We consider the inverse function $z=g(w)$ of a (normalized) starlike function $w=f(z)$ of order $\alpha$ on the unit disk of the complex plane with $0<\alpha<1.$ Krzy{\. z}, Libera and Z\l otkiewicz obtained sharp estimates of the second and the third coefficients of $g(w)$ in their 1979 paper. Prokhorov and Szynal gave sharp estimates of the fourth coefficient of $g(w)$ as a consequence of the solution to an extremal problem in 1981. We give a straightforward proof of the estimate of the fourth coefficient of $g(w)$ together with explicit forms of the extremal functions.

Astringency is an important sensory characteristic of food and beverages containing polyphenols. However, astringency perception in elderly people has not been documented. The aim of the present work was to evaluate sensitivity to astringency as a function of age and salivary flow. Fifty-four panellists, including 30 elderly people (age=75±4.2 years) and 24 young people (age=29.4±3.8 years), participated in this study. Astringency sensitivity was evaluated by the 2-alternative forced choice (2-AFC) procedure using tannic acid solutions. Whole saliva was collected for 5 min before and after sensory tests. The results showed that the astringency threshold was significantly higher in the elderly group than in the young group. Moreover, a negative correlation between salivary flow and threshold was observed in the young group only. These results showed a difference in oral astringency perception as a function of age for the first time. This difference can be linked to salivary properties that differ as a function of age.

With a highly efficient optical absorption capability, bismuth selenide (Bi2Se3) nanomaterial can be used as an outstanding photothermal agent for anti-tumor treatment and shows promise in the field of nanotechnology-based biomedicine. However, little research has been done on the relevant mechanism underlying the photothermal killing effect of Bi2Se3 nanomaterial. Herein, the photothermal effects of Bi2Se3 nanoparticles on A549 cells were explored with emphasis put on autophagy. Firstly, we characterized the structure and physicochemical property of the synthesized Bi2Se3 and confirmed their excellent photothermal conversion efficiency (35.72%), photostability, biocompatibility and ability of photothermal killing on A549 cells. Enhanced autophagy was detected in Bi2Se3-exposed cells under an 808 nm laser. Consistently, an elevated expression ratio of LC3-II to LC3-I, a marker of autophagy occurrence, was induced in Bi2Se3-exposed cells upon NIR irradiation. Meanwhile, the expression of cleaved-PARP was increased in the irradiated cells dependently on the exposure concentrations of Bi2Se3 nanoparticles. Pharmacological inhibition of autophagy by 3-methyladenine (3-MA) further strengthened the photothermal killing effect of Bi2Se3. Meanwhile, stress-related signaling pathways including p38 and SAPK/JNK were activated coupled with the attenuated PI3K/Akt signaling. Our study figures out that autophagy and the activation of stress-related signaling pathways were involved in the photothermal killing of cancerous cells by Bi2Se3, which provides a more understanding of photothermal nanomaterials.

Background:Malignant pleural effusion (MPE),a frequent complication of advanced malignancies. This pilot study characterized and compared the immune landscapes of breast carcinoma (BC) and lung adenocarcinoma (LADC) primary tumors(PTs) and their corresponding MPEs and tested the incorporation of multiplexed image technology for the study of malignant fluids. Methods: We studied the immune contexture of 6 BC and 5 LADC PT samples and their MPEs using 3 multiplex immunofluorescence panels. We explored associations between sample characteristics and pleural effusion–free survival. Results: Although we found 3 out of 11 PTs PD-L1 positive more than 1% by malignant cells, no MPE samples reached positive expression by malignant cells. In addition, CD3+ T cells and CD3+CD8+ cytotoxic T cells predominated (median percentages for MPEs vs. PTs: 45.5% vs. 40.7% and 4.7% vs. 6.6%, respectively). In the BC samples, CD68+ macrophages predominated (median percentages for MPEs vs. PTs:61% vs. 57.1%). Generally, CD3+CD8+FOXP3+ T cells in PTs and the distances from the malignant cells to CD3+CD8+Ki67+ and CD3+PD-1+ T cells were correlated in the first event of MPE after diagnosis. Conclusions: The immune cell phenotypes in the MPEs and PTs were similar within each cancer type but were different for LADC vs. BC.MPE analysis could be used as a substitute for PT analysis, but an expanded study on this topic is essential.

The electroencephalogram (EEG) is a record of brain activity. Brain Computer Interface (BCI) technology formed by the EEG signal has become one of the hotspots at present. How to extract the feature signal of EEG is the most basic research of BCI technology. In this paper, A new method of recognizing fatigue, conscious, concentrated state of human brain is proposed by the combination of discrete wavelet transform and the neural network based on EEG signal. First of all, the law signal is preprocessed by the wavelet denoising method because the law EEG signal contains a large number of high frequency noise, which is decomposed into multi-layer high frequency signal and low frequency signal. thus, δ wave, θ wave, α wave, β wave are obtained by the wavelet transform. And then, frequency band energy of the different wave is regards as the feature signal of EEG. In the experiment, the feature signal is classified by radial basic function (RBF) and annealed chaotic competitive learning network (ACCLN). RBF and ACCLN networks are trained with 500 sets of sample data and are tested by 100 sets of samples in different mental states. The experimental results show that the average accuracy of RBF network under three conditions are 88.75%, 88.25%, 88.5%, respectively, and the correct rate of ACCLN network is 97%, 98%, 98%, respectively.