Contraction of the proximal mapping and applications to the equilibrium problem

In this paper, we introduce a new definition of Lipschitz-type continuity of a bifunction. Using this definition, we prove the contraction of the proximal mapping and apply it to the equilibrium problem over the fixed-point set of a nonexpansive mapping. We present a new algorithm for this problem. Under classical conditions, the convergence of the algorithm is proved. Finally, we present some numerical results for the proposed algorithm.     

The existence of a positive solution for nonlinear fractional differential equations with integral boundary value conditions

In this paper, first, we consider the existence of a positive solution for the nonlinear fractional differential equation boundary value problem where 0≤λ < 1,^CD^α is the Caputo's differential operator of order α, and f:[0,1] × [0,∞)→[0,∞) is a continuous function. Using some cone theoretic techniques, we deduce a general existence theorem for this problem. Then, we consider two following more general problems for arbitrary α, 1≤n < α≤n + 1: Problem 1: where , 0≤λ < k + 1; Problem 2: where 0≤λ≤α and D^α is the Riemann–Liouville fractional derivative of order α. For these problems, we give existence results, which improve recent results in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Analytic invariant curves for an iterative equation related to dissipative standard map

In this paper, we study existence of invariant curves of an iterative equation which is from dissipative standard map. By constructing an invertible analytic solution g (x ) of an auxiliary equation of the form invertible analytic solutions of the form g (λ g  ^? 1(x )) for the original iterative functional equation are obtained. Besides the hyperbolic case 0 < |λ | < 1, we focus on those λ on the unit circle S ¹, that is, |λ | = 1. We discuss not only those λ at resonance, that is, at a root of the unity, but also those λ near resonance under the Brjuno condition. Copyright © 2016 John Wiley & Sons, Ltd.     

Hybrid projection methods for equilibrium problems with non‐Lipschitz type bifunctions

Based on the extended extragradient‐like method and the linesearch technique, we propose three projection methods for finding a common solution of a finite family of equilibrium problems. The linesearch used in the proposed algorithms has allowed to reduce some conditions imposed on equilibrium bifunctions. The strongly convergent theorems are established without the Lipschitz‐type condition of bifunctions. The paper also helps in the design and analysis of practical algorithms and gives us a generalization of some previously known problems. Copyright © 2017 John Wiley & Sons, Ltd.     

Delay‐dependent criteria on the global attractivity of Nicholson's blowflies model with patch structure

In this paper, we investigate the effect of delay on the asymptotic behavior of Nicholson's blowflies model with patch structure and multiple time‐varying delays. By using the fluctuation lemma and some differential inequality technique, delay‐dependent criteria are obtained for the global attractivity of the addressed system. Meanwhile, some numerical examples are given to illustrate the feasibility of the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.     

Exact boundary controllability for 1‐D quasilinear wave equations with dynamical boundary conditions

By equivalently replacing the dynamical boundary condition by a kind of nonlocal boundary conditions, and noting a hidden regularity of solution on the boundary with a dynamical boundary condition, a constructive method with modular structure is used to get the local exact boundary controllability for 1‐D quasilinear wave equations with dynamical boundary conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

A half-space projection method for solving generalized Nash equilibrium problems

The generalized Nash equilibrium problem (GNEP) is an n-person noncooperative game in which each player’s strategy set depends on the rivals’ strategy set. In this paper, we presented a half-space projection method for solving the quasi-variational inequality problem which is a formulation of the GNEP. The difference from the known projection methods is due to the next iterate point in this method is obtained by directly projecting a point onto a half-space. Thus, our next iterate point can be represented explicitly. The global convergence is proved under the minimal assumptions. Compared with the known methods, this method can reduce one projection of a vector onto the strategy set per iteration. Numerical results show that this method not only outperforms the known method but is also less dependent on the initial value than the known method.     

Practical Synthesis of 2-Iodosobenzoic Acid (IBA) without Contamination by Hazardous 2-Iodoxybenzoic Acid (IBX) under Mild Conditions

We report a convenient and practical method for the preparation of nonexplosive cyclic hypervalent iodine(III) oxidants as efficient organocatalysts and reagents for various reactions using Oxone^® in aqueous solution under mild conditions at room temperature. The thus obtained 2-iodosobenzoic acids (IBAs) could be used as precursors of other cyclic organoiodine(III) derivatives by the solvolytic derivatization of the hydroxy group under mild conditions of 80 °C or lower temperature. These sequential procedures are highly reliable to selectively afford cyclic hypervalent iodine compounds in excellent yields without contamination by hazardous pentavalent iodine(III) compound.     

Extremely Low Vapor-Pressure Data as Access to PC-SAFT Parameter Estimation for Ionic Liquids and Modeling of Precursor Solubility in Ionic Liquids

Precursor solubility is a crucial factor in industrial applications, dominating the outcome of reactions and purification steps. The outcome and success of thermodynamic modelling of this industrially important property with equations of states, such as Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT), vastly depends on the quality of the pure-component parameters. The pure-component parameters for low-volatile compounds such as ionic liquids (ILs) have been commonly estimated using mixture properties, e. g. the osmotic pressure of aqueous solutions. This leads to parameters that depend on the solvent, and transferability to other mixtures often causes poor modeling results. Mixture-independent experimental properties would be a more suitable basis for the parameter estimation offering a way to universal parameter sets. Model parameters for ILs are available in the literature [10.1016/j.fluid.2012.05.029], but they were estimated using pure-IL density data. The present work focuses on a step towards a more universal estimation strategy that includes new experimental vapor-pressure data of the pure IL. ILs exhibit an almost negligible vapor pressure in magnitude of usually 10⁻⁵ Pa even at elevated temperatures. In this work, such vapor-pressure data of a series of 1-ethyl-3-methyl-imidazolium-based [C₂mim]-ILs with various IL-anions (e. g. tetrafluoroborate [BF₄]⁻, hexafluorophosphate [PF₆]⁻, bis(trifluoromethylsulfonyl)imide [NTf₂]⁻) were experimentally determined and subsequently used for PC-SAFT parameter estimation. The so-determined parameters were used to predict experimental molecular precursor solubility in ILs and infinitely diluted activity coefficients of various solvents in ILs. The parameters were further compared to modeling results using classical parametrization methods (use of liquid-density data only for the molecular PC-SAFT and the ion-based electrolyte PC-SAFT). As a result, the modeled precursor solubilities using the new approach are much more precise than using the classical parametrization methods, and required binary parameters were found to be much smaller (if needed). In sum, including the pure-component vapor-pressure data of ILs opens the door towards parameter estimation that is not biased by mixture data. This procedure might be suitable also for polymers and for all kind of ionic species but needs extension to ion-specific parametrization in the long term.     

Dynamic Ring-chain Equilibrium of Nucleophilic Thiol-yne “Click” Polyaddition for Recyclable Poly(dithioacetal)s

We report a dynamic polymerization system based on the reversible nucleophilic Michael polyaddition of activated alkynes and dithiols. Four poly(dithioacetal)s(P1-P4) were prepared via the base-catalyzed thiol-yne "click" polyaddition of two dithiols(1,4-butanedithiol(4 S) and 1,5-pentanedithiol(5 S)) and two alkynones(3-butyn-2-one(Y1) and 1-phenyl-2-propyn-1-one(Y2)) at high concentrations. We systematically investigated the base-catalyzed polymerization of 4 S and Y1(for polymer P1) under different conditions, and found that this polymerization was a highly concentration-dependent dynamic system: polymer P1 was formed at high concentration, while seven-membered dithioacetal, 1-(1,3-dithiepan-2-yl) propan-2-one(C1), was obtained at low concentration. The polymerization of 4 S and Y2(for polymer P4)displayed similar polymerization behavior, generating 2-(1,3-dithiepan-2-yl)-1-phenylethanone(C4) at low concentration. On the contrary,polymer P2(from Y1 and 5 S) was exclusively obtained with no formation of eight-membered dithioacetal. The polymerizations of Y1 with 1,2-ethanedithiol(2 S) and 1,3-dimercaptopropane(3 S) only afforded corresponding five-and six-membered dithioacetals, 1-(1,3-dithiolan-2-yl)propan-2-one(C2) and 1-(1,3-dithian-2-yl) propan-2-one(C3). This dynamic behavior of P1 and P4 was attributed to the concentrationdependent retro-Michael addition reaction between a thiol and a β-sulfido-α,β-unsaturated carbonyl compound catalyzed by bases.Furthermore, polymers P1 and P4 could be depolymerized into C1 and C4 in yields of 58% and 95%, respectively. The ring-opening polymerization of C1 at high concentration could successfully regenerate polymer P1. Thus, a new type of closed-loop recyclable poly(dithioacetal)s was developed.