2,337 research outputs found
On the asymptotic stabilization of the hyperelastic-rod wave equation
No full textWe discuss the problem of asymptotic stabilization of the hyper\-elastic-rod wave equation on the real line
\partial_t u-\partial_{txx}^3 u+3u \partial_x u=\gamma\left(2\partial_x u\, \partial_{xx}^2 u+u\, \partial_{xxx}^3 u\right),\quad t > 0,\>\>x\in \mathbb{R}.
We consider the equation with an additional force term of the form f:H^1(\mathbb{R})\to H^{-1}(\mathbb{R}),\, f[u]=-\lambda(u-\partial_{xx}^2 u),
for some \lambda>0. We resume the results of [F. Ancona and G. M. Coclite, 2015] on the existence of a semigroup of global weak dissipative solutions of the corresponding closed-loop system defined for every initial data u_0\in H^1(\mathbb{R}). Any such solution decays esponentially to 0 as t\to\infty
Decomposition of homogeneous vector fields of degree one and representation of the flow
No full textSummary:
The paper gives a decomposition theorem for the elements of the nonsemisimple Lie algebra of the vector fields on that are homogeneous of degree one with respect to a dilation Each is proved to be equal to with and linear semisimple. As a consequence, the author proves that "in absence of esonance" the vector field is equivalent to its linear part. Finally, the above results are applied to obtain a representation formula for the trajectories of a vector field and those of the affine control system with constant of minimum degree
Jonghi Lavarini G.M.: Atti del convegno Fiera di Genova, RIABITAT"98 - L'adeguamento delle Chiese, prospettive progetti.CHIESA OGGI, vol. 30/1998, ISS: 1125-1360 - G.Domenici, R. Gagliardi: Le chiese Monumentali dell'Arcidiocesi di Ancona-Osimo - Studi e disegni - Ed. Aniballi - Ancona 1996.
No full textLa Fiera di Genova ha avuto l'opportunità e il piacere di ospitare, nel corso dell'edizione di "RIABITAT" del 1997, una prima iniziativa, presentata sotto il titolo "Centomila cantieri per centomila Chiese" in previsione dell'imminente Giubileo 2000 e delle opere di manutenzione e adeguamento edilizio di cui il prezioso patrimonio degli edifici del culto avrebbe avuto necessità in vista dell'evento. Per l'occasione sono stati riportati numerosi interventi di specialisti del settore ed esposti i disegni ripresi dalla pubblicazione "Chiese monumentali dell'Arcidiocesi di Ancona-Osimo, Studi e disegni" redatti da G. Domenici e R. Gagliardi dell'Università di Ancona
Asymptotic stabilization of systems of conservation laws by controls acting at a single boundary point
No full textWe consider a strictly hyperbolic system of conservation laws in one space dimension on the bounded interval . Assuming that the boundaries at and are non characteristic, we establish a general result on the asymptotic stabilization near an equilibrium state by means of controls acting only at
On Kolmogorov entropy compactness estimates for scalar conservation laws without uniform convexity
No full textIn the case of scalar conservation laws u_t +f(u)_x = 0; t > 0; x in R, with uniformly strictly convex flux, quantitative compactness estimates-in terms of Kolmogorov entropy in L^1_{loc}- were established in [C. De Lellis and F. Golse, Comm. Pure Appl. Math., 58 (2005), pp. 989{998; F. Ancona, O. Glass, and K. T. Nguyen, Comm. Pure Appl. Math., 65 (2012), pp. 1303{1329] for sets of entropy weak solutions evaluated at a fixed time t > 0, whose initial data have a uniformly bounded support and vary in a bounded subset of L1. These estimates reflct the irreversibility features of entropy weak discontinuous solutions of these nonlinear equations. We provide here an extension of such estimates to the case of scalar conservation laws with a smooth flux function f that either is strictly (but not necessarily uniformly) convex or has a single inflection point with a polynomial degeneracy
Ancona "città greca" nel II sec. a.C.
No full textThe great quantity of oriental luxury items from the Hellenistic necropolis at Ancona (3rd -1st century BC) attest the existence of a wealthy local mercantile community as well as the presence of few individuals of Greek origin, as attested by the source used by Strabo, who defines Ancona as a Greek polis. Greek-oriental stylistic and iconographic motifs are in the funerary stele, which date between the second half of the 2nd century BC and the Augustan period, if not later; the onomastics and the language testify to the presence of Greek speaking individuals, probably tied to the trade activites carried out in Ancona. Among the documents considered there is an honorary degree from Delphi, which mentions the proxeny granted to Nikostratos, son of Sotikos, from Ankon, in 167 BC.
The onomastics, the honors, typically Greek, and the historical context highlight the interest developped by Delphi after the third Macedonian war towards the Greek cities of Italy, especially Ancona, which became the base of the Roman fleet in the Adriatic.
Antolini S.: pp. 524-530
On the asymptotic stabilization of a generalized hyperelastic-rod wave equation
No full textWe discuss the problem of asymptotic stabilization of the hyper-elastic-rod wave equation on the real line
egin{equation*}
partial_t u-partial_{txx}^3 u+3u partial_x u=
gammaleft(2partial_x u, partial_{xx}^2 u+u, partial_{xxx}^3 u
ight),quad t > 0,>>xin mathbb{R}.
end{equation*}
We consider the equation with
an additional forcing term of the form
%
for some lambda>0. We resume the results of cite{AC} on the existence of a semigroup of global weak dissipative solutions of
the corresponding closed-loop system
defined for every initial data . Any such solution
decays exponentially to 0 as
Homogeneous Tangent Vectors and High Order Necessary Conditions for Optimal Controls
No full textSummary:
The author introduces and analyzes "homogeneous" tangent vectors which provide high-order approximations to the attainable set for an affine control system of the form . Homogeneous tangent vectors are defined relative to one-parameter families of dilations on . Adjoint equations associated with the corresponding homogeneous variational equation are derived and used to transport homogeneous tangent vectors along the flow of a reference trajectory. These constructions are then used to derive a homogeneous high-order test for optimality of control problems in Mayer form without terminal constraints. Essentially, it is shown that if is a homogeneous tangent vector with respect to a dilation generated by a control variation, then it is a necessary condition for optimality that , where denotes the solution of the corresponding homogeneous adjoint equation
Le regole processuali dell'accertamento probatorio. Il dibattito contemporaneo al vaglio di un testo tommasiano
No full textThis essay deals with some procedural issues related
to the forensic pursuance of truth, especially
the latest law trends about the judge’s powers of
investigation and the prohibition of judge’s personal knowledge. In the second part the author
shows how the same problems are considered and
solved in an article of Aquinas’ Summa Theologiae
A Big Step from Finite to Infinite Computations (SCICO Journal-first)
No full textThe known is finite, the unknown infinite - Thomas Henry Huxley
The behaviour of programs can be described by the final results of computations, and/or their interactions with the context, also seen as observations. For instance, a function call can terminate and return a value, as well as have output effects during its execution.
Here, we deal with semantic definitions covering both results and observations. Often, such definitions are provided for finite computations only. Notably, in big-step style, infinite computations are simply not modelled, hence diverging and stuck terms are not distinguished. This becomes even more unsatisfactory if we have observations, since a non-terminating program may have significant infinite behaviour.
Recently, examples of big-step semantics modeling divergence have been provided [Davide Ancona et al., 2017; Davide Ancona et al., 2018] by means of generalized inference systems [Davide Ancona et al., 2017; Francesco Dagnino, 2019], which allow corules to control coinduction. Indeed, modeling infinite behaviour by a purely coinductive interpretation of big-step rules would lead to spurious results [Xavier Leroy and Hervé Grall, 2009] and undetermined observation, whereas, by adding appropriate corules, we can correctly get divergence (∞) as the only result, and a uniquely determined observation. This approach has been adopted in [Davide Ancona et al., 2017; Davide Ancona et al., 2018] to design big-step definitions including infinite behaviour for lambda-calculus and a simple imperative Java-like language. However, in such works the designer of the semantics is in charge of finding the appropriate corules, and this is a non-trivial task.
In this paper, we show a general construction that extends a given big-step semantics, modeling finite computations, to include infinite behaviour as well, notably by generating appropriate corules. The construction consists of two steps:
1) Starting from a monoid O modeling finite observations (e.g., finite traces), we construct an ω-monoid ⟨O, O_∞⟩ also modeling infinite observations (e.g., infinite traces). The latter structure is a variation of the notion of ω-semigroup [Dominique Perrin and Jean-Eric Pin, 2004], including a mixed product composing a finite with a possibly infinite observation, and an infinite product mapping an infinite sequence of finite observations into a single one (possibly infinite).
2) Starting from an inference system defining a big-step judgment c⇒⟨r, o⟩, with c denoting a configuration, r ∈ R a result, and o ∈ O a finite observation, we construct an inference system with corules defining an extended big-step judgment c⇒c ⇒ ⟨r_∞, o_∞⟩ with r_∞ ∈ R_∞ = R+{∞}, and o_∞ ∈ O_∞ a "possibly infinite" observation. The construction generates additional rules for propagating divergence, and corules for introducing divergence in a controlled way.
The exact corules added in the construction depend on the type of observations that one starts with. To show the effectiveness of our approach, we provide several instances of the framework, with different kinds of (finite) observations.
Finally, we prove a correctness result for the construction. To this end, we assume the original big-step semantics to be equivalent to (finite sequences of steps in) a reference small-step semantics, and we show that, by applying the construction, we obtain an extended big-step semantics which is still equivalent to the small-step semantics, where we consider possibly infinite sequences of steps.} As hypotheses, rather than {just} equivalence in the finite case {(which would be not enough)}, we assume a set of equivalence conditions between individual big-step rules and the small-step relation. This proof of equivalence holds for deterministic semantics; issues arising in the non-deterministic case and a possible solution are sketched in the conclusion of the full paper
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