一个R2上含双曲函数核的Hilbert型不等式

通过引入参数，构造了一个全平面上的、含双曲函数的非齐次核函数。利用正切函数的有理分式展开，建立了最佳常数因子与正切函数高阶导数相关联的Hilbert型积分不等式。 作为应用，通过赋予参数不同的值，建立了一些有意义的特殊结果。     

Design,synthesis and evaluation of novel dehydroabietic acid-dithiocarbamate hybrids as potential multi-targeted compounds for tumor cytotoxicity

In the present study, novel representatives of the important group of biologically-active, dehydroabietic acid-bearing dithiocarbamate moiety, were synthesized and characterized by ¹H NMR, ¹³C NMR, HR-MS. The in vitro antiproliferative activity evaluation (MTT) indicated that these compounds exhibited potent inhibitory activities in various cancer cell lines (HepG-2, MCF-7, HeLa, T-24, MGC-803). Particularly, compound III-b possessed extraordinary cytotoxicity with low micromolar IC₅₀ values ranging from 4.07 to 38.84 µM against tested cancer cell lines, while displayed weak cytotoxicity on two normal cell lines (LO-2 and HEK 293 T). Subsequently, the potential mechanisms of representative compound III-b were elementarily investigated by Transwell experiment, which showed III-b can inhibit cancer cells migration. Annexin-V/PI dual staining showed that the compound can induce HepG-2 cells apoptosis in a dose-dependent manner. Meanwhile this apoptosis may be related to the upregulated protein expression of cleaved-caspase 3, cleaved-caspase 9, Bax and downregulated of Bcl-2 indicated by Western Blot. Later study further confirmed that ROS levels in HepG-2 cells increased significantly with the rise of concentrations. In addition, through the network pharmacology data analyzing, the core targets and signaling pathways of compound III-b for treatment of liver neoplasms were forecasted. Molecular docking model showed that compound III-b had high affinity with hub targets (CASP3, EGFR, HSP90AA1, MAPK1, ERBB2, MDM2), suggesting that compound III-b might target the hub protein to modulate signaling activity. Taken together, these data indicated that dehydroabietic acid structural modification following the “Molecular hybridization” principle is a feasible way to discover the potential multi-targeted antitumor compounds.     

Intensification of delignification of Tectona grandis saw dust as sustainable biomass using acoustic cavitational devices

Delignification of sawdust was studied using ultrasound assisted alkali peroxide approach using longitudinal horn for the first time and the efficacy compared with more commonly used configurations of ultrasonic reactors. Comparison with the conventional approach based on stirring has also been presented to establish the process intensification benefits. Effect of different operating parameters such as sodium carbonate concentration (0.1, 0.15, 0.2, 0.25 M), hydrogen peroxide concentration (0.2, 0.4, 0.6, 0.8, 1 M) and biomass loading (2, 4, 6, 8, 10 wt%), on the efficacy of lignin extraction has been investigated for different ultrasonic reactors. The optimum conditions for probe type ultrasonic horn were established as 150 W, 50% duty cycle and 80% amplitude with optimum process conditions as Na₂CO₃ concentration as 0.2 M, H₂O₂ concentration as 1 M, biomass loading of 10 wt% and operating time of 70 min. Longitudinal horn resulted in best efficacy (both in terms of yield and energy requirements) followed by ultrasonic horn and ultrasonic bath whereas the conventional approach was least effective. The obtained lignin was also analyzed using different characterization techniques. The presence of peaks at wavelength range of 875–817, 1123–1110, and at 1599 cm⁻¹ for the extracted sample confirmed the presence of lignin. Increase in the crystallinity index of the processed sample (maximum for longitudinal horn) also confirmed the lignin removal as lignin is amorphous in nature. Overall it has been concluded that ultrasound can be effectively used for delignification with longitudinal horn as best configuration.     

Stratification phenomenon in an inclined rheology of UCM nanomaterial

This investigation presents the unsteady rheology of Maxwell nanomaterial induced to flow over an inclined surface. Simultaneous effects of stratification, thermal radiation, heat source/sink and magnetic field are taken into account. Viscous dissipation and mixed convection due to concentration and temperature differences are also analyzed. The governing partial differential equations for the Maxwell nanofluid which incorporate the effects of Brownian and thermophoresis effects are simplified by using appropriate similarity transformations, and solved analytically by using homotopy analysis method (HAM). The effects of involved physical parameters on the flow field are analyzed graphically and numerically.     

Improving breakdown strength and energy storage efficiency of poly(vinylidene fluoride-co-chlorotrifluoroethylene) and polyurea blend films by double layer structure design

All-organic composites are widely used in energy storage application due to the high breakdown strength performance, but the improvement of energy storage was limited by the relatively low dielectric constant. Therefore, to satisfy the high demands of dielectric materials, energy storage properties of polymer composites should be further enhanced. In this article, poly(vinylidene fluoride-co-chlorotrifluoroethylene) (P(VDF-CTFE)) and polyurea (PUA), which are known as high dielectric ferroelectric material and linearly high energy storage efficiency material respectively, are composited through double layer (DL) casting method for the first time. The properties of DL structured composite film is contrasted with solution blending structure especially in energy storage efficiency, and the results demonstrate that DL structure design can make great use of advantages of two materials and also can avoid the influence of phase separation between P(VDF-CTFE) and PUA efficiently. Moreover, high breakdown strength (6180 kV/cm) and high energy storage efficiency (77%) of DL composites can be realized simultaneously by incorporating PUA as an insulating layer, and the mechanism is discussed in detail. This work provides an effective route to improve the energy storage properties of polymer dielectric materials and shows great application potential.     

Evolution processes of coupled thermal qubits

We investigate the quantum speed limit time (QSLT) of quantum evolution before thermal equilibrium of two coupled qubits each of which is coupled to a separate thermal bath at the same temperature within the Born-Markov approximation. The evolution process in one particular initial state can change between speed-up and speed-down two times before reaching equilibrium. We call this double cusp behaviour. This behaviour is an anomalous phenomenon in evolution processes in the weak-coupling Markovian regime. We study QSLT corresponding to all pure initial energy eigenstates and categorise them. In addition, we also display the conditions for double cusp behaviour in terms of temperature, qubit interaction and frequency.