A DC programming approach for solving the symmetric Eigenvalue Complementarity Problem

In this paper, we investigate a DC (Difference of Convex functions) programming technique for solving large scale Eigenvalue Complementarity Problems (EiCP) with real symmetric matrices. Three equivalent formulations of EiCP are considered. We first reformulate them as DC programs and then use DCA (DC Algorithm) for their solution. Computational results show the robustness, efficiency, and high speed of the proposed algorithms.     

Uncertainty propagation in stochastic fractional order processes using spectral methods: A hybrid approach

Stochastic spectral methods are widely used in uncertainty propagation thanks to its ability to obtain highly accurate solution with less computational demand. A novel hybrid spectral method is proposed here that combines generalized polynomial chaos (gPC) and operational matrix approaches. The hybrid method takes advantage of gPC’s efficient handling of large parameter uncertainties and overcomes its limited applicability to systems with relatively highly correlated inputs. The hybrid method’s use of operational matrices allows analyses of systems with low input correlations without suffering its restriction to small parameter uncertainties. The hybrid method is aimed to propagate uncertainties in fractional order systems with random parameters and random inputs with low correlation lengths. It is validated through several examples with different stochastic uncertainties. Comparison with Monte Carlo and gPC demonstrates the superior computational efficiency of the proposed method.     

Exact solutions of a two-fluid model of two-phase compressible flows with gravity

We aim at determining and computing a class of exact solutions of a two-fluid model of two-phase flows with/without gravity. The model is described by a non-hyperbolic system of balance laws whose characteristic fields may not be given explicitly, making it perhaps impossible to solve the Riemann problem. First, we investigate Riemann invariants in the linearly degenerate characteristic fields and obtain a surprising result on the corresponding contact waves of the model without gravity. Second, even when gravity is allowed, we show that smooth stationary solutions can be governed by a system of differential equations in divergence form, which determines jump relations for any stationary discontinuity wave. Using these relations, we establish a nonlinear equation for the pressure and propose a method to compute the pressure and then the equilibria resulted by a stationary wave.     

Novel flavanes from Livistona halongensis

A study of the chemical constituents of a methanolic extract of the roots of Livistona halongensis (Arecaceae) led to the isolation of two new flavanes, 2S,3S-3,5,7,3'-tetrahydroxy-5'-methoxyflavane (1) and 3,7,3'-trihydroxy-5'-methoxyflavane 5-O-beta-glucopyranoside (2), together with trans-3,5,3',5'-tetrahydroxy-4-methoxystilbene, saccharose and beta-sitosterol-3-O-beta-glucopyranoside. The structures of these compounds were elucidated on the basis of spectroscopic data.     

Time to Face the Fats: What Can Mass Spectrometry Reveal about the Structure of Lipids and Their Interactions with Proteins?

Since the 1950s, X-ray crystallography has been the mainstay of structural biology, providing detailed atomic-level structures that continue to revolutionize our understanding of protein function. From recent advances in this discipline, a picture has emerged of intimate and specific interactions between lipids and proteins that has driven renewed interest in the structure of lipids themselves and raised intriguing questions as to the specificity and stoichiometry in lipid-protein complexes. Herein we demonstrate some of the limitations of crystallography in resolving critical structural features of ligated lipids and thus determining how these motifs impact protein binding. As a consequence, mass spectrometry must play an important and complementary role in unraveling the complexities of lipid-protein interactions. We evaluate recent advances and highlight ongoing challenges towards the twin goals of (1) complete structure elucidation of low, abundant, and structurally diverse lipids by mass spectrometry alone, and (2) assignment of stoichiometry and specificity of lipid interactions within protein complexes.     

Magnetic-state tuning of the rhombohedral graphite film by interlayer spacing and thickness

Based on first-principles total-energy calculations, we systematically investigate how the electronic and magnetic properties of rhombohedral graphite thin films depend on the interlayer spacing and number of layers. Our calculations show that the magnetic ordering of the thin films depends on the interlayer spacing. Thin films under compression normal to the layers possess finite magnetic moments, indicating parallel spin coupling between the two surfaces. We also find that thin graphite films with seven or more atomic layers exhibit magnetic ordering while films with six or less atomic layers are metallic with no magnetic ordering.     

Time discretization and quantization methods for optimal multiple switching problem

In this paper, we study probabilistic numerical methods based on optimal quantization algorithms for computing the solution to optimal multiple switching problems with regime-dependent state process. We first consider a discrete-time approximation of the optimal switching problem, and analyse its rate of convergence. Given a time step h$h$, the error is in general of order (hlog(1/h))^1/2${(hlog(1/h))}^{1/2}$, and of order h^1/2$h^{1/2}$ when the switching costs do not depend on the state process. We next propose quantization numerical schemes for the space discretization of the discrete-time Euler state process. A Markovian quantization approach relying on the optimal quantization of the normal distribution arising in the Euler scheme is analysed. In the particular case of uncontrolled state process, we describe an alternative marginal quantization method, which extends the recursive algorithm for optimal stopping problems as in Bally (2003) [1]. A priori L^p$L^p$-error estimates are stated in terms of quantization errors. Finally, some numerical tests are performed for an optimal switching problem with two regimes.     

Emission characteristics of SPAN-80 activated ZnS nanocolloids

Quantum surface effects (new emission bands, blueshifts, intensity enhancement) were observed in SPAN-80 activated ZnS nanocolloids and explained in terms of time-dependent density functional theory. The experimental evidences were demonstrated for both undoped and Cu, Mn-doped colloidal phases. The photoluminescence spectra of these materials showed a new green band at 520 nm (ZnS:Cu) and a yellow-orange band at 576 nm (ZnS:Mn) besides a blue band at 465 nm. All bands lie in the visible region and are blueshifted, show sharp emissions with narrow widths and have approximately 20-times stronger intensities in comparison with those of the bulk samples. The time-resolved luminescence spectra showed that the life-times of free electrons were 0.12 μs and 1.9 ms in ZnS:Cu and ZnS:Mn correspondingly.