Nonnegative solutions to reaction–diffusion system with cross-diffusion and nonstandard growth conditions

We establish the existence of nonnegative weak solutions to nonlinear reaction–diffusion system with cross-diffusion and nonstandard growth conditions subject to the homogeneous Neumann boundary conditions. We assume that the diffusion operators satisfy certain monotonicity condition and nonstandard growth conditions and prove that the existence of weak solutions using Galerkin's approximation technique.     

安培环路定理的拓扑学描述

近年来拓扑学在量子力学中得到了广泛的运用.本文将安培环路定理积分式重新表达为一矢量场在轮胎参数面上的第一类陈数积分.数值模拟展示了该积分值为一整数即第一陈数,其代表矢量场的整体性质:当经历连续变换时,矢量场的局部数值发生改变但整体积分值即陈数仍保持不变;若陈数发生改变,则表明矢量场变换的连续性条件发生破坏,矢量场出现奇点.进一步通过高斯映射将该矢量场从参数轮胎面映射到单位球面上,并给出了第一陈数的直观几何意义.理论和数值结果揭示了安培环路定理的拓扑学本质,表明拓扑概念在经典物理学中也会有广泛应用.     

Can Anti-Aufbau DFT Calculations Estimate Singlet Excited State Aromaticity? Correspondence on “Dibenzoarsepins: Planarization of 8π-Electron System in the Lowest Singlet Excited State”

The simple anti-aufbau DFT approach for estimating singlet excited state aromaticity suggested in a recent Communication published in this journal is shown to produce incorrect results because it targets a linear combination of the singlet and triplet configurations involving the HOMO and LUMO rather than the first singlet excited state. If the S₁ state of a molecule is dominated by the HOMO→LUMO excitation, a comparably simple but theoretically consistent and qualitatively correct approximation to the S₁ wavefunction can be achieved by performing a small “two electrons in two orbitals” CASSCF(2,2) calculation which can be followed by the evaluation of magnetic aromaticity criteria such as NICS.     

The recent progress of functionally graded CNT reinforced composites and structures

In the last decade,the functionally graded carbon nanotube reinforced composites(FG-CNTRCs)have attracted considerable interest due to their excellent mechanical properties,and the structures made of FG-CNTRCs have found broad potential applications in aerospace,civil and ocean engineering,automotive industry,and smart structures.Here we review the literature regarding the mechanical analysis of bulk CNTR nanocomposites and FG-CNTRC structures,aiming to provide a clear picture of the mechanical modeling and properties of FG-CNTRCs as well as their composite structures.The review is organized as follows:(1)a brief introduction to the functionally graded materials(FGM),CNTRCs and FG-CNTRCs;(2)a literature review of the mechanical modeling methodologies and properties of bulk CNTRCs;(3)a detailed discussion on the mechanical behaviors of FG-CNTRCs;and(4)conclusions together with a suggestion of future research trends.     

Sharper uncertainty principles associated with Lp-norm

Motivated by the well-established phase derivative embedded technique, this study devotes to sharper uncertainty principles related to the L^p-norm type of uncertainty product, giving rise to two kinds of uncertainty inequalities that improve the classical result through providing tighter lower bounds. The conditions that truly reach these better estimates are obtained. Examples and simulations are carried out to verify the correctness of the derived results, and finally, possible applications in time-frequency analysis are also given.     

Aeroelastic analysis of cantilever plates using Peters’ aerodynamic model,and the influence of choosing beam or plate theories as the structural model

In this paper, the aeroelastic analyses of a rectangular cantilever plate of varying aspect ratio is presented. The classical plate theory has been selected as the structural model. The main point that distinguishes this study from previously reported research is employing Peters’ theory to model aerodynamic effect which is not straightforward. The Peters’ aerodynamic model was originally developed to provide lift and moment, which is only applicable to the structural model based on the beam theories. In this study, using the basic concept of the Peters’ aerodynamic model in addition to utilizing the Fourier series, the pressure distribution is derived, which makes Peters’ model applicable to structural models based on plate theory. This combination provides a much simpler state–space aeroelastic model for plates in comparison to the prevalent panel methods, which could lead to a significant reduction in computational time. In addition, the aeroelastic response of the plate with respect to changes in the structural model from the beam theory to the plate theory is evaluated. By using data from an experiment carried out at Duke University, the theoretical results are evaluated. Furthermore, the differences in structural models obtained from the plate and beam theories can be divided into two distinct parts, which are responsible for differences in bending and torsional behaviors of the structure, separately. This approach enables us to measure the effects of differences of each behavior separately, which could provide with a new insight into the problem. It has been determined that the flutter speeds obtained from the beam and plate aeroelastic models are little affected by the difference in bending behavior, but rather is mainly caused by the difference in torsional frequencies.     

Certain fractional calculus and integral transform results of incomplete ℵ-functions with applications

In this paper, we study certain interesting and useful properties of incomplete $\aleph$-functions. The incomplete $\aleph$-function is an extension of the $\aleph$-function. We find several useful classical integral transforms of these functions. Further, we examine the fractional calculus with the incomplete $\aleph$-functions and point out several special cases. Finally, we give the applications of incomplete $\aleph$-functions in detecting glucose supply in human blood.     

Modeling the drying of ultrasound and glucose pretreated sweet potatoes: The impact on phytochemical and functional groups

The influence of ultrasonic frequency (20 kHz) and glucose pretreatments either alone or in combination on the drying of sweet potato slices (3 mm) using a hot-air dryer at 60 °C was tested to study the kinetics modeling, phytochemicals, antioxidant activities, and functional and textural changes of the final dried product. The results indicated that total phenolic content and total flavonoid content were significantly higher in glucose-pretreated samples while antioxidant activities were higher in ultrasound- and glucose-pretreated samples. For vitamin C, much degradation occurred in the glucose-pretreated samples when compared with the other pretreated samples apart from the control. Enzymatic browning made a minor contribution to the ultrasound/glucose-pretreated samples, while no significant differences were noted in the glucose-pretreated samples. A modified Henderson and Pabis (MHP) model, followed by the two-term and Hii models, fitted best among the 15 selected mathematical models. Fourier Transform Infrared Spectroscopy (FTIR) analysis revealed the presence of glucose, phenols, and flavonols in all samples. Microstructural analysis confirmed the hardness (N) in the final glucose-pretreated samples due to glucose layers and less cell damage.