2024-03-28T19:15:55Z
http://eprints.biblio.unitn.it/cgi/oai2
oai:eprints.biblio.unitn.it:658
2012-02-28T14:17:38Z
7374617475733D756E707562
7375626A656374733D51:5141:51413239392E36
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Optimal control of finite horizon type for a dimensional delayed switching system
Bagagiolo, Fabio
QA299.6 Analysis
We consider a finite horizon optimal control problem for an ODE system, with trajectories presenting a delayed two-values switching along a fixed direction. In particular the system exhibits hysteresis. Due to the presence of the switching component of the trajectories, several definitions of value functions are possible. No one of this value functions is in general continuous. We prove that, under general hypotheses, the "least value function", i.e. the value function of the more relaxed problem, is the unique semicontinuous viscosity solution of two suitably coupled Hamilton-Jacobi-Bellman equations. Such a coupling involves boundary conditions in the viscosity sense.
2003
Departmental Technical Report
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/658/1/UTM647.pdf
Bagagiolo, Fabio (2003) Optimal control of finite horizon type for a dimensional delayed switching system. UNSPECIFIED. (Unpublished)
http://eprints.biblio.unitn.it/658/
oai:eprints.biblio.unitn.it:659
2012-02-28T14:17:38Z
7374617475733D756E707562
7375626A656374733D51:5141:51413239392E36
74797065733D746563687265706F7274
Kazhdan-Lusztig R-polynomials of permutations containing a 231 or 312 pattern
Pagliacci, Michela
QA299.6 Analysis
We consider the Kazhdan-Lusztig R-polynomials, Ru,v(q) , indexed by permutations u,v of Sn, where u contains a pattern of type 231 or 232 and v is obtained from u by applying a transposition and an appropriate 3-cycle. We prove, using combinatorial techniques, that these polynomials are given by a closed product formula. The case of permutation which contain a pattern of type 321 follows from the others.
2003
Departmental Technical Report
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/659/1/UTM648.pdf
Pagliacci, Michela (2003) Kazhdan-Lusztig R-polynomials of permutations containing a 231 or 312 pattern. UNSPECIFIED. (Unpublished)
http://eprints.biblio.unitn.it/659/
oai:eprints.biblio.unitn.it:661
2012-02-28T14:17:39Z
7374617475733D756E707562
7375626A656374733D51:5141:51413239392E36
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Convergence Analysis of a Domain Decomposition FEM Approximation of the Isentropic Euler Equation
Gerardo Giorda, Luca
QA299.6 Analysis
We analyze an interation-by-subdomain algorithm of Dirichlet\Dirichlet type for the isentropic Euler equation. Focusing on subsonic flows, which are the ones showing the most interesting features in a domain decomposition framework. The main attention is paid to the spatial decomposition, and the problem is advanced in time by means of a semi-implicit Euler scheme. We enforce the continuity on the interface of the inviscid flux, and, in the one-dimentional case, we prove convergence of the algorithm in characteristic variables for both the semi-discrete problem and the fully discrete one, where the equation is discretized in space via Streamline Diffusion Finite Elements. In both cases, the interface mapping is showed to be a contraction: in the semi discrete case, for any choice of the time step Dt, with constant of order e (-c/Dt) (c>0), in the fully discrete case, provided the entries of the stabilizing matrix are sufficiently small. Finally, some error estimates of energy type are given.
2003
Departmental Technical Report
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/661/1/UTM651.pdf
Gerardo Giorda, Luca (2003) Convergence Analysis of a Domain Decomposition FEM Approximation of the Isentropic Euler Equation. UNSPECIFIED. (Unpublished)
http://eprints.biblio.unitn.it/661/
oai:eprints.biblio.unitn.it:666
2012-02-28T14:17:40Z
7374617475733D756E707562
7375626A656374733D51:5141:51413239392E36
74797065733D746563687265706F7274
Quaternionic Regular Functions and the @-Neumann Problem in C2
Perotti, Alessandro
QA299.6 Analysis
In this paper we give a boundary differential criterium that characterizes regular functions (in the sense of Fueter) among harmonic functions.
2003
Departmental Technical Report
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/666/1/UTM654.pdf
Perotti, Alessandro (2003) Quaternionic Regular Functions and the @-Neumann Problem in C2. UNSPECIFIED. (Unpublished)
http://eprints.biblio.unitn.it/666/
oai:eprints.biblio.unitn.it:673
2012-02-28T14:17:43Z
7374617475733D756E707562
7375626A656374733D51:5141:51413239392E36
74797065733D746563687265706F7274
Limit cycle's uniqueness for a class of plane system
Sabatini, M.
QA299.6 Analysis
A uniqueness theorem for limit cycles of a class of plane differential system is proved. The main results is applicable to second order O.D.E.'s with dissipative term depending both on the position and the velocity.
2004
Departmental Technical Report
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/673/1/UTM662.pdf
Sabatini, M. (2004) Limit cycle's uniqueness for a class of plane system. UNSPECIFIED. (Unpublished)
http://eprints.biblio.unitn.it/673/
oai:eprints.biblio.unitn.it:779
2012-02-28T14:18:05Z
7374617475733D756E707562
7375626A656374733D51:5141:51413239392E36
74797065733D746865736973
Cycle type and Kazhdan Lustig R-polynomials
Pagliacci, Michela
QA299.6 Analysis
Not available
2003
Thesis
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/779/1/PhDTS38.pdf
Pagliacci, Michela (2003) Cycle type and Kazhdan Lustig R-polynomials. UNSPECIFIED thesis, UNSPECIFIED.
http://eprints.biblio.unitn.it/779/
oai:eprints.biblio.unitn.it:784
2012-02-28T14:18:07Z
7374617475733D756E707562
7375626A656374733D51:5141:51413239392E36
74797065733D746563687265706F7274
Limit cycle's uniqueness for a class of planar dynamical systems
Sabatini, M.
Villari, G.
QA299.6 Analysis
A uniqueness theorem for limit cycles of a class of plane differential system is proved. The main result is applicable to secord order O.D.E.'s with dissipative term depending both on the position and the velocity.
2004-06
Departmental Technical Report
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/784/1/UTM668.pdf
Sabatini, M. and Villari, G. (2004) Limit cycle's uniqueness for a class of planar dynamical systems. UNSPECIFIED. (Unpublished)
http://eprints.biblio.unitn.it/784/
oai:eprints.biblio.unitn.it:789
2012-02-28T14:18:09Z
7374617475733D756E707562
7375626A656374733D51:5141:51413239392E36
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About limit cycle's uniqueness for a class of generalized Liénard systems
Sabatini, Marco
Villari, Gabriele
QA299.6 Analysis
Available in the file.
2004-08
Departmental Technical Report
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/789/1/UTM672.pdf
Sabatini, Marco and Villari, Gabriele (2004) About limit cycle's uniqueness for a class of generalized Liénard systems. UNSPECIFIED. (Unpublished)
http://eprints.biblio.unitn.it/789/
oai:eprints.biblio.unitn.it:793
2012-02-28T14:18:10Z
7374617475733D756E707562
7375626A656374733D51:5141:51413239392E36
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Period function's convexity for Hamiltonian centers with separable variables
Sabatini, Marco
QA299.6 Analysis
A convexity theorem for the period function T of Hamiltonian systems with separable variables is proved. We are interested in systems with a non-monotone T. The result is applied to prove the uniqueness of critical orbits in second order ODE's.
2004-09
Departmental Technical Report
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/793/1/UTM676.pdf
Sabatini, Marco (2004) Period function's convexity for Hamiltonian centers with separable variables. UNSPECIFIED. (Unpublished)
http://eprints.biblio.unitn.it/793/
oai:eprints.biblio.unitn.it:807
2012-02-28T14:18:12Z
7375626A656374733D51:5141:51413239392E36
74797065733D7072657072696E74
On regular harmonics of one quaternionic variable
Perotti, Alessandro
QA299.6 Analysis
We prove some results about the Fueter-regular homogeneous polynomials, which appear as components in the power series of any quaternionic regular function. Let B denote the unit ball in C2 ≅ H and S = δ B the group of unit quaternions. In §2.1 we obtain a differential condition that characterize the homogeneous polynomials whose restrictions to S extend as a regular polynomial. This result generalizes a similar characterization for holomorphic extensions of polynomials proved by Kytmanov. In §2.2 we show how to define an injective linear operator R: Hk(S)-> Uk Ψ between the space of complex-valued spherical harmonics and the H-module of regular homogeneous polynomials of degree k. In particular, we show how to construct bases of the module of regular homogeneous polynomials of a fixed degree starting from any choice of C-bases of the spaces of complex harmonic homogeneous polynomials.
2005
Preprint
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/807/1/RegBall.pdf
Perotti, Alessandro (2005) On regular harmonics of one quaternionic variable. [Preprint]
http://eprints.biblio.unitn.it/807/
oai:eprints.biblio.unitn.it:883
2012-02-28T14:18:38Z
7374617475733D7375626D6974746564
7375626A656374733D51:5141:51413239392E36
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On regular harmonics of one quaternionic variable
Perotti, Alessandro
QA299.6 Analysis
We prove some results about the Fueter-regular homogeneous polynomials, which appear as components in the power series of any quaternionic regular function. We obtain a differential condition that characterizes the homogeneous polynomials whose trace on the unit sphere extends as a regular polynomial. We apply this result to define an injective linear operator from the space of complex spherical harmonics to the module of regular homogeneous polynomials of a fixed degree $k$.
2005
Preprint
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/883/2/RegBallIJPAM.pdf
Perotti, Alessandro (2005) On regular harmonics of one quaternionic variable. [Preprint] (Submitted)
http://eprints.biblio.unitn.it/883/
oai:eprints.biblio.unitn.it:884
2012-02-28T14:18:38Z
7374617475733D7375626D6974746564
7375626A656374733D51:5141:51413239392E36
74797065733D636F6E667061706572
Holomorphic functions and regular quaternionic functions on the hyperkähler space H
Perotti, Alessandro
QA299.6 Analysis
Let H be the space of quaternions, with its standard hypercomplex structure. Let $\mathcal R(\Omega)$ be the module of \emph{$\psi$-regular} functions on $\Omega$. For every $p\in H$, $p^2=-1$, $\mathcal R(\Omega)$ contains the space of holomorphic functions w.r.t. the complex structure $J_p$ induced by $p$. We prove the existence, on any bounded domain $\Omega$, of $\psi$-regular functions that are not $J_p$-holomorphic for any $p$. Our starting point is a result of Chen and Li concerning maps between hyperk\"ahler manifolds, where a similar result is obtained for a less restricted class of quaternionic maps. We give a criterion, based on the energy-minimizing property of holomorphic maps, that distinguishes $J_p$-holomorphic functions among $\psi$-regular functions.
World Scientific
2005
Conference paper
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/884/1/RegIsaacProcs.pdf
Perotti, Alessandro (2005) Holomorphic functions and regular quaternionic functions on the hyperkähler space H. World Scientific. (Submitted)
http://eprints.biblio.unitn.it/884/
oai:eprints.biblio.unitn.it:973
2012-02-28T14:19:00Z
7374617475733D756E707562
7375626A656374733D51:5141:51413239392E36
74797065733D746563687265706F7274
A Rigorous Approach to the Feynman-Vernon Influence Functional and its Applications. I
Albeverio, S.
Cattaneo, L.
Di Persio, L.
Mazzucchi, S.
QA299.6 Analysis
A rigorous representation of the Feynman-Vernon influence functional used to describe open quantum systems is given, based on the theory of infinite dimensional oscillatory integrals. An application to the case of the density matrices describing the Caldeira-Leggett model of two quantum systems with a quadratic interaction is treated.
2006-04
Departmental Technical Report
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/973/1/UTM696.pdf
Albeverio, S. and Cattaneo, L. and Di Persio, L. and Mazzucchi, S. (2006) A Rigorous Approach to the Feynman-Vernon Influence Functional and its Applications. I. UNSPECIFIED. (Unpublished)
http://eprints.biblio.unitn.it/973/
oai:eprints.biblio.unitn.it:1189
2012-02-28T14:19:58Z
7374617475733D756E707562
7375626A656374733D51:5141:51413239392E36
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Wick powers in stochastic PDEs: an introduction
Da Prato, Giuseppe
Tubaro, Luciano
QA299.6 Analysis
not available
2007-03
Departmental Technical Report
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/1189/1/UTM711.pdf
Da Prato, Giuseppe and Tubaro, Luciano (2007) Wick powers in stochastic PDEs: an introduction. UNSPECIFIED. (Unpublished)
http://eprints.biblio.unitn.it/1189/
oai:eprints.biblio.unitn.it:1442
2012-02-28T14:21:49Z
7374617475733D756E707562
7375626A656374733D51:5141:5141313530
7375626A656374733D51:5141:51413239392E36
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Feynman Path Integrals for the Inverse Quartic Oscillator
Mazzucchi, Sonia
QA152 Algebra
QA299.6 Analysis
Available in the .pdf
2008-04
Departmental Technical Report
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/1442/1/UTM722.pdf
Mazzucchi, Sonia (2008) Feynman Path Integrals for the Inverse Quartic Oscillator. UNSPECIFIED. (Unpublished)
http://eprints.biblio.unitn.it/1442/
oai:eprints.biblio.unitn.it:1675
2012-02-28T14:23:06Z
7374617475733D756E707562
7375626A656374733D51:5141:51413735
7375626A656374733D51:5141:51413239392E36
74797065733D746563687265706F7274
Which is the Right Source for Vulnerability Studies? An Empirical Analysis on Mozilla Firefox
Massacci, Fabio
Nguyen, Viet Hung
QA075 Electronic computers. Computer science
QA299.6 Analysis
The last years have seen a major trend towards the notion of quantitative security assessment and the use of empirical methods to analyze or predict vulnerable components. Many past researches focused on vulnerability discovery models. The common method is to rely upon either a public vulnerability database (CVE, NVD), or vendor vulnerability database. Some combine these databases. Most of these works address a knowledge problem: can we understand the empirical causes of vulnerabilities? Can we predict them? Still, if the data sources do not completely capture the phenomenon we are interested in predicting, then our predictor might be optimal with respect to the data we have but unsatisfactory in practice. In our work, we focus on a more fundamental question: the quality of vulnerability database. How good we are at sampling? Or, with respect to the research objectives of current papers on empirical study in security, are we sampling the right data?
2010-05
Departmental Technical Report
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/1675/1/esem10.pdf
Massacci, Fabio and Nguyen, Viet Hung (2010) Which is the Right Source for Vulnerability Studies? An Empirical Analysis on Mozilla Firefox. UNSPECIFIED. (Unpublished)
http://eprints.biblio.unitn.it/1675/
oai:eprints.biblio.unitn.it:1784
2012-02-28T14:23:47Z
7374617475733D756E707562
7375626A656374733D51:5141:5141323733
7375626A656374733D51:5141:51413239392E36
7375626A656374733D51:5141:51413337342E37
74797065733D746563687265706F7274
Optimal control for stochastic Volterra equations with completely monotone kernels
Bonaccorsi, Stefano
Confortola, Fulvia
Mastrogiacomo, Elisa
QA273 Probabilities
QA374.7 Partial differential equations
QA299.6 Analysis
In this paper, we study a class of stochastic optimal control problems, where the drift term of the equation has a linear growth on the control variable, the cost functional has a quadratic growth, and the control process belongs to the class of square integrable, adapted processes with no bound assumed on it.
2010-01
Departmental Technical Report
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/1784/1/article.pdf
Bonaccorsi, Stefano and Confortola, Fulvia and Mastrogiacomo, Elisa (2010) Optimal control for stochastic Volterra equations with completely monotone kernels. UNSPECIFIED. (Unpublished)
http://eprints.biblio.unitn.it/1784/
oai:eprints.biblio.unitn.it:1949
2012-02-28T14:24:43Z
7374617475733D696E7072657373
7375626A656374733D51:5141:51413239392E36
74797065733D61727469636C656A6F75726E616C
Zeros of regular functions of quaternionic and octonionic variable: a division lemma and the camshaft effect
Ghiloni, Riccardo
Perotti, Alessandro
QA299.6 Analysis
We study in detail the zero set of a slice regular function of a quaternionic or octonionic variable. By means of a division lemma for convergent power series, we find the exact relation existing between the zeros of two octonionic regular functions and those of their product. In the case of octonionic polynomials, we get a strong form of the fundamental theorem of algebra. We prove that the sum of the multiplicities of zeros equals the degree of the polynomial and obtain a factorization in linear polynomials. The original publication is available at www.springerlink.com
Springer Verlag
2010
Article in journal
PeerReviewed
application/pdf
http://eprints.biblio.unitn.it/1949/1/ZerosAMPAarXiv.pdf
Ghiloni, Riccardo and Perotti, Alessandro (2010) Zeros of regular functions of quaternionic and octonionic variable: a division lemma and the camshaft effect. In «Annali di Matematica Pura ed Applicata», Springer Verlag. ISBN 0373-3114 (In Press)
http://eprints.biblio.unitn.it/1949/
oai:eprints.biblio.unitn.it:1950
2012-02-28T14:24:43Z
7374617475733D707562
7375626A656374733D51:5141:51413239392E36
74797065733D626F6F6B63686170746572
A new approach to slice regularity on real algebras
Ghiloni, Riccardo
Perotti, Alessandro
QA299.6 Analysis
We expose the main results of a theory of slice regular functions on a real alternative algebra A, based on a well-known Fueter's construction. Our general theory includes the theory of slice regular functions of a quaternionic or octonionic variable and the theory of slice monogenic functions of a Clifford variable. Our approach permits to extend the range of these function theories and to obtain new results. In particular, we show that a fundamental theorem of algebra with multiplicities holds for an ample class of polynomials with coefficients in A. We give several examples to illustrate some interesting aspects of the theory. The original publication is available at www.springerlink.com
Birkhäuser; Springer Basel AG
Sabadini , Irene
Sommen, Frank
2011
Book chapter or Essay in book
PeerReviewed
application/pdf
http://eprints.biblio.unitn.it/1950/1/Slice_regular_Hypercomplex_Analysis.pdf
Ghiloni, Riccardo and Perotti, Alessandro (2011) A new approach to slice regularity on real algebras. Trends in Mathematics . Birkhäuser; Springer Basel AG, pp. 109-123.
http://eprints.biblio.unitn.it/1950/
oai:eprints.biblio.unitn.it:1952
2012-02-28T14:24:44Z
7374617475733D707562
7375626A656374733D51:5141:51413239392E36
74797065733D61727469636C656A6F75726E616C
Slice regular functions on real alternative algebras
Ghiloni, Riccardo
Perotti, Alessandro
QA299.6 Analysis
In this paper we develop a theory of slice regular functions on a real alternative algebra $A$. Our approach is based on a well-known Fueter's construction. Two recent function theories can be included in our general theory: the one of slice regular functions of a quaternionic or octonionic variable and the theory of slice monogenic functions of a Clifford variable. Our approach permits to extend the range of these function theories and to obtain new results. In particular, we get a strong form of the fundamental theorem of algebra for an ample class of polynomials with coefficients in $A$ and we prove a Cauchy integral formula for slice functions of class $C^1$.
Elsevier
2011-01
Article in journal
PeerReviewed
application/pdf
http://eprints.biblio.unitn.it/1952/1/AIMarXiv.pdf
Ghiloni, Riccardo and Perotti, Alessandro (2011) Slice regular functions on real alternative algebras. In «Advances in Mathematics», vol. 226, n. 2 Elsevier, pp. 1662-1691. ISBN 0001-8708
http://eprints.biblio.unitn.it/1952/
oai:eprints.biblio.unitn.it:2291
2012-02-28T14:27:00Z
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7375626A656374733D51:5141:51413239392E36
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The period functions' higher order derivatives
Sabatini, Marco
QA299.6 Analysis
We prove a formula for the $n$-th derivative of the period function $T$ in a period annulus of a planar differential system. For $n = 1$, we obtain Freire, Gasull and Guillamon formula for the period's first derivative \cite{FGG}. We apply such a result to hamiltonian systems with separable variables and other systems. We give some sufficient conditions for the period function of conservative second order O.D.E.'s to be convex.
2012-02
Departmental Technical Report
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/2291/1/SABATINI_The_period_functions_higher_order_derivatives.pdf
Sabatini, Marco (2012) The period functions' higher order derivatives. UNSPECIFIED. (Unpublished)
http://eprints.biblio.unitn.it/2291/
oai:eprints.biblio.unitn.it:3987
2013-02-13T11:07:58Z
7374617475733D6163636570746564
7375626A656374733D51:5141:5141343430
7375626A656374733D51:5141:51413239392E36
74797065733D746563687265706F7274
Volume Cauchy formulas for slice functions on real associative *-algebras
Ghiloni, Riccardo
Perotti, Alessandro
QA299.6 Analysis
QA445 Geometry
We introduce a family of Cauchy integral formulas for slice and slice regular functions on a real associative *-algebra. For each suitable choice of a real vector subspace of the algebra, a different formula is given, in which the domains of integration are subsets of the subspace. In particular, in the quaternionic case, we get a volume Cauchy formula. In the Clifford algebra case, the choice of the paravector subspace R^(n+1) gives a volume Cauchy formula for slice monogenic functions.
Università degli Studi di Trento
2012-09-25
Departmental Technical Report
PeerReviewed
application/pdf
http://eprints.biblio.unitn.it/3987/1/volume%2Dcauchy%2Dghiloni%2Dperotti%2DarXiv.pdf
http://www.tandfonline.com/10.1080/17476933.2012.709851
Ghiloni, Riccardo and Perotti, Alessandro (2012) Volume Cauchy formulas for slice functions on real associative *-algebras. UTM; 754 . Trento : Università degli Studi di Trento.
http://eprints.biblio.unitn.it/3987/
oai:eprints.biblio.unitn.it:3997
2012-11-26T13:32:32Z
7374617475733D707562
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A note on entire functions
Goldoni, Luca
QA299.6 Analysis
In this article we consider certain power series with real coefficients that represent an entire function and provide sufficient conditions for the unboundedness of these functions on the real axis.
Università degli Studi di Trento. Dipartimento di Matematica
2012-07-03
Departmental Technical Report
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/3997/4/02.pdf
Goldoni, Luca (2012) A note on entire functions. Trento : Università degli Studi di Trento. Dipartimento di Matematica.
http://eprints.biblio.unitn.it/3997/
oai:eprints.biblio.unitn.it:4013
2012-09-04T09:17:14Z
7374617475733D707562
7375626A656374733D51:5141:51413239392E36
74797065733D746563687265706F7274
Linearizations, normalizations and isochrones of planar differential systems
Sabatini, Marco
QA299.6 Analysis
In the first section we collect some unpublished results presented in [17], related to linearizations and normalizations of planar centers. In the second section we consider both the problem of finding isochrones of isochronous systems (centers or not) and its inverse, i. e. given a family of curves filling an open set, how to construct a system having such curves as isochrones. In particular, we show that for every family of curves y = mx + d(x), m ∈ IR there exists a Lienard system having such curves as isochrones.
Università degli Studi di Trento. Dipartimento di Matematica
2012-08-30
Departmental Technical Report
PeerReviewed
application/pdf
http://eprints.biblio.unitn.it/4013/1/Sabatini%2DLNI%2Drevised.pdf
Sabatini, Marco (2012) Linearizations, normalizations and isochrones of planar differential systems. Trento : Università degli Studi di Trento. Dipartimento di Matematica.
http://eprints.biblio.unitn.it/4013/
oai:eprints.biblio.unitn.it:4029
2012-10-16T14:18:58Z
7374617475733D756E707562
7375626A656374733D51:5141:5141343430
7375626A656374733D51:5141:51413239392E36
74797065733D6F74686572
Looking for the Stokes Theorem in an elementary trapezoid
Goldoni, Luca
QA299.6 Analysis
QA445 Geometry
The aim of this very short note it to show that even in
a totally elementary framework, it is possible to glimpse the Stokes
theorem.
2012-10-13
Other
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/4029/1/03.pdf
Goldoni, Luca (2012) Looking for the Stokes Theorem in an elementary trapezoid. [Other] (Unpublished)
http://eprints.biblio.unitn.it/4029/
oai:eprints.biblio.unitn.it:4067
2013-04-05T07:48:01Z
7374617475733D756E707562
7375626A656374733D51:5141:51413239392E36
74797065733D6F74686572
A Theorem about Limits with Application to MacLaurin’s Polynomial of certain Functions
Goldoni, Luca
QA299.6 Analysis
In this article we consider a theorem for the limit of certain functions at x = 0. We shall prove that in some cases, the existence of the first derivative at x = 0 and the existence of a “functional equation” let us able to infer the existence of some derivatives of higher order.
2013-01-02
Other
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/4067/1/04.pdf
Goldoni, Luca (2013) A Theorem about Limits with Application to MacLaurin’s Polynomial of certain Functions. [Other] (Unpublished)
http://eprints.biblio.unitn.it/4067/
oai:eprints.biblio.unitn.it:4096
2013-03-28T15:59:24Z
7374617475733D696E7072657373
7375626A656374733D51:5141:5141343430
7375626A656374733D51:5141:51413239392E36
74797065733D61727469636C656A6F75726E616C
Power and spherical series over real alternative *-algebras
Ghiloni, Riccardo
Perotti, Alessandro
QA299.6 Analysis
QA445 Geometry
We study two types of series over a real alternative $^*$-algebra $A$. The first type are series of the form $\sum_{n} (x-y)^{\punto n}a_n$, where $a_n$ and $y$ belong to $A$ and $(x-y)^{\punto n}$ denotes the $n$--th power of $x-y$ w.r.t.\ the usual product obtained by requiring commutativity of the indeterminate $x$ with the elements of $A$.
In the real and in the complex cases, the sums of power series define, respectively, the real analytic and the holomorphic functions.
In the quaternionic case, a series of this type produces, in the interior of its set of convergence, a function belonging to the recently introduced class of slice regular functions. We show that also in the general setting of an alternative algebra $A$, the sum of a power series is a slice regular function. We consider also a second type of series, the spherical series, where the powers are replaced by a different sequence of slice regular polynomials. It is known that on the quaternions, the set of convergence of these series is an open set, a property not always valid in the case of power series. We characterize the sets of convergence of this type of series for an arbitrary alternative $^*$-algebra $A$. In particular, we prove that these sets are always open in the quadratic cone of $A$. Moreover, we show that every slice regular function has a spherical series expansion at every point.
Indiana University. Department of Mathematics
2013
Article in journal
PeerReviewed
application/pdf
http://eprints.biblio.unitn.it/4096/1/Power_series_revised.pdf
http://www.iumj.indiana.edu/IUMJ/forthcoming.php?indexorder=lastname2
Ghiloni, Riccardo and Perotti, Alessandro (2013) Power and spherical series over real alternative *-algebras. In «Indiana University Mathematics Journal», Bloomington (IN) : Indiana University. Department of Mathematics. (In Press)
http://eprints.biblio.unitn.it/4096/
oai:eprints.biblio.unitn.it:4145
2013-04-08T12:26:14Z
7374617475733D756E707562
7375626A656374733D51:5141:51413239392E36
7375626A656374733D51:5141:5141313031
74797065733D6F74686572
A Test for the Divergence of Certain Series with Positive Terms
Goldoni, Luca
QA101 Arithmetic
QA299.6 Analysis
In this short note we prove a simple divergent test for certain series with positive terms which are related in some way with the Theory of Dirichlet’s series.
2013-04-07
Other
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/4145/1/05.pdf
Goldoni, Luca (2013) A Test for the Divergence of Certain Series with Positive Terms. [Other] (Unpublished)
http://eprints.biblio.unitn.it/4145/
oai:eprints.biblio.unitn.it:4146
2013-04-08T12:27:59Z
7374617475733D756E707562
7375626A656374733D51:5141:51413239392E36
74797065733D6F74686572
On Certain Conditionally Convergent Series
Goldoni , Luca
QA299.6 Analysis
In this paper we investigate the problem of the convergence
of a very special kind of non absolutely convergent series
which can not be solved by means of traditional tests as Dirichlet test.
2013-04-07
Other
NonPeerReviewed
application/pdf
http://eprints.biblio.unitn.it/4146/1/07a.pdf
Goldoni , Luca (2013) On Certain Conditionally Convergent Series. [Other] (Unpublished)
http://eprints.biblio.unitn.it/4146/