On Necessary Optimality Conditions with Higher-Order Complementarity Slackness for Set-Valued Optimization Problems

Set-Valued and Variational Analysis - We aim to establish Karush-Kuhn-Tucker multiplier rules involving higher-order complementarity slackness under Hölder metric subregularity. These rules...     

Two Optimal Value Functions in Parametric Conic Linear Programming

Journal of Optimization Theory and Applications - We consider the conic linear program given by a closed convex cone in an Euclidean space and a matrix, where vector on the right-hand side of the...     

Analysing dynamic deep stall recovery using a nonlinear frequency approach

Nonlinear Dynamics - Based on bifurcation theory, nonlinear frequency response analysis is a recent development in the field of flight dynamics studies. Here, we consider how this method can be...     

Data assimilation and pollution forecasting in Burgers' equation with model error function

This article presents a correction method for a better resolution of the problem of estimating and predicting pollution, governed by Burgers' equations. The originality of the method consists in the introduction of an error function into the system's equations of state to model uncertainty in the model. The initial conditions and diffusion coefficients, present in the equations for pollution and concentration, and also those in the model error equations, are estimated by solving a data assimilation problem. The efficiency of the correction method is compared with that produced by the traditional method without introduction of an error function.Three test cases are presented in this study in order to compare the performances of the proposed methods. In the first two tests, the reference is the analytical solution and the last test is formulated as part of the “twin experiment”.The numerical results obtained confirm the important role of the model error equation for improving the prediction capability of the system, in terms of both accuracy and speed of convergence.     

Conformational Changes and Redox Properties of Bimetallic Single Helicates of Hexapyrrole-α,ω-dicarbaldehydes

The hexapyrrole-α,ω-dicarbaldehydes 1 a and 1 b were metallated with Cu^II, Ni^II, and Pd^II to give bimetallic complexes where a pair of 3 N+O four-coordinate metal planes are helically distorted and the central 2,2′-bipyrrole subunit adopts a cis or trans conformation. X-ray crystallographic analysis of the bisCu complex revealed a closed form with a cis-2,2′-bipyrrole subunit and an open form with a trans-2,2′-bipyrrole subunit. The bisPd complexes took a closed form both in the solid state and in solution. They are regarded as single helicates of two turns and the energy barrier for the interchange between an M helix and a P helix was remarkably influenced by the bulky 3,3′-substituent of the central 2,2′-bipyrrole subunit. Although the bisNi complexes adopt a closed form in the solid state, they exist as a homohelical open C₂-symmetric form or a heterohelical open C_i-symmetric form in solution. A theoretical study suggested that the closed form of 1 a Pd was stabilized by the Pd–Pd interaction. Compound 1 a Pd was reversibly oxidized by one electron at 0.14 V versus ferrocene/ferrocenium (Fc/Fc⁺) and this oxidized species showed Vis/NIR absorption bands at λ=767 and 1408 nm.     

A new dimeric alkylresorcinol from the stem barks of Swintonia floribunda (Anacardiaceae)

From an EtOAc-soluble fraction of the stem barks of Swintonia floribunda (Anacardiaceae), one new dimeric alkylresorcinol named integracin E (1), together with 4 known compounds (2–5) were isolated. Their chemical structures were elucidated based on the spectroscopic data interpretation. The absolute configuration of 1 was determined by the specific rotation analysis of its acid-catalyzed hydrolysis product. Compound 1 showed potent tyrosinase inhibitory activity with an IC₅₀ value of 48.2?μM.     

Regularized gap functions and error bounds for split mixed vector quasivariational inequality problems

In this paper, we consider a class of split mixed vector quasivariational inequality problems in real Hilbert spaces and establish new gap functions by using the method of the nonlinear scalarization function. Further, we obtain some error bounds for the underlying split mixed vector quasivariational inequality problems in terms of regularized gap functions. Finally, we give some examples to illustrate our results. The results obtained in this paper are new.     

Caesium carbonate supported on hydroxyapatite‐encapsulated Ni0.5Zn0.5Fe2O4 nanocrystallites as a novel magnetically basic catalyst for the one‐pot synthesis of pyrazolo[1,2‐b]phthalazine‐5,10‐diones

A novel nanomagnetic basic catalyst of caesium carbonate supported on hydroxyapatite‐coated Ni_0.5Zn_0.5Fe₂O₄ magnetic nanoparticles (Ni_0.5Zn_0.5Fe₂O₄@HAP‐Cs₂CO₃) was prepared. This new catalyst was fully characterized using Fourier transform infrared spectroscopy, transmission and scanning electron microscopy, X‐ray diffraction and vibrating sample magnetometry techniques, and then the catalytic activity of this catalyst was investigated in the synthesis of 1H‐pyrazolo[1,2‐b]phthalazine‐5,10‐dione derivatives. Also, Ni_0.5Zn_0.5Fe₂O₄@HAP‐Cs₂CO₃ could be reused at least five times without significant loss of activity and could be recovered easily by applying an external magnet. Thus, the developed nanomagnetic catalyst is potentially useful for the green and economic production of organic compounds. Copyright © 2015 John Wiley & Sons, Ltd.