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Federico Cafiero
Federico Cafiero (24 May 1914 – 7 May 1980) was an Italian mathematician known for his contributions in real analysis, measure and integration theory, and in the theory of ordinary differential equations. In particular, generalizing the Vitali convergence theorem, the Fichera convergence theorem and previous results of Vladimir Mikhailovich Dubrovskii, he proved a necessary and sufficient condition for the passage to the limit under the sign of integral: this result is, in some sense, definitive. In the field of ordinary differential equations, he studied existence and uniqueness problems under very general hypotheses for the left member of the given first order equation, developing an important approximation method and proving a fundamental uniqueness theorem. Life and academic career Cafiero was born in Riposto, Province of Catania, on May 24, 1914. He obtained his Laurea in mathematics, cum laude, from the University of Naples Federico II in 1939.See . During the 1939–194 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riposto
Riposto ( scn, Ripostu) is a ''comune'' (municipality) in the Catania area of southern Italy. The small seafront town is located about southeast of Palermo and about north of Catania. History Riposto is both historically and literally connected to Mascali, a once fiefdom of which it had been apart of as its commercial port in the 16th century and until it had finally gained local autonomy from in the 18th century. In the early 19th century, the town would be administratively merged with Giarre and become Giarre-Riposto by Fascist Italy. It was not until 1945 would the two towns be administratively divided once again, following the end of World War II. Geography The town is located on the Ionian Coast, and borders with the municipalities of Acireale, Giarre and Mascali. Its '' frazioni'' are Altarello, Archi, Carruba, Praiola, Quartirello and Torre Archirafi. People *Franco Battiato (1945–2021), singer-songwriter *Federico Cafiero (1914–1980), mathematician See a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Benemeriti Della Scuola, Della Cultura, Dell'Arte
The Italian honours system is a means to reward achievements or service to the Italian Republic, formerly the Kingdom of Italy including the Italian Social Republic. Orders of chivalry Italian Republic There are five orders of knighthood awarded in recognition of service to the Italian Republic. Below these sit a number of other decorations, associated and otherwise, that do not confer knighthoods. The degrees of knighthood, not all of which apply to all orders, are Knight (''Cavaliere'' abbreviated ''Cav.''), Officer (''Ufficiale'' abbreviated ''Uff.''), Commander (''Commendatore'' abbr. ''Comm.''), Grand Officer (''Grand'Ufficiale'', abbr. ''Gr. Uff.''), Knight Grand Cross (''Cavaliere di Gran Croce'', abbr. ''Cav. Gr. Croce'') and Knight Grand Cross with cordon (''Cavaliere di Gran Croce con cordone''). Italian citizens may not use within the territory of the Republic honours or distinctions conferred on them by non-national orders or foreign states, unless authorised ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laurea
In Italy, the ''laurea'' is the main post-secondary academic degree. The name originally referred literally to the laurel wreath, since ancient times a sign of honor and now worn by Italian students right after their official graduation ceremony and sometimes during the graduation party. A graduate is known as a ''laureato'', literally "crowned with laurel." The ''Laurea'' degree before the Bologna process Early history In the early Middle Ages Italian universities awarded both bachelor's and doctor's degrees. However very few bachelor's degrees from Italian universities are recorded in the later Middle Ages and none after 1500. Students could take the doctoral examination without studying at the university. This was criticised by northern Europeans as taking a degree la, per saltum, label=none because they had leapt over the regulations requiring years of study at the university. Twentieth century To earn a ''laurea'' (degree) undergraduate students had to complete four to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meta Di Sorrento
Meta (or, wrongly, Meta di Sorrento) is a ''comune'' (municipality) in the Metropolitan City of Naples in the Italian region Campania, located about 25 km southeast of Naples. Meta borders the municipalities of Piano di Sorrento and Vico Equense. See also *Sorrentine Peninsula *Amalfi Coast The Amalfi Coast ( it, Costiera amalfitana) is a stretch of coastline in southern Italy overlooking the Tyrrhenian Sea and the Gulf of Salerno. It is located south of the Sorrentine Peninsula and north of the Cilentan Coast. Celebrated worldwide ... References External links Meta di Sorrento Interactive Map Cities and towns in Campania {{Campania-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Province Of Catania
The Province of Catania ( it, Provincia di Catania; scn, Pruvincia di Catania) was a province in the autonomous island region of Sicily in southern Italy. Its capital was the city of Catania. It had an area of and a total population of about 1,116,917 as of 31 December 2014. Historically known also as ''Val di Catania'',, with the administrative meaning of Province of Catania, from sqr, وَلاية, wālāya (based on ar, وَلِيّ, wālī), but also used with the geographical meaning of Catania Valley, from la, vallis. it included until 1927 a large part of the Province of Enna. It was replaced by the Metropolitan City of Catania starting from 4 August 2015. History The Province of Catania was founded by Greeks, in 729 B.C. It was conquered by the Roman, in the First Punic War, in 263 BC. It had experienced many volcanic eruptions from the Mount Etna, of which the first eruption was recorded in 475 BC. It was hit by a devastating earthquake in 1169, which caused an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Limit (mathematics)
In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory. In formulas, a limit of a function is usually written as : \lim_ f(x) = L, (although a few authors may use "Lt" instead of "lim") and is read as "the limit of of as approaches equals ". The fact that a function approaches the limit as approaches is sometimes denoted by a right arrow (→ or \rightarrow), as in :f(x) \to L \text x \to c, which reads "f of x tends to L as x tends to c". History Grégoire de Saint-Vincent gave the first definition of limit (terminus) of a geometric series in his work ''Opus Geometricum'' (1647): "The ''terminus'' of a pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir Mikhailovich Dubrovskii
Vladimir may refer to: Names * Vladimir (name) for the Bulgarian, Croatian, Czech, Macedonian, Romanian, Russian, Serbian, Slovak and Slovenian spellings of a Slavic name * Uladzimir for the Belarusian version of the name * Volodymyr for the Ukrainian version of the name * Włodzimierz (given name) for the Polish version of the name * Valdemar for the Germanic version of the name * Wladimir for an alternative spelling of the name Places * Vladimir, Russia, a city in Russia * Vladimir Oblast, a federal subject of Russia * Vladimir-Suzdal, a medieval principality * Vladimir, Ulcinj, a village in Ulcinj Municipality, Montenegro * Vladimir, Gorj, a commune in Gorj County, Romania * Vladimir, a village in Goiești Commune, Dolj County, Romania * Vladimir (river), a tributary of the Gilort in Gorj County, Romania * Volodymyr (city), a city in Ukraine Religious leaders * Metropolitan Vladimir (other), multiple * Jovan Vladimir (d. 1016), ruler of Doclea and a saint of the Se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fichera Convergence Theorem (born 1993), Italian fencer
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Fichera is a surname. Notable people with the surname include: *Gaetano Fichera (1922–1996), Italian mathematician **Fichera's existence principle * Joseph Fichera, American business executive *Marco Fichera Marco Fichera (born 15 April 1993) is an Italian male épée fencer. Career Fichera took up fencing when he was ten years old under the guidance of maestro Domenico Patti at C.S. Acireale. In 2010 he took a double gold haul at the U17 European C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vitali Convergence Theorem
In real analysis and measure theory, the Vitali convergence theorem, named after the Italian mathematician Giuseppe Vitali, is a generalization of the better-known dominated convergence theorem of Henri Lebesgue. It is a characterization of the convergence in ''Lp'' in terms of convergence in measure and a condition related to uniform integrability In mathematics, uniform integrability is an important concept in real analysis In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties .... Preliminary definitions Let (X,\mathcal,\mu) be a measure space, i.e. \mu : \mathcal\to ,\infty/math> is a set function such that \mu(\emptyset)=0 and \mu is countably-additive. All functions considered in the sequel will be functions f:X\to \mathbb, where \mathbb=\R or \mathbb. We adopt the following definitions according to Bogachev's terminology. * A set of functions \mathcal \sub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinary Differential Equation
In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast with the term partial differential equation which may be with respect to ''more than'' one independent variable. Differential equations A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form :a_0(x)y +a_1(x)y' + a_2(x)y'' +\cdots +a_n(x)y^+b(x)=0, where , ..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of the unknown function of the variable . Among ordinary differential equations, linear differential equations play a prominent role for several reasons. Most elementary and special functions that are encountered in physics and applied mathematics are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Measure Theory
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures ( length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical context. Measures are foundational in probability theory, integration theory, and can be generalized to assume negative values, as with electrical charge. Far-reaching generalizations (such as spectral measures and projection-valued measures) of measure are widely used in quantum physics and physics in general. The intuition behind this concept dates back to ancient Greece, when Archimedes tried to calculate the area of a circle. But it was not until the late 19th and early 20th centuries that measure theory became a branch of mathematics. The foundations of modern measure theory were laid in the works of Émile Borel, Henri Lebesgue, Nikolai Luzin, Johann Radon, Const ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Analysis
In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include convergence, limits, continuity, smoothness, differentiability and integrability. Real analysis is distinguished from complex analysis, which deals with the study of complex numbers and their functions. Scope Construction of the real numbers The theorems of real analysis rely on the properties of the real number system, which must be established. The real number system consists of an uncountable set (\mathbb), together with two binary operations denoted and , and an order denoted . The operations make the real numbers a field, and, along with the order, an ordered field. The real number system is the unique ''complete ordered field'', in the sense that any other complete ordered field is isomorphic to it. Intuitively, completeness means ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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