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Academic literature on the topic 'GEP EQUATION'

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Published: 11 September 2023

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Journal articles on the topic "GEP EQUATION"

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Salmasi, Farzin, and John Abraham. "Discharge coefficients for ogee weirs including the effects of a sloping upstream face." Water Supply 20, no. 4 (April 17, 2020): 1493–508. http://dx.doi.org/10.2166/ws.2020.064.

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Abstract Discharge coefficients (C0) for ogee weirs are essential factors for predicting the discharge-head relationship. The present study investigates three influences on the C0: effect of approach depth, weir upstream face slope, and the actual head, which may differ from the design head. This study uses experimental data with multiple non-linear regression techniques and Gene Expression Programming (GEP) models that are applied to introduce practical equations that can be used for design. Results show that the GEP method is superior to the regression analysis for predicting the discharge coefficient. Performance criteria for GEP are R2 = 0.995, RMSE = 0.021 and MAE = 0.015. Design examples are presented that show that the proposed GEP equation correlates well with the data and eliminates linear interpolation using existing graphs.
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Wang, Leizhi, Qingfang Hu, Yintang Wang, Yong Liu, Lingjie Li, and Tingting Cui. "Regional Calibration of Hargreaves Equation in the Xiliaohe Basin." Journal of Geoscience and Environment Protection 04, no. 07 (2016): 28–36. http://dx.doi.org/10.4236/gep.2016.47004.

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Jiang, Huanjun, Ahmed Salih Mohammed, Reza Andasht Kazeroon, and Payam Sarir. "Use of the Gene-Expression Programming Equation and FEM for the High-Strength CFST Columns." Applied Sciences 11, no. 21 (November 8, 2021): 10468. http://dx.doi.org/10.3390/app112110468.

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The ultimate strength of composite columns is a significant factor for engineers and, therefore, finding a trustworthy and quick method to predict it with a good accuracy is very important. In the previous studies, the gene expression programming (GEP), as a new methodology, was trained and tested for a number of concrete-filled steel tube (CFST) samples and a GEP-based equation was proposed to estimate the ultimate bearing capacity of the CFST columns. In this study, however, the equation is considered to be validated for its results, and to ensure it is clearly capable of predicting the ultimate bearing capacity of the columns with high-strength concrete. Therefore, 32 samples with high-strength concrete were considered and they were modelled using the finite element method (FEM). The ultimate bearing capacity was obtained by FEM, and was compared with the results achieved from the GEP equation, and both were compared to the respective experimental results. It was evident from the results that the majority of values obtained from GEP were closer to the real experimental data than those obtained from FEM. This demonstrates the accuracy of the predictive equation obtained from GEP for these types of CFST column.
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Onen, Fevzi. "GEP PREDICTION OF SCOUR AROUND A SIDE WEIR IN CURVED CHANNEL." JOURNAL OF ENVIRONMENTAL ENGINEERING AND LANDSCAPE MANAGEMENT 22, no. 3 (March 17, 2014): 161–70. http://dx.doi.org/10.3846/16486897.2013.865632.

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Side-weirs have been widely used in hydraulic and environmental engineering applications. Side-weir is known as a lateral intake structure, which are significant parts of the distribution channel in irrigation, land drainage, and urban sewerage system, by flow diversion device. Local scour involves the removal of material around piers, abutments, side-weir, spurs, and embankments. Clearwater scour depth based on five dimensional parameters: approach flow velocity (V1/Vc), water head ratio (h1–p)/h1, side-weir length (L/r), side-weir crest height (b/p) and angle of bend θ. The aim of this study is to develop a new formulation for prediction of clear-water scour of side-weir intersection along curved channel using Gene Expression Programming (GEP) which is an algorithm based on genetic algorithms (GA) and genetic programming (GP). In addition, the explicit formulations of the developed GEP models are presented. Also equations are obtained using multiple linear regressions (MLR) and multiple nonlinear regressions (MNRL). The performance of GEP is found more influential than multiple linear regression equation for predicting the clearwater scour depth at side-weir intersection along curved channel. Multiple nonlinear regression equation was quite close to GEP, which serve much simpler model with explicit formulation.
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Azaiez, Naima. "Improved Modelling of Soil Loss in El Badalah Basin: Comparing the Performance of the Universal Soil Loss Equation, Revised Universal Soil Loss Equation and Modified Universal Soil Loss Equation Models by Using the Magnetic and Gravimetric Prospection Outcomes." Journal of Geoscience and Environment Protection 09, no. 04 (2021): 50–73. http://dx.doi.org/10.4236/gep.2021.94005.

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Ashteyat, Ahmed, Yasmeen T. Obaidat, Yasmin Z. Murad, and Rami Haddad. "COMPRESSIVE STRENGTH PREDICTION OF LIGHTWEIGHT SHORT COLUMNS AT ELEVATED TEMPERATURE USING GENE EXPRESSION PROGRAMING AND ARTIFICIAL NEURAL NETWORK." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 26, no. 2 (February 10, 2020): 189–99. http://dx.doi.org/10.3846/jcem.2020.11931.

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The experimental behavior of reinforced concrete elements exposed to fire is limited in the literature. Although there are few experimental programs that investigate the behavior of lightweight short columns, there is still a lack of formulation that can accurately predict their ultimate load at elevated temperature. Thus, new equations are proposed in this study to predict the compressive strength of the lightweight short column using Gene Expression Programming (GEP) and Artificial neural networks (ANN). A total of 83 data set is used to establish GEP and ANN models where 70% of the data are used for training and 30% of the data are used for validation and testing. The predicting variables are temperature, concrete compressive strength, steel yield strength, and spacing between stirrups. The developed models are compared with the ACI equation for short columns. The results have shown that the GEP and ANN models have a strong potential to predict the compressive strength of the lightweight short column. The predicted compressive strengths of short lightweight columns using the GEP and ANN models are closer to the experimental results than that obtained using the ACI equations.
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., Hoang Nguyen, Nam Xuan Bui ., Hieu Quang Tran ., and Giang Huong Thi Le. "A novel soft computing model for predicting blast - induced ground vibration in open - pit mines using gene expression programming." Journal of Mining and Earth Sciences 61, no. 5 (October 10, 2020): 107–16. http://dx.doi.org/10.46326/jmes.ktlt2020.09.

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The efforts of this study are to develop and propose a state - of - the - art model for predicting blast - induced ground vibration in open - pit mines with high accuracy anf ability based on the gene expression programming (GEP) technique. 25 blasts were conducted in the Tan Dong Hiep quarry mines with a total of 83 blasting events that were collected for this study. The GEP method was then applied to develop a non - linear equation for predicting blast - induced ground vibration based on a variety of influential parameters. A traditional empirical equation, namely Sadovski, was also applied to compare with the proposed GEP model. The results indicated that the GEP model can predict blast - induced ground vibration in open - pit mines better than the Sadovski model with an RMSE of 0.986 and R2 of 0.867. Meanwhile, the traditional empirical model (Sadovski) only provided an accuracy with an RMSE of 1.850 và R2 of 0.767.
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Hajihassani, Mohsen, Shahrum Shah Abdullah, Panagiotis G. Asteris, and Danial Jahed Armaghani. "A Gene Expression Programming Model for Predicting Tunnel Convergence." Applied Sciences 9, no. 21 (November 1, 2019): 4650. http://dx.doi.org/10.3390/app9214650.

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Underground spaces have become increasingly important in recent decades in metropolises. In this regard, the demand for the use of underground spaces and, consequently, the excavation of these spaces has increased significantly. Excavation of an underground space is accompanied by risks and many uncertainties. Tunnel convergence, as the tendency for reduction of the excavated area due to change in the initial stresses, is frequently observed, in order to monitor the safety of construction and to evaluate the design and performance of the tunnel. This paper presents a model/equation obtained by a gene expression programming (GEP) algorithm, aiming to predict convergence of tunnels excavated in accordance to the New Austrian Tunneling Method (NATM). To obtain this goal, a database was prepared based on experimental datasets, consisting of six input and one output parameter. Namely, tunnel depth, cohesion, frictional angle, unit weight, Poisson’s ratio, and elasticity modulus were considered as model inputs, while the cumulative convergence was utilized as the model’s output. Configurations of the GEP model were determined through the trial-error technique and finally an optimum model is developed and presented. In addition, an equation has been extracted from the proposed GEP model. The comparison of the GEP-derived results with the experimental findings, which are in very good agreement, demonstrates the ability of GEP modeling to estimate the tunnel convergence in a reliable, robust, and practical manner.
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Al-Aboodi, Ali H. "ESTIMATION OF MONTHLY MEAN REFERENCE EVAPOTRANSPIRATION USING GENE EXPRESSION PROGRAMMING." Kufa Journal of Engineering 8, no. 1 (February 16, 2017): 37–50. http://dx.doi.org/10.30572/2018/kje/811189.

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Evapotranspiration is a main component of the water cycle and is important in crop growth. Monthly mean reference evapotranspiration (ETo) is estimated using gene expression programming (GEP) in Basrah City, south of Iraq. Various climatic data, such as air temperature, relative humidity, and wind speed are used as inputs of GEP model to estimate the values of reference evapotranspiration (ETo) given by the FAO-56 (Penman-Monteith equation). Nine input combinations tested with GEP are coded as model No. (1-9). Root relative squared error (RRSE) is taken as fitness function in each of GEP models. GEP models with three climatic input variables (temperature, relative humidity, and wind speed) take the highest level in the performance. The GEP technique was successfully employed to estimate ETo in the study area. The explicit formulas obtained can be used as powerful models for estimating the mean monthly ETo in the irrigation practices with limited climatic data.
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Mutakela, Patrick S., Joyce P. Lepetu, Gofaone Rammotokara, Melusi Rampart, and Sarah Assem Ibrahim. "Biomass Prediction Equation for <i>Colophospermum mopane</i> (Mopane) in Botswana." Journal of Geoscience and Environment Protection 11, no. 06 (2023): 1–22. http://dx.doi.org/10.4236/gep.2023.116001.

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Dissertations / Theses on the topic "GEP EQUATION"

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Baek, Chin-wook. "Finite-gap solutions of the defocusing nonlinear Schrodinger equation." Thesis, Imperial College London, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.485428.

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The subject of this thesis is a study of the two-component nonlinear Schrodinger equation (NSE) in (1+1)-dimension. Two aitemative cases are possible, referred to as the focusing and defocusing cases in applications to studies in nonlinear optics. The main focus of the work in this thesis is on the defocusing case, but results known for the focusing case are also discussed and compared, where relevant. This thesis is comprised of two themes. The first is the effective integration of the NSE, using techniques of algebrogeometric theory. Here, the Baker-Akheizer formalism is developed and applied to the Manakov system. This formalism is used to derive the finite-gap solution, expressed in terms of Riemann theta-functions. The second is the derivation of soliton solutions from these finite-gap solutions, by considering an important limit; namely, the closing ofthe gap in the Riemanu surface associated with. the spectral curve yields explicit representations for soliton solutions. The scalar NSE is first considered by way of introducing and discussing relevant techniques. Then, it is shown how these methods can be extended to the vector case. Next, two particular cases are considered. Firstly, it is shown that the genus 1 case yields a dark-dark soliton solution in the limiting case. An aspect of the vector problem not found with the scalar case is the existence of dark-bright solitons. A single dark-bright soliton can be obtained by considering genus 2, not genus 1, in the soliton limit. A discussion of these derivations is an important feature of the thesis. We discuss next a solution obtained elsewhere introducing a separable ansatz for both components shown to be a genus 2 solution. We discuss the fact that the appropriate curve is hyperelliptic, and indicate how it is related to our trigonal curve by a birational map.
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Kamli, Ali Ahmed. "Reliability of the Dyson-Schwinger gap equation in technicolor theories." Thesis, University of Southampton, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358369.

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Warren, Oliver H. "A study of finite gap solutions to the nonlinear Schrödinger equation." Thesis, Imperial College London, 2007. http://hdl.handle.net/10044/1/1255.

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The vector nonlinear Schrödinger equation is an envelope equation which models the propagation of ultra-short light pulses and continuous-wave beams along optical fibres. Previous work has focused almost entirely on soliton solutions to the equation using a Lax representation originally developed by Manakov. We prove recursion formulae for the family of higher-order nonlinear Schrödinger equations, along with its associated Lax hierarchy, before investigating finite gap solutions using an algebrogeometric approach which introduces Baker-Akhiezer functions defined upon the Riemann surface of the relevant spectral curve. We extend this approach to account for solutions of arbitrary genus and compare it with an alternative method describing solutions of genus two. The scalar nonlinear Schrödinger and Heisenberg ferromagnet equations were shown to be equivalent following work by Lakshmanan; we generalise this idea by introducing the Heisenberg ferromagnet hierarchy and show it is entirely gauge equivalent to the scalar nonlinear Schrödinger hierarchy in the attractive case. We also investigate the polarisation state evolution of general solutions to the vector nonlinear Schrödinger equation and study possible degenerations to the Heisenberg ferromagnet equation.
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Fullwood, Elliot J. "Quasiparticle dynamics at the superfluid '3He A-B interface." Thesis, University of Sussex, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.321464.

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Sancier-Barbosa, Flavia Cabral. "Closing the memory gap in stochastic functional differential equations." OpenSIUC, 2011. https://opensiuc.lib.siu.edu/dissertations/346.

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In this paper, we obtain convergence of solutions of stochastic differential systems with memory gap to those with full finite memory. More specifically, solutions of stochastic differential systems with memory gap are processes in which the intrinsic dependence of the state on its history goes only up to a specific time in the past. As a consequence of this convergence, we obtain a new existence proof and approximation scheme for stochastic functional differential equations (SFDEs) whose coefficients have linear growth. In mathematical finance, an option pricing formula with full finite memory is obtained through convergence of stock dynamics with memory gap to stock dynamics with full finite memory.
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Sticksel, Christoph. "Efficient equational reasoning for the Inst-Gen Framework." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/efficient-equational-reasoning-for-the-instgen-framework(67ead780-3ec9-4897-ac17-48d3de011b4b).html.

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We can classify several quite different calculi for automated reasoning in first-order logic as instantiation-based methods (IMs). Broadly speaking, unlike in traditional calculi such as resolution where the first-order satisfiability problem is tackled by deriving logical conclusions, IMs attempt to reduce the first-order satisfiability problem to propositional satisfiability by intelligently instantiating clauses. The Inst-Gen-Eq method is an instantiation-based calculus which is complete for first-order clause logic modulo equality. Its distinctive feature is that it combines first-order reasoning with efficient ground satisfiability checking, which is delegated in a modular way to any state-of-the-art ground solver for satisfiability modulo theories (SMT). The first-order reasoning modulo equality employs a superposition-style calculus which generates the instances needed by the ground solver to refine a model of a ground abstraction or to witness unsatisfiability. The thesis addresses the main issue in the Inst-Gen-Eq method, namely efficient extraction of instances, while providing powerful redundancy elimination techniques. To that end we introduce a novel labelled unit superposition calculus with sets, AND/OR trees and ordered binary decision diagrams (OBDDs) as labels. The different label structures permit redundancy elimination each to a different extent. We prove completeness of redundancy elimination from labels and further integrate simplification inferences based on term rewriting. All presented approaches, in particular the three labelled calculi are implemented in the iProver-Eq system and evaluated on standard benchmark problems.
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Capdevilla, Roldan Rodolfo Maia [UNESP]. "Dynamical chiral symmetry breaking: the fermionic gap equation with dynamical gluon mass and confinement." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/92026.

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Made available in DSpace on 2014-06-11T19:25:34Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-02-28Bitstream added on 2014-06-13T20:53:39Z : No. of bitstreams: 1 capdevillaroldan_rm_me_ift.pdf: 1695600 bytes, checksum: 56f8cc2724bbe924e0b430ebe1a3b24e (MD5)
Alguns aspectos da quebra de simetria quiral para quarks na representação fundamental são discutidos no contexto das equações de Schwinger-Dyson. Estudamos a equação de gap fermionica incluindo o efeito de uma massa dinêmica para os gluons. Ao estudar esta equação de gap verificamos que a intenção não é forte o suficiente para gerar uma massa dinâmica dos quarks compatível com os dados experimentais. Também discutimos como a introdução de um propagador confinante pode mudar este cenário, exatamente como foi proposto por Cornwall [1] recentemente, desta forma estudamos uma equação de gap completa, composta pela troca de um gluon massivo e por um termo confinante; M('p POT 2') = 'M IND. c('p POT 2') + 'M IND. 1g'('p POT 2'). Encontramos soluções assintótica desta equação de gap nos casos de constante de acoplamento constante e corredora. Este último caso corresponde a um aprimoramento do cálculo com constante de acoplamento constante feito por Doff, Machado e Natale [2]
Some aspects of chiral symmetry breaking for quarks in the fundamental representation are discussed in the framework of the Schwinger-Dyson equations. We study the fermionic gap equation including effects of dynamical gluon mass. Studying the bifurcation equation of this gap equation we verify that the interaction is not strong enough to generate a satisfactory dynamical quark mass. We also discuss how the introduction of a confining propagator may change this scenario as recently pointed out by Cornwall [1], so we study a complete gap equation composed by the one-dressed-gluon exchange term and a confining term: M('p POT 2') = 'M IND. c('p POT 2') + 'M IND. 1g'('p POT 2'). We find asymptotic solutions for this gap equation in the cases of constant coupling and running coupling constant. This last case is an improvement of the constant coupling calculation of Doff, Machado and Natale [2]
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Capdevilla, Roldan Rodolfo Maia. "Dynamical chiral symmetry breaking : the fermionic gap equation with dynamical gluon mass and confinement /." São Paulo, 2013. http://hdl.handle.net/11449/92026.

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Orientador: Adriano Antonio Natale
Banca: Adriano Doff Sotta Gomes
Banca: Alex Gomes Dias
Resumo: Alguns aspectos da quebra de simetria quiral para quarks na representação fundamental são discutidos no contexto das equações de Schwinger-Dyson. Estudamos a equação de gap fermionica incluindo o efeito de uma massa dinêmica para os gluons. Ao estudar esta equação de gap verificamos que a intenção não é forte o suficiente para gerar uma massa dinâmica dos quarks compatível com os dados experimentais. Também discutimos como a introdução de um propagador confinante pode mudar este cenário, exatamente como foi proposto por Cornwall [1] recentemente, desta forma estudamos uma equação de gap "completa", composta pela troca de um gluon massivo e por um termo confinante; M('p POT 2') = 'M IND. c('p POT 2') + 'M IND. 1g'('p POT 2'). Encontramos soluções assintótica desta equação de gap nos casos de constante de acoplamento "constante" e "corredora". Este último caso corresponde a um aprimoramento do cálculo com constante de acoplamento "constante" feito por Doff, Machado e Natale [2]
Abstract: Some aspects of chiral symmetry breaking for quarks in the fundamental representation are discussed in the framework of the Schwinger-Dyson equations. We study the fermionic gap equation including effects of dynamical gluon mass. Studying the bifurcation equation of this gap equation we verify that the interaction is not strong enough to generate a satisfactory dynamical quark mass. We also discuss how the introduction of a confining propagator may change this scenario as recently pointed out by Cornwall [1], so we study a "complete" gap equation composed by the one-dressed-gluon exchange term and a confining term: M('p POT 2') = 'M IND. c('p POT 2') + 'M IND. 1g'('p POT 2'). We find asymptotic solutions for this gap equation in the cases of "constant coupling" and "running coupling constant". This last case is an improvement of the constant coupling calculation of Doff, Machado and Natale [2]
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9

Hudson, Melanie. "Studies of the formation of homogeneous mixed silicon-titanium/zirconium oxides by the sol-gel route." Thesis, Brunel University, 1994. http://bura.brunel.ac.uk/handle/2438/5371.

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This thesis is concerned with the preparation of mixed silicon-titanium oxides (Ti02=4.1-21.9wt%) and silicon-zirconium oxides (Zr02=4.1-22.Iwt%) by the sol-gel route. Methods of preparing homogeneous Si02-TiO2 gels and SiO2-Zr02 gels have been explored. In this work bis(acetylacetonato)titanium diisopropoxide or bis(acetylacetonato)zirconium dipropoxide and tetraethyl orthosilicate (TEOS) have been hydrolysed simultaneously in iso-propanol to form homogeneous gels. Using these systems, the effects of the reaction conditions, amount of titania/zirconia present in the gel, drying conditions and thermal treatment of the dry gels on the bulk and structural properties have been investigated by a variety of experimental methods including X-ray diffraction, mid- and near-infrared spectroscopy and gas adsorption techniques. For SiO2-TiO2 powders and monoliths, and SiO2-ZrO3 monoliths, thermal treatment has been found to significantly reduce the surface area (from 750-1.0m2g-1), pore volume (from 0.56-0.001cm3g-1') and relative number of silanol groups on the surface of the sample above 700°C. Average pore diameters remain constant at temperatures below 900°C (ca 54-21Å for monoliths), although the micropore volume does decrease (0.04-0.0cm3g-1) suggesting that smaller pores are destroyed by the heating process. For SiO2-TiO2 powders, the average pore diameter was ca IOÅ larger than for the corresponding monolith suggesting that small pores are destroyed during powdering. At 1100°C, gas adsorption data indicate that the samples are fully densified. This is supported by NIR spectra which detect no silanol groups on the surface of the sample. Structural changes arising from compositional changes and differing thermal treatment regimes have been monitored using mid-infrared spectroscopy and X-ray diffraction. With increasing temperature the silica matrix strengthens and titanium/zirconium are incorporated into the matrix. Monolithic SiO2-TiO2 gels (Ti02=6.34 weight%) remained amorphous at 1100°C, whereas powders began to exhibit diffraction patterns predominantly from anatase at 700°C. Anatase crystallite sizes have been calculated using the Scherrer equation and have been found to be between 16.3 and 5.4nm. Monolithic SiO2-ZrO2 gels containing 4.1 and 4.9 weight% zirconia were found to be amorphous after treatment at 1100°C. Increasing the zirconia content to 6.4 and 22.1 weight% resulted in gels that were amorphous up to 900°C. Further treatment at 1100°C, resulted in tetragonal zirconia and some cristobalite being formed. Crystallite sizes have been calculated as being between 2.7 and 1.6nm for tetragonal zirconia and from 4.1 to 2.8nm for cristobalite. Increasing the levels of titania/zirconia in the sample resulted in higher relative levels of hydrogen-bonded silanol groups. On hydration, the increased levels of titania/zirconia resulted in no observable free silanol groups on the surface suggesting that the surface becomes more hydrophilic as the amount of titania/zirconia present in the sample increases. This suggests that water becomes more tightly bound to Ti-OH /Zr-OH groups on the surface and within the pores, resulting in fewer free silanol type groups. A double alkoxide bis(acetylacetonato)titanium di(triethoxysilane) [Ti(acac)2(OSi(OC2H5)3)2] has also been synthesised and characterised. Mixed Si02-TiO2 gels have also been prepared by the simultaneous hydrolysis of Ti(acac)2(OSi(OC2H5)3)2 and TEOS under acidic conditions in ethanol. The effects of reaction conditions and thermal treatment of the dry gels have been investigated. Increasing the treatment temperature of the samples resulted in the progressive decrease in surface area (533-3.0m2g-1), pore volume (0.18-0.003cm3g-1), micropore volume (0.06-0.00cm3g-1) and relative number of silanol groups on the surface. However, the average pore diameter remained constant at temperatures up to 700°C. Changes in pore volume (0.07-0.005cm3g-1), surface area (300-3.0m2g-1) and average pore diameter (26.9-91.9Å) were largest at 900°C, and the samples were found to be almost completely dense. This was confirmed by the absence of observable silanol groups by NIR spectroscopy. After heating at temperatures up to 900°C, the samples were found to be amorphous by XRD. However increasing the temperature to 1100°C resulted in the formation of some crystalline anatase. The anatase crystal sizes have been calculated as being from 16.3 to 10.8nm in diameter. NIR studies of silica-zirconia and silica-titania gels (prepared by both methods), indicate that decreasing the amount of acid used in the hydrolysis reaction resulted in higher relative levels of hydrogen bonded silanol species. Similarly, decreasing the amount of acid increased the micropore volume and decreased the mesoporosity of the resulting samples. Generally, decreasing the amount of acid used for the hydrolysis for silica-zirconia and silica-titania gels (prepared by both methods), results in a decrease in the overall surface area and pore volume of the resulting material. The resulting isotherms indicate that the samples became less mesoporous as the amount of acid used in the hydrolysis reaction decreased. This was accompanied by an increase in the micropore volume. For SiO2-TiO2 monoliths prepared from a double alkoxide and Si02-ZrO2 monoliths the resulting pore structure is more rigid and composed of smaller pores than that of SiO2-TiO2 powders and monoliths prepared from bis(acetylacetonato)titanium diisopropoxide.
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Lu, Kang. "The Application of Generalised Maxwell-Stefan Equations to Protein Gels." Thesis, University of Canterbury. Chemical and Process Engineering, 2007. http://hdl.handle.net/10092/1236.

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The removal of milk fouling deposits often requires the diffusion of electrolyte solutions such as sodium hydroxide through a gel. Very often more than one single anion and one single cation are involved and thus the modelling of such diffusion requires a multicomponent description. Diffusion of electrolyte solutions through gels can be modelled using the Maxwell-Stefan equation. The driving forces for diffusion are the chemical potential gradients of ionic species and the diffusion potential, i.e., the electrostatic potential induced by diffusion of the ions. A model based on the Maxwell-Stefan equation was applied to electrolyte solutions and electrolyte solutions with a gel. When modelling the diffusion of electrolyte solutions, the resulting equations were found to be a partial differential algebraic equation system with a differentiation index of two. The identification of this characteristic of the system enabled a solution method using the method of lines to be developed. When modelling the diffusion of electrolyte solutions through a gel an explicit expression for diffusion potential was developed and hence the diffusion equations were solved. Numerical solutions were presented for a number of case studies and comparisons were made with solutions from literature and between different electrolyte systems. It was found that the results of diffusion of electrolytes were in good agreement with those of experiments and literature. In the case of diffusion of electrolytes through a gel, swelling of the gel was predicted. The model can be improved by adding thermodynamic factors and can be easily extended to multiple ion systems.
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Books on the topic "GEP EQUATION"

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Gesztesy, Fritz. (m)KdV solitons on the background of quasi-periodic finite-gap solutions. Providence, R.I: American Mathematical Society, 1995.

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Simos, Th. Forecasting quarterly GDP using a system of stochastic differential equations. Athens: Centre of Planning and Economic Research, 2002.

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Dyall, Kenneth G. All-electron molecular Dirac-Hartree-Fock calculations: Properties of the Group IV monoxides GeO, SnO and Pbo. [Washington, D.C: National Aeronautics and Space Administration, 1991.

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Dyall, Kenneth G. All-electron molecular Dirac-Hartree-Fock calculations: Properties of the Group IV monoxides GeO, SnO and Pbo. [Washington, D.C: National Aeronautics and Space Administration, 1991.

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Master math: Solving word problems : analyze any word problem, translate it into mathematical terms, and get the right answer! Boston, MA: Course Technology, 2010.

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1942-, Bulla W., ed. Algebro-geometric quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies. Providence, R.I: American Mathematical Society, 1998.

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Martin, Gutting, and SpringerLink (Online service), eds. Special Functions of Mathematical (Geo-)Physics. Basel: Springer Basel, 2013.

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la, Llave Rafael de, and Seara Tere M. 1961-, eds. A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: Heuristics and rigorous verification on a model. Providence, R.I: American Mathematical Society, 2006.

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Center, Langley Research, ed. Expanded equations for torque and force on a cylindrical permanent magnet core in a large-gap magnetic suspension system. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1997.

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Groom, Nelson J. Expanded equations for torque and force on a cyclindrical permanent magnet core in a large-gap magnetic suspension system. Washington, D.C: National Aeronautics and Space Administration, 1997.

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Book chapters on the topic "GEP EQUATION"

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Pagano, Stéphane, and Marc Bonnet. "Constitutive Equation Gap." In Full-Field Measurements and Identification in Solid Mechanics, 275–300. Hoboken, NJ USA: John Wiley & Sons, Inc., 2012. http://dx.doi.org/10.1002/9781118578469.ch10.

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Volchkov, V. V. "Gap Theorems." In Integral Geometry and Convolution Equations, 366–77. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-010-0023-9_29.

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Fujita, Shigeji, Kei Ito, and Salvador Godoy. "The Energy Gap Equations." In Quantum Theory of Conducting Matter, 45–60. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-88211-6_4.

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Gould, Martin, and Edward Hurst. "Separable Differential Equations." In Bridging the Gap to University Mathematics, 1–14. London: Springer London, 2008. http://dx.doi.org/10.1007/978-1-84800-290-6_8.

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Sörensen, M. P., T. Schneider, and M. Frick. "Nonlinear Properties of the BCS Gap Equation." In NATO ASI Series, 315–27. Boston, MA: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4684-5961-6_33.

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Bao, Qiulan, Ting Yang, Ruoyu Mo, Xiujuan Zhang, and Zhousen Zhu. "Fine Linear Equation Algorithm for Geo-Fence." In Lecture Notes in Electrical Engineering, 441–56. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0416-7_45.

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De Filippis, Cristiana, and Giuseppe Mingione. "Interpolative gap bounds for nonautonomous integrals." In Harmonic Analysis and Partial Differential Equations, 67–105. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-25424-6_4.

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Roblin, Yves. "Polarization in a GeV RLA." In Polarized Beam Dynamics and Instrumentation in Particle Accelerators, 197–215. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-16715-7_8.

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AbstractPolarized beam dynamics in a Recirculated Linear Accelerator (RLA) differ markedly from their behavior in circular machines. After giving a brief overview of the topology of a RLA we discuss the unique requirements for polarized beam physics experiments carried at these types of machines and their implications on the spin transport. The Thomas BMT equation will be rewritten to emphasize the relevant features and the relationship between spin transport and global accelerator parameters such as the accelerating profiles. We will consider scenarios for which one or more experimental hall has to be provided with longitudinal polarization and discuss how this is achieved. Finally, a review of possible depolarization and spin precession effects occurring in these machines will be presented. In order to illustrate this, we will examine the case of the Stanford Linear Collider (SLC) where such effects were first observed.
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Zhang, Yifan, and Dekang Zhao. "Using Improved Genetic Algorithm to Solve the Equations." In Geo-informatics in Sustainable Ecosystem and Society, 265–71. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-7025-0_27.

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Soerensen, Mads Peter. "Bifurcations and Nonlinear Properties of the Bcs Gap Equation." In Nonlinear Superconductive Electronics and Josephson Devices, 427–36. Boston, MA: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4615-3852-3_32.

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Conference papers on the topic "GEP EQUATION"

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Elfass, Sherif, Gary Norris, and Panchaligam Vimalaraj. "A Simple Bearing Capacity Equation." In Geo-Denver 2007. Reston, VA: American Society of Civil Engineers, 2007. http://dx.doi.org/10.1061/40915(234)4.

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Witten, Benjamin, and Brad Artman. "Wave-Equation Propagation as a Body-Wave Filter." In GEO 2010. European Association of Geoscientists & Engineers, 2010. http://dx.doi.org/10.3997/2214-4609-pdb.248.410.

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Walton-Macaulay, Corrie, L. Sebastian Bryson, and Brock Kidd. "An Equation Describing the Shear Modulus of Unsaturated Soil." In Geo-Chicago 2016. Reston, VA: American Society of Civil Engineers, 2016. http://dx.doi.org/10.1061/9780784480151.021.

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Nam, BooHyun, Jinwoo An, and Michael R. Murphy. "Improvements to the AASHTO Subgrade Resilient Modulus (MR) Equation." In Geo-Congress 2014. Reston, VA: American Society of Civil Engineers, 2014. http://dx.doi.org/10.1061/9780784413272.234.

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Khosrojerdi, Mahsa, Ming Xiao, Tong Qiu, and Jennifer Nicks. "Predictive Equation for Estimating Lateral Deformation of GRS Abutments." In Geo-Congress 2020. Reston, VA: American Society of Civil Engineers, 2020. http://dx.doi.org/10.1061/9780784482797.046.

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Al Dulaijan, Khaled, and Saleh M. Al-Saleh. "Practical Implementation of Wave-Equation Datuming for Resolving Near-Surface Problems." In GEO 2010. European Association of Geoscientists & Engineers, 2010. http://dx.doi.org/10.3997/2214-4609-pdb.248.113.

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Ki, Kyung Seo, Donggeon Lee, Bugeun Kim, and Gahgene Gweon. "Generating Equation by Utilizing Operators : GEO model." In Proceedings of the 28th International Conference on Computational Linguistics. Stroudsburg, PA, USA: International Committee on Computational Linguistics, 2020. http://dx.doi.org/10.18653/v1/2020.coling-main.38.

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Ki, Kyung Seo, Donggeon Lee, Bugeun Kim, and Gahgene Gweon. "Generating Equation by Utilizing Operators : GEO model." In Proceedings of the 28th International Conference on Computational Linguistics. Stroudsburg, PA, USA: International Committee on Computational Linguistics, 2020. http://dx.doi.org/10.18653/v1/2020.coling-main.38.

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Ahn, Jaehun, Yusuk Kim, Yun-Tae Kim, and Hosung Shin. "A Constitutive Equation for Compression Behaviors of Artificially Cemented Composite Geo-Materials." In Geo-Congress 2013. Reston, VA: American Society of Civil Engineers, 2013. http://dx.doi.org/10.1061/9780784412787.006.

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Xue, Ronghui, and Qingyun Di. "Forward modeling of the three‐ dimensional integral equation based on Born approximation." In GEM Beijing 2011, edited by Xiong Li, Yaoguo Li, and Xiaohong Meng. Society of Exploration Geophysicists, 2011. http://dx.doi.org/10.1190/1.3659107.

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Reports on the topic "GEP EQUATION"

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Rosen, Richard A. Can Panel Data Methodologies Determine the Impact of Climate Change on Economic Growth? Institute for New Economic Thinking Working Paper Series, November 2021. http://dx.doi.org/10.36687/inetwp171.

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Several major papers have been published over the last ten years claiming to have detected the impact of either annual variations in weather or climate change on the GDPs of most countries in the world using panel data-based statistical methodologies. These papers rely on various multivariate regression equations which include the annual average temperatures for most countries in the world as one or more of the independent variables, where the usual dependent variable is the change in annual GDP for each country from one year to the next year over 30-50 year time periods. Unfortunately, the quantitative estimates derived in these papers are misleading because the equations from which they are calculated are wrong. The major reason the resulting regression equations are wrong is because they do not include any of the appropriate and usual economic factors or variables which are likely to be able to explain changes in GDP/economic growth whether or not climate change has already impacted each country’s economy. These equations, in short, exhibit suffer from “omitted variable bias,” to use statistical terminology.
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Lubowa, Nasser, Zita Ekeocha, Stephen Robert Byrn, and Kari L. Clase. Pharmaceutical Industry in Uganda: A Review of the Common GMP Non-conformances during Regulatory Inspections. Purdue University, December 2021. http://dx.doi.org/10.5703/1288284317442.

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The prevalence of substandard medicines in Africa is high but not well documented. Low and Middle-Income Countries (LMICs) are likely to face considerable challenges with substandard medications. Africa faces inadequate drug regulatory practices, and in general, compliance with Good Manufacturing Practices (GMP) in most of the pharmaceutical industries is lacking. The majority of pharmaceutical manufacturers in developing countries are often overwhelmed by the GMP requirements and therefore are unable to operate in line with internationally acceptable standards. Non-conformances observed during regulatory inspections provide the status of the compliance to GMP requirements. The study aimed to identify the GMP non-conformances during regulatory inspections and gaps in the production of pharmaceuticals locally manufactured in Uganda by review of the available 50 GMP reports of 21 local pharmaceutical companies in Uganda from 2016. The binary logistic generalized estimating equations (GEE) model was applied to estimate the association between odds of a company failing to comply with the GMP requirements and non-conformances under each GMP inspection parameter. Analysis using dummy estimation to linear regression included determination of the relationship that existed between the selected variables (GMP inspection parameters) and the production capacity of the local pharmaceutical industry. Oral liquids, external liquid preparations, powders, creams, and ointments were the main categories of products manufactured locally. The results indicated that 86% of the non-conformances were major, 11% were minor, and 3% critical. The majority of the non-conformances were related to production (30.1%), documentation (24.5%), and quality control (17.6%). Regression results indicated that for every non-conformance under premises, equipment, and utilities, there was a 7-fold likelihood of the manufacturer failing to comply with the GMP standards (aOR=6.81, P=0.001). The results showed that major non-conformances were significantly higher in industries of small scale (B=6.77, P=0.02) and medium scale (B=8.40, P=0.04), as compared to those of large scale. This study highlights the failures in quality assurance systems and stagnated GMP improvements in these industries that need to be addressed by the manufacturers with support from the regulator. The addition of risk assessment to critical production and quality control operations and establishment of appropriate corrective and preventive actions as part of quality management systems are required to ensure that quality pharmaceuticals are manufactured locally.
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Fasso, A. Heavy Ion Interactions From Coulomb Barrier to Few GeV/n: Boltzmann Master Equation Theory and FLUKA Code Performances. Office of Scientific and Technical Information (OSTI), December 2004. http://dx.doi.org/10.2172/839786.

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Nagahi, Morteza, Raed Jaradat, Simon Goerger, Michael Hamilton, Randy Buchanan, Sawsan Abutabenjeh, and Junfeng Ma. The impact of practitioners’ personality traits on their level of systems-thinking skills preferences. Engineer Research and Development Center (U.S.), October 2022. http://dx.doi.org/10.21079/11681/45791.

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In this study, we used a structural equation modeling method to investigate the relationship between systems engineers and engineering managers’ Systems-Thinking (ST) skills preferences and their Personality Traits (PTs) in the domain of complex system problems. As organizations operate in more and more turbulent and complex environments, it has become increasingly important to assess the ST skills preferences and PTs of engineers. The current literature lacks studies related to the impact of systems engineers and engineering managers’ PTs on their ST skills preferences, and this study aims to address this gap. A total of 99 engineering managers and 104 systems engineers provided the data to test four hypotheses posed in this study. The results show that the PTs of systems engineers and engineering managers have a positive impact on their level of ST skills preferences and that the education level, the current occupation type, and the managerial experience of the systems engineers and engineering managers moderate the main relationship in the study.
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Tossey, Brett, and Ramgopal Thodla. PR-180-094506-R01 Challenges for Safe and Reliable On-Shore Pipeline Transport of Supercritical CO2. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), September 2010. http://dx.doi.org/10.55274/r0010712.

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There is interest within the pipeline industry in transporting supercritical CO2 in pipelines. A significant issue is the lack of an independent industry standard for supercritical CO2 pipelines. Existing industry standard for liquid and gas transmission are used for mechanical design requirements, but selected properties of supercritical CO2 make it a unique product. Impurities in the gas steam, materials selection, and leak detection in supercritical CO2 require special consideration. The objective of this project is to engage the supercritical CO2 industry in a workshop and use their knowledge to complete a gap analysis. The project is divided into two main thrusts; survey of knowledge and gaps by conducting an industry workshop (Thrust 1) and to outline what efforts and work is needed to close these gaps in a limited way (Thrust 2). This report summarizes the results of both thrusts. This report summarizes the results of the gaps analysis. The primary finding is that the supercritical CO2 pipeline operators in the United States are confident that the designs of their transmission systems are safe and adequate. Another important finding was the need for improvement in the equation of state (EOS). Currently, most models fail to accurately predict the affects of coal combustion impurities on the phase behavior of supercritical CO2. Improvements in metering technology, materials selection criteria, and leak detection were also identified as gaps. The final gap that was identified was the need for a standardized �blow-down� procedure during system startup and shutdown. An industry standard specific to supercritical CO2 transportation should include sound engineering guidance covering each of these gaps. See the associated linked documents for appendices to this report.
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Nagahi, Morteza, Niamat Ullah Ibne Hossain, Safae El Amrani, Raed Jaradat, Laya Khademibami, Simon Goerger, and Randy Buchanan. Investigating the influence of demographics and personality types on practitioners' level of systems thinking skills. Engineer Research and Development Center (U.S.), March 2022. http://dx.doi.org/10.21079/11681/43622.

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Although the application of systems thinking (ST) has become essential for practitioners when dealing with turbulent and complex environments, there are limited studies available in the current literature that investigate how the ST skills of practitioners vary with regard to demographic factors and personality types (PTs). To address this gap, this article uses a structural equation modeling approach to explore the relationship be-tween practitioners’ ST skills, PT, and a set of demographic factors. The demographic factors included in the study are education level, the field of the highest degree, organizational ownership structure, job experience, and current occupation type. A total of 99 engineering managers, 104 systems engineers (SEs), and 55 practitioners with other occupations participated in this article. Results showed that the education level, the field of the highest degree, PT, organizational ownership structure, and current job experience of practitioners influenced their level of ST skills. Additionally, the current occupation type of practitioners partially affects their level of ST skills. An in-depth analysis was also conducted using multiple group analysis to show how seven ST skills of the practitioners vary across their level of education. Taken together, the findings of the study suggest that PT and a set of demographic factors influence the overall ST skill of the practitioners.
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Lee, Jusang, John E. Haddock, and Jongmyung Jeon. Development of Volumetric Acceptance and Percent Within Limits (PWL) and Criteria for Stone Metrix Asphalt (SMA) Mixtures in Indiana. Purdue University, 2022. http://dx.doi.org/10.5703/1288284317580.

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SMA is to be designed based on SMA volumetric properties in terms of air voids content (Va), voids in the mineral aggregate (VMA), and adequate stone-on-stone contact. For construction quality assurance (QA) purposes, INDOT currently accepts SMAs based on aggregate gradation and asphalt binder content. Thus, there is a discrepancy between SMA design criteria and construction acceptance. To better align design and construction, it is necessary to consider SMA volumetric properties in the use of QA. For HMA mixtures, INDOT has already transitioned from volumetric QA acceptance procedures to PWL. Today, SMA still uses adjustment points not based on robust statistics for QA acceptance. SMA QA samples and QA data sets were collected from projects constructed in 2019 and tested in the laboratory. The Hamburg Wheel Track Test (HWTT) was performed on the 2019 QA samples to evaluate SMA rutting performance. Additionally, the PWL for HMA was applied to the 2019 SMA QA data to see if the HMA PWL method would work for SMA. Possible SMA QA measurements were compared to past QA data and HMA QA measurements. In addition, Voids in the Coarse Aggregate (VCA) was evaluated as a possible SMA QA measurement. Finally, using the suitable QA measurements for SMA, a PWL parameter study was performed to find PWL that provides a Pay Factor (PF) equivalent to the current SMA Adjustment Point (AP) PF. The current SMA QA measurements (binder content, gradation, and density) are recommended for Indiana's SMA PWL. Based on the results of applying PWL to SMA QA data for the last four years, SMA PWL specification limits are recommended. Also, the SMA PF equations are suggested to get the SMA PWL to have PF equivalent to the current AP PF.
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Walmsley, Terrie. Long Run Simulations With GTAP: Illustrative Results from APEC Trade Liberalisation. GTAP Technical Paper, September 2000. http://dx.doi.org/10.21642/gtap.tp09.

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In static applied general equilibrium models, the exogenous/endogenous split between variables (or closure) is used to infer the time frame over which the effects of a shock are simulated. This paper introduces a long-run closure for the GTAP model (Hertel and Tsigas, 1997) and uses this closure to simulate and compare the short-run and long-run effects of Asia-Pacific trade liberalisation. The approach explored here incorporates some relatively minor changes to existing GTAP theory in order to define a steady state in which growth rates of all real variables are uniform. Such uniformity must apply in the initial database (as well as in the post-shock solution). So to implement the new long run in GTAP a new initial database must first be created. Details concerning the creation of the new database are given, and results under the new approach are compared with those obtained under the old. The emphasis of this paper is on the development of a long-run closure in which the percentage change form equations of the model and the relationships between the levels variables in the GTAP database are consistent. Further research is required into these types of long-run closures to incorporate changes in ownership of capital to ensure that changes in welfare are adequately modelled. In the results reported here, GDP is not a useful guide to national welfare. The long-run closures introduced here are also compared with another comparative static long-run closure developed for GTAP by Francois, MacDonald and Nordström (1996). Technical Paper Number 9 can be downloaded in PDF format. To print this you will need the Adobe Acrobat Reader. For those interested in replicating the results in this technical paper, an associated zip file can be downloaded. The zip file includes a readme file with detailed instructions.
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Pessino, Carola, Nadir Altinok, and Cristian Chagalj. Allocative Efficiency of Government Spending for Growth in Latin American Countries. Inter-American Development Bank, June 2022. http://dx.doi.org/10.18235/0004310.

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There is scant empirical economic research regarding the way that Latin American governments efficiently allocate their spending across different functions to achieve higher growth. While most papers restrict their analysis to the size of government, much less is known about the composition of spending and its implications for long-term growth. This paper sheds light on how allocating expenditures to investment in quality human and physical capital, and avoiding waste on inefficient expenditures, enhance growth in Latin America. This paper uses a novel dataset on physical and human capital and detailed public spending that includes -for the first time- Latin American countries, which is categorized by a cross-classification that provides the breakdown of government expenditure, both, by economic and by functional heads. The database covers 42 countries of the OECD and LAC between 1985 and 2017. There are five main results. First, the estimated growth equations show significant positive effects of the factors of production on growth and plausible convergence rates (about 2 percent). The estimated effect of the physical investment rate is positive and significant with a long-run elasticity of 1.2. Second, while the addition of years of education as a proxy for human capital tends to have no effect on growth, the addition of a new variable that measures quality-adjusted years of schooling as a proxy for human capital turns out to have a positive and significant effect across all specifications with a long-run elasticity of 1.1. However, if public spending on education (excluding infrastructure spending) is added to the factor specification, growth is not affected. This is mainly because, once quality is considered, spending more on teacher salaries has no effect on student outcomes. Therefore, the key is to increase quality, not just school performance or education spending. Third, both physical and human capital are equally important for growth: the effect of increasing one standard deviation of physical capital or human capital statistically has the same impact on economic growth. Fourth, increasing public investment spending (holding public spending constant) is positive and significant for growth (a 1% increase in public investment would increase the long-term GDP per capita by about 0.3 percent), in addition to the effect of the private investment rate. However, the effect of public spending on payroll, pensions and subsidies does not contribute to economic growth. Fifth, the overall effect of the size of public spending on economic growth is negative in most specifications. An increase in the size of government by about 1 percentage point would decrease 4.1 percent the long-run GDP per capita, but the more effective the government is, the less harmful the size of government is for long-term growth.
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Snyder, Victor A., Dani Or, Amos Hadas, and S. Assouline. Characterization of Post-Tillage Soil Fragmentation and Rejoining Affecting Soil Pore Space Evolution and Transport Properties. United States Department of Agriculture, April 2002. http://dx.doi.org/10.32747/2002.7580670.bard.

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Tillage modifies soil structure, altering conditions for plant growth and transport processes through the soil. However, the resulting loose structure is unstable and susceptible to collapse due to aggregate fragmentation during wetting and drying cycles, and coalescense of moist aggregates by internal capillary forces and external compactive stresses. Presently, limited understanding of these complex processes often leads to consideration of the soil plow layer as a static porous medium. With the purpose of filling some of this knowledge gap, the objectives of this Project were to: 1) Identify and quantify the major factors causing breakdown of primary soil fragments produced by tillage into smaller secondary fragments; 2) Identify and quantify the. physical processes involved in the coalescence of primary and secondary fragments and surfaces of weakness; 3) Measure temporal changes in pore-size distributions and hydraulic properties of reconstructed aggregate beds as a function of specified initial conditions and wetting/drying events; and 4) Construct a process-based model of post-tillage changes in soil structural and hydraulic properties of the plow layer and validate it against field experiments. A dynamic theory of capillary-driven plastic deformation of adjoining aggregates was developed, where instantaneous rate of change in geometry of aggregates and inter-aggregate pores was related to current geometry of the solid-gas-liquid system and measured soil rheological functions. The theory and supporting data showed that consolidation of aggregate beds is largely an event-driven process, restricted to a fairly narrow range of soil water contents where capillary suction is great enough to generate coalescence but where soil mechanical strength is still low enough to allow plastic deforn1ation of aggregates. The theory was also used to explain effects of transient external loading on compaction of aggregate beds. A stochastic forInalism was developed for modeling soil pore space evolution, based on the Fokker Planck equation (FPE). Analytical solutions for the FPE were developed, with parameters which can be measured empirically or related to the mechanistic aggregate deformation model. Pre-existing results from field experiments were used to illustrate how the FPE formalism can be applied to field data. Fragmentation of soil clods after tillage was observed to be an event-driven (as opposed to continuous) process that occurred only during wetting, and only as clods approached the saturation point. The major mechanism of fragmentation of large aggregates seemed to be differential soil swelling behind the wetting front. Aggregate "explosion" due to air entrapment seemed limited to small aggregates wetted simultaneously over their entire surface. Breakdown of large aggregates from 11 clay soils during successive wetting and drying cycles produced fragment size distributions which differed primarily by a scale factor l (essentially equivalent to the Van Bavel mean weight diameter), so that evolution of fragment size distributions could be modeled in terms of changes in l. For a given number of wetting and drying cycles, l decreased systematically with increasing plasticity index. When air-dry soil clods were slightly weakened by a single wetting event, and then allowed to "age" for six weeks at constant high water content, drop-shatter resistance in aged relative to non-aged clods was found to increase in proportion to plasticity index. This seemed consistent with the rheological model, which predicts faster plastic coalescence around small voids and sharp cracks (with resulting soil strengthening) in soils with low resistance to plastic yield and flow. A new theory of crack growth in "idealized" elastoplastic materials was formulated, with potential application to soil fracture phenomena. The theory was preliminarily (and successfully) tested using carbon steel, a ductile material which closely approximates ideal elastoplastic behavior, and for which the necessary fracture data existed in the literature.
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