Equilibrium phase behavior of aqueous two-phase systems containing 17R4/L64 and citrates

The cloud points (CPs) of the copolymers 17R4 and L64 were first measured, and then the effects of salts ((NH₄)₃C₆H₅O₇, K₃C₆H₅O₇) on 17R4 and L64 were researched. After finishing the work described above, the temperature (278.15, 283.15, and 288.15) K of aqueous two-phase systems was determined, which consist of 17R4-(NH₄)₃C₆H₅O₇, 17R4-K₃C₆H₅O₇, L64-(NH₄)₃C₆H₅O₇, and L64-K₃C₆H₅O₇. Finally, the liquid–liquid equilibrium (LLE) data of binodal curve and the tie line for 17R4-(NH₄)₃C₆H₅O₇ aqueous two- phase systems (ATPSs) 17R4-K₃C₆H₅O₇ ATPSs, L64-(NH₄)₃C₆H₅O₇ ATPSs, and L64-K₃C₆H₅O₇ ATPSs were obtained. Nonlinear fitting of the empirical equation was used for making the diagram. The results showed that the change in the size of the two-phase areas increases with the increase of temperature. The capacity of the salts to induce phase segregation follows the Hofmeister series, that is, K₃C₆H₅O₇?>?(NH₄)₃C₆H₅O₇. In addition, the findings also showed that the phase separation ability of 17R4 is better than that of L64.     

Study on convergence and error of a numerical method for solving systems of nonlinear Fredholm–Volterra integral equations of Hammerstein type

The aim of this paper is to present an efficient analytical and numerical procedure for solving systems of nonlinear Fredholm–Volterra integral equations of the Hammerstein type with the aid of fixed point techniques and the usual Schauder basis in an adequate Banach space.     

On Existence of Common Fixed Points Under Lipschitz-Type Mapping Pairs with Applications

In this paper, we propose some su?cient conditions to obtain the existence of common fixed points for a pair of self-mappings satisfying Lipschitz-type conditions in noncomplete metric space. Our results improve and extend the results of Pant [Common fixed points of Lipschitz-type mapping pairs, J. Math. Anal. Appl. 240, (1999), 280–283] and Khan et al. [Coincidences of Lipschitz-type hybrid maps and invariant approximation, Numer. Funct. Anal. Optim. 28(9–10), (2007), 1165–1177]. As an application of our results we solve an eigenvalue problem for operators defined on a normed space.     

Necessary and Sufficient Conditions for Weak Quasi Efficiency in Nonsmooth Multiobjective Problems

In this article, a multiobjective problem with a feasible set defined by inequality, equality and set constraints is considered, where the objective and constraint functions are locally Lipschitz. Several constraint qualifications are given and the relations between them are analyzed. We establish Kuhn-Tucker and strong Kuhn-Tucker necessary optimality conditions for (weak) quasi e?ciency in terms of the Clarke subdifferential. By using two new classes of generalized convex functions, su?cient conditions for local (weak) quasi e?cient are also provided. Furthermore, we study the Mond-Weir type dual problem and establish weak, strong and converse duality results.     

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.     

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.     

Difference Cochains and Reidemeister Traces

The authors consider the difference of Reidemeister traces and difference cochain of given two self-maps,and find out a relation involving these two invariants.As an application,an inductive formula of the Reidemeister traces for self-maps on a kind of CW-complex,including spherical manifolds is obtained.     

Modified classification of non-self-adjoint second-order difference equations

This paper is concerned with the classification of non-self-adjoint second-order difference equations. The relationship between the number of summable solutions of non-self-adjoint difference equations and that of the discrete linear Hamiltonian system is discussed. A classification for non-self-adjoint second-order difference equations is established, which is independent of the choice of the rotated half plane and the fixed point.