An outcome of this period is the Lotka—Volterra equations. Volterra is the only person who was a plenary speaker in the International Congress of Mathematicians four times , , , In , he joined the opposition to the Fascist regime of Benito Mussolini and in he was one of only 12 out of 1, professors who refused to take a mandatory oath of loyalty. However, Volterra was no radical firebrand; he might have been equally appalled if the leftist opposition to Mussolini had come to power, since he was a lifelong royalist and nationalist.

As a result of his refusal to sign the oath of allegiance to the fascist government he was compelled to resign his university post and his membership of scientific academies, and, during the following years, he lived largely abroad, returning to Rome just before his death. In , he had been appointed a member of the Pontifical Academy of Sciences , on the initiative of founder Agostino Gemelli. He died in Rome on 11 October He is buried in the Ariccia Cemetery. The Academy organised his funeral.

In he married Virginia Almagia, a cousin. In , he became professor of mechanics at the University of Turin and then, in , professor of mathematical physics at. The Lotka—Volterra equations, also known as the predator—prey equations, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey. The Lotka—Volterra system of equations is an example. In mathematics, the Volterra integral equations are a special type of integral equations.

They are divided into two groups referred to as the first and the second kind. A useful method to solve such equations, the Adomian decomposition method, is due to George Adomian.

## Category:Vito Volterra

In an paper, Smith discussed a nowhere-dense set of positive measure on the real line,[2] and Volterra introduced a similar example in The Smith-Volterra-Cantor set is topologically equivalent to the middle-thirds Cantor set. The Volterra series is a model for non-linear behavior similar to the Taylor series.

It differs from the Taylor series in its ability to capture 'memory' effects. The Taylor series can be used for approximating the response of a nonlinear system to a given input if the output of this system depends strictly on the input at that particular time. In the Volterra series the output of the nonlinear system depends on the input to the system at all other times. This provides the ability to capture the 'memory' effect of devices like capacitors and inductors.

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It has been applied in the fields of medicine biomedical engineering and biology, especially neuroscience. It is also used in electrical engineering to model intermodulation distortion in many devices including power amplifiers and frequency mixers. Its main advantage lies in its generality: it can represent a wide range of systems. Thus it is sometimes considered a non-parametric model. In mathematics, a Volterra series denotes a functional expansion of a. The first three steps in the construction of Volterra's function. In mathematics, in the area of functional analysis and operator theory, the Volterra operator, named after Vito Volterra, is a bounded linear operator on the space L2 0,1 of complex-valued square-integrable functions on the interval 0,1.

On the subspace C 0,1 of continuous functions it represents indefinite integration. It is the operator corresponding to the Volterra integral equations. Volterra may refer to the following: Volterra, a town in Italy Daniele da Volterra — , an Italian painter Francesco da Volterra, a 14th-century Italian painter Vito Volterra — , an Italian mathematician Volterra Semiconductor, an American semiconductor company Volterra crater , a lunar impact crater on the far side of the Moon In mathematics: Lotka—Volterra equations, also known as the predator—prey equations The Smith—Volterra—Cantor set, a Cantor set with measure greater than zero Volterra's function, a differentiable function whose derivative is not Riemann integrable Volterra integral equation, a generalization of the indefinite integral Volterra operator, a bounded linear operator on the space of square integrable functions, the operator corresponding to an indefinite integral Volterra series Volterra space, a property of topological spaces.

Volterra Semiconductor, commonly known as "Volterra," was acquired by Maxim Integrated in October The company was founded in and was headquartered in Fremont, California, United States. Volterra is named for Vito Volterra, an Italian mathematician and physicist, who is best known as the father of the Volterra series. References "Maxim Integrat. The presence of dislocations strongly influences many of the properties of materials.

The theory describing the elastic fields of the defects was originally developed by Vito Volterra in Taylor in In such a case, the surrounding planes are not straight, but instead they bend around the edge of the terminating plane so that the crystal structure is perfectly ordered on either side. This phenomenon is analogous to the following situation related to a stack of paper: If half of a piece of paper is inserted into a stack of paper, the defect in the stack is noticeable only at the edge of the half sheet.

The two pr. An American biophysicist, Lotka is best known for his proposal of the predator—prey model, developed simultaneously but independently of Vito Volterra.

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The Lotka—Volterra model is still the basis of many models used in the analysis of population dynamics in ecology. A "product integral" is any product-based counterpart of the usual sum-based integral of classical calculus. The first product integral Type I below was developed by the mathematician Vito Volterra in to solve systems of linear differential equations. The bigeometric integral, together with the bigeometric derivative, is useful in some applications of fractals[14][15][16][17][18][19][20][21].

A population model is a type of mathematical model that is applied to the study of population dynamics. Rationale Models allow a better understanding of how complex interactions and processes work. Modeling of dynamic interactions in nature can provide a manageable way of understanding how numbers change over time or in relation to each other. Many patterns can be noticed by using population modeling as a tool. This might be due to interactions with the environment, individuals of their own species, or other species.

Population models are also used to understand the spread of parasites, viruses, and disease. In continuum physics, materials with memory, also referred as materials with hereditary effects are a class of materials whose constitutive equations contains a dependence upon the past history of thermodynamic, kinetic, electromagnetic or other kind of state variables. Historical notes The study of these materials arises from the pioneering articles of Ludwig Boltzmann[1][2] and Vito Volterra,[3][4] in which they sought an extension of the concept of an elastic material.

In general, in materials with memory the local value of some constitutive quantity stress, heat flux, electric current, polarization and magnetization, etc. The hypothesis that the remote history of a variable has less influence than its values in the recent past, was stated in. In vector calculus, and more generally differential geometry, Stokes' theorem sometimes spelled Stokes's theorem, and also called the generalized Stokes theorem or the Stokes—Cartan theorem[1] is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus.

He attended secondary school in Fiume and later enrolled as a student in the Faculty of Natural Sciences at the University of Budapest. During World War I he interrupted his studies to fight as artillery officer, and became wounded and was decorated for military valor. From to he studied at the University of Rome under supervision of Giulio Cotronei.

He graduated on a thesis on the effect of starvation on the digestive tract of the eel.

He later moved to the University of Padua where he founded the hydrobiological station in Chioggia that now bears his name. He was a member of the Accademia dei Lincei and a corresponding member of the French Academy of Sciences. His work covered marine biology and his interests ranged from physiology to hydrobiology, oceanography and evolut. In mathematics, in the field of topology, a topological space is said to be a Volterra space if any finite intersection of dense G subsets is dense. Every Baire space is Volterra, but the converse is not true. In fact, any metrizable Volterra space is Baire.

The name refers to a paper of Vito Volterra in which he uses the fact that in modern notation the intersection of two dense G-delta sets in the real numbers is again dense. Gauld, D.

## Vito Volterra - The Mathematics Genealogy Project

Gruenhage, G. Volterra, V. In mathematics, the Volterra lattice, also known as the discrete KdV equation, the Kac—van Moerbeke lattice, and the Langmuir lattice, is a system of ordinary differential equations with variables indexed by some of the points of a 1-dimensional lattice. The Volterra lattice is a special case of the generalized Lotka—Volterra equation describing predator—prey interactions, for a sequence of species with each species preying on the next in the sequence.

The Volterra lattice also behaves like a discrete version of the KdV equation. The Volterra lattice is an integrable system, and is related to the Toda lattice. It is also used as a model for Langmuir waves in plasmas. One of the possible modes of vibration of an idealized circular drum head. These modes are eigenfunctions of a linear operator on a function space, a common construction in 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 e.

The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. This point of view turned out to be particularly useful for the study of differential and integral equations. The usage of the word functional as a noun goes back to the calculus of variations, implying a function whose argument is a function.

The t. These model systems are then studied in order to make predictions about the dynamics of the real system. Often, the study of inaccuracies in the model when compared to empirical observations will lead to the generation of hypotheses about possible ecological relations that are not yet known or well understood.

Models enable researchers to simulate large-scale experiments that would be too costly or u. The province of Ancona Italian: provincia di Ancona is a province in the Marche region of central Italy.

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Its capital is the city of Ancona, and the province borders the Adriatic Sea. The city of Ancona is also the capital of Marche. The population of the province is mostly located in coastal areas and in the provincial capital Ancona, which has a population of ,; the province has a total population of , as of A large area of the province's land is farmland often used for wine production; the province produces wines using the Montepulciano, Sangiovese, and Verdicchio varieties of grape.

Annually, feasts occur in the province during the harvesting period. Biography A son of the famous mathematician Vito Volterra, Enrico Volterra received in his degree in civil engineering from the Sapienza University of Rome and, in the same year, his professional qualification abilitazione in bridges and roads from the Polytechnic School of Engineering in Naples.

In January , he obtained the libera docenza in the science of structures from the University of Rome. Edoardo Volterra was an Italian scholar of Roman law.

Son of the distinguished Italian mathematician Vito Volterra, Edoardo Volterra held a series of teaching positions at the Universities of Cagliari, Camerino, Pisa, and Bologna before finally accepting a call to the Sapienza University of Rome. His first major work was on the Collatio Legum Mosaicarum et Romanarum. Opposed to the rise of fascism, the Jewish Volterra was forced out of his position in In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties.

Although Cantor himself defined the set in a general, abstract way, the most common modern construction is the Cantor ternary set, built by removing the middle third of a line segment and then repeating the process with the remaining shorter segments. Cantor himself mentioned the ternary construction only in passing, as an example of a more general idea, that of a perfect set that is nowhere dense. One starts by deleting the open middle third.

Oblique Lunar Orbiter 5 image Volterra is a lunar impact crater that is located in the northern latitudes on the far side of the Moon. This is an eroded crater formation, particularly along the western side where the rim is more uneven. A small crater lies across the northeast rim edge. The interior floor is relatively level in the eastern half, while the west is marked by several remnants of small craterlets in the surface.