12,405 research outputs found
Fractional variational problems with the Riesz-Caputo derivative
No full textIn this paper we investigate optimality conditions for fractional variational problems, with a Lagrangian depending on the Riesz-Caputo derivative. First we prove a generalized Euler-Lagrange equation for the case when the interval of integration of the functional is different from the interval of the fractional derivative. Next we consider integral dynamic constraints on the problem, for several different cases. Finally, we determine optimality conditions for functionals depending not only on the admissible functions, but on time also, and we present a necessary condition for a pair function-time to be an optimal solution to the problem. © 2011 Elsevier Ltd. All rights reserved.FCTCIDM
Fractional variational problems depending on indefinite integrals
No full textWe obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral. Main results give fractional Euler-Lagrange type equations and natural boundary conditions, which provide a generalization of the previous results found in the literature. Isoperimetric problems, problems with holonomic constraints and depending on higher-order Caputo derivatives, as well as fractional Lagrange problems, are considered. © 2011 Elsevier Ltd. All rights reserved
The free air corrections of the normal gravity field: rigor and consequences
No full textTables of the free air anomalies, as non linear function of the elevation and the latitude, computed using the formulae of the normal gravity field in space given by Benavidez and Caputo (1986) are presented together with the errors in the free air anomalies computed using the formulae in which the non linear and the latitude effects are omitted
Reactivity of ethanediyl S,S-acetals; 5. On the aromatization of the ring A in 3-oxosteroid derivatives R. Caputo; C. Ferreri; G. Palumbo; S. Pedatella; F. Russo
No full textEthanediyl S,S-acetal (1,3-dithiolane) derivatives of 3-oxosteroids, when treated with bromine in anhydrous chloroform at room temperature, undergo ring A aromatization following a dienone-benzene like steroidal skeleton rearrangement that leads to 1,4-dithian fused 4-methylestranes. The easy replacement of the sulphur atoms may afford 4-methylestranes with variously substituted A rings
On Caputo Fractional Derivatives and Caputo–Fabrizio Integral Operators via (s, m)-Convex Functions
No full textThis paper contains a variety of new integral inequalities for (s,m)-convex functions using Caputo fractional derivatives and Caputo–Fabrizio integral operators. Various generalizations of Hermite–Hadamard-type inequalities containing Caputo–Fabrizio integral operators are derived for those functions whose derivatives are (s,m)-convex. Inequalities involving the digamma function and special means are deduced as applications
Contradictions, Disagreement and Normative Error
No full textMy aim is to discuss some counterexamples to the following principle:
(P) Necessarily, for every proposition p, for every cognitive agent S and for every cognitive agent S*, if S believes that p and S* believes that ¬p, then either S makes a normative error or S* makes a normative error.
If we assume the identity between S and S*, then (P) regulates what I'm going to call psychological contradiction; conversely, if we assume the non-identity between S and S*, then (P) regulates cases of disagreement. In trying to offer counterexamples, I will compare two different approaches: a three-valued approach and a relativist approach. I will argue that adopting the latter is preferable, since, contrary to the former, in offering counterexamples to (P) it does not commit us to hold the controversial metaphysical views that I will present in section 2. Furthermore, it allows us to propose genuine counterexamples not only in cases of syntactic disagreement, but also in cases of semantic and ontological disagreement
High Order Approximation to Caputo Derivative On Graded Mesh and Time-Fractional Diffusion Equation for Non-smooth Solutions
No full textIn this paper, a high-order approximation to Caputo-type time-fractional diffusion equations involving an initial-time singularity of the solution is proposed. At first, we employ a numerical algorithm based on the Lagrange polynomial interpolation to approximate the Caputo derivative on the non-uniform mesh. Then truncation error rate and the optimal grading constant of the approximation on a graded mesh are obtained as min{4 - a, ra} and 4-a/a , respectively, where α ∈ (0, 1) is the order of fractional derivative and r ≥ 1 is the mesh grading parameter. Using this new approximation, a difference scheme for the Caputo-type time-fractional diffusion equation on the graded temporal mesh is formulated. The scheme proves to be uniquely solvable for general r. Then we derive the unconditional stability of the scheme on uniform mesh. The convergence of the scheme, in particular for r = 1, is analyzed for non-smooth solutions and concluded for smooth solutions. Finally, the accuracy of the scheme is verified by analyzing the error through a few numerical examples.The first author acknowledges the support provided by the Council of Scientific and Industrial Research, India, under grant number
09/086(1483)/2020-EMR-I. The fourth author acknowledges the support provided by the SERB, a statutory body of DST,
India, under the award SERB–POWER fellowship (grant
number SPF/2021/000103)
S. Caputo, Verità
No full textViene recensito Verità, il volume di Stefano Caputo uscito nel 2015 da Laterza
Magnitude versus faults' surface parameters: quantitative relationships from the Aegean
No full textHistorical and seismotectonic data from the broader Aegean Region have been collected and all possible information relative to ground deformation associated to earthquakes that hit the area have been re-evaluated. All events associated to co-seismic surface faulting have been selected and further investigated, while geomorphologic and geological criteria have been used to recognise and characterise the seismogenic faults associated to these ‘morphogenic earthquakes’ (sensu Caputo, 1993). In particular, in order to perform seismic hazard analyses, we compiled a list of all earthquakes where the surface rupture length (SRL), the maximum vertical displacement (MVD) or the average displacement (AD) is available. We thus obtained reliable values of these source parameters for 36 earthquakes, of which 26 occurred during the 20th century, 6 in the 19th century and the three remaining earlier. Magnitude versus SRL and MVD have been compiled for estimating empirical relationships. The calculated regression equations are: Ms = 0.90·log(SRL) + 5.48 and Ms = 0.59·log(MVD) + 6.75, showing good correlation coefficients equal to 0.84 and 0.82, respectively. Co-seismic fault rupture lengths and especially maximum displacements in the Aegean Region have systematically lower values than the same parameters world-wide, but are similar to those of the Eastern Mediterranean-Middle East region. The envelopes of our diagrams are also calculated and discussed for estimating the worst-case scenario. Furthermore, for all investigated seismogenic structures, based on several geological criteria, we measured the 'geological' fault length (GFL), that is the total length of the neotectonic faults showing cumulative recent activity. We then compared SRL with GFL and their ratio shows a clear bimodal distribution with a major peak at 0.8-1.0, indicating that about 50% of the investigated earthquakes ruptured almost the entire fault length, while a second peak around the value of 0.5, is clearly related to a segmentation process of longer neotectonic structures. Further implications of this distribution are also discussed. Eventually, from the distribution of GFL versus magnitude we also infer an important geological threshold for the occurrence of ‘morphogenic earthquakes’ at about 5.5 degrees
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