|
Federico Cafiero
Federico Cafiero (24 May 1914 – 7 May 1980) was an Italian mathematician known for his contributions in real analysis, measure theory, measure and Integral (mathematics), 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 (mathematics), limit under the sign of Integral (mathematics), 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riposto
Riposto () is a ''comune'' (municipality) in the Catania area of Sicily, southern Italy. The small seafront town is located about southeast of Palermo and about north of Catania. History Riposto is historically connected to Mascali, as its commercial port since the 16th century, until it finally gained autonomy in the 18th century. In the early 19th century, the town would be merged with Giarre, changing its name to Ionia in 1939. In 1945 the two towns were divided once again. Geography The town is located on the Ionian Sea, Ionian Coast, and borders with the municipalities of Acireale, Giarre and Mascali. Its ''Frazione, frazioni'' are Altarello, Archi, Carruba, Praiola, Quartirello and Torre Archirafi. People *Franco Battiato (1945–2021), singer-songwriter *Federico Cafiero (1914–1980), mathematician See also *Giarre-Riposto References External links Official website Riposto, {{Sicily-geo-stub ... [...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 author ... [...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" and is awarded the title of ''dottore'', or Doctor. 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 because they had leapt over the regulations requiring years of study at the university. Twentieth century To earn a ''laurea'' (degree) undergraduate student ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meta Di Sorrento
Meta (also unofficially known as Meta di Sorrento) is a (municipality) in the Metropolitan City of Naples in the Italian region Campania, located about 25 km southeast of Naples Naples ( ; ; ) is the Regions of Italy, regional capital of Campania and the third-largest city of Italy, after Rome and Milan, with a population of 908,082 within the city's administrative limits as of 2025, while its Metropolitan City of N .... Meta borders the municipalities of Piano di Sorrento and Vico Equense. See also * Sorrentine Peninsula * Amalfi Coast References External links Meta di Sorrento Interactive MapComune di Meta Official Website Cities and towns in Campania {{Campania-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Province Of Catania
The province of Catania (; ) was a province in the autonomous island region of Sicily, 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 , it included until 1927 a large part of the province of Enna. It was replaced by the Metropolitan City of Catania starting from August 4, 2013. History The area of Catania was founded by Greeks in 729 BC. It was conquered by the Romans 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 estimated death toll of about 15,000 people in the city of Catania alone. In 1669, it was also affected by the 1669 Etna eruption. It was hit by another earthquake in 1693, which resulted in the death of about 12,000 people (63% population at the time). Geography The province of Ca ... [...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 argument (or index) approaches some value. Limits of functions 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. The limit inferior and limit superior provide generalizations of the concept of a limit which are particularly relevant when the limit at a point may not exist. Notation In formulas, a limit of a function is usually written as : \lim_ f(x) = L, and is read as "the limit of of as approaches equals ". This means that the value of the function can be made arbitrarily close to , by choosing sufficiently close to . Alternatively, the fact that a function approaches the limit as approaches is sometimes denoted by a right arrow (→ or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir Mikhailovich Dubrovskii
Vladimir (, , pre-1918 orthography: ) is a masculine given name of Slavic origin, widespread throughout all Slavic nations in different forms and spellings. The earliest record of a person with the name is Vladimir of Bulgaria (). Etymology The Old East Slavic form of the name is Володимѣръ ''Volodiměr'', while the Old Church Slavonic form is ''Vladiměr''. According to Max Vasmer, the name is composed of Slavic владь ''vladĭ'' "to rule" and ''*mēri'' "great", "famous" (related to Gothic element ''mērs'', ''-mir'', cf. Theode''mir'', Vala''mir''). The modern ( pre-1918) Russian forms Владимиръ and Владиміръ are based on the Church Slavonic one, with the replacement of мѣръ by миръ or міръ resulting from a folk etymological association with миръ "peace" or міръ "world". Max Vasmer, ''Etymological Dictionary of Russian Language'' s.v. "Владимир"starling.rinet.ru [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fichera Convergence Theorem
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 (born 1993), Italian fencer {{surname ... [...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. Preliminary definitions Let (X,\mathcal,\mu) be a measure space A measure space is a basic object of measure theory, a branch of mathematics that studies generalized notions of volumes. It contains an underlying set, the subsets of this set that are feasible for measuring (the -algebra) and the method that ..., 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 \mathca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinary Differential Equation
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable (mathematics), variable. As with any other DE, its unknown(s) consists of one (or more) Function (mathematics), function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equation, ''partial'' differential equations (PDEs) which may be with respect to one independent variable, and, less commonly, in contrast with stochastic differential equations, ''stochastic'' differential equations (SDEs) where the progression is random. 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 a_0(x),\ldots,a_n(x) and b(x) are arbitrary differentiable functions that do not need to be linea ... [...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 magnitude (mathematics), magnitude, 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, integral, integration theory, and can be generalized to assume signed measure, 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 B ... [...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 (established) real number system. The real number system consists of an uncountable set (\mathbb), together with two binary operations denoted and \cdot, and a total 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, completenes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
