Exponent Equation Research Articles

Analysis of Student Ability Solving Hots Problems Material Exponent Equation Reviewed From's Beginning Ability

This study aims to describe the ability of high school students in solving HOTS-type questions in terms of initial abilities. The research method used in this research is descriptive qualitative. The subjects of this study were three students of class X consisting of 1 high-ability student, 1 medium-ability student, and 1 low-ability student. Collecting data or information in this study using written tests and interviews. The written test was conducted twice, namely the initial ability test and the problem-solving test. The instrument used was a validated test and interview guide. The result of this study is that students who have high abilities turn out to have similarities with students who have moderate abilities, which are only able to solve problem number 1 with an analytical level (C4) even though they use different methods of solving. While students who have low abilities are not able to respond to the three questions correctly. In general, the ability of SMA Negeri 1 Baureno students in solving HOTS category questions is still below average. This is because they are not used to working on HOTS category questions at school. So far, teachers only give ordinary questions found in textbooks or worksheets.

Temperature-dependent photoluminescence of r-GeO2 film deposited on r-plane sapphire by synchrotron radiation excitation

Germanium oxide (GeO2) film has been directly deposited on r-plane sapphire substrate by pulsed laser deposition. Firstly, the structure, surface morphology, and optical properties of the film have been systematically investigated by means of X-ray photoelectron spectroscopy, X-ray diffraction, Raman scattering, and atomic force microscope. The measurements results suggest that the deposited pure GeO2 film has the rutile structure with a (101) orientation. Subsequently, temperature-dependent photoluminescence was detailedly investigated by synchrotron radiation excitation. Photoluminescence spectrum at 30 K exhibits a broad blue–green emission band, which can be divided into three emission peaks at about 3.0 eV (∼415 nm), 2.7 eV (∼455 nm), and 2.4 eV (∼514 nm). As the temperature increases, these defect-related emissions experience strong thermal quenching and distinct red-shift. The variation of emission intensity and wavelength with the temperature follows the exponent equation and Bose-Einstein expression, respectively. These experimental data will provide reliable guiding value for developing r-GeO2 material.

Existence of solutions for a double-phase variable exponent equation without the Ambrosetti-Rabinowitz condition

Abstract The article deals with the existence of a pair of nontrivial nonnegative and nonpositive solutions for a nonlinear weighted quasilinear equation in R N {{\mathbb{R}}}^{N} , which involves a double-phase general variable exponent elliptic operator A {\bf{A}} . More precisely, A {\bf{A}} has behaviors like ∣ ξ ∣ q ( x ) − 2 ξ {| \xi | }^{q\left(x)-2}\xi if ∣ ξ ∣ | \xi | is small and like ∣ ξ ∣ p ( x ) − 2 ξ {| \xi | }^{p\left(x)-2}\xi if ∣ ξ ∣ | \xi | is large. Existence is proved by the Cerami condition instead of the classical Palais-Smale condition, so that the nonlinear term f ( x , u ) f\left(x,u) does not necessarily have to satisfy the Ambrosetti-Rabinowitz condition.

Exponent equations in HNN-extensions

We consider exponent equations in finitely generated groups. These are equations, where the variables appear as exponents of group elements and take values from the natural numbers. Solvability of such (systems of) equations has been intensively studied for various classes of groups in recent years. In many cases, it turns out that the set of all solutions on an exponent equation is a semilinear set that can be constructed effectively. Such groups are called knapsack semilinear. Examples of knapsack semilinear groups are hyperbolic groups, virtually special groups, co-context-free groups and free solvable groups. Moreover, knapsack semilinearity is preserved by many group theoretic constructions, e.g., finite extensions, graph products, wreath products, amalgamated free products with finite amalgamated subgroups, and HNN-extensions with finite associated subgroups. On the other hand, arbitrary HNN-extensions do not preserve knapsack semilinearity. In this paper, we consider the knapsack semilinearity of HNN-extensions, where the stable letter $t$ acts trivially by conjugation on the associated subgroup $A$ of the base group $G$. We show that under some additional technical conditions, knapsack semilinearity transfers from base group $G$ to the HNN-extension $H$. These additional technical conditions are satisfied in many cases, e.g., when $A$ is a centralizer in $G$ or $A$ is a quasiconvex subgroup of the hyperbolic group $G$.

Exponent equations in HNN-extensions

We consider exponent equations in finitely generated groups. These are equations, where the variables appear as exponents of group elements and take values from the natural numbers. Solvability of such (systems of) equations has been intensively studied for various classes of groups in recent years. In many cases, it turns out that the set of all solutions on an exponent equation is a semilinear set that can be constructed effectively. Such groups are called knapsack semilinear. Examples of knapsack semilinear groups are hyperbolic groups, virtually special groups, co-context-free groups and free solvable groups. Moreover, knapsack semilinearity is preserved by many group theoretic constructions, e.g., finite extensions, graph products, wreath products, amalgamated free products with finite amalgamated subgroups, and HNN-extensions with finite associated subgroups. On the other hand, arbitrary HNN-extensions do not preserve knapsack semilinearity. In this paper, we consider the knapsack semilinearity of HNN-extensions, where the stable letter $t$ acts trivially by conjugation on the associated subgroup $A$ of the base group $G$. We show that under some additional technical conditions, knapsack semilinearity transfers from base group $G$ to the HNN-extension $H$. These additional technical conditions are satisfied in many cases, e.g., when $A$ is a centralizer in $G$ or $A$ is a quasiconvex subgroup of the hyperbolic group $G$.

Exponent equations in HNN-extensions

We consider exponent equations in finitely generated groups. These are equations, where the variables appear as exponents of group elements and take values from the natural numbers. Solvability of such (systems of) equations has been intensively studied for various classes of groups in recent years. In many cases, it turns out that the set of all solutions on an exponent equation is a semilinear set that can be constructed effectively. Such groups are called knapsack semilinear. Examples of knapsack semilinear groups are hyperbolic groups, virtually special groups, co-context-free groups and free solvable groups. Moreover, knapsack semilinearity is preserved by many group theoretic constructions, e.g., finite extensions, graph products, wreath products, amalgamated free products with finite amalgamated subgroups, and HNN-extensions with finite associated subgroups. On the other hand, arbitrary HNN-extensions do not preserve knapsack semilinearity. In this paper, we consider the knapsack semilinearity of HNN-extensions, where the stable letter $t$ acts trivially by conjugation on the associated subgroup $A$ of the base group $G$. We show that under some additional technical conditions, knapsack semilinearity transfers from base group $G$ to the HNN-extension $H$. These additional technical conditions are satisfied in many cases, e.g., when $A$ is a centralizer in $G$ or $A$ is a quasiconvex subgroup of the hyperbolic group $G$.

Asymptotic Analysis of the Mixed-Exponential Jump Diffusion Model and Its Financial Applications

Transform inversion is a popular approach to pricing many types of path-dependent options under various dynamic models. However, it is usually difficult to guarantee the accuracy due to the lack of error control, which often depends heavily on the asymptotic property of the transform function. This article characterizes the asymptotic behaviors of all the complex roots of the exponent equation under the mixed-exponential jump diffusion model (MEM), by which one can output the error bounds and achieve any pre-specified error tolerance in the transform inversion algorithm when pricing various path-dependent options under the MEM. Numerical examples indicate that the resulting transform inversion algorithm with our computable error bounds are reliably accurate and efficient for pricing lookback options and barrier options, and evaluating a joint distribution under the MEM.

A Study on Gel/Space Ratio Development in Binary Mixture Containing Portland Cement and Meta-Illite Calcined Clay/Rice Husk Ash.

Supplementary cementitious materials (SCMs) have been widely used to enhance both the microscopic and macroscopic properties of the Portland cement (PC)–SCM composite matrix. Few studies have been undertaken to establish the gel/space ratio of meta-illite calcined clay (MCC) and rice husk ash (RHA)-based high-performance concrete (HPC) mortar. This experimental paper describes a conventional degree of hydration (non-evaporable water) and porosity routes of establishing a link amid the gel/space ratio and compressive strength of a sieved mortar from Class 1 (50–75 MPa) HPC at an early age. Using the non-evaporable water method, this paper predicted the gel/space ratio of the hardened MCC/RHA-based HPC mortars and curved fitted into Powers’ exponent equation. The results from this study revealed that MCC or RHA additions (5–30% by weight of PC) to the PC-SCM matrix led to a moderate decline in the compressive strength of the low water-binder ratio (W/B) HPC mortar. The modification aimed at void volume (superabsorbent polymers, SAP, and air) applying Bolomey’s formula and Powers’ gel/space ratio developed a suitable fitting into the Powers’ model. This experimental procedure shows feasibility to predict the MCC and RHA outcome on the compressive strength of HPC.

Finite-dimensional reduction of a supercritical exponent equation

We present a finite-dimensional reduction for a supercritical exponent PDE. We reduce the existence of a solution of the problem − Δ u = K | u | 4 ∕ ( n − 2 ) + e u in Ω (with e > 0 ) , u = 0 on ∂ Ω , to finding a critical point of a function defined in some set V⊂ℝN×ℝN×ΩN.

Active contour model based on variable exponent p-Laplace equation for image segmentation

ABSTRACTIn this paper, we propose a region-based active contour model for image segmentation. By combining the region fitting energy based on coefficient of variation with the variable exponent p-Laplace energy, the proposed method can perform well in segmenting complex images. The region fitting energy conducts the evolving curve to reach the boundaries of the objects, and the p-Laplace energy can handle the topological changes and extract the boundaries accurately. In order to eliminate the re-initialization step, an augmented Lagrangian method is employed to solve the optimization problem. The results of experiments on synthetic and real images demonstrate that our method can successfully segment complex object boundaries, and it is robust to noise and not sensitive to the initial position of contours.

Evaluation of the applicability of climate forecast system reanalysis weather data for hydrologic simulation: A case study in the Bahe River Basin of the Qinling Mountains, China

In recent years, global reanalysis weather data has been widely used in hydrological modeling around the world, but the results of simulations vary greatly. To consider the applicability of Climate Forecast System Reanalysis (CFSR) data in the hydrologic simulation of watersheds, the Bahe River Basin was used as a case study. Two types of weather data (conventional weather data and CFSR weather data) were considered to establish a Soil and Water Assessment Tool (SWAT) model, which was used to simulate runoff from 2001 to 2012 in the basin at annual and monthly scales. The effect of both datasets on the simulation was assessed using regression analysis, Nash-Sutcliffe Efficiency (NSE), and Percent Bias (PBIAS). A CFSR weather data correction method was proposed. The main results were as follows. (1) The CFSR climate data was applicable for hydrologic simulation in the Bahe River Basin (R 2 of the simulated results above 0.50, NSE above 0.33, and |PBIAS| below 14.8. Although the quality of the CFSR weather data is not perfect, it achieved a satisfactory hydrological simulation after rainfall data correction. (2) The simulated streamflow using the CFSR data was higher than the observed streamflow, which was likely because the estimation of daily rainfall data by CFSR weather data resulted in more rainy days and stronger rainfall intensity than was actually observed. Therefore, the data simulated a higher base flow and flood peak discharge in terms of the water balance, except for some individual years. (3) The relation between the CFSR rainfall data (x) and the observed rainfall data (y) could be represented by a power exponent equation: y=1.4789x 0.8875 (R 2=0.98, P<0.001). There was a slight variation between the fitted equations for each station. The equation provides a theoretical basis for the correction of CFSR rainfall data.

Влияние конструктивных решений на формирование кривой усталости боковых рам тележек грузовых вагонов

Fatigue resistance is the main parameter of the quality of cast parts. Fatigue tests allow evaluating performance of designs, feasibility of introducing structural changes, efficiency of used in the manufacture parts of technological solutions. The analysis of the results of fatigue tests of the side frames of different manufacturers is made. The main places of destruction were determined and defects in the centers of origin of the fatigue cracks were systematized. The parameters of fatigue curves (m - exponent equation, ρ - correlation coefficient), as well as limits of endurance and resistance to fatigue safety factor n were calculated in the article. In some cases, the value of the index m greatly exceeds the average level of the entire test volume. Test results of three batches of the side frames with high values of m and n were reviewed. The first batch of the side frames is represented by the base case. Analysis of the fracture of surfaces showed the presence of damage with high operating time of parts without casting defects. Also, there is destruction of parts with low operating time with presence of numerous casting defects. This indicates instability of manufacturing techniques of parts during its development in the enterprise. Side frames in the second batch are reinforced in the zone of internal angle of pedestal jaw opening by introducing additional edge, increasing the height of the vertical walls in 1.2 times and the wall thickness in 1.25 times. Efforts of pedestal opening led to a peak stresses in the lower and diagonal tension members, side frames divided into two groups of parts with different levels of damage. As a result - the formation of the fatigue curve with the magnitude | m | = 17. Side frames of third batch are an option of enhancing inner angle of pedestal opening by increasing the height of the vertical walls in 1.2 times and the thickness of the horizontal zone in 1.3 times. The rigidity of reinforced zone (pedestal opening) has led to an increase in stress in a neighbor zone - diagonal tension member. As a result, obtaining fatigue of the curve with the magnitude | m | = 25. Formation of zones with different levels of stress state distorts results of fatigue tests of the side frames, unreasonably increases the value of index m, and hence index n. When receiving m in absolute value over 10 an analysis of zones of destruction with establishing reasons behind this increase should be made as well.

Polyazomethine with m-tolylazo side groups: thermal, dielectric and conductive behaviour

Using solution polycondensation, a new polyazomethine with m-tolylazo side groups (PAz) exhibiting thermotropic liquid crystalline phase was synthesised and its chemical structure was characterised with generally accepted methods. Its phase transition temperatures were detected with both polarising optical microscopy and differential scanning calorimetry. Using dielectric spectroscopy method, both real and imaginary parts of the permittivity were investigated in wide regions of temperature (from −100°C to 170°C) and frequency (from 1 Hz to 1 MHz). Analysis of frequency dependent permittivity allowed finding three relaxations (α, β1 and β2) in PAz. β-relaxations were described with the Arrhenius equation, whereas α-relaxation was described with the Vogel–Fulcher–Tammann equation. The alternating current conductivity (ACC) of PAz was studied in the same regions of temperature and frequency. The frequency dependent ACC was described with an exponent power equation. Presentation of ACC as a function of inverse temperature allowed us to describe ACC with the Arrhenius equation.

Landslide-risk zonation along mountainous highway considering rock mass classification

Landslide and especially rockfall hazard widely occurs along cut slopes in mountainous regions. The risk assessment of mass movements is still one of most challenging problems in slope engineering geology. We propose a routine method to assess rock slide and rockfall risk of cut slopes essentially based on slope properties and rock mass structure. The method is a lean low-cost path to a risk estimate. Rock block size is simplified into two classes, {small} with a volume less than 1.0 m3 and {large}, greater than 1.0 m3. Studies indicate that for a slope with n small-medium rock blocks, the possibility of rockfalls can be estimated by 1 − (1 − P) n , in which P is the likelihood of one {small} rock block fall. The possibility of other types of mass movement can be determined by the first-order second-moment (FOSM) method. Based on this, an exponent equation was adopted to evaluate the consequence and the risk. The methodology is demonstrated by a case study from the mountains of Mentougou district, Beijing, China. Based on the investigations of geological conditions (i.e., lithology, weathering and rock mass structure) and some historical mass movement data of the cut slopes, a zonation map for rockfall and rock slide risk along a 17-km section of a road is presented. The result is supported by mass movement event observations in the recent 2 years.

The Self Exitated Induction Generator with Observation Magnetizing Characteristic in The Air Gap

This paper discusses the Self Exitated induction Generator (SEIG) by approaching the induction machine, physically and mathematically which then transformed from three-phase frame abc to-axis frame, direct axis and quadratur-axis. Based on the reactive power demand of induction machine, capacitor mounted on the stator of the induction machine then do the physical and mathematical approach of the system to obtain a state space model. Underknown relationships, magnetization reactance and magnetizing current is not linear, so do mathematical approach to the magnetization reactance equation used in the calculation. Obtained state space model and the magnetic reactance equation is simulated by Runge kutta method of fourth order. The equation of reactance, is simulated by first using the polynomial equation and second using the exponent equation. The load voltage at d axis and q axis using the polynomial laggs 640µs to the exponent equation. The polynomial voltage magnetitude is less than 0.6068 volt from the exponent voltage magnitude

Volume and Taper Equations for P. taeda (L.) and E. grandis (Hill ex. Maiden)

We compared several taper and volume equations with emphasis in testing the suitability of compatible taper equations, so that they can be used in forest inventories or decision support systems. We used data from 863 and 932 trees of Pinus taeda and Eucalyptus grandis respectively, collected from the Departments of Rivera, Tacuarembó, Paysandú, and Río Negro in Uruguay. In general, rankings of the candidate models were consistent for both species. For volume estimation the most accurate equations were the models presented by Clutter et al. (1983) and Schumacher and Hall (1933) for P. taeda and E. grandis respectively, while for describing stem profiles the most accurate model was a variable exponent equation presented by Muhairwe (1999) and modified by Methol (2001). The best compatible taper equation tested remained in an intermediate ranking position, but represented a satisfactory option for foresters seeking to use the advantages of this class of equations.

Studies on the Root Characteristics of Maize Varieties of Different Eras

Experiment was conducted at the Gongzhuling Experimental Station of Institute of Crop Sciences, Chinese Academy of Agricultural Sciences, Jilin Province, China, during 2009–2010. Six representative varieties of maize (Baihe in the 1950s, Jidan 101 in the 1960s, Zhongdan 2 in the 1970s, Yedan 13 in the 1980s, Zhengdan 958 in the 1990s, and Xianyu 335 in the 2000s) were each planted under two different densities (52 500 and 82 500 plants ha−1) and two different nitrogen application levels (150 and 300 kg ha−1). Root characteristics and distribution among soil layers were studied by the field root digging method. The results showed that root mass increased with the process of the growth and development of the plant, and it peaked at kernel filling stage, and decreased at maturity due to the root senesces. Root mass of different maize varieties from the 1950s to 1980s had a trend of increase, while it decreased for the modern varieties. Root length and root surface areas had the similar changing trend. The study suggested that early maize varieties may have root redundancy, and reducing root redundancy may be a direction for variety improvement for high yield. Root characteristics were affected by nitrogen application level and density; modern varieties were more suitable for higher fertilizer application level and density conditions. Root characteristics distribution among soil layers decreased by an exponent equation, but the regression coefficients of different varieties were different. Though the root length density (RLD) of every soil layer of different varieties also decreased by an exponent equation, there were large variations of RLD in every part of a layer.

Effects of Cyclic Loading on Interface of Liner and Propellant

During the service life of a solid rocket motor, the interface of liner and propellant is subjected to cyclic loading. In order to find the damage law of it, fixed stress amplitude cyclic loading experiment was used. In the process of the experiment, constitutive behavior and dissipative energy mainly researched. The influence of the fixed stress amplitude on properties of liner/propellant was also studied. The results show that the remains strain increased following the increase of cyclic number. The dissipative energy of every cyclic loading is random, so it does not adapt to be damage variable. The stress amplitude and natural logarithm of the cycle number accord with exponent equation.

Ground state and multiple solutions for a critical exponent problem

We study the following Brezis–Nirenberg type critical exponent equation which is related to the Yamabe problem: $$-\Delta u=\lambda u+ |u|^{2^{\ast}-2}u, \quad u\in H_0^1 (\Omega),$$ where Ω is a smooth bounded domain in $${{\mathbb R}^N(N\ge3)}$$ and 2* is the critical Sobolev exponent. We show that, if N ≥ 5, this problem has at least $${\lceil\frac{N+1}{2}\rceil}$$ pairs of nontrivial solutions for each fixed λ ≥ λ1, where λ1 is the first eigenvalue of −Δ with the Dirichlet boundary condition. For N ≥ 3, we give energy estimates from below for ground state solutions.

Effects of Soil/Solution Ratios and Cation Types on Adsorption and Desorption of Tetracycline in Soils

The adsorption and desorption behavior of tetracycline on an Alfisol and an Ultisol was investigated at varying soil/solution ratios (1:10, 1:50, and 1:100) and different cation types (CaCl2, KCl, and NaCl) and H2O using a batch equilibration experiment. Kinetic studies revealed that the adsorption of tetracycline on the two soils was rate limited, and the adsorption kinetics could be well described by the Elovich equation and exponent equation. Changes in the soil/solution ratio affected the relative equilibration time in the Ultisol, but there was no effect of the initial tetracycline concentration. The adsorption rate in the soils decreased as the soil/solution ratio increased from 1:50 to 1:10. The adsorption and desorption data on tetracycline in the two soils could be described by the Freundlich isotherm equation, with r values &gt;0.952 under all experimental treatments. The Ultisol always had stronger adsorption (higher distribution coefficient [Kd] value) than the Alfisol under all experimental conditions. The Kd values decreased with increasing soil/solution ratios in the two tested soils at 1 or 1.25 mg L−1 of tetracycline; however, this trend did not occur at 25 mg L−1 of tetracycline. The adsorption isotherm had an S‐type curve that changed into an L‐type curve with decreasing soil/solution ratios from 1:10 to 1:100. The presence of cations in the soil solution, especially CaCl2, can significantly reduce the adsorption of tetracycline in soils. The presence of cations also significantly reduced the nonlinearity of the adsorption isotherms.