Slow divergence integral and its application to classical Liénard equations of degree 5

The slow divergence integral is a crucial tool to study the cyclicity of a slow–fast cycle for singularly perturbed planar vector fields. In this paper, we deduce a useful form for this integral in order to apply it to various problems. As an example, we use it to prove that the slow divergence integral along any non-degenerate slow–fast cycle for singular perturbations of classical Liénard equations of degree 5 has at most one zero, and the zero is simple if it exists; hence the cyclicity of any non-degenerate slow–fast cycle in this class of equations is at most 2. Up to now there were many interesting results about Liénard equations of degree 3, 4 and ≥6, but almost nothing is known about degree 5. The result in this paper can be seen as a first stage to study the uniform property for classical Liénard equations of degree 5.     

Neural control of uncertain robot manipulator with fixed-time convergence

Nonlinear Dynamics - In this paper, an adaptive NN (neural network) control scheme is proposed for uncertain robot systems to achieve fixed-time convergence. With the proposed fixed-time NN...     

The Optical Characteristics of the Acousto-optic Tunable Filter with the Equivalent Point

In this paper, the interaction curves of acoustic and optical waves in a non-collinear AOTF (acousto-optic tunable filter) cell under the parallel-tangent momentum matching condition are analyzed systematically. A new theory of equivalent point for AOTF design is put forward. The wavelength characteristics and the wavelength resolution of two diffraction beams with equivalent point design in AOTF are emphatically analyzed. The optical characteristics at δ=0 (ideal case) and δ≠0 (real case) are also discussed. The advantages of the AOTF with equivalent point design include high wavelength resolution,more quantitative energy and larger incident angle aperture.     

Neglschisandrins A-B: two new dibenzocyclooctene lignans from Schisandra neglecta

Two new dibenzocyclooctene lignans, neglschisandrins A-B (1-2), were isolated from the stems of Schisandra neglecta. Their structures and stereochemistries were elucidated by spectroscopic methods, including 1D- and 2D-NMR and HR-ESI-MS techniques.     

带两个形状参数的同次Bézier曲线

构造了一种带两个形状参数的Bézier型曲线,并研究了该曲线的性质、形状参数对曲线的影响及曲线的拼接.所提出的曲线是多项式Bezier曲线的一种同次新扩展,不仅具有传统Bézier曲线的诸多性质,而且可通过修改两个形状参数的取值对其形状进行调节.由于所提出的曲线是一种带有形状参数且与传统Bézier曲线具有相似性质的同次多项式模型,因此比现有的一些带形状参数的Bézier型曲线更有优势.     

Poly(2-Oxazoline)-Based Functional Peptide Mimics: Eradicating MRSA Infections and Persisters while Alleviating Antimicrobial Resistance

Peptides have important biological functions. However, their susceptibility to proteolysis limits their applications. We demonstrated here for the first time, that poly(2-oxazoline) (POX) can work as a functional mimic of peptides. POX-based glycine pseudopeptides, a host defense peptide mimic, had potent activities against methicillin-resistant S. aureus, which causes formidable infections. The POX mimic showed potent activity against persisters that are highly resistant to antibiotics. S. aureus did not develop resistance to POX owning to the reactive oxygen species related antimicrobial mechanism. POX-treated S. aureus is sensitive to common antibiotics, demonstrating no observable antimicrobial pressure or cross-resistance in using antimicrobial POX. This study highlights POX as a new type of functional mimic of peptides and opens new avenues in designing and exploring peptide mimetics for biological functions and applications.     

Numerical investigation of the flow and heat behaviours of an impinging jet

The flow and temperature fields of a turbulent impinging jet are rather complex. In order to accurately describe the flow and heat-transfer process, two important factors that must be taken into account are the turbulence model and the wall function. Several turbulence models, including κ–? turbulence models, κ–ω turbulence models, low-Re turbulence models, the κ–κ_l–ω turbulence model, the Transition SST turbulence model, the V2F turbulence model and the RSM turbulence model, are examined and compared to experimental data. Furthermore, for the near wall region, various wall functions are presented for comparison and they include the standard wall function, the scale wall function, the non-equilibrium wall function and the enhanced wall function. The distribution features of velocity, turbulent kinetic energy and Nusselt number are determined in order to provide a reliable reference for the multiphase impinging jet in the future.     

Anaerobic conditions to reduce oxidation of proteins and to accelerate the copper-catalyzed "Click" reaction with a water-soluble bis(triazole) ligand

Oxidation of protein (bovine albumin serum) by air still occurred under the copper-catalyzed azide-alkyne cycloaddition (CuAAC) reaction conditions even in the presence of a Cu(I)-stabilizing tris(triazole) ligand. Anaerobic conditions not only avoided the oxidation of the protein, but also greatly accelerated the CuAAC reaction using a water-soluble bis(triazole) Cu(I) ligand.