Giacinto Morera
Encyclopedia
Giacinto Morera was an Italian engineer and mathematician
. He is remembered for Morera's theorem
in the theory of functions of a complex variables
and for his work in the theory of linear elasticity
.
on 18 July 1856, the son of Giacomo Morera and Vittoria Unico. His family was a wealthy one: his father was a rich merchant
. states that this occurrence eased him in his studies after the laurea
: however, he was an extraordinary hard worker and he widely used this professional skill in his researches. After studying in Turin
he went to Pavia
, Pisa
and Leipzig
: after studying in Leipzig
he went back to Pavia
for a brief period in 1885, and finally in 1886 he went to Genova
, living here for the next 15 years. writes that in Genova
he also married his fellow-citizen Cesira Faà. From 1901 to his death he was in Turin
: he died of pneumonia
on 8 February 1909.
in engineering in 1878, and his laurea
in mathematics in 1879, both from the Politecnico di Torino: refers that the title of his thesis in the mathematical sciences
was: "Sul moto di un punto attratto da due centri fissi colla legge di Newton". In Turin
he attended to the courses of Enrico d'Ovidio, Angelo Genocchi
and Francesco Siacci
: in particular he acknowledged this last one as his master, both in science and in life. After graduating, he followed several advanced courses: he studied in Pavia
from 1881 to 1882 under Eugenio Beltrami
, Eugenio Bertini
and Felice Casorati
. In 1883 he was in Pisa
under Enrico Betti
, Riccardo de Paolis and Ulisse Dini: a year later he was in Leipzig
under Felix Klein
, Adolph Mayer
and Carl Neumann
. In 1885 he went also in Berlin in order to follow the lessons of Hermann von Helmholtz
, Gustav Kirchhoff
, Leopold Kronecker
and Karl Weierstrass
at the local university
: later, in the same year, he went back to Italy
briefly working at the University of Pavia
as a professor in the then newly established "Scuola di Magistero". In 1886, after a competitive examination by a judging commission, he became professor of rational mechanics at the University of Genova: he lived there for 15 years, serving also as a dean
and as a rector. In 1901 he was invited to the chair of rational mechanics at University of Turin
, a position left open by Vito Volterra
. In 1908 he passed to the chair of "Meccanica Superiore" and was elected dean
of the Faculty of Sciences, according to .
elected him corresponding member in the meeting of the society held on 31 October 1909 (Old Calendar), being not aware of his death.
was his friend for more than twenty years and colleague from 1901 onward, discussing with him scientific matters almost every day: he describes him as a devoted friend and a precious colleague.
Described as a cheerful hearted man, he was also a witty incisive talker, according to , and .
Gifted by a sharp and penetrating intelligence, owning an uncommonly clean mind jointly with analytic and critical capabilities, he is also described as being not interested in sciences and other fields outside is own expertise, however being capable and versatile, with the ability to grasp and appreciate every kind of disclosure produced by the human mind. Morera himself, in the inaugural address , after quoting a statement attributed to Peter Guthrie Tait
, discloses the reason behind his views:-"In science, the one who has a sound and solid knowledge, even in a narrow field, holds a true strength and he can use it whenever he needs: the one who has only a superficial knowledge, however wide and striking, holds nothing, and indeed he often holds a weakness pushing him towards vanity
".
According to Somigliana
, he was also acknowledged as an honest, loyal and conscientious man, gifted with exquisite qualities of temperament and intellect, whose simple manners earned him affection even when performing the duties of dean
and rector at the University of Genoa
: describes him as a man of great moral value, being this the reason of his success in social relationships and in performing his duties as a civil servant. Somigliana remarks also that he had the ability of serenely judging men and facts.
Despite being successful in social relation
s, he did not cured nor appreciated much appearances, and was not interested in activities other than the teaching and research ones: consequently, he was not well known outside his the circle of his family and relatives and the circle of his colleagues. He did not make a display of himself, careless of being not known by everyone for his true value: his conception of life was a serious one, and he strongly disliked vanity and superficiality.
Again according to Somigliana
, his entire life was devoted to a higher unselfish ideal, i.e. scientific research: and remarks that only his beloved family shared the same attentions and care he reserved to his ideal.
and their mechanical
and physical
applications.
He was the author of more than 60 works: fairly complete lists appear in references , and . This last reference is particularly useful as Maggi classifies Morera's works according to the topics dealt: his classification is basically followed in the following subsections, however using modern terminology.
, notably Morera's theorem
, first proved in the paper , are still the best known part of his scientific research. He wrote eight research papers on this topic: these papers probably inspired the quotation by Carlo Somigliana
reported at the beginning of this section.
or partial
ones: classifies this contributions as works in the theory of the equations of dynamics
, in the theory of first-order partial differential equations and in the theory of exact differential equation
s. He wrote twelve papers on this topic: the results he obtained in this works are well described by . In the paper he gives a very brief proof of a transformation formula for the Poisson brackets first proved by Émile Léonard Mathieu
, while in the paper he simplifies the proof of a theorem of Francesco Siacci
which is substantially equivalent to Lie's third theorem
: the paper is concerned with the Pfaff problem, proving a theorem
on the minimum number of integrations to be performed in order to solve the problem.
.
s.
describes once his teaching ability as incisive. However, his teaching activity is also testified by the litographed
lecture notes
: according to the OPAC, this book had two editions, the first one being in 1901–1902.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He is remembered for Morera's theorem
Morera's theorem
In complex analysis, a branch of mathematics, Morera's theorem, named after Giacinto Morera, gives an important criterion for proving that a function is holomorphic....
in the theory of functions of a complex variables
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
and for his work in the theory of linear elasticity
Linear elasticity
Linear elasticity is the mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions. Linear elasticity models materials as continua. Linear elasticity is a simplification of the more general nonlinear theory of elasticity and is a branch of...
.
Life
He was born in NovaraNovara
Novara is the capital city of the province of Novara in the Piedmont region in northwest Italy, to the west of Milan. With c. 105,000 inhabitants, it is the second most populous city in Piedmont after Turin. It is an important crossroads for commercial traffic along the routes from Milan to Turin...
on 18 July 1856, the son of Giacomo Morera and Vittoria Unico. His family was a wealthy one: his father was a rich merchant
Merchant
A merchant is a businessperson who trades in commodities that were produced by others, in order to earn a profit.Merchants can be one of two types:# A wholesale merchant operates in the chain between producer and retail merchant...
. states that this occurrence eased him in his studies after the laurea
Laurea
In Italy, the laurea is the main post-secondary academic degree.-Reforms due to the Bologna process:Spurred by the Bologna process, a major reform was instituted in 1999 to introduce easier university degrees comparable to the bachelors...
: however, he was an extraordinary hard worker and he widely used this professional skill in his researches. After studying in Turin
Turin
Turin is a city and major business and cultural centre in northern Italy, capital of the Piedmont region, located mainly on the left bank of the Po River and surrounded by the Alpine arch. The population of the city proper is 909,193 while the population of the urban area is estimated by Eurostat...
he went to Pavia
Pavia
Pavia , the ancient Ticinum, is a town and comune of south-western Lombardy, northern Italy, 35 km south of Milan on the lower Ticino river near its confluence with the Po. It is the capital of the province of Pavia. It has a population of c. 71,000...
, Pisa
Pisa
Pisa is a city in Tuscany, Central Italy, on the right bank of the mouth of the River Arno on the Tyrrhenian Sea. It is the capital city of the Province of Pisa...
and Leipzig
Leipzig
Leipzig Leipzig has always been a trade city, situated during the time of the Holy Roman Empire at the intersection of the Via Regia and Via Imperii, two important trade routes. At one time, Leipzig was one of the major European centres of learning and culture in fields such as music and publishing...
: after studying in Leipzig
Leipzig
Leipzig Leipzig has always been a trade city, situated during the time of the Holy Roman Empire at the intersection of the Via Regia and Via Imperii, two important trade routes. At one time, Leipzig was one of the major European centres of learning and culture in fields such as music and publishing...
he went back to Pavia
Pavia
Pavia , the ancient Ticinum, is a town and comune of south-western Lombardy, northern Italy, 35 km south of Milan on the lower Ticino river near its confluence with the Po. It is the capital of the province of Pavia. It has a population of c. 71,000...
for a brief period in 1885, and finally in 1886 he went to Genova
Génova
Génova may refer to:* Spanish spelling of the city of Genoa, Italy* Génova, Quindío, a municipality in the department of Quindío, Colombia* Génova, Quetzaltenango, a municipality in the department of Quetzaltenango, Guatemala...
, living here for the next 15 years. writes that in Genova
Génova
Génova may refer to:* Spanish spelling of the city of Genoa, Italy* Génova, Quindío, a municipality in the department of Quindío, Colombia* Génova, Quetzaltenango, a municipality in the department of Quetzaltenango, Guatemala...
he also married his fellow-citizen Cesira Faà. From 1901 to his death he was in Turin
Turin
Turin is a city and major business and cultural centre in northern Italy, capital of the Piedmont region, located mainly on the left bank of the Po River and surrounded by the Alpine arch. The population of the city proper is 909,193 while the population of the urban area is estimated by Eurostat...
: he died of pneumonia
Pneumonia
Pneumonia is an inflammatory condition of the lung—especially affecting the microscopic air sacs —associated with fever, chest symptoms, and a lack of air space on a chest X-ray. Pneumonia is typically caused by an infection but there are a number of other causes...
on 8 February 1909.
Education and academic career
He earned his laureaLaurea
In Italy, the laurea is the main post-secondary academic degree.-Reforms due to the Bologna process:Spurred by the Bologna process, a major reform was instituted in 1999 to introduce easier university degrees comparable to the bachelors...
in engineering in 1878, and his laurea
Laurea
In Italy, the laurea is the main post-secondary academic degree.-Reforms due to the Bologna process:Spurred by the Bologna process, a major reform was instituted in 1999 to introduce easier university degrees comparable to the bachelors...
in mathematics in 1879, both from the Politecnico di Torino: refers that the title of his thesis in the mathematical sciences
Mathematical sciences
Mathematical sciences is a broad term that refers to those academic disciplines that are primarily mathematical in nature but may not be universally considered subfields of mathematics proper...
was: "Sul moto di un punto attratto da due centri fissi colla legge di Newton". In Turin
Turin
Turin is a city and major business and cultural centre in northern Italy, capital of the Piedmont region, located mainly on the left bank of the Po River and surrounded by the Alpine arch. The population of the city proper is 909,193 while the population of the urban area is estimated by Eurostat...
he attended to the courses of Enrico d'Ovidio, Angelo Genocchi
Angelo Genocchi
Angelo Genocchi was an Italian mathematician who specialized in number theory. He worked with Giuseppe Peano. The Genocchi numbers are named after him.-References:...
and Francesco Siacci
Francesco Siacci
Francesco Siacci , an Italian mathematician, ballistician, and officer in the Italian army, was born in Rome, Italy. He was a professor of mechanics in the University of Turin and University of Naples...
: in particular he acknowledged this last one as his master, both in science and in life. After graduating, he followed several advanced courses: he studied in Pavia
Pavia
Pavia , the ancient Ticinum, is a town and comune of south-western Lombardy, northern Italy, 35 km south of Milan on the lower Ticino river near its confluence with the Po. It is the capital of the province of Pavia. It has a population of c. 71,000...
from 1881 to 1882 under Eugenio Beltrami
Eugenio Beltrami
Eugenio Beltrami was an Italian mathematician notable for his work concerning differential geometry and mathematical physics...
, Eugenio Bertini
Eugenio Bertini
Eugenio Bertini was an Italian mathematician who introduced Bertini's theorem.-References:...
and Felice Casorati
Felice Casorati (mathematician)
Felice Casorati was an Italian mathematician best known for the Casorati-Weierstrass theorem in complex analysis...
. In 1883 he was in Pisa
Pisa
Pisa is a city in Tuscany, Central Italy, on the right bank of the mouth of the River Arno on the Tyrrhenian Sea. It is the capital city of the Province of Pisa...
under Enrico Betti
Enrico Betti
-External links:...
, Riccardo de Paolis and Ulisse Dini: a year later he was in Leipzig
Leipzig
Leipzig Leipzig has always been a trade city, situated during the time of the Holy Roman Empire at the intersection of the Via Regia and Via Imperii, two important trade routes. At one time, Leipzig was one of the major European centres of learning and culture in fields such as music and publishing...
under Felix Klein
Felix Klein
Christian Felix Klein was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory...
, Adolph Mayer
Christian Gustav Adolph Mayer
Christian Gustav Adolph Mayer was a German mathematician.Mayer was born on February 15, 1839 in Leipzig, Germany. His father was a businessman from Leipzig. He studied at the University of Leipzig, University of Göttingen, University of Heidelberg and University of Königsberg...
and Carl Neumann
Carl Neumann
Carl Gottfried Neumann was a German mathematician.Neumann was born in Königsberg, Prussia, as the son of the mineralogist, physicist and mathematician Franz Ernst Neumann , who was professor of mineralogy and physics at Königsberg University...
. In 1885 he went also in Berlin in order to follow the lessons of Hermann von Helmholtz
Hermann von Helmholtz
Hermann Ludwig Ferdinand von Helmholtz was a German physician and physicist who made significant contributions to several widely varied areas of modern science...
, Gustav Kirchhoff
Gustav Kirchhoff
Gustav Robert Kirchhoff was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects...
, Leopold Kronecker
Leopold Kronecker
Leopold Kronecker was a German mathematician who worked on number theory and algebra.He criticized Cantor's work on set theory, and was quoted by as having said, "God made integers; all else is the work of man"...
and Karl Weierstrass
Karl Weierstrass
Karl Theodor Wilhelm Weierstrass was a German mathematician who is often cited as the "father of modern analysis".- Biography :Weierstrass was born in Ostenfelde, part of Ennigerloh, Province of Westphalia....
at the local university
Humboldt University of Berlin
The Humboldt University of Berlin is Berlin's oldest university, founded in 1810 as the University of Berlin by the liberal Prussian educational reformer and linguist Wilhelm von Humboldt, whose university model has strongly influenced other European and Western universities...
: later, in the same year, he went back to Italy
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
briefly working at the University of Pavia
University of Pavia
The University of Pavia is a university located in Pavia, Lombardy, Italy. It was founded in 1361 and is organized in 9 Faculties.-History:...
as a professor in the then newly established "Scuola di Magistero". In 1886, after a competitive examination by a judging commission, he became professor of rational mechanics at the University of Genova: he lived there for 15 years, serving also as a dean
Dean (education)
In academic administration, a dean is a person with significant authority over a specific academic unit, or over a specific area of concern, or both...
and as a rector. In 1901 he was invited to the chair of rational mechanics at University of Turin
University of Turin
The University of Turin is a university in the city of Turin in the Piedmont region of north-western Italy...
, a position left open by Vito Volterra
Vito Volterra
Vito Volterra was an Italian mathematician and physicist, known for his contributions to mathematical biology and integral equations....
. In 1908 he passed to the chair of "Meccanica Superiore" and was elected dean
Dean (education)
In academic administration, a dean is a person with significant authority over a specific academic unit, or over a specific area of concern, or both...
of the Faculty of Sciences, according to .
Honours
He was member of the Accademia Nazionale dei Lincei (corresponding member in 1896, then national member in 1907) and of the Accademia delle Scienze di Torino (elected on 9 February 1902). refers also that the Kharkov Mathematical SocietyKharkov Mathematical Society
The Kharkov Mathematical Society is an association of professional mathematicians in Kharkiv aimed at advancement of mathematical research and education. It was established in 1879 by the initiative of V.G. Imshenetskii, who also founded the St...
elected him corresponding member in the meeting of the society held on 31 October 1909 (Old Calendar), being not aware of his death.
Tracts of his personality and attitudes
Carlo SomiglianaCarlo Somigliana
Carlo Somigliana was an Italian mathematician and a classical mathematical physicist faithful to the school of Enrico Betti and Eugenio Beltrami. He made important contributions in elasticity. The Somigliana integral equation for elasticity is the equivalent of Green's formula for potential...
was his friend for more than twenty years and colleague from 1901 onward, discussing with him scientific matters almost every day: he describes him as a devoted friend and a precious colleague.
Described as a cheerful hearted man, he was also a witty incisive talker, according to , and .
Gifted by a sharp and penetrating intelligence, owning an uncommonly clean mind jointly with analytic and critical capabilities, he is also described as being not interested in sciences and other fields outside is own expertise, however being capable and versatile, with the ability to grasp and appreciate every kind of disclosure produced by the human mind. Morera himself, in the inaugural address , after quoting a statement attributed to Peter Guthrie Tait
Peter Guthrie Tait
Peter Guthrie Tait FRSE was a Scottish mathematical physicist, best known for the seminal energy physics textbook Treatise on Natural Philosophy, which he co-wrote with Kelvin, and his early investigations into knot theory, which contributed to the eventual formation of topology as a mathematical...
, discloses the reason behind his views:-"In science, the one who has a sound and solid knowledge, even in a narrow field, holds a true strength and he can use it whenever he needs: the one who has only a superficial knowledge, however wide and striking, holds nothing, and indeed he often holds a weakness pushing him towards vanity
Vanity
In conventional parlance, vanity is the excessive belief in one's own abilities or attractiveness to others. Prior to the 14th century it did not have such narcissistic undertones, and merely meant futility. The related term vainglory is now often seen as an archaic synonym for vanity, but...
".
According to Somigliana
Carlo Somigliana
Carlo Somigliana was an Italian mathematician and a classical mathematical physicist faithful to the school of Enrico Betti and Eugenio Beltrami. He made important contributions in elasticity. The Somigliana integral equation for elasticity is the equivalent of Green's formula for potential...
, he was also acknowledged as an honest, loyal and conscientious man, gifted with exquisite qualities of temperament and intellect, whose simple manners earned him affection even when performing the duties of dean
Dean (education)
In academic administration, a dean is a person with significant authority over a specific academic unit, or over a specific area of concern, or both...
and rector at the University of Genoa
University of Genoa
The University of Genoa is one of the largest universities in Italy.Located in Liguria on the Italian Riviera, the university was founded in 1471. It currently has about 40,000 students, 1,800 teaching and research staff and about 1,580 administrative staff.- Campus :The University of Genoa is...
: describes him as a man of great moral value, being this the reason of his success in social relationships and in performing his duties as a civil servant. Somigliana remarks also that he had the ability of serenely judging men and facts.
Despite being successful in social relation
Social relation
In social science, a social relation or social interaction refers to a relationship between two , three or more individuals . Social relations, derived from individual agency, form the basis of the social structure. To this extent social relations are always the basic object of analysis for social...
s, he did not cured nor appreciated much appearances, and was not interested in activities other than the teaching and research ones: consequently, he was not well known outside his the circle of his family and relatives and the circle of his colleagues. He did not make a display of himself, careless of being not known by everyone for his true value: his conception of life was a serious one, and he strongly disliked vanity and superficiality.
Again according to Somigliana
Carlo Somigliana
Carlo Somigliana was an Italian mathematician and a classical mathematical physicist faithful to the school of Enrico Betti and Eugenio Beltrami. He made important contributions in elasticity. The Somigliana integral equation for elasticity is the equivalent of Green's formula for potential...
, his entire life was devoted to a higher unselfish ideal, i.e. scientific research: and remarks that only his beloved family shared the same attentions and care he reserved to his ideal.
Research activity
As Somigliana remarks, he was not gifted by a strong inventiveness, meaning also that he never created new theories: this ability was not his main one. He perfected already developed theories: nearly each of his works appear as the natural result of a deep analysis work on theories that have already reached a high degree of perfection, clearly and precisely exposed. He also had an exquisite sense for the applicability of his work, due to his engineering knowledges: he mastered perfectly all known branches of mathematical analysisMathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
and their mechanical
Mechanics
Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....
and physical
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
applications.
He was the author of more than 60 works: fairly complete lists appear in references , and . This last reference is particularly useful as Maggi classifies Morera's works according to the topics dealt: his classification is basically followed in the following subsections, however using modern terminology.
Complex analysis
classifies his works on this topics as pertaining to "analytic function theory". His contributions to complex analysisComplex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
, notably Morera's theorem
Morera's theorem
In complex analysis, a branch of mathematics, Morera's theorem, named after Giacinto Morera, gives an important criterion for proving that a function is holomorphic....
, first proved in the paper , are still the best known part of his scientific research. He wrote eight research papers on this topic: these papers probably inspired the quotation by Carlo Somigliana
Carlo Somigliana
Carlo Somigliana was an Italian mathematician and a classical mathematical physicist faithful to the school of Enrico Betti and Eugenio Beltrami. He made important contributions in elasticity. The Somigliana integral equation for elasticity is the equivalent of Green's formula for potential...
reported at the beginning of this section.
Differential equations
This section includes all his works on the theory of differential equations, ordinaryOrdinary differential equation
In mathematics, an ordinary differential equation is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable....
or partial
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
ones: classifies this contributions as works in the theory of the equations of dynamics
Analytical dynamics
In classical mechanics, analytical dynamics, or more briefly dynamics, is concerned about the relationship between motion of bodies and its causes, namely the forces acting on the bodies and the properties of the bodies...
, in the theory of first-order partial differential equations and in the theory of exact differential equation
Exact differential equation
In mathematics, an exact differential equation or total differential equation is a certain kind of ordinary differential equation which is widely used in physics and engineering.-Definition:...
s. He wrote twelve papers on this topic: the results he obtained in this works are well described by . In the paper he gives a very brief proof of a transformation formula for the Poisson brackets first proved by Émile Léonard Mathieu
Émile Léonard Mathieu
Émile Léonard Mathieu was a French mathematician. He is most famous for his work in group theory and mathematical physics. He has given his name to the Mathieu functions, Mathieu groups and Mathieu transformation...
, while in the paper he simplifies the proof of a theorem of Francesco Siacci
Francesco Siacci
Francesco Siacci , an Italian mathematician, ballistician, and officer in the Italian army, was born in Rome, Italy. He was a professor of mechanics in the University of Turin and University of Naples...
which is substantially equivalent to Lie's third theorem
Lie's third theorem
In mathematics, Lie's third theorem often means the result that states that any finite-dimensional Lie algebra g, over the real numbers, is the Lie algebra associated to some Lie group G. The relationship to the history has though become confused....
: the paper is concerned with the Pfaff problem, proving a theorem
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...
on the minimum number of integrations to be performed in order to solve the problem.
Equilibrium of continuous bodies in elasticity theory
classifies four of his works within the realm of elasticity theory: his contribution are well described by and by in their known monographs. The works within this section are perhaps the second best known part of his research, after his contributions to complex analysisComplex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
.
Mathematical analysis
classifies four of his works under the locution "Questioni varie di Analisi".Potential theory of harmonic functions
His contribution of this topics are classified by under two sections, named respectively "Fondamenti della teoria della funzione potenziale" and "Attrazione dell'elissoide e funzioni armoniche ellissoidali". The work deals with the definition and properties of ellipsoidal harmonics and the related Lamé functionLamé function
In mathematics, a Lamé function is a solution of Lamé's equation, a second-order ordinary differential equation. It was introduced in the paper . Lamé's equation appears in the method of separation of variables applied to the Laplace equation in elliptic coordinates...
s.
Rational mechanics and mathematical physics
includes in this class twelve works: his first published work is included among them.Varia: algebraic analysis and differential geometry
This section includes the only two papers of Morera on the subject of algebraic analysis and his unique paper on differential geometry: they are, respectively, the papers , and .Teaching activity
References , and do not say much about the teaching activity of Giacinto Morera: SomiglianaCarlo Somigliana
Carlo Somigliana was an Italian mathematician and a classical mathematical physicist faithful to the school of Enrico Betti and Eugenio Beltrami. He made important contributions in elasticity. The Somigliana integral equation for elasticity is the equivalent of Green's formula for potential...
describes once his teaching ability as incisive. However, his teaching activity is also testified by the litographed
Lithography
Lithography is a method for printing using a stone or a metal plate with a completely smooth surface...
lecture notes
Textbook
A textbook or coursebook is a manual of instruction in any branch of study. Textbooks are produced according to the demands of educational institutions...
: according to the OPAC, this book had two editions, the first one being in 1901–1902.
See also
- Linear elasticityLinear elasticityLinear elasticity is the mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions. Linear elasticity models materials as continua. Linear elasticity is a simplification of the more general nonlinear theory of elasticity and is a branch of...
- Morera's theoremMorera's theoremIn complex analysis, a branch of mathematics, Morera's theorem, named after Giacinto Morera, gives an important criterion for proving that a function is holomorphic....
- Potential theoryPotential theoryIn mathematics and mathematical physics, potential theory may be defined as the study of harmonic functions.- Definition and comments :The term "potential theory" was coined in 19th-century physics, when it was realized that the fundamental forces of nature could be modeled using potentials which...
- Morera stress functions