Techniques of Discrete Function Transfers into Continuous Function in Practice

The discrete Lotka power function describes the number of sources (e.g., authors) with n = 1, 2, 3, … items (e.g., publications). As in econometrics, informetrics theory requires functions of a continuous variable j, replacing the discrete variable n. Now j represents item densities instead of number of items. The continuous Lotka power function describes the density of sources with item density j. The discrete Lotka function one obtains from data, obtained empirically; the continuous Lotka function is the one needed when one wants to apply Lotkaian informetrics, i.e., to determine properties that can be derived from the (continuous) model. It is, hence, important to know the relations between the two models. We show that the exponents of the discrete Lotka function (if not too high, i.e., within limits encountered in practice) and of the continuous Lotka function are approximately the same. This is important to know in applying theoretical results (from the continuous model), derived from practical data.

Previous work has shown that the S-distribution is a valuable tool for data analysis and for the classification of continuous and discrete distribution functions. The distribution has four parameters: one determines its location, one is related to the variance, and two control its shape. The distributional structure allows symmetry as well as skewness to the right or the left. This offers great flexibility and, among other analyses, facilitates the simultaneous investigation of random variables whose distributions differ in shape. The present paper demonstrates that mean, variance, and quantiles of any S-distribution can be computed with simple algebraic operations from corresponding properties of a standard S-distribution,sSd, which is characterized by only the two shape parameters. This scalability is comparable with the use of z-scores when dealing with normal distributions. Die seit einiger Zeit bekannte S-Verteilung ist ein nützliches Hilfsmittel für verschiedenartige Datenanalysen und zur Klassifizierung von Wahrscheinlichkeitsverteilungen. Die Verteilung hat vier Parameter, von denen zwei den Median und die Standardabweichung festlegen und zwei die Form charakterisieren. Je nach Wahl der Formparameter ist die Verteilung symmetrisch oder weist positive oder negative Schiefe auf. Die vorliegende Arbeit zeigt, daß Mittelwerte, Standardabweichungen und Perzentile beliebiger S-Verteilungen mit einfachen algebraischen Mitteln von den entsprechenden Maßen einer Standard-S-Verteilung, sSd, berechnet werden können, die nur durch zwei Formparameter bestimmt ist. Diese Skalierung ähnelt dem Übergang von einer normalverteilten Zufallsvariable auf die Standardnormalvariable Z.

This article focuses on the integral theory of discrete regular quaternionic functions and the connection between discrete and classical quaternionic analysis. We develop a new approach to the discrete integral theory based on the concepts ‘discrete boundary measure’ and ‘discrete normal vector’. By combining the discrete integral theory and our results on discrete approximations to domains in \({\mathbb {R}}^4\), we reveal a convergence relation between the discrete and continuous regular functions: a quaternionic function is regular if and only if it is the scaling limit of some discrete regular functions.

Energy and population balances in comminution process modelling based on the informational entropy

We studied the phase transitions of the [Formula: see text] spin-1/2 Ising model in the square lattice by considering [Formula: see text] fixed and [Formula: see text] as random interactions following discrete and continuous probability distribution functions. The configuration of [Formula: see text] in the lattice evolves in time through a competing kinetics using the Metropolis algorithm leading to a steady state without reaching the free-energy minimum. So, different phase diagrams were obtained according to the distribution of [Formula: see text]. For fixed and random values of [Formula: see text], we noted that the amplitude of the correlation length is different from the Ising value at the critical point of the superantiferromagnetic–paramagnetic frontier.

Binding of small molecules to heterogeneous ligands and/ or adsorption on heterogeneous surfaces with a multiplicity of specific binding sites is of great importance in many fields, ranging from the analysis of interactions between receptors and ligands in biochemistry to environmental sciences. This paper presents the application of the Maximum Entropy (MaxEnt) formalism to the calculation of the Langmuirian affinity distribution function or affinity spectrum, describing the interactions between small molecules and a surface or a macromolecule. Discrete, continuous, and mixed affinity distribution functions are successfully reproduced using a very reduced number of simulated data of coverage versus free complexing agent concentration and without any a priori assumption on the number of kinds of sites. MaxEnt is also applied to experimental data previously reported in the literature. Finally, the advantages and drawbacks of applying MaxEnt formalism to the spectral analysis of coverage data are discussed.

Comparison between error correcting output codes and fuzzy support vector machines

In the present investigation, a QSAR analysis on structurally diverse α-glucosidase inhibitors (andrographolide, chromenone, triazole derivatives) was performed and the developed models were validated by various validation methods (LMO, LOO, LSO, bootstrapping, Y-randomization and test set). The statistical parameters calculated for the models show that the developed models are statistically significant and have predicted the activities with small residual errors. The crossvalidated correlation coefficient (Q2) values obtained from different validation methods show >0.7 for both the models. Other correlations coefficient statistical parameters (R2pred and R2m) show that the developed models are reliable and robust. The leave-series-out (LSO) results reveal that the developed models can predict the activity of new compounds and its crossvalidated correlation coefficients’ values are comparable with the Q2 values obtained from other validation methods. The descriptors contributed in the selected models are suggested that the lower/reduced polarizability on the vdW surface area of the molecules and the presence of flexible bonds allow the substituents/side chains in the molecules with free movement and with lesser stretching energy which are favourable for the α-glucosidase inhibitory activity. These results reveal that the developed models are statistically significant and can be used with other molecular modelling works for designing novel α-glucosidase inhibitors with multiple activities (HIV, diabetics, cancer, etc).

A genetic algorithm with discrete cost functions is used to design and optimise a 42 V-14 V/8 A buck converter. The use of discrete and continuous cost functions are confronted. Discrete cost functions produces better designs. Electrical time domain simulation is used for verification. Experimental measurement, electrical and thermal, validates the design.

Water is one of the essential resources of a country, which controls human development activities and very much influences living things. Hydrologists had been interested in the discharge and runoff caused by precipitation. This study compares two daily conceptual models, TANK and SimHyd, using the Rainfall-Runoff Library (RRL) tool and suggests which model is suitable for the Hemavathi watershed. The daily rainfall and evapotranspiration were the inputs in the TANK and SimHyd to determine daily discharge. The daily streamflow was utilized to calibrate models from 1990 to 2006 and then validated for 2007 to 2015. These model parameters are optimized using the genetic algorithm technique. Model prediction effectiveness was assessed using Nash–Sutcliffe efficiency (NSE) and Correlation coefficient (CC) values. NSE and CC values during calibration was 0.71, 0.85 for TANK model, 0.66, 0.83 for SIMHYD model, and during verification was 0.64, 0.74 for TANK model, 0.62, 0.72 for SIMHYD model. From the obtained results, the TANK model performs satisfactorily in terms of NSE and CC compared to the SimHyd model. This paper evaluates the model abilities in streamflow simulation, which policy makers can use.KeywordsHemavathi watershedTANK modelSimHydNSERRL

Biosynthesis of Leucaena Leucocephala leaf mediated ZnO, CuO, MnO2, and MgO based nano-adsorbents for Reactive Golden Yellow-145 (RY-145) and Direct Red-31 (DR-31) dye removal from textile wastewater to reuse in agricultural purpose

We consider the m-Peripatetic Salesman Problem (m-PSP) on random inputs with discrete distribution function. In this paper we present a polynomial approximation algorithm which, under certain conditions, with high probability (w.h.p.) gives optimal solution for both the m-PSP on random inputs with identical weight functions and the m-PSP with different weight functions.

The realization of fractional-order controllers is based on the approximation of the irrational operators by continuous or discrete transfer functions. However, at high sampling frequencies, discrete z-transfer functions approximations can be very sensitive even to small changes in coefficient values. This technical note proposes a realization of sν , in terms of transfer functions in the complex delta-domain, which improves considerably the robustness of the approximation to parameter changes and then to truncation in transfer function coefficients applied for implementation with finite word length.

Abstract. The spatiotemporal variations of integrated precipitable water vapor (IPWV) are very important in understanding the regional variability of water vapor. Traditional in situ measurements of IPWV in the Indian region are limited, and therefore the performance of satellite and Copernicus Atmosphere Meteorological Service (CAMS) retrievals with the Indian Global Navigation Satellite System (GNSS) as reference were analyzed. In this study the CAMS reanalysis data of 1 year (2018) and the Indian GNSS and INSAT-3DR sounder retrieval data for 1.5 years (January 2017 to June 2018) were utilized, and statistics were computed. It is noticed that seasonal correlation coefficient (CC) values between INSAT-3DR and Indian GNSS data mainly lie within the range of 0.50 to 0.98 for all the selected 19 stations except Thiruvananthapuram (0.1), Kanyakumari (0.31) and Karaikal (0.15) during the monsoon season and Panjim (0.2) during the post-monsoon season. The seasonal CC values between CAMS and GNSS IPWV range from 0.73 to .99 except for Jaipur (0.16) and Bhubaneswar (0.29) during the pre-monsoon season, Panjim (0.38) during the monsoon season, Nagpur (0.50) during the post-monsoon season, and Dibrugarh (0.49) Jaipur (0.58) and Bhubaneswar (0.16) during the winter season. The root mean square error (RMSE) values are higher under the wet conditions (pre-monsoon and monsoon season) than under dry conditions (post-monsoon and winter season), and we found differences in magnitude and sign of bias for INSAT-3DR and CAMS with respect to GNSS IPWV from station to station and season to season. This study will help to improve understanding and utilization of CAMS and INSAT-3DR data more effectively along with GNSS data over land, coastal and desert locations in terms of the seasonal flow of IPWV, which is an essential integrated variable in forecasting applications.

A direct-sequence spread-spectrum communication system which uses a form of trellis coding is considered. The authors analyze the performance of this system for a channel model which includes the effects of multiple-access interference, Gaussian noise and Rician fading. Upper and lower bounds on the probability of occurrence of dominant error events are obtained by modeling the continuous probability density functions of noise and interference as discrete probability mass functions. Bit error rates are reported for coded and uncoded systems with equivalent power, bandwidth and transmission rates. It is found that while coded systems without interleaving yield only modest performance improvements over uncoded systems, coded systems with interleaving perform dramatically better. >