A class of operator equilibrium problems

In this paper, we consider a class of operator equilibrium problems (OEP for short) with operator solutions and derive a Minty type lemma for this class of problems. Further, using this lemma and KKM theorem, we establish some existence theorems for OEP. The theorems presented in this paper generalize, improve and unify many known results.     

Decomposition of Order Statistics of Semimartingales Using Local Times

Given a finite collection of continuous semimartingales, a semimartingale decomposition of the corresponding ranked (order-statistics) processes was derived recently in [1 Banner , A.D. , and Ghomrasni , R. 2008 . Local times of ranked continuous semimartingales . Stochastic Processes and Applications 118 : 1244 – 1253 . [Google Scholar]]. In this paper, we obtain a more general result for semimartingales (not necessarily continuous) using a simpler approach. Furthermore, we also give a generalization of Ouknine [7 Ouknine , Y. 1988 . Généralisation d'un lemme de S. Nakao et applications . Stochastics 23 : 149 – 157 .[Taylor & Francis Online] , [Google Scholar], 8 Ouknine , Y. 1990 . Temps local du produit et du sup de deux semimartingales . Séminaire de Probabilités XXIV, 1988/89 . Lecture Notes in Mathematics , Vol. 1426 , pp. 477 – 479 . [Google Scholar]] and Yan's [11 Yan , J.A. 1985 . A formula for local times of semimartingales . Northeast. Math. J. 1 : 138 – 140 . [Google Scholar]] formula for local times of ranked processes.     

Inelastic impact dynamics of ships with one-sided barriers. Part I: analytical and numerical investigations

This two-part paper deals with impact interaction of ships with one-sided ice barrier during roll dynamics. The first part presents analytical and numerical studies for the case of inelastic impact. An analytical model of a ship roll motion interacting with ice is developed based on Zhuravlev and Ivanov non-smooth coordinate transformations. These transformations have the advantage of converting the vibro-impact oscillator into an oscillator without barriers such that the corresponding equation of motion does not contain any impact term. Such approaches, however, account for the energy loss at impact times in different ways. The present work, in particular, demonstrates that the impact dynamics may have qualitatively different response characteristics to different dissipation models. The difference between localized and distributed equivalent damping approaches is discussed. Extensive numerical simulations are carried out for all initial conditions covered by the ship grazing orbit for different values of excitation amplitude and frequency of external wave roll moment. The basins of attraction of safe operation are obtained and reveal the coexistence of different response regimes such as non-impact periodic oscillations, modulation impact motion, period added impact oscillations, chaotic impact motion and rotational motion. The second part will consider experimental validations of predicted results.     

A facile preparation of trisubstituted amino-furan and -thiophene derivatives

β-Alkylation of amino-furan and -thiophene heterocycles is described through metal-, acid- and base-free carbon-carbon bond formation. The ability of both heterocycles to undergo selective β-alkylation is compared by mean of experimental and theoretical data. The presence of chiral amine substituents induced the diastereoselective generation of the newly formed additional stereocenter.     

Synthesis of biosourced polyether-amides from 1,4-3,6-dianhydrohexitols: Characterization by NMR and MALDI–ToF mass spectrometry

New series of polyether-amides were prepared by polycondensation in solution of three diamines based on 1,4-3,6-dianhydrohexitols with two types of diacyl chlorides (sebacoyl and isophtaloyl). Unprecedented diamines based on isomannide and isoidide were elaborated. The corresponding polyether-amides (PeA) were obtained with high yields. They were characterized by different analytical techniques (NMR, MALDI–ToF MS, DSC). The combination of MALDI–ToF MS with NMR spectroscopy allowed us to confirm structure types. DSC measurements revealed an amorphous character for the isophtaloyl family with a high T_g value. The sebacoyl series proved to be semi-crystalline with a high T_m value. Isosorbide-based PeAs demonstrated interesting properties (T_g above 210 °C and T_m above 240 °C) and high viscosity (0.32).     

Cyclacenes and short zigzag nanotubes with alternanting Ge―C bonds: theoretical impacts of Ge on the ground state,strain, and band gap

[6]_n Cyclacenes and short zigzag [6]_n carbon nanotubes (n = 5–10) have unstable singlet open‐shell (S_os) ground states. We have boosted their stability by implementing altering Ge―C bonds that acquire S_cs ground states with larger band gap (ΔE_LUMO–HOMO) at B3LYP and BPW91 levels of theory. Fascinatingly, homodesmic calculations indicated release of almost two folds of strain energy upon substitution of germanium for carbon. This may turn the green lights for synthesis of germanium–carbon cyclacenes and short zigzag nanotubes. Copyright © 2014 John Wiley & Sons, Ltd.     

A new and efficient one-pot synthesis of 2-hydroxy-1,4-dihydrobenzoxazines via a three-component Petasis reaction

The secondary amines synthesized by the reaction between 2-aminophenols and aromatic aldehydes, via the reduction of the corresponding imines, were employed in the synthesis of new 2-hydroxy-2H-1,4-benzoxazine derivatives through a one-pot Petasis multicomponent reaction in good to excellent yields.     

Synthesis of organosoluble polyamides with bulky triaryl imidazole pendent group

New unsymmetrical diamine monomer containing triaryl imidazole pendent group,4-[4-(4,5-diphenyl-1H-imidazol-2-yl)phenoxy] -1,3-benzenediamine,was synthesized via aromatic substitution reaction of 1-chloro-2,4-dinitrobenzene with 4-(4,5- diphenyl-1H-imidazol-2-yl)phenol,followed by palladium-catalyzed hydrazine reduction.This new monomer was further confirmed by FT-IR,~1H NMR and ~(13)C NMR.Novel polyamides having pendant triaryl imidazole group were prepared by the phosphorylation polycondensation of fou...