Spectral shift function for a discretized continuum

A spectral shift function (SSF) is an important object in the scattering theory which is related both to the spectral density and to the scattering matrix. In the paper, it is shown how to employ the SSF formalism to solve scattering problems when the continuum is discretized, e.g. when solving a scattering problem in a finite volume or in the representation of some finite square-integrable basis. A new algorithm is proposed for reconstructing integrated densities of states and the SSF using a union of discretized spectra corresponding to a set of Gaussian bases with the shifted scale parameters. The examples given show that knowledge of the discretized spectra of the total and asymptotic Hamiltonians is sufficient to find the scattering partial phase shifts at any required energy, as well as the resonances parameters.

The Bayes Estimators of the Variance and Scale Parameters of the Normal Model With a Known Mean for the Conjugate and Noninformative Priors Under Stein’s Loss

For the normal model with a known mean, the Bayes estimation of the variance parameter under the conjugate prior is studied in Lehmann and Casella (1998) and Mao and Tang (2012). However, they only calculate the Bayes estimator with respect to a conjugate prior under the squared error loss function. Zhang (2017) calculates the Bayes estimator of the variance parameter of the normal model with a known mean with respect to the conjugate prior under Stein’s loss function which penalizes gross overestimation and gross underestimation equally, and the corresponding Posterior Expected Stein’s Loss (PESL). Motivated by their works, we have calculated the Bayes estimators of the variance parameter with respect to the noninformative (Jeffreys’s, reference, and matching) priors under Stein’s loss function, and the corresponding PESLs. Moreover, we have calculated the Bayes estimators of the scale parameter with respect to the conjugate and noninformative priors under Stein’s loss function, and the corresponding PESLs. The quantities (prior, posterior, three posterior expectations, two Bayes estimators, and two PESLs) and expressions of the variance and scale parameters of the model for the conjugate and noninformative priors are summarized in two tables. After that, the numerical simulations are carried out to exemplify the theoretical findings. Finally, we calculate the Bayes estimators and the PESLs of the variance and scale parameters of the S&P 500 monthly simple returns for the conjugate and noninformative priors.

Variability in rainfall dispersion in Madhya Pradesh

An attempt has been made to examine distribution and dispersion in rainfall variability in Madhya Pradesh by applying Gamma distribution probability model, The spatial and regional distribution of shape and scale parameters of the Gamma distribution have been examined, Periods of water surpluses and deficiencies have been identified by comparing the probability rainfall with the water requirement. Regression equations have been developed to find probabilitistic rainfall from the mean rainfall. Agronomic practices have been evaluated for efficient utilization of water resources for crop planning.

The Improved Element-Free Galerkin Method for 3D Helmholtz Equations

The improved element-free Galerkin (IEFG) method is proposed in this paper for solving 3D Helmholtz equations. The improved moving least-squares (IMLS) approximation is used to establish the trial function, and the penalty technique is used to enforce the essential boundary conditions. Thus, the final discretized equations of the IEFG method for 3D Helmholtz equations can be derived by using the corresponding Galerkin weak form. The influences of the node distribution, the weight functions, the scale parameters of the influence domain, and the penalty factors on the computational accuracy of the solutions are analyzed, and the numerical results of three examples show that the proposed method in this paper can not only enhance the computational speed of the element-free Galerkin (EFG) method but also eliminate the phenomenon of the singular matrix.

Variability of ecosystem carbon source from microbial respiration is controlled by rainfall dynamics

Soil heterotrophic respiration (Rh) represents an important component of the terrestrial carbon cycle that affects whether ecosystems function as carbon sources or sinks. Due to the complex interactions between biological and physical factors controlling microbial growth, Rh is uncertain and difficult to predict, limiting our ability to anticipate future climate trajectories. Here we analyze the global FLUXNET 2015 database aided by a probabilistic model of microbial growth to examine the ecosystem-scale dynamics of Rh and identify primary predictors of its variability. We find that the temporal variability in Rh is consistently distributed according to a Gamma distribution, with shape and scale parameters controlled only by rainfall characteristics and vegetation productivity. This distribution originates from the propagation of fast hydrologic fluctuations on the slower biological dynamics of microbial growth and is independent of biome, soil type, and microbial physiology. This finding allows us to readily provide accurate estimates of the mean Rh and its variance, as confirmed by a comparison with an independent global dataset. Our results suggest that future changes in rainfall regime and net primary productivity will significantly alter the dynamics of Rh and the global carbon budget. In regions that are becoming wetter, Rh may increase faster than net primary productivity, thereby reducing the carbon storage capacity of terrestrial ecosystems.

Improving Hillslope Link Model Performance from Non-Linear Representation of Natural and Artificially Drained Subsurface Flows

This study evaluates the potential for a newly proposed non-linear subsurface flux equation to improve the performance of the hydrological Hillslope Link Model (HLM). The equation contains parameters that are functionally related to the hillslope steepness and the presence of tile drainage. As a result, the equation provides better representation of hydrograph recession curves, hydrograph timing, and total runoff volume. The authors explore the new parameterization’s potential by comparing a set of diagnostic and prognostic setups in HLM. In the diagnostic approach, they configure 12 different scenarios with spatially uniform parameters over the state of Iowa. In the prognostic case, they use information from topographical maps and known locations of tile drainage to distribute parameter values. To assess performance improvements, they compare simulation results to streamflow observations during a 17-year period (2002–2018) at 140 U.S. Geological Survey (USGS) gauging stations. The operational setup of the HLM model used at the Iowa Flood Center (IFC) serves as a benchmark to quantify the overall improvement of the model. In particular, the new equation provides better representation of recession curves and the total streamflow volumes. However, when comparing the diagnostic and prognostic setups, the authors found discrepancies in the spatial distribution of hillslope scale parameters. The results suggest that more work is required when using maps of physical attributes to parameterize hydrological models. The findings also demonstrate that the diagnostic approach is a useful strategy to evaluate models and assess changes in their formulations.

Determine the parameters of PID algorithm in liquid level control controlled by PLC s7 1500 using 3d virtual reality model

It is very common to stabilize the preset value (Wanted value) of analog signals such as temperature, pressure, weight, flow, speed in automatic control. However, these control objects often have some problems such as overshooting, taking a long time to bring the system to a steady value, and large errors. One of the most used systems to overcome these problems is the PID, which is a preset stabilizing system with a quick function that returns the system to the set value in a short time without overshooting. error is close to zero. However, determining the scale parameters Ki, integral Kp, and differential Kd for the system to work optimally is a problem that needs to be studied. This paper presents how to accurately determine differential, integral, and scale coefficients according to 3D virtual reality model. Used a lot in simulation modeling for training and practical applications.

Non-Parametric Tests for Testing of Scale Parameters

One of the fundamental problems in testing of equality of populations is of testing the equality of scale parameters. The subsequent usages for scale are dispersion, spread and variability. In this paper, we proposed non-parametric tests based on U-Statistics for the testing of equality of scale parameters. The null distribution of proposed tests is developed and its Pitman efficiency is worked out to compare proposed tests with respect to some existing tests. Simulation study is carried out to compute the asymptotic power of proposed tests. An illustrative example is also provided.

Attribution of typhoon-induced torrential precipitation in Central Vietnam, October 2020

In October 2020, Central Vietnam was struck by heavy rain resulting from a sequence of 5 tropical depressions and typhoons. The immense amount of water led to extensive flooding and landslides that killed more than 200 people, injured more than 500 people, and caused direct damages valued at approximately 1.2 billion USD. Here, we quantify how the intensity of the precipitation leading to such exceptional impacts is attributable to anthropogenic climate change. First, we define the event as the regional maximum of annual maximum 15-day average rainfall (Rx15day). We then analyse the trend in Rx15day over Central Vietnam from the observations and simulations in the PRIMAVERA and CORDEX-CORE ensembles, which pass our evaluation tests, by applying the generalised extreme value (GEV) distribution in which location and scale parameters exponentially covary with increasing global temperatures. Combining these observations and model results, we find that the 2020 event, occurring about once every 80 years (at least 17 years), has not changed in either probability of occurrence (a factor 1.0, ranging from 0.4 to 2.4) or intensity (0%, ranging from −8 to +8%) in the present climate in comparison with early-industrial climate. This implies that the effect of human-induced climate change contributing to this persistent extreme rainfall event is small compared to natural variability. However, given the scale of damage of this hazard, our results underline that more investment in disaster risk reduction for this type of rainfall-induced flood hazard is of importance, even independent of the effect of anthropogenic climate change. Moreover, as both observations and model simulations will be extended with the passage of time, we encourage more climate change impact investigations on the extreme in the future that help adaptation and mitigation plans and raise awareness in the country.