On the complexity of extending the convergence ball of Wang’s method for finding a zero of a derivative

Ball convergence results are very important, since they demonstrate the complexity in choosing initial points for iterative methods. One of the most important problems in the study of iterative methods is to determine the convergence ball. This ball is small in general restricting the choice of initial points. We address this problem in the case of Wang’s method utilized to determine a zero of a derivative. Finding such a zero has many applications in computational fields, especially in function optimization. In particular, we find the convergence ball of Wang’s method using hypotheses up to the second derivative in contrast to earlier studies using hypotheses up to the fourth derivative. This way, we also extend the applicability of Wang’s method. Numerical experiments used to test the convergence criteria complete this study.     

Malliavin and Dirichlet structures for independent random variables

On any denumerable product of probability spaces, we construct a Malliavin gradient and then a divergence and a number operator. This yields a Dirichlet structure which can be shown to approach the usual structures for Poisson and Brownian processes. We obtain versions of almost all the classical functional inequalities in discrete settings which show that the Efron–Stein inequality can be interpreted as a Poincaré inequality or that the Hoeffding decomposition of $U$-statistics can be interpreted as an avatar of the Clark representation formula. Thanks to our framework, we obtain a bound for the distance between the distribution of any functional of independent variables and the Gaussian and Gamma distributions.     

与 Cauchy 微分中值定理相关的几个问题

根据Cauchy微分中值定理表达式的结构引入辅助函数 F（x ，c）＝ f （x）- f （c）g（x）- g（c）（a＜ c＜ b），通过讨论其可导性，得到相关的几个不等式，由此得出Cauchy微分中值定理存在唯一“中值点”的一个条件，并给出其逆定理的一个较弱表述。     

一类极限为1的未定式

对于一类00型或∞0型未定式，给出其极限为1的一个充分条件，并通过实例展示其应用。     

Treatment by serum up-conversion nanoparticles in the fluoride matrix changes the mechanism of cell death and the elasticity of the membrane

Nanoparticles are increasingly being used for treatment and diagnostic purposes, but their effects on cells is not fully understood. Here, the interaction of fluorescent up-conversion nanoparticles (UpC-NPs) with neutrophils was investigated by imaging and measurement of membrane-cytosceletal elasticity by atomic force microscopy. It was found that UpC-NPs induce the death of neutrophils mainly by necrosis, and to a smaller extent by a novel process called ‘mummification'. Necrosis occurs by gradual loss of intracellular contents and nuclei, 45–110 min after exposure to UpC-NPs. Mummification is apparent as an increase in the rigidity of the neutrophils' membrane and acquisition of a characteristic bumpy shape with numerous protrusions; this structure does not change during atomic force microscopy scanning. Coating UpC-NPs with protein by incubation with serum leads to (1) formation of nanoparticle aggregates in the nm and μm size range, (2) a reduction in toxicity, (3) reduced mummification of neutrophils, and (4) no significant reduction of the elasticity of the membrane-cytoskeletal complex of neutrophils 30 min after exposure to coated UpC-NPs. The study shows that serum proteins greatly curb the toxicity of nanoparticles and reveals mummification as a novel mechanism of UpC-NP-induced cell death.     

The solubility of bosentan in aqueous-2-propanol mixtures at several temperatures,measurement and data correlation

ABSTRACT

The solubilities of bosentan (BST) in binary aqueous mixtures of 2-propanol at temperatures ranging from 293.15 to 313.15 K were determined using a shake-flask method. The produced data were modelled with the Jouyban-Acree-van’t Hoff model and difference between the predicted data and experimental ones were illustrated by percent average relative deviations (%ARD). Moreover, the thermodynamic functions of dissolution for BST in the aqueous 2-propanol solutions were computed which suggest that the dissolution process is endothermic and not spontaneous.     

Dumbbell-Shaped 2,2’-Bipyridines: Controlled Metal Monochelation and Application to Ni-Catalyzed Cross-Couplings

2,2’-Bipyridine ligands (dsbpys) with dumbbell-like shapes and differently substituted triarylmethyl groups at the C5 and C5’ positions showed high ligand performance in the Ni-catalyzed cross-electrophile coupling and the Ni/photoredox-synergistically catalyzed decarboxylative coupling reactions. The superior ligand effects of dsbpys compared to the conventional bpy ligands were attributed to the monochelating nature of dsbpys.     

Dispersion and localisation in structured Rayleigh beams

This paper brings a comparative analysis between dynamic models of couple-stress elastic materials and structured Rayleigh beams on a Winkler foundation. Although physical phenomena have different physical origins, the underlying equations appear to be similar, and hence mathematical models have a lot in common. In the present work, our main focus is on the analysis of dispersive waves, band-gaps and localised waveforms in structured Rayleigh beams. The Rayleigh beam theory includes the effects of rotational inertia which are neglected in the Euler–Bernoulli beam theory. This makes the approach applicable to higher frequency regimes. Special attention is given to waves in pre-stressed Rayleigh beams on elastic foundations.