical nature. Etymology The word comes from the ''Academy'' in ancient Greece, which derives from the Athenian hero, ''Akademos''. Outside the city walls of Athens, the Gymnasium (ancient Greece), gymnasium was made famous by Plato as a center of learning. The sacred space, dedicated to the goddess of wisdom, Athena, had formerly been an olive Grove (nature), grove, hence the expression "the groves of Academe". In these gardens, the philos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From The Province Of Brandenburg
The term "the people" refers to the public or common mass of people of a polity. As such it is a concept of human rights law, international law as well as constitutional law, particularly used for claims of popular sovereignty. In contrast, a people is any plurality of persons considered as a whole. Used in politics and law, the term "a people" refers to the collective or community of an ethnic group or nation. Concepts Legal Chapter One, Article One of the Charter of the United Nations states that "peoples" have the right to self-determination. Though the mere status as peoples and the right to self-determination, as for example in the case of Indigenous peoples (''peoples'', as in all groups of indigenous people, not merely all indigenous persons as in ''indigenous people''), does not automatically provide for independent sovereignty and therefore secession. Indeed, judge Ivor Jennings identified the inherent problems in the right of "peoples" to self-determination, as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematicians From Berlin
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria ( – 415). She succeed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19th-century German Mathematicians
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 ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1889 Deaths
Events January * January 1 ** The total solar eclipse of January 1, 1889 is seen over parts of California and Nevada. ** Paiute spiritual leader Wovoka experiences a Vision (spirituality), vision, leading to the start of the Ghost Dance movement in the Dakotas. * January 4 – An Act to Regulate Appointments in the Marine Hospital Service of the United States is signed by President Grover Cleveland. It establishes a Commissioned Corps of officers, as a predecessor to the modern-day U.S. Public Health Service Commissioned Corps. * January 8 – Herman Hollerith receives a patent for his electric tabulating machine in the United States. * January 15 – The Coca-Cola Company is originally Incorporation (business), incorporated as the Pemberton Medicine Company in Atlanta, Georgia (U.S. state), Georgia. * January 22 – Columbia Phonograph is formed in Washington, D.C. * January 30 – Mayerling incident: Rudolf, Crown Prince of Austria, and his mistress Baroness Mary Vetsera co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1831 Births
Events January–March * January 1 – William Lloyd Garrison begins publishing '' The Liberator'', an anti-slavery newspaper, in Boston, Massachusetts. * January 10 – Japanese department store, Takashimaya in Kyoto established. * February–March – Revolts in Modena, Parma and the Papal States are put down by Austrian troops. * February 2 – Pope Gregory XVI succeeds Pope Pius VIII, as the 254th pope. * February 5 – Dutch naval lieutenant Jan van Speyk blows up his own gunboat in Antwerp rather than strike his colours on the demand of supporters of the Belgian Revolution. * February 7 – The Belgian Constitution of 1831 is approved by the National Congress. *February 8 – French-born botanical explorer Aimé Bonpland leaves Paraguay for Argentina. * February 14 – Battle of Debre Abbay: Ras Marye of Yejju marches into Tigray, and defeats and kills the warlord Sabagadis. * February 25 – Battle of Olsz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinitesimal
In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally referred to the "infinity- th" item in a sequence. Infinitesimals do not exist in the standard real number system, but they do exist in other number systems, such as the surreal number system and the hyperreal number system, which can be thought of as the real numbers augmented with both infinitesimal and infinite quantities; the augmentations are the reciprocals of one another. Infinitesimal numbers were introduced in the development of calculus, in which the derivative was first conceived as a ratio of two infinitesimal quantities. This definition was not rigorously formalized. As calculus developed further, infinitesimals were replaced by limits, which can be calculated using the standard real numbers. In the 3rd century BC Archimedes used what ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
