Exponential Functional Equation Research Articles

Adaptive Quick Sliding Mode Reaching Law and Disturbance Observer for Robust PMSM Control Systems

The permanent magnet synchronous motor (PMSM) has been of interest to eco-friendly industries on account of its advantages such as high performance, efficiency, and precision control. However, perturbations due to PMSM parameter uncertainty, load torque, and external disturbance interfere with the construction of PMSM precision control systems. Therefore, a robust control system is needed to avoid unnecessary system movement caused by perturbations. In this paper, sliding mode control (SMC) is adopted to implement a robust control system for the PMSM. In order to reduce the reaching time from the initial system state to the sliding surface and the chattering phenomenon that can cause the system to malfunction, the adaptive quick sliding mode reaching law based on an exponential function and power equation is proposed. Although the SMC is robust to disturbance and parameter uncertainty, unexpected disturbances can destabilize the system. To estimate the unmatched disturbance in a short time, the second-order fast terminal sliding mode observer (SFTSMO) is proposed. The results show that the motor control system based on the proposed method has a fast convergence speed to an objective value, position tracking performance, and robustness.

Exploring the inhibitory effect of H2O on CO2/CH4 adsorption in coal: Insights from experimental and simulation approaches

To investigate the inhibitory effect of H2O on the adsorption of CH4/CO2 in coal, the anthracite was selected for physical adsorption experiments on CH4/CO2 gases in this study. Combined with Materials Studio software, the effect of moisture on the isothermal adsorption characteristics of CH4/CO2 in coal was investigated by using density functional theory and giant canonical Monte Carlo simulation. The intermolecular interaction energies were obtained, as well as the effects of electrostatic potentials, adsorption sites, and hydrogen bonding of oxygen-containing functional groups. The results show that: ①According to the CH4/CO2 isothermal adsorption experiments, it was found that moisture significantly inhibited the adsorption of CH4/CO2 by coal. For CH4, the relationship between adsorption constants a/b and moisture content can be expressed by the equations y = 43.447-3.348x and y = 3.225-0.751x. For CO2, adsorption constant a follows a power function relationship with moisture content, expressed as y = 29.114x-0.063, while adsorption constant b is represented by the polynomial fitting equation y = 1.672+0.508x+0.083x2. ② The findings have revealed correlations between the moisture influence coefficient and moisture content. The exponential functional equation η = exp(-0.188ω) was found to be more accurate for coal adsorbing CH4, whereas the linear functional equation η = 1/(1 + 0.243ω) was considered more appropriate for CO2. ③ The van der Waals and electrostatic energies between coal and CH4/CO2 decreased with an increase in moisture content, whereas the van der Waals and electrostatic energies between coal and H2O increased. ④ The orders of hydrogen bond formation ability between CH4/CO2 and functional groups were as follows: –CHO > –COOH > –OH > –CH3 and –OH > –COOH > –CHO > –CH3. The ability of H2O to form hydrogen bonds with –COOH, –OH, –CHO, and –CH3 is as follows: –COOH > –OH > –CHO> –CH3. This study provides a theoretical basis for the integrated use of hydraulic fracturing techniques and coalbed gas injection and replacement.

Modeling of gas emission in coal mine excavation workface: a new insight into the prediction model.

Coalbed methane (CBM) is a clean energy source, but its utilization is inefficient due to the complexity and low accuracy of its emission prediction model. In this research, we constructed a mathematical model of gas emission from the excavation workface, and combined the experimental results to propose a new model for accurate and concise prediction. The new model was validated in the field workface and compared with the traditional prediction model. Moreover, the sensitivity of gas emission parameters and the participation ratio of gas emission sources were analyzed. The study results show that the new model has higher calculation accuracy than the old model prediction, with an average error reduction of 4.693%. In the excavation workface, the coal fall gas emission conforms to the negative power function equation, and the coal wall gas emission conforms to the negative exponential function equation. In the early stage of excavation, the proportion of coal fall gas emission is higher than that of coal wall gas emission, and the peak proportion reaches 58.5%. In the later stage, the proportion of coal fall gas emission gradually decreases to below 30%. The order of the sensitivity of gas emission parameters is coal wall gas initial velocity > coal fall gas decay coefficient > coal fall gas initial velocity > coal wall gas decay coefficient. The new model is successfully applied in engineering, which helps to improve the efficiency of coal mine gas disaster control and utilization.

PCNs, PCBs, and PCDD/Fs in Soil around a Cement Kiln Co-Processing Municipal Wastes in Northwestern China: Levels, Distribution, and Potential Human Health Risks.

To evaluate the impact of the first cement kiln co-processing municipal wastes in northwest China on the surrounding environment, the concentrations of polychlorinated naphthalenes (PCNs), polychlorinated biphenyls (PCBs), and polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs) were determined in 17 soil samples collected around the plant. The concentration ranges of PCNs, PCBs, and PCDD/Fs were 132–1288, 10.8–59.5, and 2.50–5.95 pg/g, and the ranges of toxic equivalents (TEQ) were 1.98–20.8, 2.36–48.0, and 73.2–418 fg/g, respectively. The concentrations of PCNs, PCBs, and PCDD/Fs in this study were generally lower than those in soil around municipal waste incinerators and industrial parks in other areas. An exponential function equation was applied for the relationship between the concentration of the target compounds and the distance from the cement kiln stack, the results showed that PCN and PCB concentrations declined with the increasing of distance from the stack. Furthermore, it was found that the effect of the cement kiln on surrounding soil contaminations with PCNs and PCBs was stronger than that of PCDD/Fs by comparing the PCN, PCB, and PCDD/F homologue profiles in the fly ash sample from the plant and soil samples at different distances. The total carcinogenic risks (CR) of PCNs, PCBs, and PCDD/Fs for children and adults in soil were 1.65 × 10−8–8.93 × 10−8 and 1.70 × 10−8–9.16 × 10−8, respectively, which was less than the risk threshold (CR = 1 × 10−6), and there was no health risk.

内蒙古东北段森林衰退现状及种群竞争对其生长的影响

PDF HTML阅读 XML下载 导出引用 引用提醒 内蒙古东北段森林衰退现状及种群竞争对其生长的影响 DOI: 10.5846/stxb202106101549 作者: 作者单位: 作者简介: 通讯作者: 中图分类号: 基金项目: 内蒙古自治区科技重大专项（2021ZD0011）；国家自然科学基金委优秀青年科学基金项目（41922001）；国家自然科学基金面上项目（4217010260） The status quo of forest decline and the impact of population competition on its growth in the northeast of the Inner Mongolia Author: Affiliation: Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:随着气候变化加剧，中国半干旱区东段发现大量森林衰退现象，威胁到社会生产和环境保护的可持续发展。种群竞争是森林动态的内在驱动因子，当前对该区域森林种群竞争与森林衰退关系的研究尚缺乏足够的依据。选取内蒙古大兴安岭典型森林作为研究对象，依据Hegyi单木竞争指数模型计算个体水平上和样地水平上的竞争指数，利用树木个体树轮指数(TRI)年表作为个体水平上的衰退指标，利用样地年表(TRI)和胸高断面积增量(BAI)来分析样地水平上的衰退指标，探讨不同尺度上森林衰退状况。探讨个体水平上和样地水平上竞争指数与不同尺度上森林衰退指标之间的关系，分析研究区森林衰退的内因特征。主要结论如下：第一，样地年表与树木个体年表所指示的衰退时段基本一致，结合两者的重合结果，可以得出各样地的衰退年份。不同样地的生长衰退时段有重合的现象，个体年表中超过阈值50%的样地的严重衰退时期年份基本在2001-2005年间，而在样地年表中，样地五岔沟林场(L-WCG1)、五岔沟林场大样地(L-WCG2)、乌尔根(L-WRG)在1989年至1997年都出现生长衰退，样地军达盖林场(L-HDG)、L-WCG1、L-WCG2、L-WRG和s根河(L-GH1)衰退重合期在1998-2003年期间。这是由于这一阶段研究区发生了大规模的干旱事件，导致不同地点的树木生长都受到抑制。第二，各样地中树木个体的五年平均相对胸高断面积增量(rBAI5)与个体竞争指数相关的显著性最高，两者的关系可用指数函数方程表达，即rBAI5随着个体水平竞争指数的上升而下降。这说明了竞争指数对于树木生长存在显著的影响。而样地竞争指数与近2年、5年和10年内样地胸高断面积均值(BAI2、BAI5、BAI10)之间的关系不明显。从种群竞争方面研究中国半干旱区东段的森林衰退影响因素，旨在为森林衰退机理研究提供依据，为半干旱区森林资源可持续发展提供支持。 Abstract:The ecosystem service values and functions of forests are important in the semi-arid region of eastern China. With the increasing of climate change and the degradation of the aridification, forest declines have been monitored in the region in recent years. It eventually changed the species composition, nutrient cycling and biomass accumulation cycle of the ecosystem, and then affected the forest regeneration and structure, caused disturbance to the service function and biodiversity of the forest ecosystem and to a certain extent threatened the human society, culture and ecological function, and promoted the sustainable development of social production and environmental protection. Population competition is an intrinsic driving factor of forest dynamics. But there is still lack of evidences on the relationships between population competitions and forest decline in the area. Using typical forest types in Daxing'anling, the Inner Mongolia as cases, a suitable competition index model was used to analyze the competition status at both individual and population levels; then individual tree chronology (TRI) was selected as an indicator of individual growth reduction; Plot chronology and basal area increment (BAI) were applied to assess forest decline at the plot level. After that, the relationships between the competition indices and the forest decline indicators at different levels were analyzed. Results indicated that the chronology of the plot was basically same as the decay period indicated by the individual chronology of the tree. The decay period of each plot could be concluded by combining the coincidence results. There was also a coincidence between periods of growth decline in different plots. At the individual chronology, most plots had similar periods of 2000-2005, with serious decline over the threshold defined by that the percentage of trees with growth decline exceeding 50%. At the plot chronology, plots L-WCG1, L-WCG2, and L-WRG had the same period of growth decline from 1989 to 1997, and plots L-HDG, L-WCG1, L-WCG2, L-WRG and L-GH1 had the same periods of growth decline from 1998 to 2003. The reason may be that the serious drought events appeared in the stage, causing the growth of trees to be inhibited at a large scale. The individual five-year averagely relative basal area increment (rBAI5) in each plot had the highest correlation with the individual competition index. The relationship between the two can be expressed by an exponential function equation through trend fitting. That is, rBAI5 decreased as the individual level competition index increased. Thus the individual competition index had a significant impact on the growth of trees in five years. The relationships between the competition index at plot level and the mean values of the basal area increment in recent two, five and ten years (BAI2, BAI5 and BAI10) were insignificant. The research explored the factors of forest decline in semi-arid area of eastern China from the perspective of population competition. It aims at providing bases for the analyses of the driving mechanism of forest decline and the sustainable development of forest resources in semi-arid area. 参考文献 相似文献 引证文献

On superstability of exponential functional equations

The aim of this paper is to prove the superstability of the following functional equations: \t\t\tf(P(x,y))=g(x)h(y),f(x+y)=g(x)h(y).\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document} $$\\begin{aligned}& f \\bigl(P(x,y) \\bigr)= g(x)h(y), \\\\& f(x+y)=g(x)h(y). \\end{aligned}$$ \\end{document}

Alienation of Drygas’ and Cauchy’s Functional Equations

Abstract Inspired by the papers [2, 10] we will study, on 2-divisible groups that need not be abelian, the alienation problem between Drygas’ and the exponential Cauchy functional equations, which is expressed by the equation f ( x + y ) + g ( x + y ) g ( x - y ) = f ( x ) f ( y ) + 2 g ( x ) + g ( y ) + g ( - y ) . f\left( {x + y} \right) + g\left( {x + y} \right)g\left( {x - y} \right) = f\left( x \right)f\left( y \right) + 2g\left( x \right) + g\left( y \right) + g\left( { - y} \right). We also consider an analogous problem for Drygas’ and the additive Cauchy functional equations as well as for Drygas’ and the logarithmic Cauchy functional equations. Interesting consequences of these results are presented.

A Theoretical Study on the Macrocyclic Strain of Zigzag Molecular Belts

Zigzag molecular belts have captured the imagination of scientists for over a half century because of their aesthetically appealing structures and tantalizing properties. One of the formidable challenges in synthesis is to circumvent the energy accumulated in the construction of strained structures. Reported herein is our theoretical study to quantify the molecular strain energies. A general exponential function equation E strain = a·n·e −n/b was obtained to estimate strain energies of both conjugated and partially hydrogenated hydrocarbon belts and their heteroatom-embedded analogs. The deformation of aromatic rings from planarity was revealed to contribute dominantly to the high strain energies. The method enabled the convenient quantification of the energetics of aromatization processes from partially hydrogenated double-stranded macrocycles, and facilitated the design and optimization of practical routes to synthesize the long-awaited zigzag molecular belts.

Catalytic Steam Reforming of Bio-Oil-Derived Acetic Acid over CeO2-ZnO Supported Ni Nanoparticle Catalysts.

The steam reforming of bio-oil-derived acetic acid over the developed Ni/CeO2-ZnO nanoparticle catalysts for hydrogen production was studied. The correlations of CeO2 to ZnO mass ratio (CZMR) and nickel loading with the properties and performances of Ni/CeO2-ZnO catalysts were explored. The H2, CO, and potential H2 yields followed a Gaussian normal distribution with increasing the CZMR. An exponential function equation was established to correlate the H2, CO, and potential H2 yields with Ni loading. As the CZMR increased from 0 to 1/3, the H2 yield increased from 57.8 to 69.4%, with a growth rate of 20.1%. Further, on increasing the CZMR from 1/3 to 3, the H2 yield decreased by 37.6%. The CO yield showed a similar trend for the H2 yield on increasing the CZMR, which first increased to a peak value, then started to decrease rapidly and finally stabilized. The yield of H2 increased significantly from 20.6 to 73.5%, with the increase of nickel loading from 0 to 15%. Further, on increasing the nickel loading from 15 to 25%, the H2 yield increased by only 5.8%. With the CZMR of 1/3 and the nickel loading of 15%, the selectivities of H2 and CO were as high as 91.6 and 42.3%, respectively.

Low-cycle fatigue behavior of 7075-T6 aluminum alloy at different strain amplitudes

Low-cycle fatigue (LCF) life and failure mechanism of 7075-T6 high strength aluminum alloys were investigated under MTS 809. The cycling stress response and the cyclic stress—strain relationships under different strain amplitudes were investigated. Using Manson-Coffin law, the three parameter exponential function equation and the damage function model of tensile hysteresis energy (Ostergren equation), the regression analysis of LCF test data was carried out, it was found that the fatigue life prediction results of the three parameter exponential function equation were better than the other two life prediction methods in terms of statistical analysis methods of standard deviation and dispersion band. Analysis of microstructure and fatigue failure fracture revealed that fatigue crack initiated at the interface of precipitations and α-phase aluminium substrate in surface or near surface of the sample.

Mechanical and electrical properties of coarse-grained soil affected by cyclic freeze-thaw in high cold regions

To evaluate the geotechnical properties of coarse-grained soil affected by cyclic freeze-thaw, the electrical resistivity and mechanical tests are conducted. The soil specimens are prepared under different water contents, dry densities and exposed to 0-20 freeze-thaw cycles. As a result, the stress-strain behavior of the specimen (w =14.0% and ρd=1.90 g/cm3) changes from strain-hardening into strain-softening due to the freeze-thaw effect. The electrical resistivity of test specimen increases with the freeze-thaw cycles change, but the mechanical parameters (the unconfined compressive strength qu and the deformation modulus E) and brittleness index decrease considerably at the same conditions. All of them tend to be stable after 7−9 cycles. Moreover, both the dry density and the water content have reciprocal effects on the freeze-thaw actions. The failure and pore characteristics of specimens affected by freeze-thaw cycles are discussed by using the image analysis method. Then, an exponential function equation is developed to assess the electrical resistivity of specimens affected by the cyclic freeze-thaw. Linear relations between the mechanical parameters and the electrical resistivity of specimens are established to evaluate the geotechnical properties of the soil exposed to freeze-thaw actions through the corresponding electrical resistivity.

GENERAL STABILITY OF THE EXPONENTIAL AND LOBAČEVSKIǏ FUNCTIONAL EQUATIONS

Let $S$ be a semigroup possibly with no identity and $f:S\rightarrow \mathbb{C}$. We consider the general superstability of the exponential functional equation with a perturbation $\unicode[STIX]{x1D713}$ of mixed variables $$\begin{eqnarray}\displaystyle |f(x+y)-f(x)f(y)|\leq \unicode[STIX]{x1D713}(x,y)\quad \text{for all }x,y\in S. & & \displaystyle \nonumber\end{eqnarray}$$ In particular, if $S$ is a uniquely $2$-divisible semigroup with an identity, we obtain the general superstability of Lobačevskiǐ’s functional equation with perturbation $\unicode[STIX]{x1D713}$$$\begin{eqnarray}\displaystyle \biggl|f\biggl(\frac{x+y}{2}\biggr)^{2}-f(x)f(y)\biggr|\leq \unicode[STIX]{x1D713}(x,y)\quad \text{for all }x,y\in S. & & \displaystyle \nonumber\end{eqnarray}$$

Microstructural evolution of Mg, Ag and Zn micro-alloyed Al–Cu–Li alloy during homogenization

The microstructural evolution of a Mg, Ag and Zn micro-alloyed Al–3.8Cu–1.28Li (mass fraction, %) alloy ingot during two-step homogenization was examined in detail by optical microscopy (OM), differential scanning calorimetry (DSC), electron probe micro-analysis (EPMA) and X-ray diffraction (XRD) methods. The results show that severe dendritic segregation exists in the as-cast ingot. There are many secondary phases, including TB (Al7Cu4Li), θ(Al2Cu), R(Al5CuLi3) and S(Al2CuMg) phases, and a small amount of (Mg+Ag+Zn)-containing and AlCuFeMn phases. The fractions of intermetallic phases decrease sharply after 2 h of second-step homogenization. By prolonging the second-step homogenization time, the TB, θ, R, S and (Mg+Ag+Zn)-containing phases completely dissolve into the matrix. The dendritic segregation is eliminated, and the homogenization kinetics can be described by a constitutive equation in exponential function. However, it seems that the AlCuFeMn phase is separated into Al7Cu2Fe and AlCuMn phases, and the size of Al7Cu2Fe phase exhibits nearly no change when the second-step homogenization time is longer than 2 h.

Alienation of the logarithmic and exponential functional equations

We study the logarithmic–exponential functional equation and check whether the alienation phenomenon takes place.

Superstability of the functional equation with a cocycle related to distance measures

In this paper, we obtain the superstability of the functional equation f(pr,qs)+f(ps,qr)=θ(pq,rs)f(p,q)f(r,s) for all p,q,r,s∈G, where G is an Abelian group, f a functional on G 2 , and θ a cocycle on G 2 . This functional equation is a generalized form of the functional equation f(pr,qs)+f(ps,qr)=f(p,q)f(r,s), which arises in the characterization of symmetrically compositive sum-form distance measures, and as products of some multiplicative functions. In reduction, they can be represented as exponential functional equations. Also we investigate the superstability with following functional equations: f(pr,qs)+f(ps,qr)=θ(pq,rs)f(p,q)g(r,s), f(pr,qs)+f(ps,qr)=θ(pq,rs)g(p,q)f(r,s), f(pr,qs)+f(ps,qr)=θ(pq,rs)g(p,q)g(r,s), f(pr,qs)+f(ps,qr)=θ(pq,rs)g(p,q)h(r,s).MSC:39B82, 39B52.

Microstructural Evolution of High Purity Al-Cu-Mg Alloy during Homogenization

The microstructure, composition distribution and phase evolution of a high-purity Al-Cu-Mg alloy under homogenization were investigated by optical microscopy (OM), scanning electron microscopy (SEM), energy dispersive spectrometry (EDS) and differential scanning calorimeter (DSC). The results show that severe dendritic segregation exists in Al-Cu-Mg alloy ingot. There are a lot of eutectic phases at grain boundary and the primary phases at grain boundary are Al2Cu and Al2CuMg. The primary phases dissolve into the matrix gradually during homogenization with increasing temperature and holding time, which can be described by a constitutive equation in exponential function. The optimum parameter of homogenization is 500°C for 18 h, which is consistent with the result of homogenization kinetic analysis.

Concentration and distribution of PCNs in ambient soil of a municipal solid waste incinerator

The impact of a typical municipal solid waste incinerator (MSWI) on polychlorinated naphthalene (PCN) concentrations in surrounding soil was studied. We collected 6 stack gas samples from the MSWI and 21 soil samples from sampling sites at distances of between 300 and 1700m from the MSWI stack. Total dl-PCN (dioxin-like PCN) concentrations in the stack gas samples ranged from 6898 and 89,032pgm−3, with a mean value of 36,241pgm−3. The total dl-PCN concentrations in the soil samples ranged from 30.35 to 280.9pgg−1, with a mean value of 87.03 and a median value of 70.32pgg−1, while the TEQ values were between 7.7 and 130.2fg TEQ g−1, with a mean value of 41.12fg TEQ g−1 and a median value of 31.52fg TEQ g−1. The PCN homologue patterns and the results of Principal Component Analysis suggested that the MSWI may be a source of PCNs in the soils. A contour map, created using an ordinary Kriging interpolation technique, showed that a limited area (≤1000m radius) surrounding the MSWI was influenced by the emissions from the MSWI. Furthermore, an exponential function equation was proposed to quantify the relationship between TEQs of PCNs and the distance from the stack.

Stability of the Exponential Functional Equation in Riesz Algebras

We deal with the stability of the exponential Cauchy functional equationF(x+y)=F(x)F(y)in the class of functionsF:G→Lmapping a group (G, +) into a Riesz algebraL. The main aim of this paper is to prove that the exponential Cauchy functional equation is stable in the sense of Hyers-Ulam and is not superstable in the sense of Baker. To prove the stability we use the Yosida Spectral Representation Theorem.

Stability of Exponential Functional Equations with Involutions

LetSbe a commutative semigroup if not otherwise specified andf:S→ℝ. In this paper we consider the stability of exponential functional equations|f(x+σ(y))-g(x)f(y)|≤ϕ(x)or ϕ(y),|f(x+σ(y))-f(x)g(y)|≤ϕ(x)orϕ(y)for allx,y∈Sand whereσ:S→Sis an involution. As main results we investigate bounded and unbounded functions satisfying the above inequalities. As consequences of our results we obtain the Ulam-Hyers stability of functional equations (Chung and Chang (in press); Chávez and Sahoo (2011); Houston and Sahoo (2008); Jung and Bae (2003)) and a generalized result of Albert and Baker (1982).

Microstructural evolution during homogenization of Al-Cu-Li-Mn-Zr-Ti alloy

The microstructure evolution of Al-Cu-Li-Mn-Zr-Ti alloy during homogenization was investigated by optical microscopy (OM), scanning electron microscopy (SEM), energy dispersive X-ray spectrometry (EDX), and differential scanning calorimeter (DSC) methods. The results show that severe dendritic segregation exists in the experimental alloy ingot. Numerous eutectic phases can be observed in the grain boundary, and the distribution of the main elements along the interdendritic region varies periodically. The main secondary phase is Al2Cu. The overburnt temperature of the alloy is 520 °C. The second phases are gradually dissolved into the matrix, and the grain boundaries become spare and thin during homogenization with increasing temperature or prolonging holding time. Homogenization can be described by a constitutive equation in exponential function. The suitable homogenization treatment for the alloy is (510 °C, 18 h), which agrees well with the results of homogenization kinetic analysis.