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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 ceremony ... from Sapienza University in 1984. Her dissertation, ''Programmazione dinamica ed equazione di Bellman'' 'dynamic programming and the Bellman equation">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 '' ... [...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 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sapienza University Of Rome
The Sapienza University of Rome ( it, Sapienza – Università di Roma), also called simply Sapienza or the University of Rome, and formally the Università degli Studi di Roma "La Sapienza", is a Public university, public research university located in Rome, Italy. It is one of the List of largest universities by enrollment, largest European universities by enrollments and List of oldest universities in continuous operation, one of the oldest in history, founded in 1303. The university is one of the most prestigious Italian universities in the world, commonly ranking first in national rankings and in Southern Europe. In 2018, 2019, 2021 and 2022 it ranked first in the world for classics and ancient history. Most of the Italian ruling class studied at the Sapienza. The Sapienza has educated numerous notable alumni, including many List of Nobel laureates, Nobel laureates, President of the European Parliament, Presidents of the European Parliament and European Commissioners, heads ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control Theory
Control theory is a field of mathematics that deals with the 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; often with the aim to achieve a degree of 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 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 which are also studied are controllability and observability. Control theory is used in control system eng ... [...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 notation, 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 (mathematics), set of all ''β''-expansions that have a finite representation is a subset of the ring (mathematics), 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... = 0.9 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Komornik–Loreti Constant
In the mathematical theory of Non-integer representation, 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 Non-integer representation, \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 and ceiling functions, 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. Howev ... [...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] |
Dynamic Programming
Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. In both contexts it refers to simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive manner. While some decision problems cannot be taken apart this way, decisions that span several points in time do often break apart recursively. Likewise, in computer science, if a problem can be solved optimally by breaking it into sub-problems and then recursively finding the optimal solutions to the sub-problems, then it is said to have ''optimal substructure''. If sub-problems can be nested recursively inside larger problems, so that dynamic programming methods are applicable, then there is a relation between the value of the larger problem and the values of the sub-problems.Cormen, T. H.; Leiserson, C. E.; Rives ... [...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 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 '' Theory of Games and Econ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Year Of Birth Missing (living People)
A year or annus is the orbital period of a planetary body, for example, the Earth, moving in its orbit around the Sun. Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by change in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the planet, four seasons are generally recognized: spring, summer, autumn and winter. In tropical and subtropical regions, several geographical sectors do not present defined seasons; but in the seasonal tropics, the annual wet and dry seasons are recognized and tracked. A calendar year is an approximation of the number of days of the Earth's orbital period, as counted in a given calendar. The Gregorian calendar, or modern calendar, presents its calendar year to be either a common year of 365 days or a leap year of 366 days, as do the Julian calendars. For the Gregorian calendar, the average length of the calendar year (the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...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, an ethnic group 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 marinade * Italian or Italian-A, alternative names for the Ping-Pong virus, an extinct computer virus See also * * * Italia (other) * Italic (other) * Italo (other) * The Italian (other) * Italian people (other) Italian people may refer to: * in terms of ethnicity: all ethnic Italians, in and outside of Italy * in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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