Two‐Photon Probes for Zn2+ Ions with Various Dissociation Constants. Detection of Zn2+ Ions in Live Cells and Tissues by Two‐Photon Microscopy

A series of Zn²⁺‐selective two‐photon fluorescent probes (AZnM1−AZnN) that had a wide range of dissociation constants (K_d^TP=8 nm‐ 12 μM ) were synthesized. These probes showed appreciable water solubility (>3 μM ), cell permeability, high photostability, pH insensitivity at pH>7, significant two‐photon action cross‐sections (86–110 GM) upon complexation with Zn²⁺, and can detect the Zn²⁺ ions in HeLa cells and in living tissue slices of rat hippocampal at a depth of >80 μm without mistargeting and photobleaching problems. These probes can potentially find application in the detection of various amounts of Zn²⁺ ions in live cells and intact tissues.     

Treatment of TiO2 with COOH‐Functionalized Germanium Nanoparticles to Enhance the Photocurrent of Dye‐Sensitized Solar Cells

A dye‐sensitized solar cell (DSSC) containing a TiO₂ film treated with COOH‐functionalized germanium nanoparticles (Ge COOH Nps) exhibited a higher short‐circuit photocurrent density (J_sc; 15.4 mA cm⁻²) compared to the corresponding untreated DSSC (13.4 mA cm⁻²) using N719 and a 12 μm thick TiO₂ film at 100 mW cm⁻². The amount of N719 attached to the treated TiO₂ film was 21 % greater than that attached to the untreated TiO₂ film. Enhancement of the J_sc value by 15 % was attributed mostly to an intramolecular charge transfer from N719 attached to the Ge COOH Nps to the TiO₂ conduction band through the Ge COOH Nps.     

New,real fundamental solutions to the transient thermal contact problem in a piezoelectric strip under the coupling actions of a rigid punch and a convective heat supply

A thermo-electro-mechanical contact analysis has been performed for a finite piezoelectric strip, which is subjected to the joint actions of a rigid, flat punch and a transient convective heat supply. The Laplace transform and Fourier sine and cosine transforms were applied in solving the governing equations. A detailed analysis of the characteristic roots of the corresponding characteristic equation was made. Real fundamental solutions were derived, which can readily lead to real solutions to the thermo-electro-mechanical quantities. A Cauchy-type singular integral equation was obtained for the stated problem and then solved numerically. Closed form solutions of a special case were obtained. To obtain the accurate solution in the time domain, an effective numerical inversion algorithm of the Laplace transform was applied. Detailed analyses were performed to reveal the variation law of temperature, contact stress beneath the punch, stress intensity factor at the punch edge and strain with time. Parametric studies were performed to discover the effects of the layer thickness on the distribution of temperature, contact stress beneath the punch and stress intensity factor at the punch edge.     

Linear maps that strongly preserve regular matrices over the Boolean algebra

The set of all m × n Boolean matrices is denoted by $ \mathbb{M} $ \mathbb{M} _m,n . We call a matrix A ∈ $ \mathbb{M} $ \mathbb{M} _m,n regular if there is a matrix G ∈ $ \mathbb{M} $ \mathbb{M} _n,m such that AGA = A. In this paper, we study the problem of characterizing linear operators on $ \mathbb{M} $ \mathbb{M} _m,n that strongly preserve regular matrices. Consequently, we obtain that if min{m, n} ⩽ 2, then all operators on $ \mathbb{M} $ \mathbb{M} _m,n strongly preserve regular matrices, and if min{m, n} ⩾ 3, then an operator T on $ \mathbb{M} $ \mathbb{M} _m,n strongly preserves regular matrices if and only if there are invertible matrices U and V such that T(X) = UXV for all X ε $ \mathbb{M} $ \mathbb{M} _m,n , or m = n and T(X) = UX ^T V for all X ∈ $ \mathbb{M} $ \mathbb{M} _n .     

关于一类择优增长系统的度分布的注记

本文研究文[1]中提出的一类择优增长系统,说明文[1]中利用主方程法求解系统的平均度分布及稳态度分布是值得商榷的,然后通过考虑系统中空团体的存在的可能性,对系统进行修正,并证明空团体存在的必要性。     

Optimal estimates of the field enhancement in presence of a bow-tie structure of perfectly conducting inclusions in two dimensions

This paper deals with the field enhancement due to insertion of a bow-tie structure of perfectly conducting inclusions into the two-dimensional space with a given field. The field enhancement is represented by the gradient blow-up of a solution to the conductivity problem. The bow-tie structure consists of two disjoint bounded domains which have corners with possibly different aperture angles. The domains are parts of cones near the vertices which are nearly touching to each other. We construct functions explicitly which characterize the field enhancement. As consequences, we derive optimal estimates of the gradient in terms of the distance between two inclusions and aperture angles of the corners. The estimates show in quantitatively precise way that the field is enhanced beyond the corner singularities due to the interaction between two inclusions, and the blow-up rate is much higher than the one for the case of inclusions with smooth boundaries.     

Modelling the Effects of Pest Control with Development of Pesticide Resistance

In this paper,we assume that the pest population is divided into susceptible pests and infected pests,and only susceptible pests do harm to crops.Considering the two methods of spraying pesticides and releasing infected pests and natural enemies to control susceptible pests(the former is applied more frequently),and assuming that only susceptible pests develop resistance to pesticides,a pest control model with resistance development is established.By using the basic theory of impulsive differential systems and analytical methods,the sufficient condition for the global attractiveness of the susceptible pest eradication periodic solution is given.Combined with numerical simulations,the effects of spraying frequency of pesticides on critical threshold conditions for eradicating susceptible pests are discussed.The results confirm that it is not that the more frequently the pesticides are sprayed,the better the result of the pest control is.Two control strategies for eradicating susceptible pests are proposed:switching pesticides and releasing natural enemies elastically.Finally,the parameters in the critical threshold are analyzed from the following two aspects:(1)The key factors affecting pest control are determined by parameter sensitivity analyses.The results indicate that the correlation of the critical threshold concerning the killing efficiency rate and the decay rate of pesticides to susceptible pests varies due to the resistance development of susceptible pests.(2)Three-dimensional graphs and contours of susceptible pest eradication critical threshold with two parameters are simulated,and the effects of the main parameters on the critical threshold are analyzed.     

Singular Functions and Characterizations of Field Concentrations: a Survey

In the presence of closely located inclusions of the extreme material property, the physical fields, such as the electric field and the stress tensor, may be concentrated and arbitrarily large in the narrow region between two inclusions. Recently there has been significant progress on the quantitative characterization of the field concentration in the contexts of electrostatics(Laplace equation), linear elasticity(Lamé system), and viscous flow(Stokes system). This paper is to review such progress in a coherent way.     

Rubesanolides F and G: Two Novel Lactone-Type Norditerpenoids from Isodon rubescens

A phytochemical investigation of the leaves of the medicinal plant Isodon rubescens led to the isolation of the two new degraded abietane lactone diterpenoids rubesanolides F (1) and G (2). Their structures were elucidated based on the analyses of the HRESIMS and 1D/2D NMR spectral data, and their absolute configurations were determined by ECD spectrum calculations and X-ray single crystal diffraction methods. Compounds 1 and 2, with a unique γ-lactone subgroup between C-8 and C-20, were found to form a carbonyl carbon at C-13 by removal of the isopropyl group in an abietane diterpene skeleton. Rubesanolide G (2) is a rare case of abietane that possesses a cis-fused configuration between rings B and C. The two isolates were evaluated for their biological activities against two cancer cell lines (A549 and HL60), three fungal strains (Candida alba, Aspergillus niger and Rhizopus nigricans) and three bacterial strains (Escherichia coli, Staphylococcus aureus and Bacillus subtilis).     

Enhancement of Near-Cloaking. Part II: The Helmholtz Equation

The aim of this paper is to extend the method of Ammari et al. (Commun. Math. Phys., 2012) to scattering problems. We construct very effective near-cloaking structures for the scattering problem at a fixed frequency. These new structures are, before using the transformation optics, layered structures and are designed so that their first scattering coefficients vanish. Inside the cloaking region, any target has near-zero scattering cross section for a band of frequencies. We analytically show that our new construction significantly enhances the cloaking effect for the Helmholtz equation.