A generalized super AKNS hierarchy associated with orthosymplectic Lie superalgebra OSP(2,2) and its super bi-Hamiltonian structures

For the orthosymplectic Lie superalgebra $\text{◂⋅▸}OSP(2,2)$, we choose a set of basis matrices. A linear combination of those basis matrices presents a spatial spectral matrix. The compatible condition of the spatial part and the corresponding temporal parts of the spectral problem leads to a generalized super AKNS (GSAKNS) hierarchy. By making use of the supertrace identity, the obtained GSAKNS hierarchy can be written as the super bi-Hamiltonian structures.     

Uniform local well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation

In this paper, we study the Cauchy problem for the Benjamin-Ono-Burgers equation \({\partial _t}u - \epsilon \partial _x^2u + {\cal H}\partial _x^2u + u{u_x} = 0\), where \({\cal H}\) denotes the Hilbert transform operator. We obtain that it is uniformly locally well-posed for small data in the refined Sobolev space \({\tilde H^\sigma }(\mathbb{R})\,\,(\sigma \geqslant 0)\), which is a subspace of L²(ℝ). It is worth noting that the low-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is scaling critical, and thus the small data is necessary. The high-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is equal to the Sobolev space H^σ (ℝ) (σ ⩾ 0) and reduces to L²(ℝ). Furthermore, we also obtain its inviscid limit behavior in \({\tilde H^\sigma }(\mathbb{R})\) (σ ⩾ 0).

     

Finding any given 2‐factor in sparse pseudorandom graphs efficiently

Given an $n$‐vertex pseudorandom graph $G$ and an $n$‐vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$, that is, an embedding $\phi :V\left(H\right)\to V\left(G\right)$ so that $\phi \left(u\right)\phi \left(v\right)\in E\left(G\right)$ for all $uv\in E\left(H\right)$. Particular instances of this problem include finding a triangle‐factor and finding a Hamilton cycle in $G$. Here, we provide a deterministic polynomial time algorithm that finds a given $H$ in any suitably pseudorandom graph $G$. The pseudorandom graphs we consider are $\left(p,\lambda \right)$‐bijumbled graphs of minimum degree which is a constant proportion of the average degree, that is, $\mathrm{\Omega }\left(pn\right)$. A $\left(p,\lambda \right)$‐bijumbled graph is characterised through the discrepancy property: $|e\left(A,B\right)?p|A||B||<\lambda \sqrt{|A||B|}$ for any two sets of vertices $A$ and $B$. Our condition $\lambda =O(p^{2}n/\log n)$ on bijumbledness is within a log factor from being tight and provides a positive answer to a recent question of Nenadov. We combine novel variants of the absorption‐reservoir method, a powerful tool from extremal graph theory and random graphs. Our approach builds on our previous work, incorporating the work of Nenadov, together with additional ideas and simplifications.     

Recent advances and challenges in the recovery and purification of cellular exosomes

Exosomes are nanovesicles secreted by most cellular types that carry important biochemical compounds throughout the body with different purposes, playing a preponderant role in cellular communication. Because of their structure, physicochemical properties and stability, recent studies are focusing in their use as nanocarriers for different therapeutic compounds for the treatment of different diseases ranging from cancer to Parkinson's disease. However, current bioseparation protocols and methodologies are selected based on the final exosome application or intended use and present both advantages and disadvantages when compared among them. In this context, this review aims to present the most important technologies available for exosome isolation while discussing their advantages and disadvantages and the possibilities of being combined with other strategies. This is critical since the development of novel exosome‐based therapeutic strategies will be constrained to the effectiveness and yield of the selected downstream purification methodologies for which a thorough understanding of the available technological resources is needed.     

Microwave‐assisted polycondensation of 4‐octylaniline with dibromoarylene

The Pd‐catalyzed polycondensation of 4‐octylaniline with various dibromoarylenes was carried out under microwave heating. Microwave heating led to a decrease in the reaction time and an increase in the molecular weight of the polymers as compared to conventional heating. Microwave heating also allowed the catalyst loading to be reduced to 1 mol %, yielding polymerization results that were comparable to those under conventional heating and 5 mol % catalyst. Investigations regarding field‐effect transistors and organic photovoltaic cells using the obtained poly(arylamine) with azobenzene units revealed that increasing the molecular weight of the polymer led to improved device performance, including hole mobility and power conversion efficiency. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 536–542     

Separation and analysis of triazine herbcide residues by capillary electrophoresis

Triazines are widely used in agriculture around the world as selective pre‐ and post‐emergence herbicides for the control of broad leaf and grassy weeds. With high toxicity and persistence, triazines can contaminate the environment and crops, so the development of rapid and sensitive methods for the determination of different triazines is necessary. Capillary electrophoresis comprises a group of techniques used to separate chemical mixtures. Analytical separation is based on different electrophoretic mobilities. This review focuses on the analysis of triazine herbicides with different modes of capillary electrophoresis, including capillary zone electrophoresis, micellar electrokinetic capillary electrophoresis, capillary electrochromatography and nonaqueous capillary electrophoresis. Determinations of triazines in various matrices such as surface water, groundwater, vegetables, soil and grains are emphasized. Copyright © 2014 John Wiley & Sons, Ltd.     

Lipase‐Supported Metal–Organic Framework Bioreactor Catalyzes Warfarin Synthesis

A green and sustainable strategy synthesizes clinical medicine warfarin anticoagulant by using lipase‐supported metal–organic framework (MOF) bioreactors (see scheme). These findings may be beneficial for future studies in the industrial production of chemical, pharmaceutical, and agrochemical precursors.