Pub Date : 2023-11-11DOI: 10.1142/s0218348x23501347
XIAOHUA ZHANG, YUNXIU ZHOU, TINGSONG DU
The fractal [Formula: see text]-preinvex mappings are put forward and their properties are investigated firstly. Meanwhile, some fractal Hermite–Hadamard-type ([Formula: see text]) and Fejér–Hermite–Hadamard-type ([Formula: see text]) inequalities concerning [Formula: see text]-preinvexity are popularized. Then, two weighted parameterized [Formula: see text]-fractal identities are proposed, which involve twice the local fractional differentiable mappings. Based upon these identities and taking advantage of the fractal [Formula: see text]-preinvex mappings as well as [Formula: see text]-Lipschitzian mappings, a range of error estimations are deduced in the fractal domains. Finally, certain fractal inequalities with relation to the weighted formula and random variable are correspondingly presented as applications.
{"title":"PROPERTIES AND 2α̃-FRACTAL WEIGHTED PARAMETRIC INEQUALITIES FOR THE FRACTAL (m,h)-PREINVEX MAPPINGS","authors":"XIAOHUA ZHANG, YUNXIU ZHOU, TINGSONG DU","doi":"10.1142/s0218348x23501347","DOIUrl":"https://doi.org/10.1142/s0218348x23501347","url":null,"abstract":"The fractal [Formula: see text]-preinvex mappings are put forward and their properties are investigated firstly. Meanwhile, some fractal Hermite–Hadamard-type ([Formula: see text]) and Fejér–Hermite–Hadamard-type ([Formula: see text]) inequalities concerning [Formula: see text]-preinvexity are popularized. Then, two weighted parameterized [Formula: see text]-fractal identities are proposed, which involve twice the local fractional differentiable mappings. Based upon these identities and taking advantage of the fractal [Formula: see text]-preinvex mappings as well as [Formula: see text]-Lipschitzian mappings, a range of error estimations are deduced in the fractal domains. Finally, certain fractal inequalities with relation to the weighted formula and random variable are correspondingly presented as applications.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"21 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135086385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-11DOI: 10.1142/s0218348x23501311
HUAIZHI ZHU, JUN GAO, BOQI XIAO, YIDAN ZHANG, YANBIN WANG, PEILONG WANG, BILIANG TU, GONGBO LONG
The microspatial structure of porous media affects the electrical properties of reservoir rocks significantly. In this work, a dual-porosity model is established to investigate the electrical properties of porous media, in which tree-like networks and capillary channels represent fractures and pores. By using fractal theory, we established an analytical equation for the conductivity of water-saturated dual-porosity media. The analytical equation, devoid of any empirical constants, expresses the electrical properties of the porous media as a function of some structural parameters ([Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]. We also examine the impact of various matrix structural parameters on conductivity. It is found that increasing the length of mother channel ([Formula: see text], length ratio ([Formula: see text], the number of branching layers ([Formula: see text], and tortuosity fractal dimension ([Formula: see text] leads to a decrease in conductivity, whereas increasing the diameter of mother channel ([Formula: see text], diameter ratio ([Formula: see text], the cross-sectional porosity ([Formula: see text], [Formula: see text], and the channel bifurcation number ([Formula: see text] enhances conductivity. Furthermore, we validated this analytical model by comparing it with the experimental data available, and the results demonstrate good agreement. This research has proposed an advanced conductivity model that enables us to better understand the underlying physical mechanisms of the electrical properties in porous media.
{"title":"PREDICTING THE ELECTRICAL CONDUCTIVITY OF DUAL-POROSITY MEDIA WITH FRACTAL THEORY","authors":"HUAIZHI ZHU, JUN GAO, BOQI XIAO, YIDAN ZHANG, YANBIN WANG, PEILONG WANG, BILIANG TU, GONGBO LONG","doi":"10.1142/s0218348x23501311","DOIUrl":"https://doi.org/10.1142/s0218348x23501311","url":null,"abstract":"The microspatial structure of porous media affects the electrical properties of reservoir rocks significantly. In this work, a dual-porosity model is established to investigate the electrical properties of porous media, in which tree-like networks and capillary channels represent fractures and pores. By using fractal theory, we established an analytical equation for the conductivity of water-saturated dual-porosity media. The analytical equation, devoid of any empirical constants, expresses the electrical properties of the porous media as a function of some structural parameters ([Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]. We also examine the impact of various matrix structural parameters on conductivity. It is found that increasing the length of mother channel ([Formula: see text], length ratio ([Formula: see text], the number of branching layers ([Formula: see text], and tortuosity fractal dimension ([Formula: see text] leads to a decrease in conductivity, whereas increasing the diameter of mother channel ([Formula: see text], diameter ratio ([Formula: see text], the cross-sectional porosity ([Formula: see text], [Formula: see text], and the channel bifurcation number ([Formula: see text] enhances conductivity. Furthermore, we validated this analytical model by comparing it with the experimental data available, and the results demonstrate good agreement. This research has proposed an advanced conductivity model that enables us to better understand the underlying physical mechanisms of the electrical properties in porous media.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"21 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135086527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-11DOI: 10.1142/s0218348x23501293
ZUN LI, AIMIN CHEN, XIAOMENG SHEN, TONGJUN MIA
Aiming to solve the problem of blind image inpainting, this study proposed a blind image inpainting model integrated with rational fractal interpolation information. First, wavelet decomposition and closed operations were adopted to obtain masks and transform blind inpainting into non-blind inpainting. Then, on the basis of similar structural groups, rational fractal interpolation functions were introduced to complete the restoration. On the one hand, this model can sufficiently express the texture features of the image with high fidelity. On the other hand, it can better represent the structural features of the image, avoid serrated edges, enhance the restoration effect, and approximate the original image. The experimental results show that the restoration effect of this model can reserve texture details and ensure edges without distortion, possessing great practical application value.
{"title":"A BLIND IMAGE INPAINTING MODEL INTEGRATED WITH RATIONAL FRACTAL INTERPOLATION INFORMATION","authors":"ZUN LI, AIMIN CHEN, XIAOMENG SHEN, TONGJUN MIA","doi":"10.1142/s0218348x23501293","DOIUrl":"https://doi.org/10.1142/s0218348x23501293","url":null,"abstract":"Aiming to solve the problem of blind image inpainting, this study proposed a blind image inpainting model integrated with rational fractal interpolation information. First, wavelet decomposition and closed operations were adopted to obtain masks and transform blind inpainting into non-blind inpainting. Then, on the basis of similar structural groups, rational fractal interpolation functions were introduced to complete the restoration. On the one hand, this model can sufficiently express the texture features of the image with high fidelity. On the other hand, it can better represent the structural features of the image, avoid serrated edges, enhance the restoration effect, and approximate the original image. The experimental results show that the restoration effect of this model can reserve texture details and ensure edges without distortion, possessing great practical application value.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"21 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135086523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-11DOI: 10.1142/s0218348x23501359
YELİZ KARACA, MATI UR RAHMAN, MOHAMMED A. EL-SHORBAGY, DUMITRU BALEANU
The exploration of nonlinear phenomena entails the representation of intricate systems with space-time variables, and across this line, Itô calculus, as the stochastic calculus version of the change pertaining to the variables formula and chain rules, involves the second derivative of f, coming from the property that Brownian motion has non-zero quadratic variation. To this end, the extended ([Formula: see text])-dimensional two-component Itô equation, as an applicable mathematical tool employed in this study for enhancing our understanding of the complex dynamics inherent in multidimensional physical systems, serves the purpose of modeling and understanding dynamic phenomena pervading various disciplines. For modeling complex phenomena, fractional differential equations (FDEs), ordinary differential equations (ODEs), partial differential equations (PDEs) as well as the other ones provide benefits in terms of accuracy and tractability. Accordingly, our study provides the analysis of the two-component nonlinear extended ([Formula: see text])-dimensional Itô equation using the Hirota bilinear method to derive multiple soliton solutions, including novel variations along with their dispersion coefficients, which shed light into the intriguing attributes of the Itô equation. The investigation further encompasses diverse soliton types, such as the general first-order soliton, second-order soliton with fission and bifurcation, third-order soliton, and fourth-order soliton with fission and bifurcation. Besides these, the study also explores the rogue wave and lump solutions by varying parameters across distinct planes. Consequently, these results validate the characteristics and utility of the two-component nonlinear extended ([Formula: see text])-dimensional Itô equation and its relevance to related systems. The novel findings based on the Itô calculus systems revealed, through the analyses, theoretical and experimental aspects in combination with the graphical presentation of the parameter effects on solitons in line with the analyses obtained. These have enhanced the understanding of the dynamics of intricate attributes governed by the two-component nonlinear extended ([Formula: see text])-dimensional Itô equation, particularly concerning chaotic patterns, fission and bifurcation soliton nonlinear complexities.
{"title":"MULTIPLE SOLITONS, BIFURCATIONS, CHAOTIC PATTERNS AND FISSION/FUSION, ROGUE WAVES SOLUTIONS OF TWO-COMPONENT EXTENDED (2+1)-D ITÔ CALCULUS SYSTEM","authors":"YELİZ KARACA, MATI UR RAHMAN, MOHAMMED A. EL-SHORBAGY, DUMITRU BALEANU","doi":"10.1142/s0218348x23501359","DOIUrl":"https://doi.org/10.1142/s0218348x23501359","url":null,"abstract":"The exploration of nonlinear phenomena entails the representation of intricate systems with space-time variables, and across this line, Itô calculus, as the stochastic calculus version of the change pertaining to the variables formula and chain rules, involves the second derivative of f, coming from the property that Brownian motion has non-zero quadratic variation. To this end, the extended ([Formula: see text])-dimensional two-component Itô equation, as an applicable mathematical tool employed in this study for enhancing our understanding of the complex dynamics inherent in multidimensional physical systems, serves the purpose of modeling and understanding dynamic phenomena pervading various disciplines. For modeling complex phenomena, fractional differential equations (FDEs), ordinary differential equations (ODEs), partial differential equations (PDEs) as well as the other ones provide benefits in terms of accuracy and tractability. Accordingly, our study provides the analysis of the two-component nonlinear extended ([Formula: see text])-dimensional Itô equation using the Hirota bilinear method to derive multiple soliton solutions, including novel variations along with their dispersion coefficients, which shed light into the intriguing attributes of the Itô equation. The investigation further encompasses diverse soliton types, such as the general first-order soliton, second-order soliton with fission and bifurcation, third-order soliton, and fourth-order soliton with fission and bifurcation. Besides these, the study also explores the rogue wave and lump solutions by varying parameters across distinct planes. Consequently, these results validate the characteristics and utility of the two-component nonlinear extended ([Formula: see text])-dimensional Itô equation and its relevance to related systems. The novel findings based on the Itô calculus systems revealed, through the analyses, theoretical and experimental aspects in combination with the graphical presentation of the parameter effects on solitons in line with the analyses obtained. These have enhanced the understanding of the dynamics of intricate attributes governed by the two-component nonlinear extended ([Formula: see text])-dimensional Itô equation, particularly concerning chaotic patterns, fission and bifurcation soliton nonlinear complexities.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"21 11","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135086524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-11DOI: 10.1142/s0218348x23501281
YONGFANG QI, GUOPING LI
In this paper, we introduce [Formula: see text]-convex function, and obtain a new identity by the method called integrating by parts. Based on the identity, many Ostrowski type inequalities are presented through the Hölder’s inequality and the well-known power-mean inequality. Under certain conditions, the results we obtained can be transformed into the classical results. Of course, at the end of the paper, some examples are given to support the main results.
{"title":"FRACTIONAL OSTROWSKI TYPE INEQUALITIES FOR (s,m)-CONVEX FUNCTION WITH APPLICATIONS","authors":"YONGFANG QI, GUOPING LI","doi":"10.1142/s0218348x23501281","DOIUrl":"https://doi.org/10.1142/s0218348x23501281","url":null,"abstract":"In this paper, we introduce [Formula: see text]-convex function, and obtain a new identity by the method called integrating by parts. Based on the identity, many Ostrowski type inequalities are presented through the Hölder’s inequality and the well-known power-mean inequality. Under certain conditions, the results we obtained can be transformed into the classical results. Of course, at the end of the paper, some examples are given to support the main results.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"21 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135086528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-10DOI: 10.1142/s0218348x2350113x
Jian Wang, Wenjing Jiang, Mengdie Yang, Wei Shao
In this paper, we explore whether the activity of SARS-CoV-2 was associated with seasonality. MF-DFA model is utilized to calculate multifractal strength and multifractal complexity to evaluate the change state of SARS-CoV-2 activity. We select 10 countries with serious epidemic in the world, which are distributed in different latitudes of the northern and southern hemispheres. The study utilized the time series data of daily new cases and daily new deaths recorded in these countries. We regard May to October as the “high temperature season” for countries in the northern hemisphere, November to April as the “low temperature season”, and the southern hemisphere is just the opposite. By comparing the multifractal intensity [Formula: see text] and multifractal complexity [Formula: see text] of the two time series in the two seasons, we draw a conclusion that, for both the sequence of the daily newly diagnosed persons and the daily newly increased number of deaths, in the countries of both the northern and southern hemispheres, [Formula: see text] and [Formula: see text] are weaker in the “low temperature season”. That is, in the low temperature environment, SARS-CoV-2 can survive for a long time and be more infectious. In addition, we also observe that in the northern hemisphere, Iran is at a lower latitude, and although the SARS-CoV-2 activity in the low temperature season is higher than that in the high temperature season, the difference is not significant. Therefore, the lower latitude may resist this phenomenon. However, most of the countries in the southern hemisphere are within 30[Formula: see text] of south latitude, with low latitude, and other meteorological characteristics such as humidity in the countries in the southern hemisphere are also relatively unique. Although SARS-CoV-2 is characterized by high activity in low temperature seasons, no direct evidence related to the characteristics of latitude distribution has been found.
{"title":"Analysis of transmission dynamics of SARS-CoV-2 under seasonal change","authors":"Jian Wang, Wenjing Jiang, Mengdie Yang, Wei Shao","doi":"10.1142/s0218348x2350113x","DOIUrl":"https://doi.org/10.1142/s0218348x2350113x","url":null,"abstract":"In this paper, we explore whether the activity of SARS-CoV-2 was associated with seasonality. MF-DFA model is utilized to calculate multifractal strength and multifractal complexity to evaluate the change state of SARS-CoV-2 activity. We select 10 countries with serious epidemic in the world, which are distributed in different latitudes of the northern and southern hemispheres. The study utilized the time series data of daily new cases and daily new deaths recorded in these countries. We regard May to October as the “high temperature season” for countries in the northern hemisphere, November to April as the “low temperature season”, and the southern hemisphere is just the opposite. By comparing the multifractal intensity [Formula: see text] and multifractal complexity [Formula: see text] of the two time series in the two seasons, we draw a conclusion that, for both the sequence of the daily newly diagnosed persons and the daily newly increased number of deaths, in the countries of both the northern and southern hemispheres, [Formula: see text] and [Formula: see text] are weaker in the “low temperature season”. That is, in the low temperature environment, SARS-CoV-2 can survive for a long time and be more infectious. In addition, we also observe that in the northern hemisphere, Iran is at a lower latitude, and although the SARS-CoV-2 activity in the low temperature season is higher than that in the high temperature season, the difference is not significant. Therefore, the lower latitude may resist this phenomenon. However, most of the countries in the southern hemisphere are within 30[Formula: see text] of south latitude, with low latitude, and other meteorological characteristics such as humidity in the countries in the southern hemisphere are also relatively unique. Although SARS-CoV-2 is characterized by high activity in low temperature seasons, no direct evidence related to the characteristics of latitude distribution has been found.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135087349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-10DOI: 10.1142/s0218348x23501335
YI JIN, JINGYAN ZHAO, JIABIN DONG, JUNLING ZHENG, QING ZHANG, DANDAN LIU, HUIBO SONG
As a multi-scale system featuring fractal hierarchical branching structure, the quantitative characterization of natural river networks is of fundamental significance for the assessment of the hydrological and ecological issues. However, as already evidenced, the fractal behavior cannot be uniquely inverted by fractal dimension, which induces a challenge in accurately describing the arbitrary scale-invariance properties in natural river networks. In this work, as per fractal topography theory, an open mathematical framework for the description of arbitrary fractal river networks is proposed by clarifying the assembly mechanisms of complexity types (i.e. the original and behavioral complexities) in a river network. On this basis, a general algorithm for the characterization of complexities is developed, and the effects of the original and behavioral complexities on the structure of a river network are systematically explored. The results indicate that the original complexity determines the tortuosity and spatial coverage of a river network, and the behavioral complexity dominates the river patterns, heterogeneity, and scale-invariance properties. Our investigation lays a foundation for assessing and predicting accurately the effect on environments, ecology and humans from river networks.
{"title":"A MATHEMATICAL FRAMEWORK TO CHARACTERIZE COMPLEXITY ASSEMBLY IN FRACTAL RIVER NETWORKS","authors":"YI JIN, JINGYAN ZHAO, JIABIN DONG, JUNLING ZHENG, QING ZHANG, DANDAN LIU, HUIBO SONG","doi":"10.1142/s0218348x23501335","DOIUrl":"https://doi.org/10.1142/s0218348x23501335","url":null,"abstract":"As a multi-scale system featuring fractal hierarchical branching structure, the quantitative characterization of natural river networks is of fundamental significance for the assessment of the hydrological and ecological issues. However, as already evidenced, the fractal behavior cannot be uniquely inverted by fractal dimension, which induces a challenge in accurately describing the arbitrary scale-invariance properties in natural river networks. In this work, as per fractal topography theory, an open mathematical framework for the description of arbitrary fractal river networks is proposed by clarifying the assembly mechanisms of complexity types (i.e. the original and behavioral complexities) in a river network. On this basis, a general algorithm for the characterization of complexities is developed, and the effects of the original and behavioral complexities on the structure of a river network are systematically explored. The results indicate that the original complexity determines the tortuosity and spatial coverage of a river network, and the behavioral complexity dominates the river patterns, heterogeneity, and scale-invariance properties. Our investigation lays a foundation for assessing and predicting accurately the effect on environments, ecology and humans from river networks.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":" 19","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135191593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-08DOI: 10.1142/s0218348x23501323
J. ALVAREZ-RAMIREZ, E. RODRIGUEZ, L. CASTRO
Complex time series appear commonly in a large diversity of the science, engineering, economy, financial and social fields. In many instances, complex time series exhibit scaling behavior over a wide range of scales. The traditional rescaled-range (R/S) analysis and the detrended fluctuation analysis (DFA) are commonly used to characterize the scaling behavior via the Hurst exponent. These methods perform well for long-time series. However, the performance may be poor for short times resulting from scarce measurements (e.g. less than a hundred). This work proposes an approach based on singular value decomposition (SVD) entropy for estimating the Hurst exponent for short-time series. In the first step, synthetic time series were used to find the relationship between Hurst exponent and SVD entropy. In the second step, an empirical relationship was proposed to estimate the Hurst exponent from SVD entropy computations of the time series. The performance of the approach was illustrated with two examples of real-time series (consumer price index (CPI) and El Niño Oceanic Index), showing that the estimated Hurst exponent provides valuable insights into the physical mechanisms involved in the generation of the time series.
{"title":"HURST EXPONENT ESTIMATION FOR SHORT-TIME SERIES BASED ON SINGULAR VALUE DECOMPOSITION ENTROPY","authors":"J. ALVAREZ-RAMIREZ, E. RODRIGUEZ, L. CASTRO","doi":"10.1142/s0218348x23501323","DOIUrl":"https://doi.org/10.1142/s0218348x23501323","url":null,"abstract":"Complex time series appear commonly in a large diversity of the science, engineering, economy, financial and social fields. In many instances, complex time series exhibit scaling behavior over a wide range of scales. The traditional rescaled-range (R/S) analysis and the detrended fluctuation analysis (DFA) are commonly used to characterize the scaling behavior via the Hurst exponent. These methods perform well for long-time series. However, the performance may be poor for short times resulting from scarce measurements (e.g. less than a hundred). This work proposes an approach based on singular value decomposition (SVD) entropy for estimating the Hurst exponent for short-time series. In the first step, synthetic time series were used to find the relationship between Hurst exponent and SVD entropy. In the second step, an empirical relationship was proposed to estimate the Hurst exponent from SVD entropy computations of the time series. The performance of the approach was illustrated with two examples of real-time series (consumer price index (CPI) and El Niño Oceanic Index), showing that the estimated Hurst exponent provides valuable insights into the physical mechanisms involved in the generation of the time series.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135341963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-08DOI: 10.1142/s0218348x23501268
LU-LU GENG, XIAO-JUN YANG
In this paper, we first propose two Chebyshev-type inequalities associated with the general fractional-order (Yang–Abdel–Aty–Cattani) integrals with the Rabotnov fractional-exponential kernel under the condition that [Formula: see text] and [Formula: see text] are synchronous functions. What is more, by the mathematical induction, we prove a new Chebyshev-type inequality in the case that [Formula: see text] be [Formula: see text] positive increasing functions. Finally, we introduce a novel Chebyshev-type inequality via the general fractional-order integrals with the Rabotnov fractional-exponential kernel under the condition that [Formula: see text] and [Formula: see text] are monotonic functions.
本文首先在[公式:见文]和[公式:见文]为同步函数的条件下，提出了两个与一般分数阶(yang - abdel - ati - cattani)积分与Rabotnov分数阶-指数核相关的chebyshev型不等式。并利用数学归纳法，证明了[公式:见文]是[公式:见文]正递增函数时的一个新的切比雪夫不等式。最后，在[公式:见文]和[公式:见文]为单调函数的条件下，利用Rabotnov分数指数核的一般分数阶积分，引入了一个新的chebyshev型不等式。
{"title":"NOVEL CHEBYSHEV-TYPE INEQUALITIES FOR THE GENERAL FRACTIONAL-ORDER INTEGRALS WITH THE RABOTNOV FRACTIONAL EXPONENTIAL KERNEL","authors":"LU-LU GENG, XIAO-JUN YANG","doi":"10.1142/s0218348x23501268","DOIUrl":"https://doi.org/10.1142/s0218348x23501268","url":null,"abstract":"In this paper, we first propose two Chebyshev-type inequalities associated with the general fractional-order (Yang–Abdel–Aty–Cattani) integrals with the Rabotnov fractional-exponential kernel under the condition that [Formula: see text] and [Formula: see text] are synchronous functions. What is more, by the mathematical induction, we prove a new Chebyshev-type inequality in the case that [Formula: see text] be [Formula: see text] positive increasing functions. Finally, we introduce a novel Chebyshev-type inequality via the general fractional-order integrals with the Rabotnov fractional-exponential kernel under the condition that [Formula: see text] and [Formula: see text] are monotonic functions.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"102 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135341965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"HAUSDORFF DIMENSION OF SKELETON NETWORKS OF SIERPIŃSKI CARPET","authors":"QINGCHENG ZENG, LIFENG XI","doi":"10.1142/s0218348x2350127x","DOIUrl":"https://doi.org/10.1142/s0218348x2350127x","url":null,"abstract":"We obtain the Hausdorff dimension of the skeleton networks of Sierpiński carpet by the self-similarity and induction, which will not touch networks.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"101 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135341968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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