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71.
72.
Ewa M. Bednarczuk Enrico Miglierina Elena Molho 《Set-Valued and Variational Analysis》2011,19(4):569-587
The mountain pass theorem for scalar functionals is a fundamental result of the minimax methods in variational analysis. In this work we extend this theorem to the class of \(\mathcal{C}^{1}\) functions \(f:\mathbb{R}^{n}\rightarrow\mathbb{R}^{m}\), where the image space is ordered by the nonnegative orthant \(\mathbb{R}_{+}^{m}\). Under suitable geometrical assumptions, we prove the existence of a critical point of f and we localize this point as a solution of a minimax problem. We remark that the considered minimax problem consists of an inner vector maximization problem and of an outer set-valued minimization problem. To deal with the outer set-valued problem we use an ordering relation among subsets of \(\mathbb{R}^{m}\) introduced by Kuroiwa. In order to prove our result, we develop an Ekeland-type principle for set-valued maps and we extensively use the notion of vector pseudogradient. 相似文献
73.
We present an optical setup for generating a sequence of light pulses in which the orbital angular momentum (OAM) degree of freedom is correlated with the temporal one. The setup is based on a single q plate within a ring optical resonator. By this approach, we demonstrate the generation of a train of pulses carrying increasing values of OAM, or, alternatively, of a controlled temporal sequence of pulses having prescribed OAM superposition states. Finally, we exhibit an "OAM-to-time conversion" apparatus that divides different input OAM states into different time bins. The latter application provides a simple approach to digital spiral spectroscopy of pulsed light. 相似文献
74.
For a sequence $\underline{u}=(u_n)_{n\in \mathbb{N }}$ of integers, let $t_{\underline{u}}(\mathbb{T })$ be the group of all topologically $\underline{u}$ -torsion elements of the circle group $\mathbb{T }:=\mathbb{R }/\mathbb{Z }$ . We show that for any $s\in ]0,1[$ and $m\in \{0,+\infty \}$ there exists $\underline{u}$ such that $t_{\underline{u}}(\mathbb{T })$ has Hausdorff dimension $s$ and $s$ -dimensional Hausdorff measure equal to $m$ (no other values for $m$ are possible). More generally, for dimension functions $f,g$ with $f(t)\prec g(t), f(t)\prec \!\!\!\prec t$ and $g(t)\prec \!\!\!\prec t$ we find $\underline{u}$ such that $t_{\underline{u}}(\mathbb{T })$ has at the same time infinite $f$ -measure and null $g$ -measure. 相似文献
75.
Enrico Jabara 《Rendiconti del Circolo Matematico di Palermo》1995,44(1):107-112
An automorphism σ of order (a divisor of)n of the groupG is calledn-splitting if
for everyg∈G.
In this paper we prove that a 2-group admitting a 4-splitting automorphism, is locally finite. 相似文献
76.
Elena Bosetto Enrico Serra 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2000,17(6):673
We prove that a class of problems containing the classical periodically forced pendulum equation displays the main features of chaotic dynamics. The approach is based on the construction of multibump type heteroclinic solutions to periodic orbits by the use of global variational methods. 相似文献
77.
Tiziana Parasassi Ewa K. Krasnowska Luis Bagatolli Enrico Gratton 《Journal of fluorescence》1998,8(4):365-373
The steady-state and dynamic fluorescence spectral properties of 2-dimethylamino-6-lauroylnaphthalene (LAURDAN) and several other naphthalene derivatives are summarized to illustrate their sensitivity to the polarity of the environment. Results obtained both in solvents of different polarity and in phospholipid vesicles in two phase states are presented. The emission red shift observed in polar solvents and in the phospholipid liquid–crystalline phase is explained on the basis of dipolar relaxation of solvent molecules surrounding the fluorescent naphthalene moiety of these probes. In phospholipid environments, experimental evidence is shown that excludes the intramolecular relative reorientation of the dimethylamino and carbonyl groups in the naphthalene and the reorientation of the entire fluorescent moiety. The solvent dipolar relaxation observed for LAURDAN and PRODAN in phospholipid bilayers has been attributed to a small number of water molecules present at the membrane interface. A comparison between LAURDAN emission in phospholipid vesicles prepared in D2O and in H2O is also presented. The definition and the derivation of the generalized polarization function are also discussed. 相似文献
78.
79.
80.
Giuseppe Di Maio Enrico Meccariello Somashekhar A. Naimpally 《Mediterranean Journal of Mathematics》2006,3(2):189-204
In this paper we use Bartle’s technique to study duality between a topological space and a function space. Normally such a
duality forms an essential part of Functional Analysis. We introduce several new topologies such as the topology of even convergence Te, the closed-cocompact topology Tk ′, the (strong) local proximal convergence.
We explore the topological groups of self-homeomorphisms of a topological space and shed light on the earlier work of Arens,
Dieudonné, Di Concilio. We also study the concepts such as evenly equidistant, functionally equicontinuous, due to Bouziad-Troallic
and topologically equicontinuous due to Royden.
In memory of Professor Enrico Meccariello who made a considerable contribution to this work and who suddenly passed away before
his time 相似文献