This paper establishes the phase space in the light of spacial series data , discusses the fractal structure of geological data in terms of correlated functions and studies the chaos of these data . In addition , it i...This paper establishes the phase space in the light of spacial series data , discusses the fractal structure of geological data in terms of correlated functions and studies the chaos of these data . In addition , it introduces the R/S analysis for time series analysis into spacial series to calculate the structural fractal dimensions of ranges and standard deviation for spacial series data -and to establish the fractal dimension matrix and the procedures in plotting the fractal dimension anomaly diagram with vector distances of fractal dimension . At last , it has examples of its application .展开更多
In this paper, the statistical averaging method and the new statistical averaging methods have been used to solve the fuzzy multi-objective linear programming problems. These methods have been applied to form a single...In this paper, the statistical averaging method and the new statistical averaging methods have been used to solve the fuzzy multi-objective linear programming problems. These methods have been applied to form a single objective function from the fuzzy multi-objective linear programming problems. At first, a numerical example of solving fuzzy multi-objective linear programming problem has been provided to validate the maximum risk reduction by the proposed method. The proposed method has been applied to assess the risk of damage due to natural calamities like flood, cyclone, sidor, and storms at the coastal areas in Bangladesh. The proposed method of solving the fuzzy multi-objective linear programming problems by the statistical method has been compared with the Chandra Sen’s method. The numerical results show that the proposed method maximizes the risk reduction capacity better than Chandra Sen’s method.展开更多
The significance of the fluctuation and randomness of the time series of each pollutant in environmental quality assessment is described for the first time in this paper. A comparative study was made of three differen...The significance of the fluctuation and randomness of the time series of each pollutant in environmental quality assessment is described for the first time in this paper. A comparative study was made of three different computing methods： the same starting point method, the striding averaging method, and the stagger phase averaging method. All of them can be used to calculate the Hurst index, which quantifies fluctuation and randomness. This study used real water quality data from Shazhu monitoring station on Taihu Lake in Wuxi, Jiangsu Province. The results show that, of the three methods, the stagger phase averaging method is best for calculating the Hurst index of a pollutant time series from the perspective of statistical regularity.展开更多
Let{Xn;n≥1}be a sequence of i.i.d, random variables with finite variance,Q（n）be the related R/S statistics. It is proved that lim ε↓0 ε^2 ∑n=1 ^8 n log n/1 P{Q（n）≥ε√2n log log n}=2/1 EY^2,where Y=sup0≤t...Let{Xn;n≥1}be a sequence of i.i.d, random variables with finite variance,Q（n）be the related R/S statistics. It is proved that lim ε↓0 ε^2 ∑n=1 ^8 n log n/1 P{Q（n）≥ε√2n log log n}=2/1 EY^2,where Y=sup0≤t≤1B（t）-inf0≤t≤sB（t）,and B（t） is a Brownian bridge.展开更多
The least squares method is one of the most fundamental methods in Statistics to estimate correlations among various data. On the other hand, Deep Learning is the heart of Artificial Intelligence and it is a learning ...The least squares method is one of the most fundamental methods in Statistics to estimate correlations among various data. On the other hand, Deep Learning is the heart of Artificial Intelligence and it is a learning method based on the least squares method, in which a parameter called learning rate plays an important role. It is in general very hard to determine its value. In this paper we generalize the preceding paper [K. Fujii: Least squares method from the view point of Deep Learning: Advances in Pure Mathematics, 8, 485-493, 2018] and give an admissible value of the learning rate, which is easily obtained.展开更多
This paper mainly talks about a popular approach of volatility of a GARCH-type model in R, while the disturbances are independent and have identical Student-t distribution. It uses the Metropolis-Hastings method to pe...This paper mainly talks about a popular approach of volatility of a GARCH-type model in R, while the disturbances are independent and have identical Student-t distribution. It uses the Metropolis-Hastings method to perform the computations and gives the programs in details in R.展开更多
The study of imine-bridged organics has been the hot spot synthesis of second order nonlinear optical (SONLO) and photo-responsive materials in recent years. Herein we present a study of synthesis, growth, and charact...The study of imine-bridged organics has been the hot spot synthesis of second order nonlinear optical (SONLO) and photo-responsive materials in recent years. Herein we present a study of synthesis, growth, and characterization of ([paranitrophenyl]imino)benzene (PNPIB) NLO single crystal. The title compound was synthesized in one step by Schiff base formation. PNPIB single crystal of diameter of 40 mmand length 50 mmwas successfully grown by SR method using a seed as the nucleus. The growth rate formula is derived for the SR method. PNPIB single crystals of 10 mmdiameter and 60 mmheight have been grown at an average growth rate of 3 mmper day from the point seed in a glass crystallizer. Almost 100% stable crystal conversion efficiency was achieved. The as grown PNPIB crystals were characterized using single crystal X-ray diffraction (XRD), X-ray powder diffraction (XRPD), Fourier Transform Infrared (FTIR), Ultraviolet-Visible-Near Infrared (UV-Vis-NIR), 1H & 13C NMR spectral studies, dielectric measurement and NLO studies. Single crystal XRD analysis confirms that the grown ingot belongs to the space group of P2 of monoclinic system thus exhibiting noncentrosymmetric structure. The crystalline perfection was assessed by XRPD. The powder diffraction pattern of the grown crystal has been indexed. The presence of C=N bond with intramolecular hydrogen bonding and the protonation of ions were confirmed by FTIR analysis. The UV-Vis-NIR spectrum of the crystal shows that the crystal has a cut-off at 298 nm. The 1H & 13C NMR spectra confirm the molecular structure. The dielectric behaviour was measured in the frequency range 1 KHz - 10 KHz for the temperature range from 30℃ to 170℃. The slight decrease in dielectric constant has been observed as the frequency is increased and the dielectric loss is very low for the entire frequency range. The second harmonic generation (SHG) in the crystal was observed by Kurtz powder technique.展开更多
文摘This paper establishes the phase space in the light of spacial series data , discusses the fractal structure of geological data in terms of correlated functions and studies the chaos of these data . In addition , it introduces the R/S analysis for time series analysis into spacial series to calculate the structural fractal dimensions of ranges and standard deviation for spacial series data -and to establish the fractal dimension matrix and the procedures in plotting the fractal dimension anomaly diagram with vector distances of fractal dimension . At last , it has examples of its application .
文摘In this paper, the statistical averaging method and the new statistical averaging methods have been used to solve the fuzzy multi-objective linear programming problems. These methods have been applied to form a single objective function from the fuzzy multi-objective linear programming problems. At first, a numerical example of solving fuzzy multi-objective linear programming problem has been provided to validate the maximum risk reduction by the proposed method. The proposed method has been applied to assess the risk of damage due to natural calamities like flood, cyclone, sidor, and storms at the coastal areas in Bangladesh. The proposed method of solving the fuzzy multi-objective linear programming problems by the statistical method has been compared with the Chandra Sen’s method. The numerical results show that the proposed method maximizes the risk reduction capacity better than Chandra Sen’s method.
基金supported by the Eleventh Five-Year Key Technology R and D Program,China(Grant No.2006BAC02A15)the Colleges and Universities in Jiangsu Province Natural Science-Based Research Projects(Grant No.2006BAC02A15)+1 种基金the Jiangsu Province Post-Doctoral Fund Projects(Grant No.0801006C)the China Post-Doctoral Science Foundation(Grant No.20080441032)
文摘The significance of the fluctuation and randomness of the time series of each pollutant in environmental quality assessment is described for the first time in this paper. A comparative study was made of three different computing methods： the same starting point method, the striding averaging method, and the stagger phase averaging method. All of them can be used to calculate the Hurst index, which quantifies fluctuation and randomness. This study used real water quality data from Shazhu monitoring station on Taihu Lake in Wuxi, Jiangsu Province. The results show that, of the three methods, the stagger phase averaging method is best for calculating the Hurst index of a pollutant time series from the perspective of statistical regularity.
基金Project Supported by NSFC (10131040)SRFDP (2002335090)
文摘A law of iterated logarithm for R/S statistics with the help of the strong approximations of R/S statistics by functions of a Wiener process is shown.
文摘Let{Xn;n≥1}be a sequence of i.i.d, random variables with finite variance,Q（n）be the related R/S statistics. It is proved that lim ε↓0 ε^2 ∑n=1 ^8 n log n/1 P{Q（n）≥ε√2n log log n}=2/1 EY^2,where Y=sup0≤t≤1B（t）-inf0≤t≤sB（t）,and B（t） is a Brownian bridge.
文摘The least squares method is one of the most fundamental methods in Statistics to estimate correlations among various data. On the other hand, Deep Learning is the heart of Artificial Intelligence and it is a learning method based on the least squares method, in which a parameter called learning rate plays an important role. It is in general very hard to determine its value. In this paper we generalize the preceding paper [K. Fujii: Least squares method from the view point of Deep Learning: Advances in Pure Mathematics, 8, 485-493, 2018] and give an admissible value of the learning rate, which is easily obtained.
文摘This paper mainly talks about a popular approach of volatility of a GARCH-type model in R, while the disturbances are independent and have identical Student-t distribution. It uses the Metropolis-Hastings method to perform the computations and gives the programs in details in R.
文摘The study of imine-bridged organics has been the hot spot synthesis of second order nonlinear optical (SONLO) and photo-responsive materials in recent years. Herein we present a study of synthesis, growth, and characterization of ([paranitrophenyl]imino)benzene (PNPIB) NLO single crystal. The title compound was synthesized in one step by Schiff base formation. PNPIB single crystal of diameter of 40 mmand length 50 mmwas successfully grown by SR method using a seed as the nucleus. The growth rate formula is derived for the SR method. PNPIB single crystals of 10 mmdiameter and 60 mmheight have been grown at an average growth rate of 3 mmper day from the point seed in a glass crystallizer. Almost 100% stable crystal conversion efficiency was achieved. The as grown PNPIB crystals were characterized using single crystal X-ray diffraction (XRD), X-ray powder diffraction (XRPD), Fourier Transform Infrared (FTIR), Ultraviolet-Visible-Near Infrared (UV-Vis-NIR), 1H & 13C NMR spectral studies, dielectric measurement and NLO studies. Single crystal XRD analysis confirms that the grown ingot belongs to the space group of P2 of monoclinic system thus exhibiting noncentrosymmetric structure. The crystalline perfection was assessed by XRPD. The powder diffraction pattern of the grown crystal has been indexed. The presence of C=N bond with intramolecular hydrogen bonding and the protonation of ions were confirmed by FTIR analysis. The UV-Vis-NIR spectrum of the crystal shows that the crystal has a cut-off at 298 nm. The 1H & 13C NMR spectra confirm the molecular structure. The dielectric behaviour was measured in the frequency range 1 KHz - 10 KHz for the temperature range from 30℃ to 170℃. The slight decrease in dielectric constant has been observed as the frequency is increased and the dielectric loss is very low for the entire frequency range. The second harmonic generation (SHG) in the crystal was observed by Kurtz powder technique.
