Search results for "Continuum"
showing 10 items of 477 documents
Diffractive optics for spectral tuning of second harmonic and supercontinuum generated in nonlinear crystals
2011
It is shown that diffractive lenses can tune the spectrum of femtosecond pulses after nonlinear optical processes. We focus on spectra of second-order pulses generated in birefringent crystals and supercontinuum in sapphire crystals. The tunability is achieved by changing the relative distance between the nonlinear crystal and the diffractive lens.
Orthotropic plate dynamics by a novel meshfree method
2003
Publisher Summary This chapter deals with a novel meshfree method for the dynamic analysis of orthotropic plates under the Kirchhoff small deflection theory. The approach starts from a modified function whose stationarity conditions lead to the meshfree plate dynamic model through a discretization process—based on the use of orthotropic plate static fundamental solutions. The resolving system obtained is characterized by—frequency independent stiffness and mass matrices, which preserve the symmetry and definiteness properties of the continuum. Moreover, these operators are computed by boundary integrals of regular kernels. The method allows the application of standard numerical routines ava…
Toward an Understanding of the Molecular Mechanism of the Reaction between 1-Methylpyrrole and Dimethyl Acetylenedicarboxylate. An ab Initio Study
1998
The molecular mechanism for the reaction between 1-methylpyrrole and dimethyl acetylenedicarboxylate (DMAD) has been studied using ab initio methods. Two alternative reaction pathways have been considered, both of which correspond to stepwise processes with initial, rate-determining formation of a common zwitterionic intermediate. This intermediate is formed by nucleophilic attack of the pyrrole ring to the carbon−carbon triple bond of DMAD. Closure of this intermediate (pathway A) affords a [4 + 2] cycloadduct, whereas intramolecular proton transfer (pathway B) affords a Michael adduct. The much larger potential energy barrier of the second step in pathway B relative to pathway A is respon…
Branches of index-preserving solutions to systems of second order ODEs
2009
We investigate the existence of a continuum of index-preserving solutions to a Dirichlet problem associated with a parameter-dependent system of second order ordinary differential equations, developing a detailed analysis on the behaviour of the branches of nontrivial solutions. Our approach is based on the Rabinowitz global bifurcation Theorem combined with the notion of index and nullity of suitable linear boundary value problems. An application of the result to the study of branches of odd, periodic solutions for suitable systems of two linearly coupled pendulums of lenghts variables is also analyzed.
On the cardinality of almost discretely Lindelof spaces
2016
A space is said to be almost discretely Lindelof if every discrete subset can be covered by a Lindelof subspace. Juhasz et al. (Weakly linearly Lindelof monotonically normal spaces are Lindelof, preprint, arXiv:1610.04506 ) asked whether every almost discretely Lindelof first-countable Hausdorff space has cardinality at most continuum. We prove that this is the case under $$2^{<{\mathfrak {c}}}={\mathfrak {c}}$$ (which is a consequence of Martin’s Axiom, for example) and for Urysohn spaces in ZFC, thus improving a result by Juhasz et al. (First-countable and almost discretely Lindelof $$T_3$$ spaces have cardinality at most continuum, preprint, arXiv:1612.06651 ). We conclude with a few rel…
The terminal hyperspace of homogeneous continua
2010
Abstract We investigate the structure of the collection of terminal subcontinua in homogeneous continua. The main result is a reduction of this structure to six specific types. Three of these types are of one-dimensional spaces, and examples representing these types are known. It is not known whether higher dimensional examples having non-trivial terminal subcontinua and representing the three remaining types exist.
On the equivalence of McShane and Pettis integrability in non-separable Banach spaces
2009
Abstract We show that McShane and Pettis integrability coincide for functions f : [ 0 , 1 ] → L 1 ( μ ) , where μ is any finite measure. On the other hand, assuming the Continuum Hypothesis, we prove that there exist a weakly Lindelof determined Banach space X, a scalarly null (hence Pettis integrable) function h : [ 0 , 1 ] → X and an absolutely summing operator u from X to another Banach space Y such that the composition u ○ h : [ 0 , 1 ] → Y is not Bochner integrable; in particular, h is not McShane integrable.
Countably compact weakly Whyburn spaces
2015
The weak Whyburn property is a generalization of the classical sequential property that was studied by many authors. A space X is weakly Whyburn if for every non-closed set \({A \subset X}\) there is a subset \({B \subset A}\) such that \({\overline{B} \setminus A}\) is a singleton. We prove that every countably compact Urysohn space of cardinality smaller than the continuum is weakly Whyburn and show that, consistently, the Urysohn assumption is essential. We also give conditions for a (countably compact) weakly Whyburn space to be pseudoradial and construct a countably compact weakly Whyburn non-pseudoradial regular space, which solves a question asked by Angelo Bella in private communica…
Enhanced supercontinuum generation in tapered tellurite suspended core fiber
2015
Abstract We demonstrate 400-THz (0.6–3.3 µm) bandwidth infrared supercontinuum generation in a 10 cm-long tapered tellurite suspended core fiber pumped by nJ-level 200-fs pulses from an optical parametric oscillator. The increased nonlinearity and dispersion engineering extended by the moderate reduction of the fiber core size are exploited for supercontinuum optimization on both frequency edges (i.e., 155-THz overall gain), while keeping efficient power coupling into the untapered fiber input. The remaining limitation of supercontinuum bandwidth is related to the presence of the high absorption beyond 3 µm whereas spectral broadening is expected to fully cover the glass transmission window…
Theoretical study on the molecular mechanism of the [5 + 2] vs. [4 + 2] cyclization mediated by Lewis acid in the quinone system
2013
[EN] The thermal and Lewis acid (LA) catalyzed cyclizations of quinone 1 involved in the synthesis of Colombiasin A and Elipsaterosin B have been theoretically studied using DFT methods at the B3LYP/6-311G(d,p) computational level. B3LYP calculations suggest that the formal endo [4 + 2] cycloadduct allowing the synthesis of Colombiasin A is preferentially formed under thermal conditions, while in the presence of the BF3 LA catalyst the formal [5 + 2] cycloadduct is seen, allowing the synthesis of Elipsaterosin B. The BF3 LA catalyst not only accelerates the nucleophilic attack on the C2 carbon of the quinone framework through a more polar C-C bond formation, but also provokes a different el…