A note on Arzela–Ascoli's lemma in almost periodic problems

This paper is concerned with a generalized Arzela–Ascoli's lemma, which has been extensively applied in almost periodic problems by the continuation theorem of degree theory. We give a counter example to show that this lemma is incorrect, and there is a gap in the proof of some existing literature, where the addressed generalized Arzela–Ascoli's lemma was used. Moreover, we make some final comments and introduce an open problem. Copyright © 2016 John Wiley & Sons, Ltd.     

Mild solution of semilinear impulsive integro‐differential evolution equation in Banach spaces

Through solving the problem step by step and by applying the method of a C₀ semigroup of operators combined with the Banach contraction theorem, we investigate the existence and uniqueness of a mild solution of semilinear impulsive integro‐differential evolution equation in Banach spaces. In addition, an explicit iterative approximation sequence of the mild solution is derived. The assumed conditions in the present theorems are weaker and more general, and the results obtained are the generalizations and improvements of some known results. Examples are also given to illustrate our main results. Copyright © 2017 John Wiley & Sons, Ltd.     

Stability and Neimark–Sacker bifurcation of a ratio‐dependence predator–prey model

In this paper, stability and bifurcation of a two‐dimensional ratio‐dependence predator–prey model has been studied in the close first quadrant . It is proved that the model undergoes a period‐doubling bifurcation in a small neighborhood of a boundary equilibrium and moreover, Neimark–Sacker bifurcation occurs at a unique positive equilibrium. We study the Neimark–Sacker bifurcation at unique positive equilibrium by choosing b as a bifurcation parameter. Some numerical simulations are presented to illustrate theocratical results. Copyright © 2017 John Wiley & Sons, Ltd.     

Characterization of canonical classes for systems of linear ODEs

The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation to the canonical form y ⁽ⁿ⁾=0 consists of copies of the same iterative scalar equation. It is also shown that contrary to the scalar case, an iterative vector equation need not be reducible to the canonical form by an invertible point transformation. Other properties of iterative linear systems are also derived, as well as a simple algebraic formula for their general solution. Copyright © 2017 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.     

A new method for exact solutions of variant types of time‐fractional Korteweg‐de Vries equations in shallow water waves

The current article devoted on the new method for finding the exact solutions of some time‐fractional Korteweg–de Vries (KdV) type equations appearing in shallow water waves. We employ the new method here for time‐fractional equations viz. time‐fractional KdV‐Burgers and KdV‐mKdV equations for finding the exact solutions. We use here the fractional complex transform accompanied by properties of local fractional calculus for reduction of fractional partial differential equations to ordinary differential equations. The obtained results are demonstrated by graphs for the new solutions. Copyright © 2016 John Wiley & Sons, Ltd.     

Existence and multiplicity of systems of Kirchhoff‐type equations with general potentials

This paper is concerned with the following systems of Kirchhoff‐type equations: Under more relaxed assumptions on V(x) and F(x,u,v), we first prove the existence of at least two nontrivial solutions for the aforementioned system by using Morse theory in combination with local linking arguments. Then by using the Clark theorem, the existence results of at least 2k distinct pairs of solutions are obtained. Some recent results from the literature are extended. Copyright © 2016 John Wiley & Sons, Ltd.     

Selective capturing and detection of Salmonella typhi on polycarbonate membrane using bioconjugated quantum dots

Present work demonstrates the utilization of surface modified polycarbonate (PC) membrane as solid phase and antibody conjugated CdSe/ZnS quantum dots (QDs) as fluorescent label for the sensitive and selective detection of Salmonella typhi (S. typhi) in water in a period of 2.5 h. PC membrane was surface modified with glycine and activated by EDC/NHS for immobilization of S. typhi specific IgG. Antibody immobilized porous PC membrane was incubated with bacteria contaminated water for immunocapturing of S. typhi. Antibody conjugated QDs were also prepared by using carbodiimide chemistry. Both modified PC membrane and quantum dots were characterized by using various modern analytical tools. It was estimated that 1.95 molecules of QDs were successfully bio-conjugated per unit of IgG. PC membrane with captured bacteria was incubated with prepared IgG conjugated QDs for the formation of sandwich complex. Analysis of the regions of interest (ROI) in fluorescent micrographs showed that newly developed method based on PC and fluorescent QDs has 100 times higher detection sensitivity (100 cells/mL) as compared with detection using conventional dye (FITC) based methods.     

Effects of peptide density and elution pH on affinity chromatographic purification of human immunoglobulins A and M

A family of linear hexamer peptide ligands HWRGWV, HYFKFD and HFRRHL, initially identified for their affinity to the Fc portion of human immunoglobulin G (hIgG), also have potential for use in the purification of human immunoglobulins A (hIgA) and M (hIgM). HWRGWV demonstrated the strongest binding affinity to hIgM, followed by hIgA and hIgG respectively. The effects of N-terminal acetylation of the peptide, as well as elution buffer pH, on the chromatographic elution of human IgG, IgA and IgM from HWRGWV resins at various peptide densities (0.04-0.55 meq/g) were investigated. Over 80% recovery and 90% purity were achieved for human IgG and IgA isolation from complete minimum essential medium (cMEM) using HWRGWV resin at optimum peptide densities. For human IgM, 75.7% recovery and 86.0% purity were achieved by using HWRGWV at a low peptide density of 0.04 meq/g. Although HYFKFD and HFRRHL exhibited their ability for isolation of human IgG, IgA and IgM from cMEM as well, HWRGWV is the best option among them for large-scale purification of human IgG, IgA and IgM based on conditions tested.     

Dissociation and fractionation of heavy and light chains from IgG monoclonal antibodies

A basic method for dissociation and fractionation of monoclonal IgG heavy and light chain is described. It employs less noxious and hazardous reagents than the classical mercaptoethanol/propionic acid process and replaces size exclusion chromatography with cation exchange on a monolith to improve productivity. Significant scope remains to refine the conditions. The method can be applied to other disulfide bonded proteins with significant affinity for cation exchangers.