Pub Date : 2024-07-19DOI: 10.1134/s1995080224600705
V. A. Manevich
Abstract
Compares ARMA models, boosting, neural network models, HAR_RV models and proposes a new method for predicting one day ahead realized volatility of financial series. HAR_RV models are taken as compared classical volatility prediction models. In addition, the phenomenon of transfer learning for boosting and neural network models is investigated. Bitcoin and E-mini S&P500 are chosen as examples. The realized volatility is calculated based on intraday (intraday—24 hours) data. The calculation is based on the closing values of the internal five-minute intervals. Comparisons are made both within and between the two intervals. The intervals considered are January 1, 2018–January 1, 2022 and January 1, 2018–April 2, 2023. Since there were structural changes in the markets during these intervals, the models are estimated in sliding windows of 399 days length. For each time series, we compare three-parameter enumeration boosting, about 10 different neural network architectures, ARMA models, the newly proposed CTCM method, and various training transfer and training sample expansion options. It is shown that ARMA and HAR_RV models are generally inferior to other listed methods and models. The CTCM model and neural networks of CNN architecture are the most suitable for financial time series forecasting and show the best results. Although transfer learning shows no improvement in terms of forecast precision and yields little decline. It requires more extensive and detailed study. The smallest MAPEs for Bitcoin and E-mini S&P500 realized volatility forecasts are achieved by the newly proposed CTCM model and are 21.075%, 25.311% on the first interval and 21.996%, 26.549% on the second interval, respectively.
{"title":"Corrected Triple Correction Method, CNN and Transfer Learning for Prediction the Realized Volatility of Bitcoin and E-Mini S&P500","authors":"V. A. Manevich","doi":"10.1134/s1995080224600705","DOIUrl":"https://doi.org/10.1134/s1995080224600705","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Compares ARMA models, boosting, neural network models, HAR_RV models and proposes a new method for predicting one day ahead realized volatility of financial series. HAR_RV models are taken as compared classical volatility prediction models. In addition, the phenomenon of transfer learning for boosting and neural network models is investigated. Bitcoin and E-mini S&P500 are chosen as examples. The realized volatility is calculated based on intraday (intraday—24 hours) data. The calculation is based on the closing values of the internal five-minute intervals. Comparisons are made both within and between the two intervals. The intervals considered are January 1, 2018–January 1, 2022 and January 1, 2018–April 2, 2023. Since there were structural changes in the markets during these intervals, the models are estimated in sliding windows of 399 days length. For each time series, we compare three-parameter enumeration boosting, about 10 different neural network architectures, ARMA models, the newly proposed CTCM method, and various training transfer and training sample expansion options. It is shown that ARMA and HAR_RV models are generally inferior to other listed methods and models. The CTCM model and neural networks of CNN architecture are the most suitable for financial time series forecasting and show the best results. Although transfer learning shows no improvement in terms of forecast precision and yields little decline. It requires more extensive and detailed study. The smallest MAPEs for Bitcoin and E-mini S&P500 realized volatility forecasts are achieved by the newly proposed CTCM model and are 21.075%, 25.311% on the first interval and 21.996%, 26.549% on the second interval, respectively.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"25 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-19DOI: 10.1134/s1995080224600651
B. K. Temyanov, R. R. Nigmatullin
Abstract
We present the description of a quasi-spherical coordinate system that is introduced in a space of parameters of a multilayer perceptron with ReLU and Leaky ReLU activation functions. In this instance, a regression loss function that is given in these coordinates becomes the sum of functions that depend on a set of functions defined on a sphere and a quasi-radial coordinate. Conditions for a concentration of measure are satisfied for the functions on the sphere. As a number of parameters tends to infinity, these criteria cause the loss function to concentrate toward a quasi-radially symmetric function.
{"title":"Concentration of Measure and Global Optimization of Bayesian Multilayer Perceptron. Part I","authors":"B. K. Temyanov, R. R. Nigmatullin","doi":"10.1134/s1995080224600651","DOIUrl":"https://doi.org/10.1134/s1995080224600651","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We present the description of a quasi-spherical coordinate system that is introduced in a space of parameters of a multilayer perceptron with ReLU and Leaky ReLU activation functions. In this instance, a regression loss function that is given in these coordinates becomes the sum of functions that depend on a set of functions defined on a sphere and a quasi-radial coordinate. Conditions for a concentration of measure are satisfied for the functions on the sphere. As a number of parameters tends to infinity, these criteria cause the loss function to concentrate toward a quasi-radially symmetric function.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"22 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141746345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-19DOI: 10.1134/s1995080224600882
M. Sertbaş, F. Yılmaz
Abstract
In this paper, it is investigated that necessary and sufficient conditions for a minimal operator defined by a degenerate first-order differential operator expression in the Hilbert space (L_{2}(H,(a,b)),,a,binmathbb{R}) to be formally normal. Also, all normal extensions of the minimal operator are given with their domains. Moreover, the spectrum set of these normal extensions is given through the family of evolution operators.
{"title":"Normal Extensions of Differential Operators for Degenerate First-order","authors":"M. Sertbaş, F. Yılmaz","doi":"10.1134/s1995080224600882","DOIUrl":"https://doi.org/10.1134/s1995080224600882","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, it is investigated that necessary and sufficient conditions for a minimal operator defined by a degenerate first-order differential operator expression in the Hilbert space <span>(L_{2}(H,(a,b)),,a,binmathbb{R})</span> to be formally normal. Also, all normal extensions of the minimal operator are given with their domains. Moreover, the spectrum set of these normal extensions is given through the family of evolution operators.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"26 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-19DOI: 10.1134/s1995080224600791
K. S. Alybaev, A. M. Juraev, M. N. Nurmatova
Abstract
This paper considers an autonomous system of singularly perturbed equations of fast variables, consisting of (2n) first-order equations and one equation of a slow variable. The first approximation matrix of singularly perturbed equations has pairwise complex conjugate eigenvalues. The system has an equilibrium position, and the stability of the equilibrium position is lost by all eigenvalues at some value of the slow variable. It is proven that the solution of a singularly perturbed equation remains near an unstable equilibrium position during a finite time. Thus, the solution is delayed near the unstable equilibrium position. Early works considered cases when the stability of the equilibrium position is lost by one pair of complex conjugate eigenvalues.
{"title":"Delay in Solving Autonomous Singularly Perturbed Equations Near an Unstable Equilibrium Position","authors":"K. S. Alybaev, A. M. Juraev, M. N. Nurmatova","doi":"10.1134/s1995080224600791","DOIUrl":"https://doi.org/10.1134/s1995080224600791","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper considers an autonomous system of singularly perturbed equations of fast variables, consisting of <span>(2n)</span> first-order equations and one equation of a slow variable. The first approximation matrix of singularly perturbed equations has pairwise complex conjugate eigenvalues. The system has an equilibrium position, and the stability of the equilibrium position is lost by all eigenvalues at some value of the slow variable. It is proven that the solution of a singularly perturbed equation remains near an unstable equilibrium position during a finite time. Thus, the solution is delayed near the unstable equilibrium position. Early works considered cases when the stability of the equilibrium position is lost by one pair of complex conjugate eigenvalues.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"13 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-19DOI: 10.1134/s1995080224600584
D. K. Durdiev, D. A. Toshev, H. H. Turdiev
Abstract
In this paper, we study the direct and inverse problems for a model equation of a mixed parabolic-hyperbolic type. In the direct problem, an analog of the Tricomi problem for this equation with a characteristic line of type change is considered. The unknown of the inverse problem is the y-dependent source function of the parabolic equation. To determine it with respect to the solution defined in the parabolic part of the domain, an overdetermination at the point (x=x_{0}) for (y>0) condition is specified. Local theorems on the unique solvability of the problems posed in the sense of the classical solution are proved.
摘要 本文研究了抛物-双曲混合型模型方程的直接问题和逆问题。在直接问题中，我们考虑了该方程的 Tricomi 问题的类似问题，其特征线类型发生了变化。逆问题的未知数是抛物线方程的 y 依赖源函数。为了确定它与定义在抛物线部分域中的解的关系，在点(x=x_{0})处指定了一个(y>0)条件的过度确定。证明了在经典解的意义上所提出问题的唯一可解性的局部定理。
{"title":"Determining a Source Function in the Mixed Parabolic–Hyperbolic Equation with Characteristic Type Change Line","authors":"D. K. Durdiev, D. A. Toshev, H. H. Turdiev","doi":"10.1134/s1995080224600584","DOIUrl":"https://doi.org/10.1134/s1995080224600584","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we study the direct and inverse problems for a model equation of a mixed parabolic-hyperbolic type. In the direct problem, an analog of the Tricomi problem for this equation with a characteristic line of type change is considered. The unknown of the inverse problem is the y-dependent source function of the parabolic equation. To determine it with respect to the solution defined in the parabolic part of the domain, an overdetermination at the point <span>(x=x_{0})</span> for <span>(y>0)</span> condition is specified. Local theorems on the unique solvability of the problems posed in the sense of the classical solution are proved.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"27 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-19DOI: 10.1134/s1995080224600560
Youssra Bouhenache, Wided Chikouche, Imene Touil
Abstract
We present a polynomial-time primal-dual interior-point algorithm (IPA) for solving convex quadratic optimization (CQO) problems, based on a bi-parameterized bi-hyperbolic kernel function (KF). The growth term is a combination of the classical quadratic term and a hyperbolic one depending on a parameter (pin[0,1],) while the barrier term is hyperbolic and depends on a parameter (qgeqfrac{1}{2}sinh 2.) Using some simple analysis tools, we prove with a special choice of the parameter (q,) that the worst-case iteration bound for the new corresponding algorithm is (textbf{O}big{(}sqrt{n}log nlogfrac{n}{epsilon}big{)}) iterations for large-update methods. This improves the result obtained in (Optimization 70 (8), 1703–1724 (2021)) for CQO problems and matches the currently best-known iteration bound for large-update primal-dual interior-point methods (IPMs). Numerical tests show that the parameter (p) influences also the computational behavior of the algorithm although the theoretical iteration bound does not depends on this parameter. To our knowledge, this is the first bi-parameterized bi-hyperbolic KF-based IPM introduced for CQO problems, and the first KF that incorporates a hyperbolic function in its growth term while all KFs existing in the literature have a polynomial growth term exepct the KFs proposed in (Optimization 67 (10), 1605–1630 (2018)) and (J. Optim. Theory Appl. 178, 935–949 (2018)) which have a trigonometric growth term.
{"title":"A Large-update Primal-dual Interior-point Algorithm for Convex Quadratic Optimization Based on a New Bi-parameterized Bi-hyperbolic Kernel Function","authors":"Youssra Bouhenache, Wided Chikouche, Imene Touil","doi":"10.1134/s1995080224600560","DOIUrl":"https://doi.org/10.1134/s1995080224600560","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We present a polynomial-time primal-dual interior-point algorithm (IPA) for solving convex quadratic optimization (CQO) problems, based on a bi-parameterized bi-hyperbolic kernel function (KF). The growth term is a combination of the classical quadratic term and a hyperbolic one depending on a parameter <span>(pin[0,1],)</span> while the barrier term is hyperbolic and depends on a parameter <span>(qgeqfrac{1}{2}sinh 2.)</span> Using some simple analysis tools, we prove with a special choice of the parameter <span>(q,)</span> that the worst-case iteration bound for the new corresponding algorithm is <span>(textbf{O}big{(}sqrt{n}log nlogfrac{n}{epsilon}big{)})</span> iterations for large-update methods. This improves the result obtained in (Optimization <b>70</b> (8), 1703–1724 (2021)) for CQO problems and matches the currently best-known iteration bound for large-update primal-dual interior-point methods (IPMs). Numerical tests show that the parameter <span>(p)</span> influences also the computational behavior of the algorithm although the theoretical iteration bound does not depends on this parameter. To our knowledge, this is the first bi-parameterized bi-hyperbolic KF-based IPM introduced for CQO problems, and the first KF that incorporates a hyperbolic function in its growth term while all KFs existing in the literature have a polynomial growth term exepct the KFs proposed in (Optimization <b>67</b> (10), 1605–1630 (2018)) and (J. Optim. Theory Appl. <b>178</b>, 935–949 (2018)) which have a trigonometric growth term.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"24 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141746169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-14DOI: 10.1134/s1995080224600213
Adil Rashid, Zahoor Ahmad, Aafaq A. Rather, Irfan Ali
Abstract
This paper provides a lucid note on the class of Weibull–Pareto distribution (NWPD) used to denote different parametric models. We briefly discussed and commented on these models’ uniqueness and proposed alternative definitions. In particular, we concluded that the NWPD introduced by Nasiru and Luguterah (2015) needs to be more balanced, even though it does not exist. More precisely, the NWPD by Nasiru and Luguterah is identifiable with a two-parameter Weibull distribution.
{"title":"A Note on Class of Weibull–Pareto Distribution","authors":"Adil Rashid, Zahoor Ahmad, Aafaq A. Rather, Irfan Ali","doi":"10.1134/s1995080224600213","DOIUrl":"https://doi.org/10.1134/s1995080224600213","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper provides a lucid note on the class of Weibull–Pareto distribution (NWPD) used to denote different parametric models. We briefly discussed and commented on these models’ uniqueness and proposed alternative definitions. In particular, we concluded that the NWPD introduced by Nasiru and Luguterah (2015) needs to be more balanced, even though it does not exist. More precisely, the NWPD by Nasiru and Luguterah is identifiable with a two-parameter Weibull distribution.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"9 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-14DOI: 10.1134/s1995080224600262
P. Sangnawakij, R. Sittimongkol
Abstract
Assessing heterogeneity between the independent studies in a meta-analysis plays a critical role in quantifying the amount of dispersion. The well-known Higgins’ I2 statistic has been used most often for measuring heterogeneity. However, the problem of the within-study variances involved in this measure is discussed, which leads to misinterpretation. Alternatively, the between-study coefficient of variation, the ratio of the standard deviation of the random effects to the effect, is of interest. This current work is motivated by meta-analytic data on continuous outcomes reported only the sample means and sample sizes. No sampling variance estimate is available in the studies. In such a case, we introduce the mean difference estimator based on the profile likelihood and bootstrap methods and propose the coefficient of variation estimator for measuring the heterogeneity of the mean differences. The statistical power of the coefficient of variation is determined based on simulations. The results indicate that the estimated between-study coefficient of variation derived from maximum profile likelihood estimation has a lower bias than that obtained from bootstrap estimation. The Wald-type confidence interval using variance estimation derived from the delta method provides a suitable coverage probability and has a short length interval.
{"title":"Heterogeneity Measure in Meta-analysis without Study-specific Variance Information","authors":"P. Sangnawakij, R. Sittimongkol","doi":"10.1134/s1995080224600262","DOIUrl":"https://doi.org/10.1134/s1995080224600262","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Assessing heterogeneity between the independent studies in a meta-analysis plays a critical role in quantifying the amount of dispersion. The well-known Higgins’ I2 statistic has been used most often for measuring heterogeneity. However, the problem of the within-study variances involved in this measure is discussed, which leads to misinterpretation. Alternatively, the between-study coefficient of variation, the ratio of the standard deviation of the random effects to the effect, is of interest. This current work is motivated by meta-analytic data on continuous outcomes reported only the sample means and sample sizes. No sampling variance estimate is available in the studies. In such a case, we introduce the mean difference estimator based on the profile likelihood and bootstrap methods and propose the coefficient of variation estimator for measuring the heterogeneity of the mean differences. The statistical power of the coefficient of variation is determined based on simulations. The results indicate that the estimated between-study coefficient of variation derived from maximum profile likelihood estimation has a lower bias than that obtained from bootstrap estimation. The Wald-type confidence interval using variance estimation derived from the delta method provides a suitable coverage probability and has a short length interval.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"218 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-14DOI: 10.1134/s1995080224600134
T. R. Zakirov, O. S. Zhuchkova, M. G. Khramchenkov
Abstract
In this paper, we present the mathematical model describing the dynamic adsorption processes in three-dimensional porous media. The novelty of this model lies in the ability to study the mass transfer processes with immiscible multiphase flows in porous media. The governing equations describing fluid flow and convective-diffusion of the active component are based on the lattice Boltzmann equations. The phenomena on the interface between two fluids and between fluids and solid phase, including interfacial tension and wetting effects, are described using the most modern version of the color-gradient method. The kinetic of the mass transfer between active component and adsorbent particles is described using the Langmuir adsorption equation. The numerical algorithm has been validated on two benchmarks including the immiscibility of the active component and the displaced fluid, as well as the problem of mass conservation of the active component during its adsorption and transport in porous media. The mathematical model has been adapted for porous media presented by X-ray computed tomography images of natural porous media.
摘要 本文提出了描述三维多孔介质中动态吸附过程的数学模型。该模型的新颖之处在于能够研究多孔介质中不相溶多相流的传质过程。描述流体流动和活性成分对流扩散的控制方程基于晶格玻尔兹曼方程。两种流体之间以及流体与固相之间的界面现象，包括界面张力和润湿效应，采用最现代的颜色梯度法进行描述。活性成分和吸附剂颗粒之间的传质动力学采用 Langmuir 吸附方程进行描述。该数值算法已在两个基准上得到验证，包括活性成分和被置换流体的不可溶性，以及活性成分在多孔介质中的吸附和传输过程中的质量守恒问题。该数学模型适用于天然多孔介质的 X 射线计算机断层扫描图像所显示的多孔介质。
{"title":"Mathematical Model for Dynamic Adsorption with Immiscible Multiphase Flows in Three-dimensional Porous Media","authors":"T. R. Zakirov, O. S. Zhuchkova, M. G. Khramchenkov","doi":"10.1134/s1995080224600134","DOIUrl":"https://doi.org/10.1134/s1995080224600134","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we present the mathematical model describing the dynamic adsorption processes in three-dimensional porous media. The novelty of this model lies in the ability to study the mass transfer processes with immiscible multiphase flows in porous media. The governing equations describing fluid flow and convective-diffusion of the active component are based on the lattice Boltzmann equations. The phenomena on the interface between two fluids and between fluids and solid phase, including interfacial tension and wetting effects, are described using the most modern version of the color-gradient method. The kinetic of the mass transfer between active component and adsorbent particles is described using the Langmuir adsorption equation. The numerical algorithm has been validated on two benchmarks including the immiscibility of the active component and the displaced fluid, as well as the problem of mass conservation of the active component during its adsorption and transport in porous media. The mathematical model has been adapted for porous media presented by X-ray computed tomography images of natural porous media.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"17 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-14DOI: 10.1134/s1995080224600237
Yashpal Singh Raghav, Rajesh Singh, Rohan Mishra, Abdullah Ali H. Ahmadini, Nitesh Kumar Adichwal, Irfan Ali
Abstract
In survey sampling, it might happen that information on the population mean of the auxiliary variable is not available, but it can be obtained if the researcher opts for it. The sampling design to be used in such a case is the Two-Phase sampling design. This design has been studied extensively in SRSWOR, but it has not been studied when the population under study is rare or clumped. It is known that when the population under study is rare or clumped, adaptive cluster sampling (ACS) design is more efficient, and therefore in this paper we have proposed the Two-Phase Adaptive Cluster Sampling Under Transformed Population Approach and further proposed ratio and product estimator and a generalized robust ratio type estimator in this design. The bias and MSE of the proposed estimators have been derived and presented up to the first order of approximation. Further, the performance of the proposed estimators has been analyzed using simulation studies.
{"title":"Two Phase Adaptive Cluster Sampling Under Transformed Population Approach","authors":"Yashpal Singh Raghav, Rajesh Singh, Rohan Mishra, Abdullah Ali H. Ahmadini, Nitesh Kumar Adichwal, Irfan Ali","doi":"10.1134/s1995080224600237","DOIUrl":"https://doi.org/10.1134/s1995080224600237","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In survey sampling, it might happen that information on the population mean of the auxiliary variable is not available, but it can be obtained if the researcher opts for it. The sampling design to be used in such a case is the Two-Phase sampling design. This design has been studied extensively in SRSWOR, but it has not been studied when the population under study is rare or clumped. It is known that when the population under study is rare or clumped, adaptive cluster sampling (ACS) design is more efficient, and therefore in this paper we have proposed the Two-Phase Adaptive Cluster Sampling Under Transformed Population Approach and further proposed ratio and product estimator and a generalized robust ratio type estimator in this design. The bias and MSE of the proposed estimators have been derived and presented up to the first order of approximation. Further, the performance of the proposed estimators has been analyzed using simulation studies.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"37 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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