Gauss Functions Research Articles

On the uniqueness of continuous and discrete hard models of NMR-spectra

AbstractLorentz, Gauss, Voigt and pseudo-Voigt functions play an important role in hard modeling of NMR spectra. This paper shows the uniqueness of continuous NMR hard models in terms of these functions by proving their linear independence. For the case of discrete hard models, where the spectra are represented by finite-dimensional vectors, criteria are given under which the models are also unique.

Temperature-dependent photoluminescence of lead-free cesium tin halide perovskite microplates

Tin halide perovskites recently have attracted extensive research attention due to their similar electronic and band structures but non-toxicity compared with their lead analogues. In this work, we prepare high-quality CsSnX 3 (X = Br, I) microplates with lateral sizes of around 1–4 μm by chemical vapor deposition and investigate their low-temperature photoluminescence (PL) properties. A remarkable splitting of PL peaks of the CsSnBr3 microplate is observed at low temperatures. Besides the possible structural phase transition at below 70 K, the multi-peak fittings using Gauss functions and the power-dependent saturation phenomenon suggest that the PL could also be influenced by the conversion from the emission of bound excitons into free excitons. With the increase of temperature, the peak position shows a blueshift tendency for CsSnI3, which is governed by thermal expansion. However, the peak position of the CsSnBr3 microplate exhibits a transition from redshift to blueshift at ∼160 K. The full width at half maximum of CsSnX 3 broadens with increasing temperature, and the fitting results imply that longitudinal optical phonons dominate the electron–phonon coupling and the coupling strength is much more robust in CsSnBr3 than in CsSnI3. The PL intensity of CsSnX 3 microplates is suppressed due to the enhanced non-radiative relaxation and exciton dissociation competing with radiative recombination. According to the Arrhenius law, the exciton binding energy of CsSnBr3 is ∼38.4 meV, slightly smaller than that of CsSnI3.

SPECTRAL ANALYSIS OF HEART RATE VARIABILITY BASED ON THE HILBERT-HUANG METHOD

Analysis of heart rate variability (HRV) is widely used for noninvasive assessment of the state of its regulation systems. The aim of the research was to evaluate the capabilities of the Hilbert-Huang method for calculating spectral parameters of HRV in comparison with the commonly used Fourier analysis. Fourier analysis allows to estimate averaged spectral amplitudes and power of HRV oscillations in fixed frequency intervals, which are associated with the activity of sympathetic, parasympathetic and humoral regulation systems. Using the Hilbert-Huang method, we revealed 4 spectral components, described by Gauss functions, in which HRV oscillations are concentrated, and showed the absence of fixed boundaries between them. The obtained energy quantitative characteristics of the spectral components of heart rhythm oscillations can serve as the basis for diagnostic methods of its regulation, supplementing the commonly used ones.

Twisted dust-acoustic waves in a self-gravitating dusty plasma with nonextensive q-distributed electrons and ions

We have investigated the twisted dust-acoustic waves (TDAWs) in an electrostatic self-gravitating dusty plasma whose electrons and ions are modelled by nonextensive q-distribution function while massive dust particles are Maxwellian distributed. A well-known kinetic theory is employed for this purpose where perturbed distribution function, electrostatic and gravitational potentials are expressed with Laguerre–Gauss functions. The governing equations of kinetic theory are solved together under paraxial approximations. The dispersion relations and instability growth rates are obtained for two situations; a) super-extensivity (q < 1) and b) sub-extensivity (q > 1). Significant modifications concerning the wave frequencies and growth rates are presented with respect to self-gravitation parameter, twist parameter, nonextensive parameter and streaming speed. It is observed that wave frequency and growth rate of TDAWs reduces in the presence of self-gravitating effects. Furthermore, the growth rates exhibit a significant enhancement in amplitude with the increase in twist parameter, q-parameter and streaming speed. Our present results may have applications in interstellar dust clouds and in the dusty plasma environments of Halley’s Comet.

Bimodal distribution of amphibole-melt apparent dihedral angles in the product of the early crystallization of hydrous basaltic melts

• Amp-Melt-Amp apparent dihedral angle distribution shows bimodality. • Bimodality becomes obvious after annealing for more than 1 h at 0.6 GPa and 970 °C. • Median-standard deviation evolution obeys no longer a unidirectional change. • The high anisotropy of amphibole is the main cause of the bimodality. The dihedral angle of mineral-melt is a very important parameter for further understanding the textural evolution of magma crystallization. In this study, we have investigated the amphibole-melt dihedral angle distribution of four previous experimental samples at 0.6 GPa and 970 °C with annealing time of 1 h, 10 h, 60 h, and 100 h, as well as two additional experiments with annealing time of 5 h and 30 h. In this experiment, we have achieved the assemblage of amphibole + granodioritic melt ± traces of other minerals in the process of melt crystallization under the above experimental conditions. The apparent dihedral angles of amphibole-melt of the experimental products were obtained by randomly measuring the dihedral angles in the backscattered images. The results indicate that the apparent dihedral angle presents a gradually obvious bimodal distribution with the increasing annealing time. The high anisotropy of amphibole is believed to be the main cause of the bimodal characteristics of the apparent dihedral angle distribution. Consequently, two Gauss functions are used to fit one distribution. As the annealing time increases, the median-standard deviation relationships of the apparent dihedral angle for these two Gauss functions show great differences. Therefore, our experiments proved that in the amphibole-melt system, the median-standard deviation with the growth of textural equilibrium in the early crystallization is no longer a unidirectional change. Furthermore, combining the results of this study and the previous work, whether the dihedral angle distribution in the early crystallization is unimodal or bimodal may have great relationship with the anisotropy of minerals.

Stochastic Modeling of Surfaces with Modified Gauss Functions

In this paper, we construct a mathematical model for estimating the mass of water flooding the coastline of a basin. The models of the relief of the bottom of the basin and the relief of the flooding part of the coastline are constructed by stochastic methods. The simulation is based on empirical data of measurements of depths of the basin and the study of level lines on maps of the coastal zone. The equations of the surface relief of the coastal zone are constructed by using empirical data from maps with level lines.

Thermal-gradient analysis of soil organic matter using an elemental analyser – A tool for qualitative characterization?

Analysing the thermal stability of soil organic matter (SOM) by heating soil material up to 900 °C and recording the time/temperature-dependent evolution of CO2, using an elemental analyser, may be an easily available tool to obtain information on the composition and stabilization of SOM. We studied four sample sets, including size fractions of mineral horizons, particulate organic matter (POM), soil aggregates, and thermally treated materials. All analyses were conducted with a thermal gradient of 70 K min−1, with i) stages of constant temperature at 400, 600 and 900 °C (‘DIN 19359′), ii) stages at 450, 600 and 900 °C (modified DIN method), or iii) continual heating. With both stage methods, the large majority of organic carbon (OC) was present in the least thermally stable fraction, thermally decomposing at T ≤400 or 450 °C, respectively. However, neither did these methods result in the same relative proportions of fractions of similar thermal stability, nor did they result in time/temperature-dependent CO2-evolution patterns characteristically reflecting the different sample sets. Thus, results of the stage-heating methods were operationally defined, as different SOM fractions in terms of composition or stabilization mechanism were combusted, but showing similar patterns. Nonetheless, most POM samples revealed less thermal stability than the other fractions with any method. Evaluation of CO2 development during continual heating provided more options, including T of maximum CO2 evolution, T50, that is, T at which 50% of CO2 has evolved, and peak deconvolution using Gauss functions. The mineral samples showed at least two maxima and variable T50 values up to 550 °C. Most POM fractions had lower T50, but not in general, possibly caused by the presence of black carbon or strongly complexing cations. The aggregate samples were mostly in between the mineral and POM samples. Irrespective of the method applied, direct unambiguous identification of samples in terms of composition or stabilization mechanisms was not possible. Nonetheless, we consider an elemental analyser a valuable tool to evaluate the thermal stability of large samples sets at relatively low cost and time effort. Particularly peak deconvolution from continual heating offers the option of quantifying OC fractions, differing in thermal stability.

Smooth solutions to the Gauss image problem

In this paper we study the the Gauss image problem, which is a generalization of the Aleksandrov problem in convex geometry. By considering a geometric flow involving Gauss curvature and functions of normal vectors and radial vectors, we obtain the existence of smooth solutions to this problem.

Analytical solution of the nonlinear equations of acoustic in the form of Gaussian beam

The nonlinear acoustics equation for a dissipative medium is analytically solved. Continuous wave stimulation and an axisymmetric Gaussian spatial profile of the boundary conditions were assumed. The approximation of the D'Alambert operator by the wave diffusion operator was applied and justified. In this approximation and assuming classical absorption (dispersion), the equation to be solved is presented by the Khokhlov-Zabolotskaya-Kuznetsov model.A sequence of functions describing the spatial distribution of the harmonic components of the disturbance was determined. They are the form of spatially modulated Gauss functions for harmonic wave numbers (frequencies).For a lossless medium a universal numerical sequence describing non-linear interactions and harmonic generations was determined. In other cases, the description of the cooperation of dispersion and non-linear interactions in the harmonic generation process is given by a sequence of functions dependent on the dispersion coefficient and with boundary values given by the universal sequence mentioned above.It was unexpectedly discovered that the influence of geometrical parameters of the beam on nonlinear interactions depends on dispersion, and component of the dispersion, absorption may strengthen harmonic generation. In general, dispersion spatially modulates the amplitude and phase of nonlinear interactions. This is not against the law of conservation of energy. The energy exchange between the fundamental (initiating) component and other harmonics is described.The analytical solution was compared with the numerical one. The numerical solution was obtained in the scheme implementing the full Helmholtz operator (no axial - wave diffusion- approximation).

Existence of Smooth Even Solutions to the Dual Orlicz–Minkowski Problem

In this paper, we study the dual Orlicz–Minkowski problem, which is a generalization of the dual Minkowski problem in convex geometry. By considering a geometric flow involving Gauss curvature and functions of normal vectors and radial vectors, we obtain a new existence result of smooth even solutions to this problem for smooth even measures.

A new NMR-data-based method for predicting petrophysical properties of tight sandstone reservoirs

Evaluating the permeability and irreducible water saturation of tight sandstone reservoirs is challenging. This study uses distribution functions to fit measured NMR T2 distributions of tight sandstone reservoirs and extract parameters for characterizing pore size distribution. These parameters are then used to establish prediction models for permeability and irreducible water saturation of reservoirs. Results of comparing the fit of the T2 distributions by the Gauss and Weibull distribution functions show that the fitting accuracy with the Weibull distribution function is higher. The physical meaning of the statistical parameters of the Weibull distribution function is defined to establish nonlinear prediction models of permeability and irreducible water saturation using the radial basis function (RBF) method. Correlation coefficients between the predicted values by the established models and the measured values of the tight sandstone core samples are 0.944 for permeability and 0.851 for irreducible water saturation, which highlight the effectiveness of the prediction models.

Integrals of Special Functions and Umbral Methods

We derive integrals of combination of Gauss and Bessel functions, by the use of umbral techniques. We show that the method allows the possibility of pursuing new and apparently fruitful avenues in the theory of special functions, displaying interesting links with the theory and the formalism of integral transforms.

Efficient spherical surface integration of Gauss functions in three-dimensional spherical coordinates and the solution for the modified Bessel function of the first kind

An efficient solution of calculating the spherical surface integral of a Gauss function defined as $$h\left( {s,{\mathbf{Q}}} \right) = \int_{0}^{2\pi } {\int_{0}^{\pi } {\left( {{\mathbf{s}} + {\mathbf{Q}}} \right)_{x}^{i} \left( {{\mathbf{s}} + {\mathbf{Q}}} \right)_{y}^{j} \left( {{\mathbf{s}} + {\mathbf{Q}}} \right)_{z}^{k} e^{{ - \gamma \left( {{\mathbf{s}} + {\mathbf{Q}}} \right)^{2} }} } } \sin \theta d\theta d\varphi$$ is provided, where $$\gamma \ge 0$$ , and i, j, k are nonnegative integers. A computationally concise algorithm is proposed for obtaining the expansion coefficients of polynomial terms when the coordinate system is transformed from cartesian to spherical. The resulting expression for $$h\left( {s,{\mathbf{Q}}} \right)$$ includes a number of cases of elementary integrals, the most difficult of which is $$II\left( {n,\mu } \right) = \int_{0}^{\pi } {\cos^{n} \theta e^{ - \mu \cos \theta } } d\theta$$ , with a nonnegative integer n and positive μ. This integral can be formed by linearly combining modified Bessel functions of the first kind $$B(n,\mu ) = \frac{1}{\pi }\int\limits_{0}^{\pi } {e^{\mu \cos \theta } \cos \left( {n\theta } \right)d\theta }$$ , with a nonnegative integer n and negative μ. Direct applications of the standard approach using Mathematica and GSL are found to be inefficient and limited in the range of the parameters for the Bessel function. We propose an asymptotic function for this expression for n = 0,1,2. The relative error of asymptotic function is in the order of 10−16 with the first five terms of the asymptotic expansion. At last, we give a new asymptotic function of $$B\left( {n,\mu } \right)$$ based on the expression for $$e^{ - \mu } II\left( {n,\mu } \right)$$ when n is an integer and μ is real and large in absolute value.

РАЗРАБОТКА НЕЧЕТКОЙ СИСТЕМЫ УПРАВЛЕНИЯ ПРИВОДОМ ПРОДОЛЬНОЙ ПОДАЧИ ТОКАРНОГО СТАНКА С ЧПУ НА ОСНОВЕ СОВМЕСТНО ИСПОЛЬЗУЕМЫХ ФУНКЦИЙ ПРИНАДЛЕЖНОСТИ

Relevance As part of the study, a control system for driving the supply of a CNC lathe based on fuzzy logic was developed using the MATLAB software package. The development is carried out on the basis of experimentally defined (both theoretically and empirically) shared functions of belonging (including Gauss functions and sigmoidal functions built on a single basis). This avoids the appearance of stagnant zones where the regulator does not respond to changes in the incoming parameters of the control object. The results obtained showed the development efficiency, which is expressed by the economical use of the synchronous motor life. Economy is achieved due to surface roughness sensor provided in control system. As a result of the design of the control system, it is possible to adjust the speed of rotation of the motor, and the quality of the machined surface of the part. It is worth noting that the regulation is based on the empirical dependence of the roughness of the processed surface of the part on the radius at the tip of the cutter and the supply. Coherence and sequence of functioning of system components allowing for control of fuzzy values of electric motor parameters is ensured by developed transfer function of ball-screw pair. To share the two components of the system, the transfer function is mathematically derived, the correctness of its calculations is confirmed graphically. For the operation of the CNC lathe motor control system based on fuzzy logic, a fuzzy rule unit has been developed. The unit functionality provides for stabilization of the motor rotation speed in case of three main situations: with an increase in the indicator from the norm, with its mismatch to the lower side and with full compliance. Its operation is arranged in such a way that due to the previously specified conditions it is possible to detect inconsistencies of fuzzy values of the set of parameters. In general, it is worth noting that the effectiveness of the resulting development was confirmed experimentally, the results of the experiment make it possible to assert that the electric motor control system functions properly and is effective at all stages of the electric drive operation. Aim of research Develop a fuzzy logic control system model to drive the longitudinal feed of the CNC lathe. To form a rule block of a fuzzy control system that facilitates its operation on the entire surface of a fuzzy set without stagnant zones. Research methods As part of the study, a model of a fuzzy control system was developed using the MATLAB package, the results showed that the development functions on the entire surface of a fuzzy set, without stagnant zones. Fuzzy regulator rule block is formed. This facilitates the operation of the control system on the entire response surface, that is, the ability to control the synchronous motor performance at all stages of the part processing process. Results As part of the study, a fuzzy logic control system was developed to drive the longitudinal supply of the CNC lathe. The system is based on shared membership functions built on a single basis. A number of mathematically formulated transfer functions have been developed, which provide correction of the rotation speed of the synchronous motor, consistent transmission of the obtained data to subsequent control system units for further control of the rotation speed of the cutting tool. To ensure the operation of the control system, a fuzzy rule unit has been developed, which consists of three control directions, the operation of which is automatically determined by the control system based on data on non-conformity of parameters obtained from a specially provided surface roughness sensor of the machined part.

EXPLORING EFFICIENT KERNEL FUNCTIONS FOR SUPPORT VECTOR CLUSTERING

Clustering is an effective tool that divides data into different classes to reveal internal and previously unknown data schemes. However, in conventional clustering algorithms such as the k-means, k-NN, fuzzy c tool, the selection of the appropriate number of clusters for each data set is uncertain and varies with the data sets. Furthermore, the data sets to which the clustering algorithm is applied generally have nonlinear boundaries between clusters. Determining these nonlinear boundaries in the input space causes a complex problem. To overcome these problems, kernel-based clustering methods have been developed in recent years, which automatically determine the number and boundaries of clusters. In particular, the Support Vector Clustering (SVC) algorithm has received great attention in data analysis because of its features such as automatically determining the number of clusters and recognizing nonlinear boundaries based on the Gaussian kernel parameter. The number of clusters and region boundaries produced by SVC may show variation depending on the choice of the kernel function and its parameters. Therefore, the choice of kernel function plays a significant role. In this study, for the first time, the implementation of two different kernel (Cauchy and Laplacian) functions and evaluation of their performances have been realized within the framework of SVC. It was observed that the Laplacian kernel function performed better than Gauss and Cauchy kernel functions.

A decomposition method of nuclear magnetic resonance T2 spectrum for identifying fluid properties

Based on analysis of NMR T2 spectral characteristics, a new method for identifying fluid properties by decomposing T2 spectrum through signal analysis has been proposed. Because T2 spectrum satisfies lognormal distribution on transverse relaxation time axis, the T2 spectrum can be decomposed into 2 to 5 independent component spectra by fitting the T2 spectrum with Gauss functions. By analyzing the free relaxation response characteristics of crude oil and formation water, the dynamic response characteristics of the core mutual drive between oil and water, the petrophysical significance of each component spectrum is clarified. T2 spectrum can be decomposed into clay bound water component spectrum, capillary bound fluid component spectrum, micropores fluid component spectrum and macropores fluid component spectrum. According to the nature of crude oil in the target area, the distribution range of T2 component spectral peaks of oil-bearing reservoir is 165–500 ms on T2 time axis. This range can be used to accurately identify fluid properties. This method has high adaptability in identifying complex oil and water layers in low porosity and permeability reservoirs.

Improved cellulose X-ray diffraction analysis using Fourier series modeling

This paper addresses two fundamental issues in the peak deconvolution method of cellulose XRD data analysis: there is no standard model for amorphous cellulose and common peak functions such as Gauss, Lorentz and Voigt functions do not fit the amorphous profile well. It first examines the effects of ball milling on three types of cellulose and results show that ball milling transforms all samples into a highly amorphous phase exhibiting nearly identical powder X-ray diffraction (XRD) profiles. It is hypothesized that short range order within a glucose unit and between adjacent units survives ball milling and generates the characteristic amorphous XRD profiles. This agrees well with cellulose I d-spacing measurements and oligosaccharide XRD analysis. The amorphous XRD profile is modeled using a Fourier series equation where the coefficients are determined using the nonlinear least squares method. A new peak deconvolution method then is proposed to analyze cellulose XRD data with the amorphous Fourier model function in conjunction with standard Voigt functions representing the crystalline peaks. The impact of background subtraction method has also been assessed. Analysis of several cellulose samples was then performed and compared to the conventional peak deconvolution methods with common peak fitting functions and background subtraction approach. Results suggest that prior peak deconvolution methods overestimate cellulose crystallinity.

A time-domain method for load identification using moving weighted least square technique

Based on the thought of Green’s kernel function method (GKFM), an improved time-domain load identification method using moving weighted least square technique (MWLST) which can accurately fit dynamic load is proposed. Better than the traditional shape function method using moving least square fitting (SFM_MLSF), the proposed method considers continuity and correlation of dynamic load between two adjacent sampling points, and involves the weighted contribution of sampling points to the fitting point. In numerical examples, Gauss, Cubic and Quartic spline weight functions are utilized in the proposed method to realize the reconstruction of kernel matrix. It is found that the accuracies of load identification are almost same when their optimum supported domain radii are adopted. Furthermore, the numerical results illustrate that the proposed method can identify dynamic load more accurately and smoothly than GKFM and SFM_MLSF significantly by the same regularization method for ill-posedness, and the proposed method has excellent stability and robustness. Additionally, a special technique combining both the whole identification and the truncated-processing identification is proposed to identify external dynamic loads during hoisting process, which solves the oscillation problem caused by using inversing methods directly.

Deconvolution of Gaussian peaks with mixed real and discrete‐integer optimization based on evolutionary computing

This study describes an alternative method for deconvolution of overlapping characteristic Gauss peaks with the help of optimization of a mixed variable genetic algorithm. Continuous and discrete variables and nonlinear discrete variables in optimization problems cause solution complexity. The processing and analysis of complex analytical signals is important not only in analytical chemistry but also in other fields of science. As the amount of data increases and linearity decreases, high‐performance computations are needed to solve analytical signals. It takes a long time to perform these calculations with traditional processor systems and algorithms. We have used NVIDIA graphical processing units (GPUs) to shorten the duration of these calculations. Solving such analytical signals with genetic algorithms is widely used in computational sciences. In this study, we present a new curve‐fitting method using a genetic algorithm based on Gauss functions used to deconvolve overlapping peaks and find the exact peak number in absorption spectroscopy. The deconvolution of individual bands in the UV‐VIS region is a complex task, because the absorption bands are broad and often strongly overlap. Useful information about the molecular structure and environment can only be obtained by appropriate and truthful separation of these peaks.

Model Data Mining dan Rasio Altman untuk Prediksi Financial Distress Perusahaan

Financial distress is the stage or situation of a decline in the company's financial condition before a business failure occurs. This failure is related to liquidation, where the company fails to run its operations for profit. Financial distress prediction methods have been long developed in the field of finance using Multiple Discriminant Analyst (MDA). The most widely used MDA method is the Altman model ratio. This method is used as an early warning to the company's financial condition. This study aims to analyze the neuro fuzzy data mining algorithm with input data from the financial ratio of the Altman model to predict the company's financial distress. Research data are from the Indonesia Stock Exchange (IDX) website at www.idx.co.id. Data population between 2012-2017 LQ45 issuers are 80 companies. Preliminary data from the company's financial statements are calculated by Altman's ratio to get zscore values ??of three types of categories. These values ??are arranged in time series of four backward periods which will be used as input data for the neuro fuzzy algorithm ANFIS model. The next step is the formation of algorithms, training, testing, simulation and model evaluation using the GUI application from the Matlab program. The results of the model are predictive values ??that are compared with the results of the Altman ratio calculation of predicted years. The final results of the study show the predicted value of the ANFIS model of the Triangle membership function looks very optimal, consistent, and efficient. It was proven that the average predicted value of 9.95% was close to the actual value of the calculated year, while the results of the ANFIS model of the Trapezoid, Gauss and G-bell membership functions seemed less than optimal.&#x0D; Keywords: Financial Distress, Neuro Fuzzy, Prediction, Altman Ratio.