Linear restrictions and two step least squares with applications

In this paper we consider the full rank regression model with arbitrary covariance matrix: Y = Xß + ε. It is shown that the effect of restricting the information Y to T = A′Y may be analyzed through an associatedi regression problem which is amenable to solution by two step least squares. The results are applied to the important case of missing observations, where some classical results are rederived.     

Examining the balance between efficiency and resilience in closed-loop supply chains

Central European Journal of Operations Research - We study a hybrid system where the demand of customers can be satisfied by both manufacturing new products and remanufacturing used products. To...     

Nonlinear Schrödinger equations: concentration on weighted geodesics in the semi-classical limit

We consider the problem

${?}^2\mathrm{\Delta }u?V(x)u+u^p=0,u>0,u\in H^1({\mathbb{R}}^2),$

where $p>1$, $?>0$ is a small parameter and V is a uniformly positive, smooth potential. Let Γ be a closed curve, nondegenerate geodesic relative to the weighted arclength ${\int }_{\Gamma }{V}^{\sigma }$, where $\sigma =\frac{p+1}{p?1}?\frac{1}{2}$. We prove the existence of a solution $u_{\mathrm{\epsilon }}$ concentrating along the whole of Γ, exponentially small in ? at any positive distance from it, provided that ? is small and away from certain critical numbers. This proves a conjecture raised in [A. Ambrosetti, A. Malchiodi, W.-M. Ni, Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I, Commun. Math. Phys. 235 (2003) 427–466] in the two-dimensional case. To cite this article: M. del Pino et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Testing goodness of fit for the distribution of errors in multivariate linear models

In this paper, to test goodness of fit to any fixed distribution of errors in multivariate linear models, we consider a weighted integral of the squared modulus of the difference between the empirical characteristic function of the residuals and the characteristic function under the null hypothesis. We study the limiting behaviour of this test statistic under the null hypothesis and under alternatives. In the asymptotics, the rank of the design matrix is allowed to grow with the sample size.     

The Brezis-Nirenberg problem near criticality in dimension 3

We consider the problem of finding positive solutions of Δu+λu+u^q=0 in a bounded, smooth domain Ω in , under zero Dirichlet boundary conditions. Here q is a number close to the critical exponent 5 and 0<λ<λ₁. We analyze the role of Green's function of Δ+λ in the presence of solutions exhibiting single and multiple bubbling behavior at one point of the domain when either q or λ are regarded as parameters. As a special case of our results, we find that if , where λ∗ is the Brezis-Nirenberg number, i.e., the smallest value of λ for which least energy solutions for q=5 exist, then this problem is solvable if q>5 and q−5 is sufficiently small.     

Ancient shrinking spherical interfaces in the Allen–Cahn flow

We consider the parabolic Allen–Cahn equation in ${\mathbb{R}}^n$, $n\ge 2$,

$u_t=\mathrm{\Delta }u+(1?u^2)u\text{ in }{\mathbb{R}}^n\times (?\infty ,0].$

We construct an ancient radially symmetric solution $u(x,t)$ with any given number k of transition layers between ?1 and +1. At main order they consist of k time-traveling copies of w with spherical interfaces distant $O(\log ?|t|)$ one to each other as $t\to ?\infty$. These interfaces are resemble at main order copies of the shrinking sphere ancient solution to mean the flow by mean curvature of surfaces: $|x|=\sqrt{?2(n?1)t}$. More precisely, if $w(s)$ denotes the heteroclinic 1-dimensional solution of $w^{″}+(1?w^2)w=0$$w(\pm \infty )=\pm 1$ given by $w(s)=\tanh ?\left(\frac{s}{\sqrt{2}}\right)$ we have

$u(x,t)\approx \sum _{j=1}^k{(?1)}^{j?1}w(|x|?{\rho }_j(t))?\frac{1}{2}(1+{(?1)}^k)\text{ as }t\to ?\infty$

where

${\rho }_j(t)=\sqrt{?2(n?1)t}+\frac{1}{\sqrt{2}}(j?\frac{k+1}{2})\log ?\left(\frac{|t|}{\log ?|t|}\right)+O(1),j=1,\dots ,k.$

     

Coumarin 314 free radical cation: formation, properties, and reactivity toward phenolic antioxidants

We have explored the photogeneration of the coumarin 314 radical cation by using nanosecond laser excitation at wavelengths longer than 400 nm in benzene, acetonitrile, dichloromethane, and aqueous media. In addition, time-resolved absorption spectroscopy measurements allowed detection of the triplet excited state of coumarin 314 (C(314)) with a maximum absorption at 550 nm in benzene. The triplet excited state has a lifetime of 90 μs in benzene. It is readily quenched by oxygen (k(q) = 5.0 × 10(9) M(-1) s(-1)). From triplet-triplet energy transfer quenching experiments, it is shown that the energy of this triplet excited state is higher than 35 kcal/mol, in accord with the relatively large singlet oxygen quantum yield (Φ(Δ) = 0.25). However, in aqueous media, the coumarin triplet was no longer observed, and instead of that, a long-lived (160 μs in air-equilibrated solutions) free radical cation with a maximum absorbance at 370 nm was detected. The free radical cation generation, which has a quantum yield of 0.2, occurs by electron photoejection. Moreover, density functional theory (DFT) calculations indicate that at least 40% of the electronic density is placed on the nitrogen atom in aqueous media, which explains its lack of reactivity toward oxygen. On the other hand, rate constant values close to the diffusion rate limit in water (>10(9) M(-1) s(-1)) were found for the quenching of the C(314) free radical cation by phenolic antioxidants. The results have been interpreted by an electron-transfer reaction between the phenolic antioxidant and the radical cation where ion pair formation could be involved.     

Oxygen Inhibition and Coating Thickness Effects on Uv Radiation Curing of Weatherfast Clearcoats Studied by Photo-DSC

Radiation curing is an environmentally-friendly technology. Furthermore, radiation curing is a faster, energy saving and more efficient industrial process than the heat-curable process. One of the most important requirements for the widespread application of UV curable coatings in the coating industry is that they are stable vs. atmospheric degradation. Today's state of the art in oxidative drying and thermosetting coatings is the use of light stabilizers to protect polymers vs. the damage of outdoor exposure. Oxygen has a detrimental effect on the cure response of free radical systems, especially in thin-film coatings. Differential photocalorimetry (photo-DSC) was used to investigate the oxygen effect and the use of light stabilizers on UV curing of photocurable formulations based on acrylate materials. Coating thickness influence was also considered. This revised version was published online in August 2006 with corrections to the Cover Date.     

Determining the stoichiometry and binding constants of inclusion complexes formed between aromatic compounds and β-cyclodextrin by solid-phase microextraction coupled to high-performance liquid chromatography

The complexation of native β-cyclodextrin (CD) and seven aromatic compounds, namely, phenetole, toluene, m-xylene, naphthalene, biphenyl, fluorene and phenanthrene, has been studied for first time utilizing a solid-phase microextraction (SPME)–high-performance liquid chromatography (HPLC) method. The stoichiometries of the analyte:β-CD complexes were found to be either 1:1 or 1:2. The formation of 1:2 complexes was confirmed for naphthalene, biphenyl, fluorene, and phenanthrene only when utilizing relatively high concentrations of β-CD (up to 6.6 mM). The 1:2 stoichiometries were confirmed using the classical modified Benesi–Hildebrand (BH) method. The calculated binding constants for 1:1 stoichiometries (K₁) using the SPME method varied from 115.3 M⁻¹ for toluene to 3510 M⁻¹ for phenanthrene, whereas the corresponding values to the 1:2 stoichiometries (K₃) varied from 7.30 × 10⁵ M⁻² for biphenyl to 9.03 × 10⁶ M⁻² for naphthalene.     

Assignment of acetyl groups to O-2 and/or O-3 of pectic oligogalacturonides using negative electrospray ionization ion trap mass spectrometry

Partially acetylated and methylated oligogalacturonides produced by enzymatic hydrolysis of sugar beet pectin were analysed by negative electrospray ionization ion trap mass spectrometry (ESI-ITMS). The (18)O labelling of the oligomer reducing end allowed the precise assignment of the fragments resulting from glycosidic bond and cross-ring cleavages. The collisional-induced dissociation of the C(i) and Z(j) fragment ions through sequential MS(n) experiments always displayed (0, 2)A-type cross-ring cleavage ions which were related to C(2)H(4)O(2) losses. These (0, 2)A ions appeared to be highly diagnostic ions allowing the precise location of the acetyl groups to the O-2 and/or O-3 of the acetylated galacturonic acid residues.