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Paola Loreti
Paola Loreti is an Italian mathematician, and a professor of mathematical analysis at Sapienza University of Rome. She is known for her research on Fourier analysis, control theory, and non-integer representations. The Komornik–Loreti constant, the smallest non-integer base for which the representation of 1 is unique, is named after her and Vilmos Komornik. Loreti earned a 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 ceremo ... from Sapienza University in 1984. Her dissertation, ''Programmazione dinamica ed equazione di Bellman'' dynamic_programming.html" ;"title="'dynamic programming">'dynamic programming and the Bellman equation''] was supervised by Italo Capuzzo-Dolcetta. With Vilmos Komornik, Loreti is the author of the book ''Fourier Series in Control Theory'' (Springer, 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (mathematics), series, and analytic functions. These theories are usually studied in the context of Real number, real and Complex number, complex numbers and Function (mathematics), functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any Space (mathematics), space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space). History Ancient Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sapienza University Of Rome
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] |
Fourier Analysis
In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics. In the sciences and engineering, the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis. For example, determining what component frequencies are present in a musical note would involve computing the Fourier transform of a sampled musical note. One could then re-synthesize the same sound by including the frequency components as revealed in the Fourier analysis. In mathematics, the term ''Fourier an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control Theory
Control theory is a field of control engineering and applied mathematics that deals with the control system, control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any ''delay'', ''overshoot'', or ''steady-state error'' and ensuring a level of control Stability theory, stability; often with the aim to achieve a degree of Optimal control, optimality. To do this, a controller with the requisite corrective behavior is required. This controller monitors the controlled process variable (PV), and compares it with the reference or Setpoint (control system), set point (SP). The difference between actual and desired value of the process variable, called the ''error'' signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-integer Representation
A non-integer representation uses non-integer numbers as the radix, or base, of a positional numeral system. For a non-integer radix ''β'' > 1, the value of :x = d_n \dots d_2d_1d_0.d_d_\dots d_ is :\begin x &= \beta^nd_n + \cdots + \beta^2d_2 + \beta d_1 + d_0 \\ &\qquad + \beta^d_ + \beta^d_ + \cdots + \beta^d_. \end The numbers ''d''''i'' are non-negative integers less than ''β''. This is also known as a ''β''-expansion, a notion introduced by and first studied in detail by . Every real number has at least one (possibly infinite) ''β''-expansion. The set of all ''β''-expansions that have a finite representation is a subset of the ring Z 'β'', ''β''−1 There are applications of ''β''-expansions in coding theory and models of quasicrystals. Construction ''β''-expansions are a generalization of decimal expansions. While infinite decimal expansions are not unique (for example, 1.000... = 0.999...), all finite decimal expansions are unique. However, even fin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Komornik–Loreti Constant
In the mathematical theory of non-standard positional numeral systems, the Komornik–Loreti constant is a mathematical constant that represents the smallest base ''q'' for which the number 1 has a unique representation, called its ''q''-development. The constant is named after Vilmos Komornik and Paola Loreti, who defined it in 1998. Definition Given a real number ''q'' > 1, the series : x = \sum_^\infty a_n q^ is called the ''q''-expansion, or \beta-expansion, of the positive real number ''x'' if, for all n \ge 0, 0 \le a_n \le \lfloor q \rfloor, where \lfloor q \rfloor is the floor function and a_n need not be an integer. Any real number x such that 0 \le x \le q \lfloor q \rfloor /(q-1) has such an expansion, as can be found using the greedy algorithm. The special case of x = 1, a_0 = 0, and a_n = 0 or 1 is sometimes called a q-development. a_n = 1 gives the only 2-development. However, for almost all 1 < q < 2, there are an infinite number of different [...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] |
Bellman Equation
A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical Optimization (mathematics), optimization method known as dynamic programming. It writes the "value" of a decision problem at a certain point in time in terms of the payoff from some initial choices and the "value" of the remaining decision problem that results from those initial choices. This breaks a dynamic optimization problem into a sequence of simpler subproblems, as Bellman's “principle of optimality" prescribes. The equation applies to algebraic structures with a total ordering; for algebraic structures with a partial ordering, the generic Bellman's equation can be used. The Bellman equation was first applied to engineering control theory and to other topics in applied mathematics, and subsequently became an important tool in economic theory; though the basic concepts of dynamic programming are prefigured in John von Neumann and Oskar Morgenstern's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Year Of Birth Missing (living People)
A year is a unit of time based on how long it takes the Earth to orbit the Sun. In scientific use, the tropical year (approximately 365 solar days, 5 hours, 48 minutes, 45 seconds) and the sidereal year (about 20 minutes longer) are more exact. The modern calendar year, as reckoned according to the Gregorian calendar, approximates the tropical year by using a system of leap years. The term 'year' is also used to indicate other periods of roughly similar duration, such as the lunar year (a roughly 354-day cycle of twelve of the Moon's phasessee lunar calendar), as well as periods loosely associated with the calendar or astronomical year, such as the seasonal year, the fiscal year, the academic year, etc. Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by changes in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the planet, four seasons a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Purpose: Because living persons may suffer personal harm from inappropriate information, we should watch their articles carefully. By adding an article to this category, it marks them with a notice about sources whenever someone tries to edit them, to remind them of WP:BLP (biographies of living persons) policy that these articles must maintain a neutral point of view, maintain factual accuracy, and be properly sourced. Recent changes to these articles are listed on Special:RecentChangesLinked/Living people. Organization: This category should not be sub-categorized. Entries are generally sorted by family name In many societies, a surname, family name, or last name is the mostly hereditary portion of one's personal name that indicates one's family. It is typically combined with a given name to form the full name of a person, although several give .... Maintenance: Individuals of advanced age (over 90), for whom there has been no new documentation in the last ten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Italian Mathematicians
Italian(s) may refer to: * Anything of, from, or related to the people of Italy over the centuries ** Italians, a Romance ethnic group related to or simply a citizen of the Italian Republic or Italian Kingdom ** Italian language, a Romance language *** Regional Italian, regional variants of the Italian language ** Languages of Italy, languages and dialects spoken in Italy ** Italian culture, cultural features of Italy ** Italian cuisine, traditional foods ** Folklore of Italy, the folklore and urban legends of Italy ** Mythology of Italy, traditional religion and beliefs Other uses * Italian dressing, a vinaigrette-type salad dressing or marination * Italian or Italian-A, alternative names for the Ping-Pong virus, an extinct computer virus * ''Italien'' (magazine), pro-Fascist magazine in Germany between 1927 and 1944 See also * * * Italia (other) * Italic (other) * Italo (other) * The Italian (other) * Italian people (other) Italian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
