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Vito Volterra
Vito Volterra (, ; 3 May 1860 – 11 October 1940) was an Italian mathematician and physicist, known for his contributions to Mathematical and theoretical biology, mathematical biology and Integral equation, integral equations, being one of the founders of functional analysis. Biography Born in Ancona, then part of the Papal States, into a very poor Jewish family: his father was Abramo Volterra and his mother, Angelica Almagià. Abramo Volterra died in 1862 when Vito was two years old. The family moved to Turin, and then to Florence, where he studied at the Dante Alighieri Technical School and the Galileo Galilei Technical Institute. Volterra showed early promise in mathematics before attending the University of Pisa, where he fell under the influence of Enrico Betti, and where he became professor of rational mechanics in 1883. He immediately started work developing his theory of functional (mathematics), functionals which led to his interest and later contributions in integra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancona
Ancona (, also ; ) is a city and a seaport in the Marche region of central Italy, with a population of around 101,997 . Ancona is the capital of the province of Ancona, homonymous province and of the region. The city is located northeast of Rome, on the Adriatic Sea, between the slopes of the two extremities of the promontory of Monte Conero, Monte Astagno and Monte Guasco. The hilly nature around Ancona is a strong contrast to the flatter coastline in areas further north. Ancona is one of the main ports on the Adriatic Sea, especially for passenger traffic, and is the main economic and demographic centre of the region. History Greek colony Before the Greek colonization, the territory was occupied by separated communities of the Picentes tribes. Ancona took a more urban shape by Greek settlers from Syracuse, Italy, Syracuse in about 387 BC, who gave it its name: ''Ancona'' stems from the Greek word (''Ankṓn''), meaning "elbow"; the harbour to the east of the town was o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Royal Society Of London
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, recognising excellence in science, supporting outstanding science, providing scientific advice for policy, education and public engagement and fostering international and global co-operation. Founded on 28 November 1660, it was granted a royal charter by King Charles II and is the oldest continuously existing scientific academy in the world. The society is governed by its Council, which is chaired by the society's president, according to a set of statutes and standing orders. The members of Council and the president are elected from and by its Fellows, the basic members of the society, who are themselves elected by existing Fellows. , there are about 1,700 fellows, allowed to use the postnominal title FRS (Fellow of the Royal Society) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Rome La Sapienza
The Sapienza University of Rome (), formally the Università degli Studi di Roma "La Sapienza", abbreviated simply as Sapienza ('Wisdom'), is a Public university, public research university located in Rome, Italy. It was founded in 1303 and is as such one of the world's oldest universities, and with 122,000 students, it is the List of largest universities by enrollment, largest university in Europe. Due to its size, funding, and numerous laboratories and libraries, Sapienza is a global major education and research centre. The university is located mainly in the ''Città Universitaria'' (University city), which covers near the monumental cemetery Campo Verano, with different campuses, libraries and laboratories in various locations in Rome. For the 14th year in a row it is ranked 1st university in Italy and in Southern Europe according tCWUR Sapienza was founded on 20 April 1303 by decree from Pope Boniface VIII as a ''Studium'' for ecclesiastical studies under more control than ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integro-differential Equation
In mathematics, an integro-differential equation is an equation that involves both integrals and derivatives of a function (mathematics), function. General first order linear equations The general first-order, linear (only with respect to the term involving derivative) integro-differential equation is of the form : \fracu(x) + \int_^x f(t,u(t))\,dt = g(x,u(x)), \qquad u(x_0) = u_0, \qquad x_0 \ge 0. As is typical with differential equations, obtaining a closed-form solution can often be difficult. In the relatively few cases where a solution can be found, it is often by some kind of integral transform, where the problem is first transformed into an algebraic setting. In such situations, the solution of the problem may be derived by applying the inverse transform to the solution of this algebraic equation. Example Consider the following second-order problem, : u'(x) + 2u(x) + 5\int_^u(t)\,dt = \theta(x) \qquad \text \qquad u(0)=0, where : \theta(x) = \left\{ \begin{ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral Equation
In mathematical analysis, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: f(x_1,x_2,x_3,\ldots,x_n ; u(x_1,x_2,x_3,\ldots,x_n) ; I^1 (u), I^2(u), I^3(u), \ldots, I^m(u)) = 0 where I^i(u) is an integral operator acting on ''u.'' Hence, integral equations may be viewed as the analog to differential equations where instead of the equation involving derivatives, the equation contains integrals. A direct comparison can be seen with the mathematical form of the general integral equation above with the general form of a differential equation which may be expressed as follows:f(x_1,x_2,x_3,\ldots,x_n ; u(x_1,x_2,x_3,\ldots,x_n) ; D^1 (u), D^2(u), D^3(u), \ldots, D^m(u)) = 0where D^i(u) may be viewed as a differential operator of order ''i''. Due to this close connection between differential and integral equations, one can often convert between the two. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional (mathematics)
In mathematics, a functional is a certain type of function. The exact definition of the term varies depending on the subfield (and sometimes even the author). * In linear algebra, it is synonymous with a linear form, which is a linear mapping from a vector space V into its field of scalars (that is, it is an element of the dual space V^*) "Let ''E'' be a free module over a commutative ring ''A''. We view ''A'' as a free module of rank 1 over itself. By the dual module ''E''∨ of ''E'' we shall mean the module Hom(''E'', ''A''). Its elements will be called functionals. Thus a functional on ''E'' is an ''A''-linear map ''f'' : ''E'' → ''A''." * In functional analysis and related fields, it refers to a mapping from a space X into the field of real or complex numbers. "A numerical function ''f''(''x'') defined on a normed linear space ''R'' will be called a ''functional''. A functional ''f''(''x'') is said to be ''linear'' if ''f''(α''x'' + β''y'') = α''f''(''x'') + β ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Florence
Florence ( ; ) is the capital city of the Italy, Italian region of Tuscany. It is also the most populated city in Tuscany, with 362,353 inhabitants, and 989,460 in Metropolitan City of Florence, its metropolitan province as of 2025. Florence was a centre of Middle Ages, medieval European trade and finance and one of the wealthiest cities of that era. It is considered by many academics to have been the birthplace of the Renaissance, becoming a major artistic, cultural, commercial, political, economic and financial center. During this time, Florence rose to a position of enormous influence in Italy, Europe, and beyond. Its turbulent political history includes periods of rule by the powerful House of Medici, Medici family and numerous religious and republican revolutions. From 1865 to 1871 the city served as the capital of the Kingdom of Italy. The Florentine dialect forms the base of Italian language, standard Italian and it became the language of culture throughout Italy due to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turin
Turin ( , ; ; , then ) is a city and an important business and cultural centre in northern Italy. It is the capital city of Piedmont and of the Metropolitan City of Turin, and was the first Italian capital from 1861 to 1865. The city is mainly on the western bank of the Po (river), River Po, below its Susa Valley, and is surrounded by the western Alpine arch and Superga hill. The population of the city proper is 856,745 as of 2025, while the population of the urban area is estimated by Eurostat to be 1.7 million inhabitants. The Turin metropolitan area is estimated by the OECD to have a population of 2.2 million. The city was historically a major European political centre. From 1563, it was the capital of the Duchy of Savoy, then of the Kingdom of Sardinia (1720–1861), Kingdom of Sardinia ruled by the House of Savoy, and the first capital of the Kingdom of Italy from 1861 to 1865. Turin is sometimes called "the cradle of Italian liberty" for having been the politi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jewish
Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of History of ancient Israel and Judah, ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, religion, and community are highly interrelated, as Judaism is their ethnic religion, though it is not practiced by all ethnic Jews. Despite this, religious Jews regard Gerim, converts to Judaism as members of the Jewish nation, pursuant to the Conversion to Judaism, long-standing conversion process. The Israelites emerged from the pre-existing Canaanite peoples to establish Kingdom of Israel (Samaria), Israel and Kingdom of Judah, Judah in the Southern Levant during the Iron Age.John Day (Old Testament scholar), John Day (2005), ''In Search of Pre-Exilic Israel'', Bloomsbury Publishing, pp. 47.5 [48] 'In this sense, the emergence of ancient Israel is viewed not as the cause of the demise of Canaanite culture but as its upshot'. Originally, J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Papal States
The Papal States ( ; ; ), officially the State of the Church, were a conglomeration of territories on the Italian peninsula under the direct sovereign rule of the pope from 756 to 1870. They were among the major states of Italy from the 8th century until the unification of Italy, which took place between 1859 and 1870, culminated in their demise. The state was legally established in the 8th century when Pepin the Short, king of the Franks, gave Pope Stephen II, as a temporal sovereign, lands formerly held by Arian Christian Lombards, adding them to lands and other real estate formerly acquired and held by the bishops of Rome as landlords from the time of Constantine onward. This donation came about as part of a process whereby the popes began to turn away from the Byzantine emperors as their foremost temporal guardians for reasons such as increased imperial taxes, disagreement with respect to iconoclasm, and failure of the emperors, or their exarchs in Italy, to pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, Inner product space#Definition, inner product, Norm (mathematics)#Definition, norm, or Topological space#Definitions, topology) and the linear transformation, linear functions defined on these spaces and suitably respecting these structures. The historical roots of functional analysis lie in the study of function space, spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining, for example, continuous function, continuous or unitary operator, unitary operators between function spaces. This point of view turned out to be particularly useful for the study of differential equations, differential and integral equations. The usage of the word ''functional (mathematics), functional'' as a noun goes back to the calculus of v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
