We consider an $N$ fermion system at low temperature $T$ in which we encounter special particle number values $N_m$ exhibiting special traits. These values arise in focusing attention upon the degree of mixture (DM) of the pertinent quantum states. Given the coupling constant of the Hamiltonian, the DMs stay constant for all $N$-values, but experience sudden jumps at the $N_m$. For a quantum state described by the matrix $\rho$, its purity is expressed by $Tr \rho^2$ and then the degree of mixture is given by $1 - Tr \rho^2$, a quantity that coincides with the entropy $S_q$ for $q=2$. Thus, Tsallis entropy of index two faithfully represents the degree of mixing of a state, that is, it measures the extent to which the state departs from maximal purity . Macroscopic manifestations of the degree of mixing can be observed through various physical quantities. Our present study is closely related to properties of many-fermion systemsn that are usually manipulated at zero temperature. Here we wish to study the subject at finite temperature. Gibbs' ensemble is appealed to. Some interesting insights are thereby gained.

Prime period sequences can serve as the fundamental tool to construct arbitrary composite period sequences. This is a review study of prime period perfect Gaussian integer sequence (PGIS). When cyclic group {1,2,…,N−1} can be partitioned into k cosets, where N=kf+1 is an odd prime number, the construction of a degree-(k+1) PGIS can be derived from either matching the flat magnitude spectrum criterion or making the sequence with ideal periodic autocorrelation function (PACF). This is a systematic approach of prime period N=kf+1 PGIS construction, and is applied to construct PGISs with degrees 1, 2, 3 and 5. However, for degrees larger than 3, matching either the flat magnitude spectrum or achieving the ideal PACF encounters a great challenge of solving a system of nonlinear constraint equations. To deal with this problem, the correlation and convolution operations can be applied upon PGIS of lower degrees to generate new PGIS with degree-4 and other higher degrees, e.g., 6, 7, 10, 11, 12, 14, 20 and 21 in this paper. In this convolution based scheme, both degree and pattern of a PGIS vary and can be indeterminant, which is rather nonsystematic compared with the systematic approach. The combination of systematic and nonsystematic schemes contributes the great efficiency for constructing abundant PGISs with various degrees and patterns for the associated applications.

In this study, we focused on the eco-driving of electric vehicles (EVs). The target vehicle is an electric bus developed by our research team. Using the parameters of the bus and speed pattern optimization algorithm, we derived the EV eco-driving speed pattern. Compared to eco-driving of internal combustion engine vehicles (ICVs), we found several different characteristics. We verified these characteristics with actual vehicle driving test data of the target bus, and the results confirmed its rationality. The EV eco-driving method can improve electricity consumption by about 10% - 20% under the same average speed.

The paper presents the main experimental capabilities of the automatic system for the study of the interaction between porous media and atmosphere. This system is one of the possible variants of patent 2-241-477. The paper shows the result of a drying and wetting study of a tailings sample. The sample is 32 cm in height and 29 cm in diameter. The saturation and drying process was carried out at 26 degrees Celsius at the sample surface, an air velocity of 2 m/s and a relative humidity of 60%. The recharge applied to the column surface was 0.3 cm3/cm2/minute. The results show the effectiveness of the system in controlling the spatial-temporal variation of different physical properties of the porous medium in the vertical and surface profile. The controlled variables include volumetric water content, suction, relative humidity, sample weight variation due to recharge or drying, shrinkage, temperature, etc. The experiment shows how the tailings saturate very quickly but dry very slowly. Tailings consolidation occurs in the drying and wetting processes, being higher in the first one.

This article deals with special curves similar to those known in mathematics as Lamé curves. Their equations have a certain similarity with the equations of Lamé curves. But these curves are more like ellipses in appearance. Like ellipses, they have major and minor axes. These are such curves that their major and minor semi-axis coincide with an ellipse but are different than an ellipse. The main feature of these curves is that for any triangle whose base coincides with the axis of a given curve and the vertex is on a given curve, the condition aⁿ+bⁿ=cⁿ is obtained. The number “n” is called the degree or rank of this curve. To distinguish this group of curves, we called them Elbe curves. The equations of these lines are also provided in the paper.

To study the anti-cracking performance of cast-in-place concrete inner shaft lining structure under the combined effects of temperature and constraint, this paper first developed a novel temperature stress test machine suitable for the shape of the inner shaft lining structure and with adjustable endpoint constraint, providing specialized experimental equipment for subsequent cast-in-place concrete inner shaft lining temperature stress simulation experiments. Then, this paper preliminarily studied the temperature, strain, and stress changes of the cast-in-place inner shaft lining under the condition of 100% endpoint constraint by simulating the internal hydration heating and cooling process of the cast-in-place inner shaft lining and using the temperature stress test machine to accurately control the endpoint constraint conditions of the inner shaft lining scaled model.

A comprehensive evaluation system of rural building energy consumption from a innovative composite perspective is established, which is suitable for southwest China. the brainstorming method and Delphi method were used to establish the indicator system, the ANP method was applied to calculate the weights of the comprehensive evaluation model, the scoring criteria of all evaluation indexes are constructed based on fuzzy evaluation theory, the applicability of the model is verified by an example of the countryside around Chengdu. The results showed that the score of some factors is low, whole or part area, just like the percentage of clean energy use(C24), the thermal performance of external walls(E21), the implementation of energy-saving measures(S22), were key factors affecting the target level, which has greater potential for improvement. The distribution of comprehensive indicators and evaluation factors have certain spatial distribution characteristics, the overall spatial distribution shows the characterwastic of "high in the southeast and low in the northwest". The key factors and spatial distribution characteristics found can be used as an important basis for the improvement of green energy-saving promotion measures, energy-saving retrofit programmes were proposed in terms of additional solar room, energy-saving of external walls and air-conditioning temperature setting guidance.

In recent years, there has been a wave of research on complex networks. The purpose of this paper is to study the graph theoretic mathematical properties of random cyclooctatetraene chain. We obtain the explicit analytical expressions for the variances of the Gutman index, Schultz index, multiplicative degree-Kirchhoff index and additive degree-Kirchhoff index of a random cyclooctatetraene chain with $n$ octagons, which plays a crucial role in the research and application of topological indices.

Ultralight power generation equipment has high requirements for the power density, continuous operation, and transient stability of the whole machine, and there is a direct conflict between high power density design and substantial stability control in the power unit design. In order to meet the power density requirements of ultra-light power stations, three main problems need to be solved, namely engine speed oscillation and flameout in the process of load power mutation, matching of the generator and engine torque, and stabilizing the voltage waveform of the AC output end. In this paper, we proposed an exquisite control strategy for ultralight power generation systems in engines, generators, and inverters. The effectiveness and practicability of the proposed strategy are verified by both simulation and experiment. The results show that the proposed control strategy can effectively solve the instability problem of the ultralights generator set and improve the stability of the system, where the response recovery can be achieved within 0.9 seconds under the condition of total load increase or decrease, and the mismatching degree of the generator following the engine is reduced by 90%. The strategy could also guarantee long-term stable operation with high-quality electrical energy output.

UN Convention on Climate Change 2015 mandates reducing carbon footprint to reduce global warming. Considering environmental concerns, Electric Vehicles (EVs) spearhead the move towards green mobility. Niti Aayog (Indian Government) has envisaged an “EV only” scenario by 2030. Two wheelers dominate the Indian automobile industry with almost 80% market share. With the transportation sector accounting for 70% of world’s fossil fuels use, the need for a sustainable supply chain which addresses environment, economy and societal issues, has, of late, aroused interest in the business academic community and industries. Sustainability in business decision-making promotes efficiency, controls expenditure, enhances customer delight, increases sales and market share, optimises risk management strategy, and promotes profitability. This study intends to develop a conceptual framework after examining research gaps in sustainable supply chain management (SSCM) and allied topics like sustainability, green supply chain management, and vendor partnerships through collaborative efforts. Even the UN vide Goal 9 of sustainable goals pertaining to industry, highlights the importance of this framework.

The accompanying mechanical behavior during the flow of ore-rock dispersion is an important factor leading to the instability and failure of the orepass in the ore storage section. It is of great significance to accurately understand the instability characteristics of the well wall in the ore section, during the ore drawing process by understanding the flow characteristics and internal mechanical transfer mechanism of ore-rock dispersion. Using the discrete element method to analyze the flow characteristics, contact compactness, stress distribution characteristics and contact force probability distribution of the ore-rock dispersion, it realizes the quantitative characterization of the damage degree of ore-rock flow, and reveals the damage mechanism of mine storage wall. The results show that: (1) The friction between ore-rock particles, between ore-rock and well wall is an important reason for the change of the macroscopic flow form of ore-rock from “one” to “V” type. (2) The compactness and stress concentration of ores are increasing with the increase of storage depth, which is shown that with the increase of storage depth, the greater the probability of well wall instability. (3) The probability distribution of contact force strength between particles decreases exponentially in the whole process of ore drawing, in which the strong chain plays a major role in the stability of the dispersion system. (4) The number of overpressure and the overpressure coefficient can be used to quantitatively characterize the wall damage degree under the action of ore-rock flow. The dynamic side pressure decreases periodically in the form of exponential fluctuations, and the dynamic load formed by the ore-rock flow mainly played a role in the lower area of the ore storage section.

The notion of Critical Point Theory has extensive application in the filed of Partial Differential Equations, one of which is studying the existence and commenting on the uniqueness and multiplicity (in case when the solution is not unique) of weak solutions to Elliptic PDEs under certain boundary conditions.\par This article provides a brief survey about specific concepts like : differentiation on Banach Spaces, maxima and minima and its applications to PDEs. Furthermore, we've discussed the notion of defining a weak topology on Banach Spaces, before introducing the Variational Principle and its applications.\par The epilogue of the article primarily deals with results which studies the existence of weak solutions to Dirichlet Boundary Value Problems under specific conditions. The most notable aspect of this article is the proof of \textit{Rabinowitz's Saddle Point Theorem} using the method of \textit{Brouwer Degree}. Readers who are highly motivated in pursuing research in any of the topics relevent to the contents of this paper will surely find the \texttt{References} section to be extremely resourceful.

In 2023, residential and commercial sectors together consumed approximately 27.6% of total U.S. energy, equivalent to about 20.6 quadrillion Btu. Factoring in the electrical system energy losses, the residential sector represented approximately 19.7% of total U.S. energy consumption during that time. There were approximately 144 million housing units in the United States in 2023, which is increasing yearly. In this study, information on energy usage in the United States (U.S.) residential sector has been analyzed and then represented as energy intensities to establish benchmark data and to compare energy consumption of varying sizes and locations. First, public sources were identified, and data from these previously published sources were aggregated to determine the energy use of the residential sector within the US. Next, as part of this study, the energy data for seven houses/apartments from five different United States climate zones were collected firsthand. That data was analyzed, and the energy intensity of each home was calculated and then compared with the energy intensities of the other homes in the same states using RECS data. The energy intensity for each facility was calculated based on the actual energy bills. Finally, the study evaluated the carbon footprint associated with residential energy consumption in all 50 states to reinforce the importance of sustainable development initiatives.

China’s leading development of a complete battery value chain for Electric Vehicles (EV) is restructuring the global automotive sector. The competitive advantage of China's EV battery industry lies on its firms’ core competency and political economic geography. Based on first-hand empirical material and data obtained from years of fieldwork in an EV battery cluster in South China, this paper identifies what the Chinese EV battery industry’s core competency is and details how it is built up from below. The current core competency of Chinese battery firms is their mass manufacturing capability to supply lithium-ion batteries vehicle manufacturers (OEMs) with stable and consistent quality as well as competitive prices. This competency is acquired by firms through technological learning at workshop level while taking use of their experiences accumulated in mass production of batteries for consumer electronics sectors. Furthermore, the rapid learning and accumulation of knowledge on battery manufacturing at large scale is also facilitated by the industrial cluster environment where firms are embedded. Supported and promoted by local government policies, Chinese EV battery clusters are composed of firms from different segments of a complete battery value chain. The findings illuminate the likely strategic strengths, weaknesses, and futures of the Chinese EV battery industry in global competition.

According to the requirement of 20kg load of casting barrel, we design a three-dimensional model of the robot and analyze the three stages of liquid level change in the casting barrel during the casting process. Through the analysis, it is determined that the time and angle function is an implicit function, and it is impossible to find the analytical expression of time about angle. The kinetic function of the casting barrel is simulated by MATLAB, and it is found that the function image has mutation points, and when the original function is fitted and approximated by fifth-degree polynomial interpolation, the fifth-degree polynomial function image of the time versus the angular acceleration has a large amplitude of oscillation, especially the mutation points. A PID algorithm based on the discretization of the time and acceleration function is introduced for correction, and the results show that this method effectively reduces the oscillation amplitude of the image and improves the coincidence with the original function.

In recent years, the potential of insects has been explored as a sustainable protein alternative to sustain the growing world population. Differences in the way insects are processed can affect their proximate composition and digestibility. This work studies the effects of the combination of different types of slaughter methods and drying temperatures on the proximate composition, organic matter digestibility (OMd), hydrolysis degree (DH/NH2 and DH/100 g DM), total hydrolysis (TH) and hygienic sanitary study of BSFL (black soldier fly larvae). Four types of slaughter methods were used: frozen (F), blanched + frozen (B), Melacide® + frozen (M) and liquid nitrogen (N), each with three drying temperatures (50, 70 and 90 °C). A negative correlation between acid detergent fibre (ADF) and protein digestibility parameters was obtained. 70 °C was the most suitable drying temperature, as it reported higher values of protein digestibility (DH, TH), resulting in hygienic and sanitary conditions suitable for food use. Slaughtering with liquid nitrogen and blanching were more convenient than traditional freezing or the use of Melacide® to achieve higher protein digestibility results.

This study provides a comprehensive analysis of global patent trends in battery recycling, focusing on secondary batteries and related technologies across Korea, China, and the United States. The data, collected from various patent databases, was quantitatively analyzed to identify technology trends and direct future development. The analysis reveals distinct emphases on technologies such as lithium-ion and waste battery recycling, highlighting notable differences in patent activities among key companies and countries. China's large number of patents in battery manufacturing processes contrasts with the USA's focus on electrochemical cell construction and storage systems, while Korea shows significant activity in waste battery technology. The study underscores the competitive landscape and innovation efforts in the battery recycling sector, providing insights into the technological focuses and priorities of each country. It also identifies key challenges, such as the need for consistent innovation and broader geographic coverage in Korea, enhancing patent influence and international presence in China, and ensuring high patent quality and fostering innovation in lagging sectors in the United States. Addressing these challenges through enhanced collaboration, increased R&D investments, and supportive policies is crucial for strengthening the global position and driving further innovation in the battery recycling sector.