The work is devoted to the numerical solution of the initial boundary value problem for the heat equation with a fractional Riesz derivative. Explicit and implicit difference schemes are constructed that approximate the boundary value problem for the heat equation with a fractional Riesz derivative with respect to the coordinate. In the case of an explicit difference scheme, a condition is obtained for the time step at which the difference scheme converges. For an implicit difference scheme, a theorem on unconditional convergence is proved. An example of a numerical calculation using an implicit difference scheme is given. It has been established that when passing to a fractional derivative, the process of heat propagation slows down.

[Objective] To understand the relationship between species diversity and tree growth in natural secondary forests in Northeast China, to determine the reasonable size of species diversity, and to carry out appropriate nurturing harvesting and artificial replanting, so as to provide a scientific and theoretical basis for secondary forest management and management. [Methods] A total of 123 sample plots were set up in the Xiaoxinganling (XXAL), Zhangguangcailing (ZGCL), Laojialing (LYL), Changbai Mountain (CBS), Hadaling (HDL) and Longgang Mountain (LGS) areas in Northeast China, they were used to investigate the species composition, importance value, diversity and tree growth in each area. [Results] A total of 48 species belonging to 17 families and 31 genera were investigated in all the sample plots, among which the sample plots in Longgang Mountain contained the largest number of families, genera and species, followed by Hada Ling, Changbai Mountain, Laoyaling, Zhangguangcai Mountain and Xiaoxinganling. The α-diversity index of species in the sample sites was the largest in Changbai Mountain and the smallest in Xiaoxinganling, and the difference between them was significant (P < 0.05), while the richness index was the largest in Longgang Mountain and the smallest in Xiaoxinganling. The difference between them was significant (P < 0.05), while the greater the difference in latitude between the regions, the more obvious the difference in β-diversity index of species in the sample sites, and the fewer species shared between the two regions. The higher the rate of community succession, the higher the average diameter at breast height and the average tree height in each region were CBS > LYL > LGS > ZGCL > HDL > XXAL. The largest breast tree species in each region was Mongolian oak in Changbai Mountain with a diameter at breast height of 64.8 cm, and the smallest breast tree species in each region was Tyrannus sylvestris in Longgang Mountain with a diameter at breast height of 4.0 cm. The highest tree species in each region was Liriodendron sylvestris in Longgang Mountain with a height of 28.9 m, and the smallest species is yellow pineapple with a height of 1.3 m in Longgang Mountain. [Conclusion] Within a certain range, species diversity has a facilitating effect on the average diameter at breast height and average tree height of species within a stand. Therefore, during the management of secondary forests, appropriate nurturing harvesting and artificial replanting should be adopted to ensure reasonable species diversity in the stands and provide optimal space for the growth of natural secondary forests.

Nanoparticle drug delivery systems are engineered technologies that use nanoparticles for the targeted delivery and controlled release of therapeutic agents. Cisplatin-loaded nanoparticle formulations were optimized utilizing response surface methods and the central composite rotating design model. This study employed a central composite rotatable design with a three-factored factorial design with three tiers. Three independent variables namely drug polymer ratio, aqueous organic phase ration, and stabilizer concentration were used to examine the particle size, entrapment efficiency, and drug loading of cisplatin PLGA nanoparticles as responses. The results revealed that this response surface approach might be able to be used to find the best formulation for the cisplatin PLGA nanoparticles. A polymer ratio of 1:8.27, organic phase ratio of 1:6, and stabilizer concentration of 0.15 were found to be optimum for cisplatin PLGA nanoparticles. Nanoparticles made under the optimal conditions found yielded a 112 nm particle size and a 95.4 percent entrapment efficiency, as well as a drug loading of 9 percent. The cisplatin PLGA nanoparticles tailored for scanning electon microscopy displayed a spherical form. A series of in vitro tests showed that the nanoparticle delivered cisplatin progressively over time. According to this work, the Response Surface Methodology (RSM) employing the central composite rotatable design may be successfully used to simulate cisplatin-PLGA nanoparticles.

The aim of the present study was to determine the effects of single and mixed infections of nematode (Meloidogyne javanica), fungus (Fusarium oxysporum) and bacterium (Xanthomonas axonopodis) on nodulation and pathological parameters of Bambara groundnut (Vigna subterrenea (L.) Verdc.) in field condition. Nematode infested field was used while other pathogens were obtained from diseased plants. The Randomized Complete Block Design (RCBD) was adopted in a 5 × 9 × 5 factorial design (5 blocks, 9 treatments and 5 replicates per treatments) resulting in 225 experimental units. In each experimental unit, three seeds were sown to a depth of 5cm and thinned to one plant per planting hole after germination at day 7. Treatments were inoculated into test plant following standard methods. As a result, the control treatment recorded the highest number of nodules (64.0 ± 6.91), followed by bacterium (45.2 ± 5.11) while N + F + B had the lowest number of root nodules (23.4 ± 2.42). Simultaneous treatment (N + F + B) gave the highest percentage reduction in nodulation (63.44%), followed by treatment N + F7 (56.25%). Fungus treatment recorded the highest mean wilted plants (3.8 + 0.20) followed by N + F7 treatment (3.40 + 0.40). Gall formation in the nematode treatment increased proportionately by 56.33% as the highest recorded, followed by treatment N + F7 with 50.0%. Treatment N + F7 had the highest reproduction factor (Rf) value of 9.30 followed by nematode (8.30), N + B7 (7.40), N + F + B (6.80) and N + F14 (6.50). Zero (0) Rf value was recorded in fungus, bacterium and control treatments. The observed differences in nodulation and pathological parameters among the treatments are significant (P < 0.05). The data provided in this work is important in the control of the three pathogens affecting the productivity of Bambara nut. Formulation of a single protectant should be designed to have potent effects on the three pathogens to achieve effective protection and good production of Bambara nut.

Based on the density-functional theory (DFT) combined with nonequilibrium Green’s function (NGF), this paper investigates the effects of either single aluminum (Al) or single phosphorus (P) atom substitutions at different edge positions of zigzag-edged silicene nanoribbons (ZGNRs) in the ferromagnetic state on the spin-dependent transport properties and spin thermoelectric effects. It has been found that the spin polarization at the Fermi level can reach 100% or –100% in the doped ZSiNRs. Meanwhile, the spin-up Seebeck effect (for –100% case) and spin-down Seebeck effect (for 100% case) are also enhanced. Moreover, the spin Seebeck coefficient is much larger than the corresponding charge Seebeck coefficient at a special doping position and electron energy. Therefore, the study shows that the Al or P doped ZSiNRs can be used to prepare the ideal thermospin devices.