Investigating heat conduction in a sphere with heat absorption using generalized Caputo fractional derivative

In this paper, we study the ρ-Laplace transform and the finite sin-Fourier transform as powerful tools in solving fractional differential equations with generalized Caputo derivative. We use these transforms to solve the time-fractional heat equation with a generalized Caputo fractional derivative associated with heat absorption in spherical coordinates. We obtain the solutions in two cases of Dirichlet boundary conditions. The effect of the parameter $\rho$, which characterizes the generalized Caputo derivative is illustrated through some numerical examples.     

The Investigation of the Fractional-View Dynamics of Helmholtz Equations Within Caputo Operator

It is eminent that partial differential equations are extensively meaningful in physics, mathematics and engineering. Natural phenomena are formulated with partial differential equations and are solved analytically or numerically to interrogate the system’s dynamical behavior. In the present research, mathematical modeling is extended and the modeling solutions Helmholtz equations are discussed in the fractional view of derivatives. First, the Helmholtz equations are presented in Caputo’s fractional derivative. Then Natural transformation, along with the decomposition method, is used to attain the series form solutions of the suggested problems. For justification of the proposed technique, it is applied to several numerical examples. The graphical representation of the solutions shows that the suggested technique is an accurate and effective technique with a high convergence rate than other methods. The less calculation and higher rate of convergence have confirmed the present technique’s reliability and applicability to solve partial differential equations and their systems in a fractional framework.     

Chlorophyll derivatives/MXene hybrids for photocatalytic hydrogen evolution: Dependence of performance on the central coordinating metals

Development of efficient photocatalytic hydrogen evolution reaction (HER) with illumination of visible light is challenging. In this work, five chlorophyll derivatives (M-Chls; M = H₂/Cu/Ni/Co/Zn) with different central ions in its cyclic tetrapyrrole ring including free base, copper, nickel, cobalt, and zinc were synthesized and employed as the effective visible-light harvester for efficient HER. In addition, two-dimensional (2D) noble metal-free co-catalyst Ti₃C₂T_x MXene was used as an excellent electron capturer due to its outstanding conductivity property. These M-Chls are modified on the surface of Ti₃C₂T_x MXene with 2D accordion-like morphology by means of a simple deposition process to form noble metal-free Chl/Ti₃C₂T_x-based photocatalysts for HER. It is found that the best HER performance as high as 49 μmol/h/g_cat was achieved with the Co-Chl@Ti₃C₂T_x hybrid, which was much higher than those of other M-Chl@Ti₃C₂T_x composites. This research provides a specific way to synthesize low-cost and environmentally friendly natural Chls for developing highly efficient photocatalytic HER through molecular engineering.     

高斯混合模型结合加权似然的目标跟踪算法

鉴于高斯混合模型对背景变化快时无法精确检测出目标和目标跟踪的适应性差等瑕疵，提出了基于加权似然跟踪器来改进高斯混合模型实现运动目标跟踪算法。主要引入了自适应高斯混合模型来实时检测运动目标，然后空间加权似然来进行视频中的目标定位，引入加权似然期望值来改进高斯混合模型处理视频中的多尺度、多角度变化的目标跟踪不精准问题。通过VOT 2014 dataset对比实验结果表明提出的基于加权似然跟踪（Weighted Likelihood Tracking，WLT）和改进高斯混合模型（Improved Gaussian Mixture Model，IGMM）的目标跟踪算法较传统高斯混合模型跟踪算法在跟踪的精度有较大提高。在应对多尺度、多角度变化的目标跟踪表现出了较大的优势。     

Analytical attractive functions and their derivatives in bulk and nanoconfined pores

In this paper, two new analytical attractive (alpha) functions and their derivatives in bulk and nanoconfined pores are developed based on the virial equation of state (EOS) and statistical thermodynamics and are evaluated at different conditions for the first time. A cubic EOS is modified to nanometer scale and applied to predict the thermodynamic and phase properties in bulk and nanoconfined pores coupled with the new analytical alpha functions. The nanoscale-extended EOS coupled with the analytical alpha functions are validated to be accurate by means of the experimental data for the thermodynamic and phase calculations. The alpha functions and dimensionless attractive term A for the O₂, Ar, CO₂, N₂, and C₁-C₁₀ are always positive and monotonically decrease with the temperature increases at T ≤ 2000 K in the bulk phase, whereas the second virial coefficients (B₂) are always negative and increase with the temperature increases. Moreover, the alpha functions, A, and B₂ for all of components remain constant with the decreasing pore radius until r_p = 50 nm, the former two of which decrease while the latter one increases by further reducing the pore radius. It should be noted that the intermolecular attractive force (ie, A) is a function of the pressure, which is gradually increased at P ≤ 10 MPa though drastically increases afterwards. Also, the enhanced confinement effects lead the same-component intermolecular attractive forces to be smaller. The analytical formulations in the SRK type slightly outperform in the gaseous or light component cases, while those in the PR type are better for the heavy component cases in terms of the thermodynamic property calculations, both of which are compatible with the modified EOS and analytical alpha functions.     

Milk feeding level and starter protein content: Effects on growth performance,blood metabolites,and urinary purine derivatives of Holstein dairy calves

The objective of this study was to investigate the effects of milk allowances equal to 526 g/d as moderate (MOD) versus 790 g/d of milk dry matter as high (HI), and starter diets containing 18% or 23% crude protein (CP), on growth performance, blood metabolites, and purine derivative (PD) excretion in the urine of dairy calves. A total of 52 female Holstein dairy calves (40.8 kg of body weight) were randomly assigned to the experimental diets. The treatments were (1) moderate milk and 18% CP starter diet (MOD-18CP); (2) MOD and 23% CP starter diet (MOD-23CP); (3) high milk and 18% CP starter diet (HI-18CP); and (4) HI and 23% CP starter diet (HI-23CP). Calves had free access to a starter feed and water and were weaned on d 53 but remained in the study until d 73. Urine samples were collected during the preweaning period (for 6 consecutive days between d 35 and 40) and postweaning period (for 6 consecutive days between d 65 and 70) to investigate urinary excretion of PD. Starter feed intake, β-hydroxybutyrate (BHB), and blood urea concentrations were reduced; however, average daily gain (ADG) and blood glucose levels increased in calves fed HI before weaning compared with MOD. During the preweaning period, high milk feeding increased total urinary PD excretion but decreased it after weaning. The 23CP diet resulted in higher feed intake and ADG before weaning and higher excretion of allantoin and total excretion of PD compared with the 18CP diet. The HI-23CP treatment resulted in the greatest withers and hip heights at weaning and final measurement, as well as the highest preweaning blood insulin concentrations. In terms of rumen development, MOD-23CP showed the greatest benefits based on starter intake, blood BHB concentration, and urinary excretion of PD. Based on the higher urinary excretion of PD found in HI-fed calves before weaning, it is possible that milk feeding overestimates estimated microbial yield. The results suggest that feeding starters with a higher proportion of CP may help maintain a more balanced ratio of CP to ME during high milk feeding, to avoid protein deficiency due to low starter intake. When calves are fed a high milk allowance, urine excretion of PD may be misinterpreted as a measure of estimated microbial growth and rumen development; this should be considered during calculations of estimated microbial yield in milk-fed calves.     

Determination of supercapacitor parameters based on fractional differential equations

In this paper, we estimate the parameter values of a fractional-order model of supercapacitors involving fractional derivatives of Liouville-Caputo, Caputo-Fabrizio, and Atangana-Baleanu and fractional conformable derivative in the Liouville-Caputo sense. We present the exact solution of the considered model using the properties of the Laplace transform operator together with the convolution theorem. They developed numerical simulations using each one of the fractional derivatives; the results were compared graphically with experimental data obtained from different supercapacitors using standard laboratory equipment. The nonlocal parameters involved in the equivalent electrical circuit for the supercapacitor model are recalculated for each fractional derivative using a particle swarm optimization algorithm for generating optimal solutions.     

A Phenylacetamide Resveratrol Derivative Exerts Inhibitory Effects on Breast Cancer Cell Growth

Resveratrol (RSV) is a natural compound that displays several pharmacological properties, including anti-cancer actions. However, its clinical application is limited because of its low solubility and bioavailability. Here, the antiproliferative and anti-inflammatory activity of a series of phenylacetamide RSV derivatives has been evaluated in several cancer cell lines. These derivatives contain a monosubstituted aromatic ring that could mimic the RSV phenolic nucleus and a longer flexible chain that could confer a better stability and bioavailability than RSV. Using MTT assay, we demonstrated that most derivatives exerted antiproliferative effects in almost all of the cancer cell lines tested. Among them, derivative 2, that showed greater bioavailability than RSV, was the most active, particularly against estrogen receptor positive (ER+) MCF7 and estrogen receptor negative (ER-) MDA-MB231 breast cancer cell lines. Moreover, we demonstrated that these derivatives, particularly derivative 2, were able to inhibit NO and ROS synthesis and PGE2 secretion in lipopolysaccharide (LPS)-activated U937 human monocytic cells (derived from a histiocytoma). In order to define the molecular mechanisms underlying the antiproliferative effects of derivative 2, we found that it determined cell cycle arrest at the G1 phase, modified the expression of cell cycle regulatory proteins, and ultimately triggered apoptotic cell death in both breast cancer cell lines. Taken together, these results highlight the studied RSV derivatives, particularly derivative 2, as promising tools for the development of new and more bioavailable derivatives useful in the treatment of breast cancer.