Euler Characteristics on virtually free products

We define Euler characteristics on classes of residually finite and virtually torsion free groups and we show that they satisfy certain formulas in the case of amalgamated free products and HNN extensions over finite subgroups. These formulas are obtained from a general result which applies to the rank gradient and the first L²?Betti number of a finitely generated group.     

双稳态结构中的1/2次谐波共振及其对隔振特性的影响

以典型的双稳态系统——屈曲梁结构为例,基于等效模型,结合解析、数值和实验手段,研究了双稳态结构中的1/2次谐波共振特性、演化过程、参数调节规律及其对隔振特性的影响.研究发现,当非线性刚度系数或激励幅值增加到一定程度时,系统会在一定带宽下产生显著的1/2次谐波共振;随着激励幅值增加,阻尼系统的1/2次谐波遵循“产生-增强-衰退-消失”的过程,该过程对峰值频率和峰值传递率有重要影响;适当提高非线性强度能有效改善双稳态结构隔振特性.针对双稳态屈曲梁结构开展的实验验证了1/2次谐波特性和隔振特性变化规律.     

Influence of ultrasound on the functional characteristics of indigenous varieties of mango (Mangifera indica L.)

The present study was conducted to evaluate the effect of ultrasonic (US) treatment on chemical characteristics and antioxidant potential of pulps obtained from eight mango varieties indigenous to Pakistan. There was a significant (p < 0.05) effect of varieties and US treatment on chemical characteristics i.e. pH, acidity, TSS, vitamin C contents, total sugars (%), reducing sugars (%) and non-reducing sugars (%). Microstructure evaluation of pulp from all mango varieties showed deshaped middle lamella and cell wall of cells after 8 min of US treatment. At 4 min of US treatment as per shaped cell wall and middle lamella, the chemical characteristics and antioxidant potential were higher. The total phenolics (TP), flavonoids (TF) and total antioxidant activity (TAA) of pulp from most varieties increased significantly (p < 0.05) after US treatment for 4 min but decreased successively after each treatment i.e. 8 and 12 min. The maximum value (314.17 μg AAE/mL pulp) of DPPH was shown by pulp from Dosehri and the minimum (158.67 μg AAE/mL pulp) was found in pulp from Langra before US treatment. The DPPH values of pulp from most of the varieties increased significantly (p < 0.05) after US treatment for 4 min but decreased successively after each treatment but pulp from Langra showed increasing trend after 8 min of US treatment which decreased after 12 min of treatment. The total anthocyanin (TA) values of pulp from Chaunsa, Dosehri, Sindhri, Gulab Khas and Langra increased abruptly after US treatment for 4 min but decreased successively after subsequent treatment. The pulp from Desi, Anwar Ratol, Gulab Khas and Langra showed an abrupt decrease in TA after 8 min of US treatment. An increasing trend of values of total carotenoids (TC) was shown by pulp from all mango varieties after 4 min of US treatment but decreasing trend was observed with subsequent increase in time of US treatment.     

Targeted Construction of Amorphous MoSx with an Inherent Chain Molecular Structure for Improved Pseudocapacitive Lithium-Ion Response

Owing to low ion/electron conductivity and large volume change, transitional metal dichalcogenides (TMDs) suffer from inferior cycle stability and rate capability when used as the anode of lithium-ion batteries (LIBs). To overcome these disadvantages, amorphous molybdenum sulfide (MoS_x) nanospheres were prepared and coated with an ultrathin carbon layer through a simple one-pot reaction. Combining X-ray photoelectron spectroscopy (XPS) with theoretical calculations, MoS_x was confirmed as having a special chain molecular structure with two forms of S bonding (S²⁻ and S₂²⁻), the optimal adsorption sites of Li⁺ were located at S₂²⁻. As a result, the MoS_x electrode exhibits superior cycle and rate capacities compared with crystalline 2H-MoS₂ (e.g., delivering a high capacity of 612.4 mAh g⁻¹ after 500 cycles at 1 A g⁻¹). This is mainly attributed to more exposed active S₂²⁻ sites for Li storage, more Li⁺ transfer pathways for improved ion conductivity, and suppressed electrode structure pulverization of MoS_x derived from the inherent chain-like molecular structure. Quantitative charge storage analysis further demonstrates the improved pseudocapacitive contribution of amorphous MoS_x induced by fast reaction kinetics. Moreover, the morphology contrast after cycling demonstrates the dispersion of active materials is more uniform for MoS_x than 2H-MoS₂, suggesting the MoS_x can well accommodate the volume stress of the electrode during discharging. Through regulating the molecular structure, this work provides an effective targeted strategy to overcome the intrinsic issues of TMDs for high-performance LIBs.     

Behavior of metal complexes of polyacrylic acid in solutions

Metal complexes of polyacrylic acid containing Li, Li, and Cu, or Li and Zn have been studied in saline aqueous solutions using molecular hydrodynamics and light scattering methods. Intrinsic viscosities, weight-average molar masses, hydrodynamic radii, and radii of gyration were obtained. It was shown that the macromolecules of polymetalloacrylates containing divalent metals form small and large supramolecular structures, their dimensions, and composition being dependent on the ionic strength of the solution.     

Analysis in protein profile,antioxidant activity and structure-activity relationship based on ultrasound-assisted liquid-state fermentation of soybean meal with Bacillus subtilis

This study investigated effects of ultrasound on the contents of peptide and soluble protein, antioxidant activity, functionalities and structural characteristics of fermented soybean meal (FSBM) with Bacillus subtilis systematically. The results showed that there were significant effects of ultrasound treatments (frequency, treatment time and power density) on the contents of peptide and soluble protein (p < 0.05). Under the optimum ultrasound conditions (power density of 0.08 W/mL, frequency of 33 kHz and treatment time of 1 h) by single factor experiment, the contents of peptide and soluble protein increased by 31.27% and 18.79% compared to those of the control, respectively. Additionally, the in vitro antioxidant activity (•OH scavenging rate, Fe²⁺ chelating capacity and DPPH radical scavenging rate) and functional properties (emulsifying activity and emulsifying stability) of FSBM were found to be noticeably improved by ultrasound (p < 0.05). The fourier transform infrared (FTIR) spectroscopy revealed that ultrasound caused protein molecules to unfold with a decrease content of α-helix and β-turn and an increase in the proportion of β-sheet and random coil. Besides, atomic force microscope (AFM) results indicated that ultrasonication generally increased the surface roughness of protein and the protein sonicated with higher frequency (≥33 kHz) exhibited a greater height compared to lower frequency ultrasonication. Structure-activity relationship analysis illustrated that there was a good linear relationship between •OH scavenging rate and β-sheet/β-turn with Pearson’s correlation coefficient r of −0.86/0.90. Collectively, the selection of ultrasonic parameters is essential for the preparation of functional protein and bioactive peptide by enhancing fermentation of agroindustrial by-products.     

Experimental study on age and gender differences in microscopic movement characteristics of students

Campus security has aroused many concerns from the whole society. Stampede is one of the most frequent and influential accidents in campus. Studies on pedestrian dynamics especially focusing on students are essential for campus security, which are helpful to improve facility design and emergency evacuation strategy. In this paper, primary and middle school students were recruited to participate in the single-file experiments. The microscopic movement characteristics,including walking speed, headway, gait characteristics(step length, step frequency and swaying amplitude) and their relations were investigated. Age and gender differences in the headway-speed diagram and space requirements were analyzed by statistical tests. The results indicated that the impacts of age and gender were significant. There were three stages for the influence of gender on the headway-speed diagram for both age groups. The impacts on students' space requirements were consistent for different age and gender groups. But the impacts of age and gender on free-flow speed were affected by each other. Due to the connection of walking speed and gait characteristics, the comparisons of gait characteristics between different ages and genders were performed to understand the corresponding differences in speed more deeply. The results showed that differences in step length and swaying amplitude between males and females were significant for both age groups. The effect of gender on step frequency was significant for primary students. But for middle school students,whether gender had significant impact on step frequency was not clear here because of the large P-value. Besides, the influence of age on gait characteristics changed with gender.     

Dynamic Modeling of the Feed Drive System of a CNC Metal Cutting Machine

Studying the vibrational behavior of feed drive systems is important for enhancing the structural performance of computer numerical control (CNC) machines. The preload on the screw and nut position have a great influence on the vibration characteristics of the feed drive as two very important operational conditions. Rotational acceleration of the screw also affects the performance of the CNC feed drive when machining small parts. This paper investigates the influence of preload and nut position on the vibration characteristics of the feed drive system of a CNC metal cutting machine in order to be able to eliminate an observed resonance occurred at high rotational speeds of the screw, corresponding to high feed rates. Additionally, rational structural parameters of the feed drive system are selected in order to increase the rotational acceleration for improving the performance of the CNC machine. Experiments and analyses showed that by selecting specific parameters of feed drive system and simultaneously applying a certain value of preload, a 97% increase in rotational acceleration and 30% time reduction considering the vibration resistance at high rotational speeds can be achieved.     

Projective well orders and coanalytic witnesses

We further develop a forcing notion known as Coding with Perfect Trees and show that this poset preserves, in a strong sense, definable P-points, definable tight MAD families and definable selective independent families. As a result, we obtain a model in which $\mathfrak{a}=\mathfrak{u}=\mathfrak{i}={\mathrm{?}}_1<2^{{\mathrm{?}}_0}={\mathrm{?}}_2$, each of $\mathfrak{a}$, $\mathfrak{u}$, $\mathfrak{i}$ has a ${\mathrm{\Pi }}_1^1$ witness and there is a ${\mathrm{\Delta }}_3^1$ well-order of the reals. Note that both the complexity of the witnesses of the above combinatorial cardinal characteristics, as well as the complexity of the well-order are optimal. In addition, we show that the existence of a ${\mathrm{\Delta }}_3^1$ well-order of the reals is consistent with $\mathfrak{c}={\mathrm{?}}_2$ and each of the following: $\mathfrak{a}=\mathfrak{u}<\mathfrak{i}$, $\mathfrak{a}=\mathfrak{i}<\mathfrak{u}$, $\mathfrak{a}<\mathfrak{u}=\mathfrak{i}$, where the smaller cardinal characteristics have co-analytic witnesses.Our methods allow the preservation of only sufficiently definable witnesses, which significantly differs from other preservation results of this type.