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Exponential Form (exponential + form)
Selected AbstractsEffective global regularity and empirical modelling of direct, inverse, and mixed demand systemsCANADIAN JOURNAL OF ECONOMICS, Issue 2 2009Keith R. McLaren Abstract This paper utilizes the notion of ,effective global regularity' and the intuition stemming from Cooper and McLaren (1996)'s General Exponential Form to develop a family of ,composite' (product and ratio) direct, inverse and mixed demand systems. Apart from having larger regularity regions, the resulting specifications are also of potentially arbitrary rank, which can better approximate non-linear Engel curves. We also make extensive use of duality theory and a numerical inversion estimation method to rectify the endogeneity problem encountered in the estimation of the mixed demand systems. We illustrate the techniques by estimating different types of demand systems for Japanese quarterly meat and fish consumption. Ce mémoire utilise la notion de régularité effective globale et l'intuition émergeant de la Forme Exponentielle Générale de Cooper et McLaren (1996) pour développer une famille de systèmes de demandes (directes, inverses et mixtes) composites (produit et ratio). En plus d'avoir de plus vastes régions de régularité, les spécifications qui en résultent sont aussi potentiellement de rang arbitraire, ce qui permet une meilleure approximation des courbes d'Engel non linéaires. On fait aussi un usage extensif de la théorie de la dualité, et d'une méthode numérique d'estimation de l'inversion pour corriger le problème d'endogénéité qu'on rencontre dans l'estimation des systèmes de demandes mixtes. On illustre les techniques en estimant différents types de systèmes de demandes trimestrielles de viande et de poisson par les consommateurs au Japon. [source] An accurate few-parameter ground state wave function for the lithium atomINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 13 2009Nicolais L. Guevara Abstract A simple, seven-parameter trial function is proposed for a description of the ground state of the Lithium atom. It includes both spin functions. Inter-electronic distances appear in exponential form as well as in a pre-exponential factor, and the necessary energy matrix elements are evaluated by numerical integration in the space of the relative coordinates. Encouragingly accurate values of the energy and the cusp parameters as well as for some expectation values are obtained. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Clustering of luminous red galaxies , II.MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2009Small-scale redshift-space distortions ABSTRACT This is the second paper of a series where we study the clustering of luminous red galaxies (LRG) in the recent spectroscopic Sloan Digital Sky Survey (SDSS) data release, DR6, which has 75 000 LRG covering over 1 Gpc3 h,3 for 0.15 < z < 0.47. Here, we focus on modelling redshift-space distortions in ,(,, ,), the two-point correlation in separate line-of-sight and perpendicular directions, at small scales and in the line-of-sight. We show that a simple Kaiser model for the anisotropic two-point correlation function in redshift space, convolved with a distribution of random peculiar velocities with an exponential form, can describe well the correlation of LRG on all scales. We show that to describe with accuracy the so-called ,fingers-of-God' (FOG) elongations in the radial direction, it is necessary to model the scale dependence of both bias b and the pairwise rms peculiar velocity ,12 with the distance. We show how both quantities can be inferred from the ,(,, ,) data. From r, 10 Mpc h,1 to r, 1 Mpc h,1, both the bias and ,12 are shown to increase by a factor of 2: from b= 2 to 4 and from ,12= 400 to 800 km s,1. The latter is in good agreement, within a 5 per cent accuracy in the recovered velocities, with direct velocity measurements in dark matter simulations with ,m= 0.25 and ,8= 0.85. [source] The 2dF Galaxy Redshift Survey: correlation functions, peculiar velocities and the matter density of the UniverseMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2003Ed Hawkins ABSTRACT We present a detailed analysis of the two-point correlation function, ,(,, ,), from the 2dF Galaxy Redshift Survey (2dFGRS). The large size of the catalogue, which contains ,220 000 redshifts, allows us to make high-precision measurements of various properties of the galaxy clustering pattern. The effective redshift at which our estimates are made is zs, 0.15, and similarly the effective luminosity, Ls, 1.4L*. We estimate the redshift-space correlation function, ,(s), from which we measure the redshift-space clustering length, s0= 6.82 ± 0.28 h,1 Mpc. We also estimate the projected correlation function, ,(,), and the real-space correlation function, ,(r), which can be fit by a power law (r/r0), with r0= 5.05 ± 0.26 h,1 Mpc, ,r= 1.67 ± 0.03. For r, 20 h,1 Mpc, , drops below a power law as, for instance, is expected in the popular , cold dark matter model. The ratio of amplitudes of the real- and redshift-space correlation functions on scales of 8,30 h,1 Mpc gives an estimate of the redshift-space distortion parameter ,. The quadrupole moment of ,(,, ,) on scales 30,40 h,1 Mpc provides another estimate of ,. We also estimate the distribution function of pairwise peculiar velocities, f(v), including rigorously the significant effect due to the infall velocities, and we find that the distribution is well fit by an exponential form. The accuracy of our ,(,, ,) measurement is sufficient to constrain a model, which simultaneously fits the shape and amplitude of ,(r) and the two redshift-space distortion effects parametrized by , and velocity dispersion, a. We find ,= 0.49 ± 0.09 and a= 506 ± 52 km s,1, although the best-fitting values are strongly correlated. We measure the variation of the peculiar velocity dispersion with projected separation, a(,), and find that the shape is consistent with models and simulations. This is the first time that , and f(v) have been estimated from a self-consistent model of galaxy velocities. Using the constraints on bias from recent estimates, and taking account of redshift evolution, we conclude that , (L=L*, z= 0) = 0.47 ± 0.08, and that the present-day matter density of the Universe, ,m, 0.3, consistent with other 2dFGRS estimates and independent analyses. [source] Predicting effective fungicide doses through observation of leaf emergencePLANT PATHOLOGY, Issue 6 2000N. D. Paveley Experimental data were used to test the hypothesis that the effective fungicide dose (ED) , the dose required to achieve a given level of disease suppression , varies in a predictable manner according to the pattern of development of the wheat canopy. Replicated and randomized field plots received a single systemic fungicide spray at either zero (control), 0·25, 0·5, 0·75 or 1·0 dose (the recommended dose), at one of eight timings from April to June. Wheat cultivars and locations for experiments were selected to promote epidemics of septoria tritici spot and yellow rust caused by Septoria tritici (anamorph of Mycosphaerella graminicola) and Puccinia striiformis, respectively. Logistic or exponential disease progress curves were fitted to disease severity data and used to estimate the date of disease onset (t0) and relative epidemic growth rate (r) on each leaf layer for each treatment. Area under the disease progress curve (AUDPC) values were used to construct fungicide dose by spray timing response surfaces for each of the upper four leaves. A parsimonious function, with an exponential form in the dose,response dimension and a normal distribution in the timing dimension described a high proportion of the variation in AUDPC (R2 values ranging from 0·73 to 0·97). Consistent patterns of treatment effect were noted across pathogen species, leaf layers, sites and seasons. Fungicide applications that coincided with full leaf emergence delayed t0 on that leaf layer. Treatments applied after full leaf emergence did not delay t0, but reduced r. Progressively earlier or later treatments, or lower doses, had decreasing effects. AUDPC was affected more by t0 than r. AUDPC response surface parameter estimates showed that curvature of the dose,response was not affected by spray timing, but appeared to be a characteristic of the fungicide,pathogen combination. However, the lower asymptote of the dose,response curve, and hence the ED, varied substantially with spray timing. The pattern of change in ED with spray timing was consistent across a range of leaf layers, pathosystems and seasons, and the spray timing at which the ED was minimized varied only within a small range, around the time of leaf emergence. In contrast, variation in untreated disease severity, resulting from variation in initial inoculum and weather, was large. It was concluded that the main value of disease forecasting schemes may be in their capacity to predict the level of untreated disease, to which the economic optimum, or ,appropriate', dose relates. Spray timing determines the part of the canopy where disease will be efficiently controlled and hence the green leaf area saved. Timing decisions should relate to observations of emergence of those leaf layers important to yield. [source] Polynomial Spline Estimation and Inference of Proportional Hazards Regression Models with Flexible Relative Risk FormBIOMETRICS, Issue 3 2006Jianhua Z. Huang Summary The Cox proportional hazards model usually assumes an exponential form for the dependence of the hazard function on covariate variables. However, in practice this assumption may be violated and other relative risk forms may be more appropriate. In this article, we consider the proportional hazards model with an unknown relative risk form. Issues in model interpretation are addressed. We propose a method to estimate the relative risk form and the regression parameters simultaneously by first approximating the logarithm of the relative risk form by a spline, and then employing the maximum partial likelihood estimation. An iterative alternating optimization procedure is developed for efficient implementation. Statistical inference of the regression coefficients and of the relative risk form based on parametric asymptotic theory is discussed. The proposed methods are illustrated using simulation and an application to the Veteran's Administration lung cancer data. [source] Power function decay of hydraulic conductivity for a TOPMODEL-based infiltration routineHYDROLOGICAL PROCESSES, Issue 18 2006Jun Wang Abstract TOPMODEL rainfall-runoff hydrologic concepts are based on soil saturation processes, where soil controls on hydrograph recession have been represented by linear, exponential, and power function decay with soil depth. Although these decay formulations have been incorporated into baseflow decay and topographic index computations, only the linear and exponential forms have been incorporated into infiltration subroutines. This study develops a power function formulation of the Green and Ampt infiltration equation for the case where the power n = 1 and 2. This new function was created to represent field measurements in the New York City, USA, Ward Pound Ridge drinking water supply area, and provide support for similar sites reported by other researchers. Derivation of the power-function-based Green and Ampt model begins with the Green and Ampt formulation used by Beven in deriving an exponential decay model. Differences between the linear, exponential, and power function infiltration scenarios are sensitive to the relative difference between rainfall rates and hydraulic conductivity. Using a low-frequency 30 min design storm with 4·8 cm h,1 rain, the n = 2 power function formulation allows for a faster decay of infiltration and more rapid generation of runoff. Infiltration excess runoff is rare in most forested watersheds, and advantages of the power function infiltration routine may primarily include replication of field-observed processes in urbanized areas and numerical consistency with power function decay of baseflow and topographic index distributions. Equation development is presented within a TOPMODEL-based Ward Pound Ridge rainfall-runoff simulation. Copyright © 2006 John Wiley & Sons, Ltd. [source] P1 Shake-and-Bake: can success be guaranteed?ACTA CRYSTALLOGRAPHICA SECTION D, Issue 2 2000Hongliang Xu The multi-trial direct-methods procedure known as Shake-and-Bake has been applied to three small proteins (alpha-1 peptide, vancomycin and lysozyme) that crystallize in space group P1. Phase refinement was accomplished through parameter-shift optimization using both the cosine and exponential forms of the minimal function. By extending error-free data to sufficiently high resolution, 100% convergence of trial structures to solution could be achieved in all three cases by using the exponential minimal function and a shift angle in the range 130,150°. These results suggest optimum parameters for other P1 structures and emphasize the importance of collecting data to the highest possible resolution. [source] | ||||||||||