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CORBO ESPOSITO ANTONIO - Professore Ordinario

Italian version

Department: Dipartimento: Ingegneria Elettrica e dell'Informazione "Maurizio Scarano"

Scientific Sector: MAT/05

Student reception: Martedì 14-16 Giovedì 14-16

Contact info:
E-Mail: antonio.corboesposito@unicas.it

  • Teaching ANALISI MATEMATICA I (30001)

    Primo anno di Ingegneria civile e ambientale (L-7), Curriculum unico
    Credits (CFU): 12,00

    Program:
    SYLLABUS
    Introductory notions about logic and inferences.
    Review of N, Z, Q, R and their ordering and algebraic properties.
    Properties of continuum of R.
    Complex numbers and their algeabraic properties.
    Notion of limits of sequences and functions.
    Theorems on limits.
    Metric spaces and topology.
    Continuous functions. Theorems on continuous functions.
    Differential calculus for univariate functions.
    Integral calculus for univariate functions.
    Numerical series.

    Reference books:
    Bertsch, Dal Passo: Analisi Matematica. Ed. McGraw-Hill
    Marcellini, Sbordone: Analisi Matematica I. Ed. Liguori.
    Alvino, Carbone, Trombetti: Esercitazioni di Matematica, vol I parte 1 e parte 2, vol. II parte 1 e parte 2. Ed. Liguori
    Marcellini, Sbordone: Esercitazioni di Analisi Matematica I- Parte I e Parte II. Ed. Liguori
    Demidovic – Esercizi e problemi di analisi matematica. Ed. Riuniti

  • Teaching ANALISI MATEMATICA I (30001)

    Primo anno di Ingegneria Informatica e delle Telecomunicazioni (L-8), Curriculum unico
    Credits (CFU): 12,00

    Program:
    SYLLABUS
    Introductory notions about logic and inferences.
    Review of N, Z, Q, R and their ordering and algebraic properties.
    Properties of continuum of R.
    Complex numbers and their algeabraic properties.
    Notion of limits of sequences and functions.
    Theorems on limits.
    Metric spaces and topology.
    Continuous functions. Theorems on continuous functions.
    Differential calculus for univariate functions.
    Integral calculus for univariate functions.
    Numerical series.

    Reference books:
    Bertsch, Dal Passo: Analisi Matematica. Ed. McGraw-Hill
    Marcellini, Sbordone: Analisi Matematica I. Ed. Liguori.
    Alvino, Carbone, Trombetti: Esercitazioni di Matematica, vol I parte 1 e parte 2, vol. II parte 1 e parte 2. Ed. Liguori
    Marcellini, Sbordone: Esercitazioni di Analisi Matematica I- Parte I e Parte II. Ed. Liguori
    Demidovic – Esercizi e problemi di analisi matematica. Ed. Riuniti

  • Teaching RICERCA OPERATIVA (32376)

    Primo anno di Ingegneria Informatica (LM-32), Generale
    Credits (CFU): 6,00

    Program:
    Introduction
    Mathematical optimizazion and mathematical programming.
    Linear programming.
    Simplex algorithm
    Duality
    Integer linear programming
    Graphs
    Combinatorial optimization
    Software (AMPL)

    Reference books:
    Paolo Serafini "Ricerca Operativa" ed. Springer

  • Teaching ANALISI MATEMATICA II (92354)

    Primo anno di Ingegneria civile e ambientale (L-7), Curriculum unico
    Credits (CFU): 12,00

    Program:
    Vectors and vector spaces (finite dimension). Linear dependence and independence. Span. Characterization of dimension of a vector space.
    Intersections and sum of vector spaces. Grassman rule. Scalar product in Rn. Schwarz' inequality.
    Gram-Schmidt orthogonalization. Matrices. Matrix multiplication. Rank and determinant.
    Properties of determinant . Pivot method for the computation of determinant or rank. Pivot method for the computation of inverse matrix.
    Binet's theorem. Linear systems. Gauss elimination method. Rouché-Capelli's theorem. Structure of affine space of solutions. Cramer's rule.
    Omomorphisms. Ker. Image spae. Coordinates. Change of base. Matrix of a change of base.
    Endomorphism. Carachteristic polynomial. Eigenvalues, eigenvectors, eigenspaces. Diagonal and triangular matrices.
    Schur's lemma (Triangularization via orthogonal matrices).
    Canonical Hermitiano product. Symmetric and hermitian matrices.
    Spectral theorem. Search of eigenvalues and eigenvectors of a symmetric matrix (algorithm).
    Conic sections . Symmetric matrix associate to a conic section and their classification.
    Canonical equations. Reduction to canonical equation via an isometry.
    Multivariate functions. Topology in Rn. Partial and directional derivative of a function. Gradient vector.
    Differentiability. Total differential theorem. Schwarz' theorem.
    Stationary points. Hessian matrix and determination of sign of its eigenvalues. Taylor formula (up to the second order).
    Ordinary differential equations (ODE). ODE of order k.
    Banach contraction theore. Integral curves. Cauchy problem. Picard's theorem.
    Linear ODE of order 1 and equations linear after change of variables. Exercises.
    Linear ODE of any order with constant coefficient. Characteristic polynomial.
    Superposition method to find a particular solution.
    Complete metric spaces. Banach spaces. Hilbert spaces.
    Sequences of functions. Point convergence, uniform convergence.
    Norm of the uniform convergence. Completeness of C°[a,b] equipped with this norm.
    Series of functions. Total convergence. Examples and exercises.
    Theorem about taking limits under the integral sign (for the uniform convergence).
    Conditions to move a limit under derivative sign.
    Power series. Convergence radius. Abel's theorem (without proof).
    Taylor series. Sufficient conditions for equality between a function and its Taylor series.
    Maclaurin series of some common functions. Examples and exercises.
    Projection on a finite dimensional subspace of a Hilbert space.
    Fourier series. Partial sums. Bessel’s (in)equality. Examples and exercises.
    Pointwise convergence theorem for Fourier series. Examples and exercises.
    Riemann multivariate integral.
    Reduction formulas for multiple integrals on normal domains. Examples and exercises.
    Jacobian matrix. Jacobian matrix of a composite function.
    Curves. Generalities. Rectifiable curves. Length of a curve.
    Line integrals. Equivalent curves. Examples and exercises.
    Equivalence of regular and simple curves with the same image.
    Surfaces in R3. Areas. Surface integral.
    Differental (1-)forms. Line integral of a differential form. Examples and exercises.
    Exact differential forms. First and second exactness criteria for differential forms.
    Integrals depending on a parameter. Differentiation under the integral sign.
    Gauss-Green-Ostrogradskij formulas. Divergence theorem in R2. Examples and exercises.
    Lagrange multipiers' method to find constrained stationary points.

    Reference books:
    Marco Abate: Algebra lineare, Mc Graw Hill
    Enrico Giusti: Analisi Matematica II, Boringhieri.
    Nicola Fusco, Paolo Marcellini, Carlo Sbordone: Analisi matematica 2, Liguori.

  • Teaching ANALISI MATEMATICA II (92354)

    Primo anno di Ingegneria Informatica e delle Telecomunicazioni (L-8), Curriculum unico
    Credits (CFU): 12,00

    Program:
    Vectors and vector spaces (finite dimension). Linear dependence and independence. Span. Characterization of dimension of a vector space.
    Intersections and sum of vector spaces. Grassman rule. Scalar product in Rn. Schwarz' inequality.
    Gram-Schmidt orthogonalization. Matrices. Matrix multiplication. Rank and determinant.
    Properties of determinant . Pivot method for the computation of determinant or rank. Pivot method for the computation of inverse matrix.
    Binet's theorem. Linear systems. Gauss elimination method. Rouché-Capelli's theorem. Structure of affine space of solutions. Cramer's rule.
    Omomorphisms. Ker. Image spae. Coordinates. Change of base. Matrix of a change of base.
    Endomorphism. Carachteristic polynomial. Eigenvalues, eigenvectors, eigenspaces. Diagonal and triangular matrices.
    Schur's lemma (Triangularization via orthogonal matrices).
    Canonical Hermitiano product. Symmetric and hermitian matrices.
    Spectral theorem. Search of eigenvalues and eigenvectors of a symmetric matrix (algorithm).
    Conic sections . Symmetric matrix associate to a conic section and their classification.
    Canonical equations. Reduction to canonical equation via an isometry.
    Multivariate functions. Topology in Rn. Partial and directional derivative of a function. Gradient vector.
    Differentiability. Total differential theorem. Schwarz' theorem.
    Stationary points. Hessian matrix and determination of sign of its eigenvalues. Taylor formula (up to the second order).
    Ordinary differential equations (ODE). ODE of order k.
    Banach contraction theore. Integral curves. Cauchy problem. Picard's theorem.
    Linear ODE of order 1 and equations linear after change of variables. Exercises.
    Linear ODE of any order with constant coefficient. Characteristic polynomial.
    Superposition method to find a particular solution.
    Complete metric spaces. Banach spaces. Hilbert spaces.
    Sequences of functions. Point convergence, uniform convergence.
    Norm of the uniform convergence. Completeness of C°[a,b] equipped with this norm.
    Series of functions. Total convergence. Examples and exercises.
    Theorem about taking limits under the integral sign (for the uniform convergence).
    Conditions to move a limit under derivative sign.
    Power series. Convergence radius. Abel's theorem (without proof).
    Taylor series. Sufficient conditions for equality between a function and its Taylor series.
    Maclaurin series of some common functions. Examples and exercises.
    Projection on a finite dimensional subspace of a Hilbert space.
    Fourier series. Partial sums. Bessel’s (in)equality. Examples and exercises.
    Pointwise convergence theorem for Fourier series. Examples and exercises.
    Riemann multivariate integral.
    Reduction formulas for multiple integrals on normal domains. Examples and exercises.
    Jacobian matrix. Jacobian matrix of a composite function.
    Curves. Generalities. Rectifiable curves. Length of a curve.
    Line integrals. Equivalent curves. Examples and exercises.
    Equivalence of regular and simple curves with the same image.
    Surfaces in R3. Areas. Surface integral.
    Differental (1-)forms. Line integral of a differential form. Examples and exercises.
    Exact differential forms. First and second exactness criteria for differential forms.
    Integrals depending on a parameter. Differentiation under the integral sign.
    Gauss-Green-Ostrogradskij formulas. Divergence theorem in R2. Examples and exercises.
    Lagrange multipiers' method to find constrained stationary points.

    Reference books:
    Marco Abate: Algebra lineare, Mc Graw Hill
    Enrico Giusti: Analisi Matematica II, Boringhieri.
    Nicola Fusco, Paolo Marcellini, Carlo Sbordone: Analisi matematica 2, Liguori.

  • Teaching METODI MATEMATICI PER L'INGEGNERIA (92356)

    Secondo anno di Ingegneria Informatica e delle Telecomunicazioni (L-8), Curriculum unico
    Credits (CFU): 6,00

    Program:
    Fourier series. Generalized Fourier series.
    Functions of one complex variable.
    Elements of Lebesgue integration theory and Lp spaces.

    .

    Reference books:
    G.C. Barozzi "Matematica per l'ingegneria dell'informazione", ed. Zanichelli
    M. Codegone "Metodi matematici per l'ingegneria", ed. Zanichelli.

  • Teaching METODI MATEMATICI PER L'INGEGNERIA (92355)

    Modulo METODI MATEMATICI PER L'INGEGNERIA (MAT/05)

    Terzo anno di Ingegneria industriale CASSINO (L-9), Elettrica
    Credits (CFU): 3,00

    Program:
    Functions of one complex variable.
    Fourier transform.
    Zeta transform.

    Reference books:
    G.C. Barozzi "Matematica per l'ingegneria dell'informazione", ed. Zanichelli
    M. Codegone "Metodi matematici per l'ingegneria", ed. Zanichelli.

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Born on 08/14/1963
23/05/1986 Degree in Mathematics (University of Naples Federico II), 110 e lode/110.
1986/1987 Fellowship at Istituto Nazionale di Alta Matematica (Roma).
1987-1991 PHD in Mathematics (3rd cycle) at University of Naples Fedetico II
21/06/1991-31/10/1992 Teaching assinstant of Mathematical Analysis at University of Naples Fedetico II
01/11/1992-31/08/2005 Associate professor of Mathematical Analysis at University of Cassino.
01/09/2005-oggi Full professor of Mathematical Analysis at University of Cassino and southern Lazio.
Winner of the prize by "classe di Scienze Matematiche Pure e Applicate" of Accademia Pontaniana di Napoli for the year 1994.
He is (co-)author of more than 30 papers of Mathematical Analysis on international journals.

Other relevant academic duties
He was director of a local unit for a research project of national interest (PRIN)
He was commissar in several selection procedures for a university professor position at his University, and at University of Naples and University of Salerno
He is director of Numerical Analysis laboratory at his University

Teaching
In academic year 1991/92 he was teaching assistant for Mathematical Analysis courses at University of Naples Fedetico II
Since 1992 to present day he has been holder of the teaching module of "Analisi Matematica I" at University of Cassino and southern Lazio.
Since 1993 to present day he has been charged, for every academic year, with at least one more teaching module at the same University.
Since "Scuola di Dottorato in Ingegneria" was born (2006) at University of Cassino to present day, he has been holder, for every academic year, of one or two teaching modules.

Research
Main reasearch interests are:
for Mathematical Analysis
- integral functionals of the Calculus of Variations
- asymptotic behaviour for sequences of variational problems
- binary digits distribution and binomil measures
- inuerical quadrature of binomial measures and refinable functionals
fot computability theory and cryptography
- generation of computationally secure pseudorandom numbers
- authentication/key exchange protocols
- best algorithms for powers of numbers or matrices

He attended many national and international meetings of Mathematics
He was invited professor in France (Paris VI) and in Russia (Steklov Institute of San Petersburg University)

From 6th edition to present day (9th edition in 2016) he is one of the organizers of the "European conference on Elliptic and Parabolic Problems"

Research
Main reasearch interests are:
for Mathematical Analysis
- integral functionals of the Calculus of Variations
- asymptotic behaviour for sequences of variational problems
- binary digits distribution and binomil measures
- inuerical quadrature of binomial measures and refinable functionals
fot computability theory and cryptography
- generation of computationally secure pseudorandom numbers
- authentication/key exchange protocols
- best algorithms for powers of numbers or matrices

1 Comparison results for some types of relaxation of variational integral functionals. 1993 A. CORBO ESPOSITO; DE ARCANGELIS R.
2 Homogenization of the p-Laplacian in a domain with oscillating boundary. 1997 A. CORBO ESPOSITO; DONATO P.; GAUDIELLO A.; PICARD C.
3 The Lavrentieff phenomenon and different processes of homogenization. 1992 A. CORBO ESPOSITO; DE ARCANGELIS R.
4 A new proposal for a material to be used in a Flywheel Energy Storage System 2007 A. CORBO ESPOSITO; MARIGNETTI F
5 Some notes on characterization of function sets described by constraints on the gradient. 1995 A. CORBO ESPOSITO; DE ARCANGELIS R.
6 Lavrentieff phenomenon for problems of homogenization with constraints on the gradient. 1997 A. CORBO ESPOSITO; SERRA CASSANO F.
7 Further results on comparison for some types of relaxation of variational integral functionals. 1995 A. CORBO ESPOSITO; DE ARCANGELIS R.
8 Homogenization of Dirichlet and Neumann problems with gradient constraints 2006 CARDONE G; A. CORBO ESPOSITO; PADERNI G
9 Refinable functions, functionals, and iterated function systems 2016 Calabrò, F.; Corbo Esposito, A.; Mantica, G.; Radice, T.
10 Homogenization of a mixed boundary value problem for a formally selfadjoint elliptic system in a periodically perforated domain. 2009 G. Cardone; A. Corbo Esposito; S. A. Nazarov
11 An efficient and reliable quadrature algorithm for integration with respect to binomial measures 2008 F. CALABRO'; CORBO ESPOSITO A
12 Korn's inequality for periodic solids and convergence rate of homogenization 2009 G. Cardone; A. Corbo Esposito; S. A. Nazarov
13 Homogenization of Neumann problems for unbounded integral functionals. 1999 CARBONE L.; A. CORBO ESPOSITO; DE ARCANGELIS R.
14 A one-dimensional variational problem with gradient constraint. 2004 CARDONE G.; A. CORBO ESPOSITO; ZHIKOV V.V.
15 Binary digits expansion of numbers: Hausdorff dimensions of intersections of level sets of averages' upper and lower limits. 2004 CARBONE L.; CARDONE G.; A. CORBO ESPOSITO
16 ”Some remarks about level sets of Cesaro averages of binary digits'' 2005 CARDONE G; CORBO ESPOSITO A; L. FAELLA; FASC; -
17 A characterization of families of function sets described by constraints on the gradient. 1994 A. CORBO ESPOSITO; DE ARCANGELIS R.
18 A Homogenization Problem in a Perforated Domain with Both Dirichlet and Neumann Conditions on the Boundary of the Holes 2002 A. CORBO ESPOSITO; D'APICE C.; GAUDIELLO A.
19 Complete representation of some functionals showing the Lavrentieff phenomenon. 2001 A. CORBO ESPOSITO; DURANTE T.
20 Homogenization of Dirichlet problems with nonnegative bounded constraints of the gradient. 1994 A. CORBO ESPOSITO; DE ARCANGELIS R.
21 A characterization of sets of functions and distributions on Rn described by constraints on the gradient. 1996 A. CORBO ESPOSITO; DE ARCANGELIS R.
22 Hausdorff dimension for level sets of upper and lower limits of generalized averages of binary digits 2006 CARDONE G; A. CORBO ESPOSITO; FAELLA L
23 Preface [6th European Conference on Elliptic and Parabolic Problems]. Held in Gaeta, May 25–29, 2009. 2010 B. Brighi; M. Chipot; A. Corbo Esposito; G. Mingione; C. Sbordone; I. Shafir; V. Valente; G. Vergara Caffarelli
24 An integral representation result for the Gamma-limit of functionals with non-standard growth conditions in the case of elasticity. 2002 CARDONE G.; A. CORBO ESPOSITO; ZHIKOV V.V.
25 Nonlinear Dirichlet problems in randomly perforated domains. 1997 BALZANO M.; A. CORBO ESPOSITO; PADERNI G.
26 HOMOGENIZATION OF SCALAR PROBLEMS FOR A COMBINED STRUCTURE WITH SINGULAR OR THIN REINFORCEMENT 2007 CARDONE G; A. CORBO ESPOSITO; PASTUKHOVA S.E
27 An evaluation of Clenshaw-Curtis quadrature rule for integration w.r.t. singular measures 2009 F. CALABRO'; CORBO ESPOSITO A
28 Binomial Measures and their Approximations 2012 F. Calabro' ; A. Corbo Esposito ; C. Perugia
29 A proposal for a new Flywheel Energy Storage System 2007 CORBO ESPOSITO A; F. MARIGNETTI
30 Homogenization of some problems with gradient constraints. 2004 CARDONE G.; A. CORBO ESPOSITO; YOSIFIAN G.A.; ZHIKOV V.V.
31 Relaxation in BV of integral functionals defined on Sobolev functions with values in the unit sphere 2007 ALICANDRO R; A. CORBO ESPOSITO, LEONE C.
32 Integration with Respect to Linearly Balanced Measures 2012 A. Corbo Esposito; F. Calabrò

[Ultima modifica: mercoledì 30 novembre 2016]