Home About us Contact
|
Home About us Contact | ||
|
|
||
Exponential Equation (exponential + equation)
Selected AbstractsUncertainties in interpretation of isotope signals for estimation of fine root longevity: theoretical considerationsGLOBAL CHANGE BIOLOGY, Issue 7 2003YIQI LUOArticle first published online: 25 JUN 200 Abstract This paper examines uncertainties in the interpretation of isotope signals when estimating fine root longevity, particularly in forests. The isotope signals are depleted ,13C values from elevated CO2 experiments and enriched ,14C values from bomb 14C in atmospheric CO2. For the CO2 experiments, I explored the effects of six root mortality patterns (on,off, proportional, constant, normal, left skew, and right skew distributions), five levels of nonstructural carbohydrate (NSC) reserves, and increased root growth on root ,13C values after CO2 fumigation. My analysis indicates that fitting a linear equation to ,13C data provides unbiased estimates of longevity only if root mortality follows an on,off model, without dilution of isotope signals by pretreatment NSC reserves, and under a steady state between growth and death. If root mortality follows the other patterns, the linear extrapolation considerably overestimates root longevity. In contrast, fitting an exponential equation to ,13C data underestimates longevity with all the mortality patterns except the proportional one. With either linear or exponential extrapolation, dilution of isotope signals by pretreatment NSC reserves could result in overestimation of root longevity by several-fold. Root longevity is underestimated if elevated CO2 stimulates fine root growth. For the bomb 14C approach, I examined the effects of four mortality patterns (on,off, proportional, constant, and normal distribution) on root ,14C values. For a given ,14C value, the proportional pattern usually provides a shorter estimate of root longevity than the other patterns. Overall, we have to improve our understanding of root growth and mortality patterns and to measure NSC reserves in order to reduce uncertainties in estimated fine root longevity from isotope data. [source] Models for recession flows in the upper Blue Nile RiverHYDROLOGICAL PROCESSES, Issue 15 2004A. Mishra Abstract Stream-flow recessions are commonly characterized by the exponential equation or in the alternative power form equation of a single linear reservoir. The most common measure of recession is the recession constant K, which relates to the power function form of the recession equation for a linear reservoir. However, in reality it can be seen that the groundwater dynamics of even the simplest of aquifers may behave in a non-linear fashion. In this study three different storage,outflow algorithms; single linear, non-linear and multiple linear reservoir were considered to model the stream-flow recession of the upper Blue Nile. The recession parameters for the linear and non-linear models were derived by the use of least-squares regression procedures. Whereas, for the multiple linear reservoir model, a second-order autoregressive AR (2) model was applied first in order to determine the parameters by the least-squares method. The modelling of the upper Blue Nile recession flow performed shortly after the wet season, when interflow and bank storage may be contributing considerably to the river flow, showed that the non-linear reservoir model simulates well with the observed counterparts. The variation related to preceding flow on a recession parameter of the non-linear reservoir remains significant, which was obtained by stratification of the recession curves. Although a similar stratification did not show any systematic variation on the recession parameters for the linear and multiple linear reservoir models. Copyright © 2004 John Wiley & Sons, Ltd. [source] Rheological properties of Josapine pineapple juice at different stages of maturityINTERNATIONAL JOURNAL OF FOOD SCIENCE & TECHNOLOGY, Issue 4 2009Rosnah Shamsudin Summary The rheological behaviour of Josapine pineapple juice with at various maturity stages was studied at a wide range of temperature (5,65 °C) and concentration (4,14 °Brix) using a rotational rheometer as the measuring system. The results show that josapine pineapples juice demonstrated a Newtonian behavior and is influenced by maturity stage, temperature and concentration. The Arrhenius typed equation successfully describe the effect of temperature on the viscosity, on the other hand, the effect of concentration can be described better using exponential equation. Finally, an equation describing the combined effect of temperature and concentration on viscosity at different stages of maturity was successfully developed. [source] Estimation of soil water content and evapotranspiration from irrigated cropland on the North China PlainJOURNAL OF PLANT NUTRITION AND SOIL SCIENCE, Issue 5 2008Jie Jiang Abstract For nearly 30 y, cropland on the North China Plain (NCP) has been irrigated primarily by pumping groundwater with no sustainable management strategy. This has caused a continuous decline of the water table. A sustainable groundwater management and irrigation strategy must be established in order to prevent further decline of the water table; to do this, one must quantify soil water content and daily rates of deep percolation and locate evapotranspiration from irrigated cropland. For that purpose, we developed a three-layer soil,water balance (SWB) model based on an approach described by Kendy et al. (2003). In this model, the unsaturated soil zone is divided into three layers: a surface active layer, a middle active soil layer, and a lowest passive soil layer. The middle and the lowest layers dynamically change with the development of crop rooting depth. A simple "tipping bucket" routine and an exponential equation are used to redistribute soil water in the three soil layers. The actual evapotranspiration estimated is partitioned into soil evaporation and crop transpiration using a dual crop coefficient reference approach. At first, the model was calibrated using data obtained from five deficiently irrigated field plots located at an experimental site in the NCP between 1998 and 2003. Then, the model was validated by comparing estimated soil water contents with measured ones at three other plots with nondeficient irrigation. The estimates of actual evapotranspiration were compared with those measured with a large-scale weighing lysimeter (3 m2). The index of agreement (IA) for soil water contents varied between 0.62 and 0.80; the concordance correlation coefficient (CCC) and the root mean square error obtained from the same comparison were 0.34,0.65 and 0.043,0.074,cm3,cm,3, respectively. The rates of 10 d mean evapotranspiration estimated by the model show a good fit to those measured by the large-scale lysimeter; this is indicated by IA = 0.94 and CCC = 0.88. Our results indicate that at the irrigated cropland on the plain, deep soil water,percolation rates are usually <200,mm y,1 under nondeficient-irrigation conditions. [source] RHEOLOGY OF MULBERRY PEKMEZJOURNAL OF TEXTURE STUDIES, Issue 5-6 2001A. KAYA The rheological behavior of mulberry pekmez (concentrated mulberry juice, °Brix = 72.0) with different solid contents (62.8, 55.8 and 46.0) was studied over the temperature range of 10, 20, 30, 40, 50 and 60C using a Controlled Stress Rheometer. Mulberry pekmez was found to exhibit Newtonian behavior. The effect of temperature can be described by means of Arrhenius equation. The activation energies for flow of samples vary from 53.11 to 12.73 kJ/mol depending on soluble solid contents. The effect of soluble solids on viscosity can be described by an exponential equation. The best model to describe the combined effects of temperature and soluble solids content on viscosity is ,= 3.40 X 10 -10 exp (0.12C + 3723/T). [source] The Characterization of Contractile and Myoelectric Activities in Paralyzed Tibialis Anterior Post Electrically Elicited Muscle FatigueARTIFICIAL ORGANS, Issue 4 2010Nan-Ying Yu Abstract This study aimed to understand the myoelectric and mechanical characteristics of muscle recovering from electrically elicited fatigue. A modified Burke fatigue protocol was delivered to activate the tibialis anterior of 13 spinal cord injured subjects for 4 min. Before and after the fatigue protocol, a series of pulse trains was delivered to induce three twitches and a fused contraction at 0, 1, 3, and 5 min and then followed every 5 min for 60 min. The recovery processes of the ankle dorsiflexion torque and the evoked electromyography (EMG) parameters were analyzed and characterized by a first-order exponential equation. The recovery process was found to be faster in regard to tetanic muscle contraction. Factors relating to low-frequency fatigue, postfatigue potentiation, and the quickly normalized relaxation rate were taken into account for the discussion of this result. During the recovery process, the disassociation was found not only between twitch and tetanic contractions but also between mechanical and myoelectric activities. After the complete normalization of EMG parameters from about 15 min post fatigue, the tetanic force recovered incompletely to an asymptotic level. [source] The relationships between half-life (t1/2) and mean residence time (MRT) in the two-compartment open body modelBIOPHARMACEUTICS AND DRUG DISPOSITION, Issue 4 2004Eyal Sobol Abstract Rationale. In the one-compartment model following i.v. administration the mean residence time (MRT) of a drug is always greater than its half-life (t1/2). However, following i.v. administration, drug plasma concentration (C) versus time (t) is best described by a two-compartment model or a two exponential equation: C=Ae,,t+Be,,t, where A and B are concentration unit-coefficients and , and , are exponential coefficients. The relationships between t1/2 and MRT in the two-compartment model have not been explored and it is not clear whether in this model too MRT is always greater than t1/2. Methods. In the current paper new equations have been developed that describe the relationships between the terminal t1/2 (or t1/2,) and MRT in the two-compartment model following administration of i.v. bolus, i.v. infusion (zero order input) and oral administration (first order input). Results. A critical value (CV) equals to the quotient of (1,ln2) and (1,,/,) (CV=(1,ln2)/(1,,/,)=0.307/(1,,/,)) has been derived and was compared with the fraction (f1) of drug elimination or AUC (AUC-area under C vs t curve) associated with the first exponential term of the two-compartment equation (f1=A/,/AUC). Following i.v. bolus, CV ranges between a minimal value of 0.307 (1,ln2) and infinity. As long as f1
| | ||||||||||||