Relevant bibliographies by topics / Equation root

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Equation root'

Author: Grafiati
Published: 8 November 2023

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Journal articles on the topic "Equation root"

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Kulkarni, Raghavendra G. "Insert a Root to Extract a Root of Quintic Quickly." Annales Mathematicae Silesianae 33, no. 1 (September 1, 2019): 153–58. http://dx.doi.org/10.2478/amsil-2018-0013.

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AbstractThe usual way of solving a solvable quintic equation has been to establish more equations than unknowns, so that some relation among the coefficients comes up, leading to the solutions. In this paper, a relation among the coefficients of a principal quintic equation is established by effecting a change of variable and inserting a root to the quintic equation, and then equating odd-powers of the resulting sextic equation to zero. This leads to an even-powered sextic equation, or equivalently a cubic equation; thus one needs to solve the cubic equation.We break from this tradition, rather factor the even-powered sextic equation in a novel fashion, such that the inserted root is identified quickly along with one root of the quintic equation in a quadratic factor of the form, u2− g2 = (u + g)(u − g). Thus there is no need to solve any cubic equation. As an extra benefit, this root is a function of only one coefficient of the given quintic equation.
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Assi, Abdullah Dhayea. "ADA Solve the Cubic Equation in a New Method with Engineering Application." Al-Qadisiyah Journal for Engineering Sciences 13, no. 3 (September 30, 2020): 223–31. http://dx.doi.org/10.30772/qjes.v13i3.659.

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Up to date the cubic equation or matrix tensor is consisting of nine values ​​such as stress tensor that turns into the cubic equation which has been used for solving classic method. This is to impose an initial root several times to get it when achieves the equation and any other party is zero. Then dividing the cubic equation on the equation of the root. After that dividing the cubic equation on the equation of the root and using the classical method to find the rest of the roots. This is a very difficult issue, especially if the roots are secret or large for those who are looking in a difficult field or even for those who are in the examination room. In this research, two equations were reached, one that calculates the angle and the other that calculates the three roots at high accuracy without any significant error rate. By taking advantage of the traditional method, not by imposing a value to get the root of that equation, but by imposing an equation to get the solution equation that gives the value of that root. After imposing that equation, the general equation was derived from which that calculated the three roots directly and without any attempts. The angle that was implicitly derived during the derive of the main equation is calculated by taking advantage of the constants that do not change (invariants) for the matrix tensor (T).
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KRUGLOV, S. I. ""SQUARE ROOT" OF THE PROCA EQUATION: SPIN-3/2 FIELD EQUATION." International Journal of Modern Physics A 21, no. 05 (February 20, 2006): 1143–55. http://dx.doi.org/10.1142/s0217751x06024980.

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New equations describing particles with spin-3/2 are derived. The nonlocal equation with the unique mass can be considered as "square root" of the Proca equation in the same sense as the Dirac equation is related to the Klein–Gordon–Fock equation. The local equation describes spin-3/2 particles with three mass states. The equations considered involve fields with spin-3/2 and spin-1/2, i.e. multispin 1/2, 3/2. The projection operators extracting states with definite energy, spin, and spin projections are obtained. All independent solutions of the local equation are expressed through projection matrices. The first order relativistic wave equation in the 20-dimensional matrix form, the relativistically invariant bilinear form and the corresponding Lagrangian are given. Two parameters characterizing nonminimal electromagnetic interactions of fermions are introduced, and the quantum-mechanical Hamiltonian is found. It is proved that there is only causal propagation of waves in the approach considered.
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Batarius, Patrisius, and Alfri Aristo SinLae. "NILAI AWAL PADA METODE SECANT YANG DIMODIFIKASI DALAM PENENTUAN AKAR GANDA PERSAMAAN NON LINEAR." Jurnal Ilmiah Matrik 21, no. 1 (July 27, 2019): 21–31. http://dx.doi.org/10.33557/jurnalmatrik.v21i1.516.

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Determining the root of an equation means making the equation equal zero, (f (f) = 0). In engineering, there are often complex mathematical equations. With the numerical method approach, the equation can be searching for the value of the equation root. However, to find a double root approach with several numerical methods such as the bisection method, regulatory method, Newton-Raphson method, and Secant method, it is not efficient in determining multiple roots. This study aims to determine the roots of non-linear equations that have multiple roots using the modified Secant method. Besides knowing the effect of determining the initial value for the Secant method that is modifying in determining the non-linear root of persistence that has multiple roots. Comparisons were also make to other numerical methods in determining twin roots with the modified Secant method. A comparison is done to determine the initial value used. Simulations are performing on equations that have one single root and two or more double roots.
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Cogan, Brian. "Use of The Analytic Method and Computer Algebra to Plot Root Loci." International Journal of Electrical Engineering & Education 35, no. 4 (October 1998): 350–56. http://dx.doi.org/10.1177/002072099803500406.

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The analytic method for plotting root loci is examined. The basic equation for this method, originally published by Bendrikov and Teodorchik4 in 1959, is derived in a very simple way. A second equation, which complements the original Bendrikov equation, is also derived. An example of how these two equations may be used to plot root loci using Mathematica is presented.
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Pulita, Andrea. "p-adic confluence of q-difference equations." Compositio Mathematica 144, no. 4 (July 2008): 867–919. http://dx.doi.org/10.1112/s0010437x07003454.

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AbstractWe develop the theory of p-adic confluence of q-difference equations. The main result is the fact that, in the p-adic framework, a function is a (Taylor) solution of a differential equation if and only if it is a solution of a q-difference equation. This fact implies an equivalence, called confluence, between the category of differential equations and those of q-difference equations. We develop this theory by introducing a category of sheaves on the disk D−(1,1), for which the stalk at 1 is a differential equation, the stalk at q isa q-difference equation if q is not a root of unity, and the stalk at a root of unity ξ is a mixed object, formed by a differential equation and an action of σξ.
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Li, Zhong, Werner A. Kurz, Michael J. Apps, and Sarah J. Beukema. "Belowground biomass dynamics in the Carbon Budget Model of the Canadian Forest Sector: recent improvements and implications for the estimation of NPP and NEP." Canadian Journal of Forest Research 33, no. 1 (January 1, 2003): 126–36. http://dx.doi.org/10.1139/x02-165.

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In the Carbon Budget Model of the Canadian Forest Sector (CBM-CFS2), root biomass and dynamics are estimated using regression equations based on the literature. A recent analysis showed that some of these equations might overestimate belowground net primary production (NPPB). The objectives of this study were to update the compilation of root biomass and turnover data, to recalculate the regression equations and to evaluate the impact of the new equations on CBM-CFS2 estimates of net primary production (NPP) and net ecosystem production (NEP). We updated all equations based on 635 pairs of aboveground and belowground data compiled from published studies in the cold temperate and boreal forests. The new parameter for the equation to predict total root biomass for softwood species changed only slightly, but the changes for hardwood species were statistically significant. A new equation form, which improved the accuracy and biological interpretation, was used to predict fine root biomass as a proportion of total root biomass. The annual rate of fine root turnover was currently estimated to be 0.641 of fine root biomass. A comparison of NPP estimates from CBM-CFS2 with results from field measurements, empirical calculations and modeling indicated that the new root equations predicted reasonable NPPB values. The changes to the root equations had little effect on NEP estimates.
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Loginov, B. V. "Branching equation in the root subspace." Nonlinear Analysis: Theory, Methods & Applications 32, no. 3 (May 1998): 439–45. http://dx.doi.org/10.1016/s0362-546x(97)00481-1.

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Plyushchay, Mikhail S., and Michel Rausch de Traubenberg. "Cubic root of Klein-Gordon equation." Physics Letters B 477, no. 1-3 (March 2000): 276–84. http://dx.doi.org/10.1016/s0370-2693(00)00190-8.

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Debiard, Amédée, and Bernard Gaveau. "Analysis on Root Systems." Canadian Journal of Mathematics 39, no. 6 (December 1, 1987): 1281–404. http://dx.doi.org/10.4153/cjm-1987-064-x.

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A great part of mathematical analysis relies directly on the methods of separation of variables and on the successive reduction of several variables problems to one-dimensional equations and to the theory of classical special functions; for example, the theory of elliptic or parabolic equations with regular coefficients (even with non constant coefficients) can be done because we know explicitly the fundamental solutions of the Laplace operator or of the heat equation; these fundamental solutions are functions of one variable; pseudodifferential or parametrices methods are thus basically small perturbations of an explicitly known problem in one variable.On the other hand, there are many problems which are not of this type: they are related to the questions of operators with singular coefficients and to the global behaviour of the solutions; in that case, the local model cannot be reduced to a one variable problem but is fundamentally a several variables problem which cannot be treated in a detailed way by one variable methods or perturbation analysis of a one variable problem.
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Dissertations / Theses on the topic "Equation root"

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Whitacre, Jonathan H. "A Hybrid Method For Solving A Single Nonlinear Equation." Youngstown State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1296145853.

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Omotere, Olumide Olubunmi. "Improvement of the Soil Moisture Diagnostic Equation for Estimating Root-Zone Soil Moisture." Thesis, University of North Texas, 2018. https://digital.library.unt.edu/ark:/67531/metadc1157607/.

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Soil moisture information can be used accurately in determining the timing and amount of irrigation applied to plants. Pan and Pan et al. proposed a robust and simple daily diagnostic equation for estimating daily soil moisture. The diagnostic equation evaluates the relationship between the soil moisture loss function and the summation weighted average of precipitation. The loss function uses the sinusoidal wave function which employs day of the year (DOY) to evaluate the seasonal variation in soil moisture loss for a given year. This was incorporated into the daily diagnostic equation to estimate the daily soil moisture for a location. Solar radiation is an energy source that drives the energy and water exchanges between vegetation and the atmosphere (i.e., evapotranspiration), and thus impacts the soil moisture dry-down. In this paper, two parameters (the actual solar radiation and the clear sky solar radiation) are introduced into loss function coefficient to improve the estimation of soil moisture. After the Introduction of the solar radiation data into soil moisture loss function, a slight improvement was observed in the estimated daily soil moisture. Pan observed that generally the correlation coefficient between the estimated and the observed soil moisture is above 0.75 and the root mean square error is below 5.0 (%v/v). The introduction solar radiation data (i.e. clear sky solar radiation and actual solar) improve the correlation coefficient average for all the sites evaluated by 0.03 when the root mean square error is generally below 4.5(%v/v) for the entire root zone.
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Pham, Tien Duc, and n/a. "A new approach to regional modelling: an Integrated Regional Equation System (IRES)." Griffith University. School of International Business and Asian Studies, 2004. http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20041022.083520.

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This thesis develops a new structure that explicitly combines two CGE models, a national and a regional, in an integrated structure that gives the thesis model the name IRES, in short for the Integrated Regional Equation System. The typical features of the integrated structure are the adding-up conditions and the two-way linkages between the national and the regional modules facilitated by the interface shifters. The adding-up conditions ensure the two modules produce consistent results and updated databases. The inclusion of the interface shifters on the one hand plays a role in ensuring compatibility of results of the two modules, i.e. no distortion occurs because technical or taste changes are transferred across modules. On the other hand, the interface shifters assist the operation of IRES in different modes: the model can be used as a top-down model, a bottom-up model or an integrated model where national and regional shocks can be introduced at the same time. Hence, IRES has more flexibility in its application than a regional model or a national model alone, as IRES can make use of availability of data at any levels in the economy. IRES has a new labour market in which regional migration is no longer the only factor that settles the labour market as in the original setting of the MMRF model. Regional unemployment and regional participation rates are modelled to response to changes in regional employment growth using elasticities estimated econometrically in this thesis. IRES implements historical patterns of regional migration so that results of regional migration are consistent with observed patterns. Altogether, regional migration, regional unemployment and participation rates determine the equilibrium of the labour market. IRES adopts new approaches to modelling margin demands and indirect taxes. These new approaches are very effective in reducing the size of IRES but they do not compromise the use of the model. These approaches are readily applicable to any other regional CGE models.
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Raybould, Michael, and n/a. "Attitudes and Information Effects in Contingent Valuation of Natural Resources." Griffith University. Australian School of Environmental Studies, 2006. http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20061009.150949.

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This thesis investigated the effects of photographic and text information on respondents' attitudes and willingness-to-pay for a proposed beach protection scheme in the erosion prone Gold Coast region on the east coast of Australia. The research developed two alternative expectancy-value attitude-behaviour models to test residents' attitudes toward relevant targets and behavioural intention, expressed through stated willingness-to-pay, and compared the proposed models with one established attitude-behaviour model. The thesis set out to investigate three central research questions; one question relating to the effects of information on attitudes and willingness-to-pay, and two questions relating to the relationships between attitudes and willingness-to-pay. It was hypothesised that photographs that depicted severe erosion damage would result in more positive attitudes toward, and greater willingness-to-pay for, beach protection than photographs that showed only mild levels of erosion damage. Positive relationships were hypothesised between variables representing attitudes toward beach erosion, attitude toward beach protection, attitude toward paying for beach protection, and willingness-to-pay. Finally, it was hypothesised that the relationships between attitudes and willingness-to-pay could be adequately explained by the proposed attitude-behaviour models. The thesis describes how seven information treatments and eight attitude measurement scales were developed and tested in a pilot experiment before use in a survey of homeowners in the region of interest. Analysis of variance showed that, while respondent's attitude toward beach protection was affected by the information treatments, their willingness-to-pay for the proposed program was insensitive to information. There were no significant effects that could be attributed exclusively to text descriptions of the good but there were significant effects that could be attributed to photographic information treatments. However, none of the effects on attitudes resulted in significant effects on the behavioural intention expressed in stated willingness-to-pay. Analysis of respondents with low previous knowledge of the proposed good revealed more extensive information effects on attitudes, but still not on willingness-to-pay, and this suggests that high levels of previous knowledge in a large proportion of the sample had a moderating effect on attitude change caused by the information treatments. Regression analysis showed that seven of the eight attitude and behaviour variables in the proposed attitude-behaviour model were significant predictors of willingness-to-pay. In the final phase of the analysis, goodness-of-fit indices, estimated using Structural Equation Modelling, indicated a good fit between the data and the attitude-behaviour models tested. Standardised coefficients on the model indicated that perceived behavioural control, expected utility of outcomes, and subjective norms all had strong direct relationships with stated willingness-to-pay, and strong indirect relationships on willingness-to-pay via attitudes toward payment. These results are consistent with the relationships proposed in attitude-behaviour models and the moderating effects of these variables explain why significant information treatment effects were observed on attitude to beach protection but not on willingness-to-pay. This research showed that respondent's willingness-to-pay in a contingent valuation experiment is quite insensitive to photographic treatments when previous knowledge is high and that costly and time consuming testing procedures, recommended by authorities, may not be necessary under these conditions. It also demonstrated that measures of attitude, consistent with an attitude-behaviour model, can be collected easily in a contingent valuation study and can contribute to understanding of participant responses and to identification of protest responses.
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Aumeerally, Manisah, and n/a. "Analytic Model Derivation Of Microfluidic Flow For MEMS Virtual-Reality CAD." Griffith University. School of Information and Communication Technology, 2006. http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20061106.095352.

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This thesis derives a first approximation model that will describe the flow of fluid in microfluidic devices such as in microchannels, microdiffusers and micronozzles using electrical network modelling. The important parameter that is of concern is the flow rates of these devices. The purpose of this work is to contribute to the physical component of our interactive Virtual Reality (VR)-prototyping tool for MEMS, with emphasis on fast calculations for interactive CAD design. Current calculations are too time consuming and not suitable for interactive CAD with dynamic animations. This work contributes to and fills the need for the development of MEMS dynamic visualisation, showing the movement of fluid within microdevices in time scale. Microfluidic MEMS devices are used in a wide range of applications, such as in chemical analysis, gene expression analysis, electronic cooling system and inkjet printers. Their success lies in their microdimensions, enabling the creation of systems that are considerably minute yet can contain many complex subsystems. With this reduction in size, the advantages of requiring less material for analysis, less power consumption, less wastage and an increase in portability becomes their selling point. Market size is in excess of US$50 billion in 2004, according to a study made by Nexus. New applications are constantly being developed leading to creation of new devices, such as the DNA and the protein chip. Applications are found in pharmaceuticals, diagnostic, biotechnology and the food industry. An example is the outcome of the mapping and sequencing of the human genome DNA in the late 1990's leading to greater understanding of our genetic makeup. Armed with this knowledge, doctors will be able to treat diseases that were deemed untreatable before, such as diabetes or cancer. Among the tools with which that can be achieved include the DNA chip which is used to analyse an individual's genetic makeup and the Gene chip used in the study of cancer. With this burgeoning influx of new devices and an increase in demand for them there is a need for better and more efficient designs. The MEMS design process is time consuming and costly. Many calculations rely on Finite Element Analysis, which has slow and time consuming algorithms, that make interactive CAD unworkable. This is because the iterative algorithms for calculating the animated images showing the ongoing proccess as they occur, are too slow. Faster computers do not solve the void of efficient algorithms, because with faster computer also comes the demand for a fasters response. A 40 - 90 minute FEA calculation will not be replaced by a faster computer in the next decades to an almost instant response. Efficient design tools are required to shorten this process. These interactive CAD tools need to be able to give quick yet accurate results. Current CAD tools involve time consuming numerical analysis technique which requires hours of numerous iterations for the device structure design followed by more calculations to achieve the required output specification. Although there is a need for a detailed analysis, especially in solving for a particular aspect of the design, having a tool to quickly get a first approximation will greatly shorten the guesswork involved in determining the overall requirement. The underlying theory for the fluid flow model is based on traditional continuum theory and the Navier-Stokes equation is used in the derivation of a layered flow model in which the flow region is segmented into layered sections, each having different flow rates. The flow characteristics of each sections are modeled as electrical components in an electrical circuit. Matlab 6.5 (MatlabTM) is used for the modelling aspect and Simulink is used for the simulation.
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Teo, Hhih-Ting, and h. teo@griffith edu au. "Tidal Dynamics in Coastal Aquifers." Griffith University. School of Engineering, 2003. http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20030729.155028.

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The prediction of coastal groundwater movement is necessary in coastal management. However, the study in this field is still a great challenge due to the involvement of tidal-groundwater interactions and the phenomena of hydrodynamic dispersion between salt-fresh water in the coastal region. To date, numerous theories for groundwater dynamic have been made available in analytical, numerical and also experimental forms. Nevertheless, most of them are based on the zeroth-order shallow flow, i.e. Boussinesq approximation. Two main components for coastal unconfined aquifer have been completed in this Thesis: the vertical beach model and the sloping beach model. Both solutions are solved in closed-form up to higher order with shallow water parameter ([epsilon]) and tidal amplitude parameter ([alpha]). The vertical beach solution contributes to the higher-order tidal fluctuations while the sloping beach model overcomes the shortcomings in the existing solutions. From this study, higher-order components are found to be significant especially for larger value of [alpha] and [epsilon]. Other parameters such as hydraulic conductivity (K) and the thickness of aquifer (D) also affect the water table fluctuations. The new sloping solution demonstrated the significant influence of beach slope ([beta]) on the water table fluctuations. A comprehensive comparison between previous solution and the present sloping solution have been performed mathematically and numerically and the present solution has been demonstrated to provide a better prediction
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Brunke, Michael A., Patrick Broxton, Jon Pelletier, David Gochis, Pieter Hazenberg, David M. Lawrence, L. Ruby Leung, Guo-Yue Niu, Peter A. Troch, and Xubin Zeng. "Implementing and Evaluating Variable Soil Thickness in the Community Land Model, Version 4.5 (CLM4.5)." AMER METEOROLOGICAL SOC, 2016. http://hdl.handle.net/10150/612995.

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One of the recognized weaknesses of land surface models as used in weather and climate models is the assumption of constant soil thickness because of the lack of global estimates of bedrock depth. Using a 30-arc-s global dataset for the thickness of relatively porous, unconsolidated sediments over bedrock, spatial variation in soil thickness is included here in version 4.5 of the Community Land Model (CLM4.5). The number of soil layers for each grid cell is determined from the average soil depth for each 0.9 degrees latitude x 1.25 degrees longitude grid cell. The greatest changes in the simulation with variable soil thickness are to baseflow, with the annual minimum generally occurring earlier. Smaller changes are seen in latent heat flux and surface runoff primarily as a result of an increase in the annual cycle amplitude. These changes are related to soil moisture changes that are most substantial in locations with shallow bedrock. Total water storage (TWS) anomalies are not strongly affected over most river basins since most basins contain mostly deep soils, but TWS anomalies are substantially different for a river basin with more mountainous terrain. Additionally, the annual cycle in soil temperature is partially affected by including realistic soil thicknesses resulting from changes in the vertical profile of heat capacity and thermal conductivity. However, the largest changes to soil temperature are introduced by the soil moisture changes in the variable soil thickness simulation. This implementation of variable soil thickness represents a step forward in land surface model development.
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Chellali, Mustapha. "Congruences, nombres de Bernoulli et polynômes de Bessel." Université Joseph Fourier (Grenoble ; 1971-2015), 1989. http://www.theses.fr/1989GRE10091.

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En premiere partie, on donne des congruences entre nombres de bernoulli-hcowitz dans le cas supersingulier. En deuxieme partie, on montre que la suite des nombres de bernoulli verifie des formules de recurrence qui servent a tester si un nombre premier est irregulier. En troisieme partie, on etudie les zeros des polynomes de bessel generalises, en particulier on encadre un zero reel, apres developpement asymptotique, et on donne des estimations uniformes des valeurs de ces polynomes
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Seiß, Matthias [Verfasser]. "Root parametrized differential equations / Matthias Seiß." Kassel : Universitätsbibliothek Kassel, 2012. http://d-nb.info/1028081170/34.

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SILVA, José Nilton. "Determinação da região robusta de estabilidade e de desempenho inspirada nos princípios da estatística clássica." Universidade Federal de Campina Grande, 2013. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/2153.

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Submitted by Maria Medeiros (maria.dilva1@ufcg.edu.br) on 2018-11-08T12:05:44Z No. of bitstreams: 1 JOSÉ NILTON SILVA - TESE (PPGEQ) 2013.pdf: 1910479 bytes, checksum: 59c6bfc5fdbee46bc17470e9b2c8c2e5 (MD5)
Made available in DSpace on 2018-11-08T12:05:44Z (GMT). No. of bitstreams: 1 JOSÉ NILTON SILVA - TESE (PPGEQ) 2013.pdf: 1910479 bytes, checksum: 59c6bfc5fdbee46bc17470e9b2c8c2e5 (MD5) Previous issue date: 2013-08-01
Este trabalho trata do desenvolvimento de uma metodologia baseada nos conceitos clássicos de estatística e probabilidade para a análise e avaliação da robustez da estabilidade e do desempenho de sistemas de controle, particularmente àqueles que usam o PID (Proporcional, Integral, Derivativo) como lei de controle. Visando estabelecer as condições para a aplicação da metodologia, um sistema de identificação do processo foi desenvolvido de forma recursiva, no qual modelos de convolução e fenomenológico foram empregados como representação do modelo e processo, agrupado a um procedimento de auto sintonia, necessário para considerar os parâmetros de sintonia como variáveis aleatórias e, por conseguinte as raízes da equação característica do sistema em malha fechada.O mapeamento da região de robustez tem sido realizado a partir das raízes da equação característica, considerando a distância estatística como a métrica representativa da robustez da estabilidade a qual permite estabelecer a região com certo grau de significância.Os resultados obtidos demonstram o potencial analítico exigido pela metodologia, permitindo também a análise online, com baixo esforço computacional e operacional mostrando ser um poderoso instrumento de avaliação de sistema de controle.
This study discusses the development of a methodology based on classical concepts of statistics and probability to analyze and evaluate the robustness of the stability and performance of the control system, particularly those that use the PID as control law. To establish the conditions for the application of the methodology, a recursive system identification method process was developed, in which convolution and phenomenological models were used to represent model and process, together with a self-tuning procedure that is necessary to consider tuning parameters as random variables, and hence the roots of the characteristic equation of the closed loop system. The mapping of the region of robustness has been achieved from the roots of the characteristic equation, considering the statistical distance as the metric represented to the robustness of stability which allows the region to establish a degree of significance. The results obtained demonstrate the potential analytical and evaluation required by the methodology, allowing such analysis also "online" with low computational effort and operational proving to be a powerful tool in the analysis of control system.
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Books on the topic "Equation root"

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Scholma, J. K. A Lie algebraic study of some integrable systems associated with root systems. Amsterdam, the Netherlands: Centrum voor Wiskunde en Informatica, 1993.

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Numerical methods for roots of polynomials. Amsterdam: Elsevier, 2007.

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Point estimation of root finding methods. [New York]: Springer, 2008.

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Completeness of root functions of regular differential operators. Essex, England: Longman Scientific & Technical, 1994.

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1948-, Teerikorpi Pekka, ed. The evolving universe and the origin of life: The search for our cosmic roots. New York, NY: Springer, 2009.

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Bardy, Nicole. Systèmes de racines infinis. [Paris, France]: Société mathématique de France, 1996.

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Young, J. R. 1799. Researches respecting the imaginary roots of numerical equations: Being a continuation of ... [Place of publication not identified]: Nabu Press, 2010.

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Young, George Paxton. Forms, necessary and sufficient, of the roots of pure uni-serial abelian equations. [Toronto?: s.n., 1993.

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Saylor, Paul E. Computing the roots of complex orthogonal and kernel polynomials. Urbana, Ill. (1304 West Springfield Ave., Urbana 61801): Dept. of Computer Science, University of Illinois at Urbana-Champaign, 1986.

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Factors influencing hotel room supply and demand in Kenya: A simultaneous equations model. Nairobi, Kenya: Kenya Institute for Public Policy Research and Analysis, 2009.

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Book chapters on the topic "Equation root"

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Barbeau, Edward J. "The Square Root of 2." In Pell’s Equation, 1–15. New York, NY: Springer New York, 2003. http://dx.doi.org/10.1007/0-387-22602-8_1.

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Gooch, Jan W. "Cube Root Color Difference Equation." In Encyclopedic Dictionary of Polymers, 185. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-6247-8_3168.

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Pan, Victor Y. "Root-Refining for a Polynomial Equation." In Computer Algebra in Scientific Computing, 283–93. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-32973-9_24.

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Sergeyev, Yaroslav D. "Finding the Minimal Root of an Equation." In Global Optimization, 441–60. Boston, MA: Springer US, 2006. http://dx.doi.org/10.1007/0-387-30927-6_18.

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Heuvers, Konrad J., Daniel S. Moak, and Blake Boursaw. "The Functional Equation of the Square Root Spiral." In Functional Equations and Inequalities, 111–17. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-011-4341-7_10.

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Nadimpalli, Vijaya Lakshmi V., Rajeev Wankar, and Raghavendra Rao Chillarige. "“Potential Interval of Root” of Nonlinear Equation: Labeling Algorithm." In Lecture Notes in Computer Science, 1–12. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-13365-2_1.

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Coppersmith, Don. "Finding a Small Root of a Univariate Modular Equation." In Advances in Cryptology — EUROCRYPT ’96, 155–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-68339-9_14.

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Dewilde, Patrick. "Riccati or Square Root Equation? The Semi-separable Case." In Mathematical Methods in Systems, Optimization, and Control, 85–112. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0411-0_9.

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Kato, Masahiro, and Toshihiro Kiuchi. "A New Square-Root-Type Pseudo-Cubic Equation of State." In A Cryogenic Engineering Conference Publication, 1045–52. Boston, MA: Springer US, 1988. http://dx.doi.org/10.1007/978-1-4613-9874-5_126.

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Qafari, Mahnaz Sadat, and Wil van der Aalst. "Root Cause Analysis in Process Mining Using Structural Equation Models." In Business Process Management Workshops, 155–67. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-66498-5_12.

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Conference papers on the topic "Equation root"

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Xie, Jin, Kaiyin Yan, and Yong Chen. "On Global Aspects of Real Newton’s Method in Synthesis of Linkages." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99087.

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Nonlinear equations arise from the synthesis of linkages. Newton’s method is one of the most accessible and easiest to implement of the iterative root-finding algorithms for these equations. As a discrete deterministic dynamical system, Newton’s method contains subsystems which have highly random motion. In a so-called chaotic zone, there is a rapid interchange between the basins of attraction for each root of the equation. Choosing initial points from such chaotic zone, one can obtain a certain number of roots or possible all of them under the Newton’s method. In this paper, how to locate the chaotic zones is addressed following the global analysis of real Newton’s method. It is show that there exist four chaotic zones for a general 4th degree polynomial. As an example, the equation derived from exact synthesis for five positions is solved.
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Qin, Taigui, and Daizong He. "Analysis of Lenardo's methods for three times equation root." In 2011 Fourth International Workshop on Advanced Computational Intelligence (IWACI). IEEE, 2011. http://dx.doi.org/10.1109/iwaci.2011.6159987.

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Choi, Ricky Y. S., and Arthur K. O. So. "On the Application of Mechanical Reinforcement of Tree Roots to Slope Stabilization." In The HKIE Geotechnical Division 41st Annual Seminar. AIJR Publisher, 2022. http://dx.doi.org/10.21467/proceedings.126.24.

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The root strengthening effects on soil behind retaining walls may be quantified by a simplified equation ΔS = 1.2TR(AR/A) where ΔS, TR and AR/A are the shear strength increase, tensile strength of root and root area ratio respectively. However, this effect is ignored during stability analysis due to the possible significant variability of the potential beneficial effect and extreme difficulty in fully characterizing the tree roots and quantifying their effects. In this paper, advancements in the last few decades in biotechnical slope stability are reviewed. Representative models to quantify the mechanical effects of tree roots are studied. If other potential beneficial effects due to existence of roots and suction effect due to transpiration of tree are ignored, the term 1.2, root tensile strength and root area ratio may still be the three key parameters to the root strengthening effect in slope stability.
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Li, Y. X., S. Y. Cao, X. Pan, D. Yuan, and Z. Cui. "A New Method for Q Inversion - Logarithmic Spectrum Equation Root." In 77th EAGE Conference and Exhibition 2015. Netherlands: EAGE Publications BV, 2015. http://dx.doi.org/10.3997/2214-4609.201413061.

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Guo De-long, Yang Nan, and Zhou Yong-quan. "Solving complex chemical equation root based on improved evolution strategy." In 2011 IEEE International Conference on Computer Science and Automation Engineering (CSAE). IEEE, 2011. http://dx.doi.org/10.1109/csae.2011.5953313.

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Li, Siwei, Sergey Fomel, and Alexander Vladimirsky. "Prestack first-break traveltime tomography using the double-square-root eikonal equation." In SEG Technical Program Expanded Abstracts 2012. Society of Exploration Geophysicists, 2012. http://dx.doi.org/10.1190/segam2012-0773.1.

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Hua, Biaolong, George McMechan, and Henri Calandra. "Nonlinear optimal approximation of square root for the one‐way wave equation." In Beijing 2009 International Geophysical Conference and Exposition. Society of Exploration Geophysicists, 2009. http://dx.doi.org/10.1190/1.3603645.

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"A symmetric solution of the Burgers equation with asymptotics described by the root of the cubic dual cusp equation." In Уфимская осенняя математическая школа - 2022. 2 часть. Baskir State University, 2022. http://dx.doi.org/10.33184/mnkuomsh2t-2022-09-28.32.

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Jing, Guodong, and Mengtian Cui. "Research of Newton method to solve the real root of the polynomial equation." In 2012 2nd International Conference on Applied Robotics for the Power Industry (CARPI 2012). IEEE, 2012. http://dx.doi.org/10.1109/carpi.2012.6356519.

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Zhang, Guanquan, and Guojian Shan. "Helical scheme for 2‐D prestack migration based on double‐square‐root equation." In SEG Technical Program Expanded Abstracts 2001. Society of Exploration Geophysicists, 2001. http://dx.doi.org/10.1190/1.1816263.

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Reports on the topic "Equation root"

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Ostashev, Vladimir, Michael Muhlestein, and D. Wilson. Extra-wide-angle parabolic equations in motionless and moving media. Engineer Research and Development Center (U.S.), September 2021. http://dx.doi.org/10.21079/11681/42043.

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Wide-angle parabolic equations (WAPEs) play an important role in physics. They are derived by an expansion of a square-root pseudo-differential operator in one-way wave equations, and then solved by finite-difference techniques. In the present paper, a different approach is suggested. The starting point is an extra-wide-angle parabolic equation (EWAPE) valid for small variations of the refractive index of a medium. This equation is written in an integral form, solved by a perturbation technique, and transformed to the spectral domain. The resulting split-step spectral algorithm for the EWAPE accounts for the propagation angles up to 90° with respect to the nominal direction. This EWAPE is also generalized to large variations in the refractive index. It is shown that WAPEs known in the literature are particular cases of the two EWAPEs. This provides an alternative derivation of the WAPEs, enables a better understanding of the underlying physics and ranges of their applicability, and opens an opportunity for innovative algorithms. Sound propagation in both motionless and moving media is considered. The split-step spectral algorithm is particularly useful in the latter case since complicated partial derivatives of the sound pressure and medium velocity reduce to wave vectors (essentially, propagation angles) in the spectral domain.
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Subrahmanyam, M. B. Roots of Certain Transcendental Equations for Elastic Angular Regions. Fort Belvoir, VA: Defense Technical Information Center, January 1998. http://dx.doi.org/10.21236/ada368632.

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Shani, Uri, Lynn Dudley, Alon Ben-Gal, Menachem Moshelion, and Yajun Wu. Root Conductance, Root-soil Interface Water Potential, Water and Ion Channel Function, and Tissue Expression Profile as Affected by Environmental Conditions. United States Department of Agriculture, October 2007. http://dx.doi.org/10.32747/2007.7592119.bard.

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Constraints on water resources and the environment necessitate more efficient use of water. The key to efficient management is an understanding of the physical and physiological processes occurring in the soil-root hydraulic continuum.While both soil and plant leaf water potentials are well understood, modeled and measured, the root-soil interface where actual uptake processes occur has not been sufficiently studied. The water potential at the root-soil interface (yᵣₒₒₜ), determined by environmental conditions and by soil and plant hydraulic properties, serves as a boundary value in soil and plant uptake equations. In this work, we propose to 1) refine and implement a method for measuring yᵣₒₒₜ; 2) measure yᵣₒₒₜ, water uptake and root hydraulic conductivity for wild type tomato and Arabidopsis under varied q, K⁺, Na⁺ and Cl⁻ levels in the root zone; 3) verify the role of MIPs and ion channels response to q, K⁺ and Na⁺ levels in Arabidopsis and tomato; 4) study the relationships between yᵣₒₒₜ and root hydraulic conductivity for various crops representing important botanical and agricultural species, under conditions of varying soil types, water contents and salinity; and 5) integrate the above to water uptake term(s) to be implemented in models. We have made significant progress toward establishing the efficacy of the emittensiometer and on the molecular biology studies. We have added an additional method for measuring ψᵣₒₒₜ. High-frequency water application through the water source while the plant emerges and becomes established encourages roots to develop towards and into the water source itself. The yᵣₒₒₜ and yₛₒᵢₗ values reflected wetting and drying processes in the rhizosphere and in the bulk soil. Thus, yᵣₒₒₜ can be manipulated by changing irrigation level and frequency. An important and surprising finding resulting from the current research is the obtained yᵣₒₒₜ value. The yᵣₒₒₜ measured using the three different methods: emittensiometer, micro-tensiometer and MRI imaging in both sunflower, tomato and corn plants fell in the same range and were higher by one to three orders of magnitude from the values of -600 to -15,000 cm suggested in the literature. We have added additional information on the regulation of aquaporins and transporters at the transcript and protein levels, particularly under stress. Our preliminary results show that overexpression of one aquaporin gene in tomato dramatically increases its transpiration level (unpublished results). Based on this information, we started screening mutants for other aquaporin genes. During the feasibility testing year, we identified homozygous mutants for eight aquaporin genes, including six mutants for five of the PIP2 genes. Including the homozygous mutants directly available at the ABRC seed stock center, we now have mutants for 11 of the 19 aquaporin genes of interest. Currently, we are screening mutants for other aquaporin genes and ion transporter genes. Understanding plant water uptake under stress is essential for the further advancement of molecular plant stress tolerance work as well as for efficient use of water in agriculture. Virtually all of Israel’s agriculture and about 40% of US agriculture is made possible by irrigation. Both countries face increasing risk of water shortages as urban requirements grow. Both countries will have to find methods of protecting the soil resource while conserving water resources—goals that appear to be in direct conflict. The climate-plant-soil-water system is nonlinear with many feedback mechanisms. Conceptual plant uptake and growth models and mechanism-based computer-simulation models will be valuable tools in developing irrigation regimes and methods that maximize the efficiency of agricultural water. This proposal will contribute to the development of these models by providing critical information on water extraction by the plant that will result in improved predictions of both water requirements and crop yields. Plant water use and plant response to environmental conditions cannot possibly be understood by using the tools and language of a single scientific discipline. This proposal links the disciplines of soil physics and soil physical chemistry with plant physiology and molecular biology in order to correctly treat and understand the soil-plant interface in terms of integrated comprehension. Results from the project will contribute to a mechanistic understanding of the SPAC and will inspire continued multidisciplinary research.
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Dinovitzer, Aaron. PR-214-114504-R02 Development of Sleeve End Fillet Weld Fitness for Service Assessment Tools. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), May 2016. http://dx.doi.org/10.55274/r0010890.

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Pipeline defects such as cracks, dents and corrosion often require permanent pressure retaining repairs. Full encirclement metallic repair sleeves with fillet-welded end connections to the pipe-line are often used for this purpose. In-service failures have occurred at pressure retaining sleeves as a result of defects associated with the sleeve welds, such as hydrogen-induced cracks, undercut at the fillet welds and inadequate weld size. At present, accurate quantitative fitness for service assessments for circumferential defects in sleeve fillet welds are difficult to carry out due to a lack of detailed stress intensity factor solutions for finite length cracks. The primary objective of the project was to improve the assessment of circumferential defects in sleeve fillet welds through the development of more accurate stress intensity factors and plastic collapse solutions for finite length sleeve-end fillet weld toe and root cracks. The stress intensity factors were estimated using detailed finite element analysis. These factors were then used to develop simplified parametric equations which are suitable for carrying out defect assessments on a wide range of pipe and sleeve geometries. These equations can be used in the assessment of fatigue crack growth and/or fracture using failure assessment diagram methods at sleeve end fillets alongside the results developed for other structural geometries in national standards.
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Willits, Daniel H., Meir Teitel, Josef Tanny, Mary M. Peet, Shabtai Cohen, and Eli Matan. Comparing the performance of naturally ventilated and fan-ventilated greenhouses. United States Department of Agriculture, March 2006. http://dx.doi.org/10.32747/2006.7586542.bard.

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The objectives of this project were to predict the performance of naturally and fan-ventilated greenhouses as a function of climate, type of crop, evaporative cooling and greenhouse size, and to estimate the effects of the two cooling systems on yield, quality and disease development in the different crops under study. Background In the competitive field of greenhouse cultivation, growers and designers in both the US and Israel are repeatedly forced to choose between naturally ventilated (NV) and fan ventilated (FV) cooling systems as they expand their ranges in an effort to remain profitable. The known advantages and disadvantages of each system do not presently allow a clear decision. Whether essentially zero operating costs can offset the less dependable cooling of natural ventilation systems is question this report hopes to answer. Major Conclusions US It was concluded very early on that FV greenhouses without evaporative pad cooling are not competitive with NV greenhouses during hot weather. During the first year, the US team found that average air temperatures were always higher in the FV houses, compared to the NV houses, when evaporative pad cooling was not used, regardless of ventilation rate in the FV houses or the vent configuration in the NV houses. Canopy temperatures were also higher in the FV ventilated houses when three vents were used in the NV houses. A second major conclusion was that the US team found that low pressure fogging (4 atm) in NV houses does not completely offset the advantage of evaporative pad cooling in FV houses. High pressure fog (65 atm) is more effective, but considerably more expensive. Israel Experiments were done with roses in the years 2003-2005 and with tomatoes in 2005. Three modes of natural ventilation (roof, side and side + roof openings) were compared with a fan-ventilated (with evaporative cooling) house. It was shown that under common practice of fan ventilation, during summer, the ventilation rate is usually lower with NV than with FV. The microclimate under both NV and FV was not homogeneous. In both treatments there were strong gradients in temperature and humidity in the vertical direction. In addition, there were gradients that developed in horizontal planes in a direction parallel to the direction of the prevailing air velocity within the greenhouse. The gradients in the horizontal direction appear to be larger with FV than with NV. The ratio between sensible and latent heat fluxes (Bowen ratio) was found to be dependent considerably on whether NV or FV is applied. This ratio was generally negative in the naturally ventilated house (about -0.14) and positive in the fan ventilated one (about 0.19). Theoretical models based on Penman-Monteith equation were used to predict the interior air and crop temperatures and the transpiration rate with NV. Good agreement between the model and experimental results was obtained with regard to the air temperature and transpiration with side and side + roof ventilation. However, the agreement was poor with only roof ventilation. The yield (number of rose stems longer than 40 cm) was higher with FV
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Lahav, Ori, Albert Heber, and David Broday. Elimination of emissions of ammonia and hydrogen sulfide from confined animal and feeding operations (CAFO) using an adsorption/liquid-redox process with biological regeneration. United States Department of Agriculture, March 2008. http://dx.doi.org/10.32747/2008.7695589.bard.

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The project was originally aimed at investigating and developing new efficient methods for cost effective removal of ammonia (NH₃) and hydrogen sulfide (H₂S) from Concentrated Animal Feeding Operations (CAFO), in particular broiler and laying houses (NH₃) and hog houses (H₂S). In both cases, the principal idea was to design and operate a dedicated air collection system that would be used for the treatment of the gases, and that would work independently from the general ventilation system. The advantages envisaged: (1) if collected at a point close to the source of generation, pollutants would arrive at the treatment system at higher concentrations; (2) the air in the vicinity of the animals would be cleaner, a fact that would promote animal growth rates; and (3) collection efficiency would be improved and adverse environmental impact reduced. For practical reasons, the project was divided in two: one effort concentrated on NH₃₍g₎ removal from chicken houses and another on H₂S₍g₎ removal from hog houses. NH₃₍g₎ removal: a novel approach was developed to reduce ammonia emissions from CAFOs in general, and poultry houses in particular. Air sucked by the dedicated air capturing system from close to the litter was shown to have NH₃₍g₎ concentrations an order of magnitude higher than at the vents of the ventilation system. The NH₃₍g₎ rich waste air was conveyed to an acidic (0<pH<~5) bubble column reactor where NH₃ was converted to NH₄⁺. The reactor operated in batch mode, starting at pH 0 and was switched to a new acidic absorption solution just before NH₃₍g₎ breakthrough occurred, at pH ~5. Experiments with a wide range of NH₃₍g₎ concentrations showed that the absorption efficiency was practically 100% throughout the process as long as the face velocity was below 4 cm/s. The potential advantages of the method include high absorption efficiency, lower NH₃₍g₎ concentrations in the vicinity of the birds, generation of a valuable product and the separation between the ventilation and ammonia treatment systems. A small scale pilot operation conducted for 5 weeks in a broiler house showed the approach to be technically feasible. H₂S₍g₎ removal: The main goal of this part was to develop a specific treatment process for minimizing H₂S₍g₎ emissions from hog houses. The proposed process consists of three units: In the 1ˢᵗ H₂S₍g₎ is absorbed into an acidic (pH<2) ferric iron solution and oxidized by Fe(III) to S⁰ in a bubble column reactor. In parallel, Fe(III) is reduced to Fe(II). In the 2ⁿᵈ unit Fe(II) is bio-oxidized back to Fe(III) by Acidithiobacillus ferrooxidans (AF).In the 3ʳᵈ unit S⁰ is separated from solution in a gravity settler. The work focused on three sub-processes: the kinetics of H₂S absorption into a ferric solution at low pH, the kinetics of Fe²⁺ oxidation by AF and the factors that affect ferric iron precipitation (a main obstacle for a continuous operation of the process) under the operational conditions. H₂S removal efficiency was found higher at a higher Fe(III) concentration and also higher for higher H₂S₍g₎ concentrations and lower flow rates of the treated air. The rate limiting step of the H₂S reactive absorption was found to be the chemical reaction rather than the transition from gas to liquid phase. H₂S₍g₎ removal efficiency of >95% was recorded with Fe(III) concentration of 9 g/L using typical AFO air compositions. The 2ⁿᵈ part of the work focused on kinetics of Fe(II) oxidation by AF. A new lab technique was developed for determining the kinetic equation and kinetic parameters (KS, Kₚ and mₘₐₓ) for the bacteria. The 3ʳᵈ part focused on iron oxide precipitation under the operational conditions. It was found that at lower pH (1.5) jarosite accumulation is slower and that the performance of the AF at this pH was sufficient for successive operation of the proposed process at the H₂S fluxes predicted from AFOs. A laboratory-scale test was carried out at Purdue University on the use of the integrated system for simultaneous hydrogen sulfide removal from a H₂S bubble column filled with ferric sulfate solution and biological regeneration of ferric ions in a packed column immobilized with enriched AFbacteria. Results demonstrated the technical feasibility of the integrated system for H₂S removal and simultaneous biological regeneration of Fe(III) for potential continuous treatment of H₂S released from CAFO. NH₃ and H₂S gradient measurements at egg layer and swine barns were conducted in winter and summer at Purdue. Results showed high potential to concentrate NH₃ and H₂S in hog buildings, and NH₃ in layer houses. H₂S emissions from layer houses were too low for a significant gradient. An NH₃ capturing system was designed and tested in a 100-chicken broiler room. Five bell-type collecting devices were installed over the litter to collect NH₃ emissions. While the air extraction system moved only 10% of the total room ventilation airflow rate, the fraction of total ammonia removed was 18%, because of the higher concentration air taken from near the litter. The system demonstrated the potential to reduce emissions from broiler facilities and to concentrate the NH₃ effluent for use in an emission control system. In summary, the project laid a solid foundation for the implementation of both processes, and also resulted in a significant scientific contribution related to AF kinetic studies and ferrous analytical measurements.
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