Pure water has been characterized for nearly a century, by its dissociation into hydronium (H3O)1+ and hydroxide (HO)1- ions. As a chemical equilibrium reaction, the equilibrium constant, known as the ion product...Pure water has been characterized for nearly a century, by its dissociation into hydronium (H3O)1+ and hydroxide (HO)1- ions. As a chemical equilibrium reaction, the equilibrium constant, known as the ion product or the product of the equilibrium concentration of the two ion species, has been extensively measured by chemists over the liquid water temperature and pressure range. The experimental data have been nonlinear least-squares fitted to chemical thermodynamic-based equilibrium equations, which have been accepted as the industrial standard for 35 years. In this study, a new and statistical-physics-based water ion product equation is presented, in which, the ions are the positively charged protons and the negatively charged proton-holes or prohols. Nonlinear least squares fits of our equation to the experimental data in the 0-100℃ pure liquid water range, give a factor of two better precision than the 35-year industrial standard.展开更多
The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lo...The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lognormal and the Gumbel distributions,respectively.The joint distribution of the horizontal and uplifting wave forces is analyzed using different probabilistic distributions,including the bivariate logistic Gumbel distribution,the bivariate lognormal distribution,and three bivariate Archimedean copulas functions constructed with different marginal distributions simultaneously.We use the fully nested copulas to construct multivariate distributions taking into account related variables.Different goodness fitting tests are carried out to determine the best bivariate copula model for wave forces on a vertical breakwater.We show that a bivariate model constructed by Frank copula gives the best reliability analysis,using marginal distributions of Gumbel and lognormal to account for uplifting pressure and horizontal wave force on a vertical breakwater,respectively.The results show that failure probability of the vertical breakwater calculated by multivariate density function is comparable to those by the Joint Committee on Structural Safety methods.As copulas are suitable for constructing a bivariate or multivariate joint distribution,they have great potential in reliability analysis for other coastal structures.展开更多
In order to solve the problem of depth classification of the underwater target in a very low frequency acoustic field, the active component of cross spectra of particle pressure and horizontal velocity (ACCSPPHV) is...In order to solve the problem of depth classification of the underwater target in a very low frequency acoustic field, the active component of cross spectra of particle pressure and horizontal velocity (ACCSPPHV) is adopted to distinguish the surface vessel and the underwater target. According to the effective depth of a Pekeris waveguide, the placing depth forecasting equations of passive vertical double vector hydrophones are proposed. Numerical examples show that when the sum of depths of two hydro- phones is the effective depth, the sign distribution of ACCSPPHV has nothing to do with horizontal distance; in addition, the sum of the first critical surface and the second critical surface is equal to the effective depth. By setting the first critical surface less than the difference between the effective water depth and the actual water depth, that is, the second critical surface is greater than the actual depth, the three positive and negative regions of the whole ocean volume are equivalent to two positive and negative regions and therefore the depth classification of the underwater target is obtained. Besides, when the 20 m water depth is taken as the first critical surface in the simulation of underwater targets (40 Hz, 50 Hz, and 60 Hz respectively), the effectiveness of the algorithm and the cor- reemess of relevant conclusions are verified, and the analysis of the corresponding forecasting performance is conducted.展开更多
In this paper, a mathematical model about the optimal booking level problem in airline overbooking rnanageanent is proposed. Firstly, the normal distribution is employed to approximate Poisson requests and binomial go...In this paper, a mathematical model about the optimal booking level problem in airline overbooking rnanageanent is proposed. Firstly, the normal distribution is employed to approximate Poisson requests and binomial goshows. By calculating the mean loss, a model to describe the relationship between booking level and flight revenue is established. Then, an equation is deduced to decide the optimal booking level. Finally, a numerical example is utilized to illustrate the proposed model and discuss the impact of refund rate on the optimal booking level and the mean loss.展开更多
The statistical characteristics of a hydrological data for the purposes of decision making in water resource planning and management is only justifiable if the data has the right attributes. This requires that the dat...The statistical characteristics of a hydrological data for the purposes of decision making in water resource planning and management is only justifiable if the data has the right attributes. This requires that the data being analysed are consistent, free of trend and being part of a stochastic process whose random characteristics is described by an appropriate distribution hypothesis. The data available for statistical analysis had a lot of missing values which could not be ordinarily filled but required a more comprehensive approach to fill these missing values. The KSOM (Kohonen Self-organising Map) was used to fill the missing runoff data from the Jidere-Bonde, Lokoja and Makundi river sites in the Niger basin. Results from the studies have shown that KSOM is the best tool for filling hydrological data with high number of missing values. After the data had been processed, some statistical applications were used to establish the runoff time-series characteristics of the three river sites of the Niger River basin. The results showed good attributes for all three river sites, except that Jidere River's data exhibited inconsistency. The presence of trend was also established for all three river sites; Jidere River was modelled based on 3-pararneter lognormal, the other two river sites were modelled based on normal distribution probability. The presence of trend and other attributes require that a more stochastic modelling process be carried out. However, the results established give reference for water resource planning and management.展开更多
The selectivity of gillnets for Oreochromis niloticus in Amerti reservoir (9°63′ N, 37°23′ E) was determined from gillnets with four mesh sizes (60, 80, 100 and 120 mm). Four selectivity models (a nor...The selectivity of gillnets for Oreochromis niloticus in Amerti reservoir (9°63′ N, 37°23′ E) was determined from gillnets with four mesh sizes (60, 80, 100 and 120 mm). Four selectivity models (a normal model assuming fixed spread, a normal model assuming that spread is proportional to mesh size, a lognormal model and a gamma model) were fitted to the data by using the share each length's catch total (SELECT) method. A total of 657 specimens of Oreochromis niloticus were caught (12.0-35.5 cm total length, TD. The sizes at first sexual maturity were 21.5 cm TL and 18.9 cm TL, respectively, for male and female Oreochromis niloticus. The lognormal selectivity curve provided the best fit to the data according to model deviance estimates with optimum selectivity of 16.66, 22.26, 27.78 and 33.38 cm TL for the 60, 80, 100 and 120 mm mesh sizes, respectively.展开更多
文摘Pure water has been characterized for nearly a century, by its dissociation into hydronium (H3O)1+ and hydroxide (HO)1- ions. As a chemical equilibrium reaction, the equilibrium constant, known as the ion product or the product of the equilibrium concentration of the two ion species, has been extensively measured by chemists over the liquid water temperature and pressure range. The experimental data have been nonlinear least-squares fitted to chemical thermodynamic-based equilibrium equations, which have been accepted as the industrial standard for 35 years. In this study, a new and statistical-physics-based water ion product equation is presented, in which, the ions are the positively charged protons and the negatively charged proton-holes or prohols. Nonlinear least squares fits of our equation to the experimental data in the 0-100℃ pure liquid water range, give a factor of two better precision than the 35-year industrial standard.
基金supported by the National Natural Science Foundation of China (51279186,51479183)the 111 Project (B14028)The first author thanks the Chinese Scholarship Council for funding his research in University of Washington
文摘The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lognormal and the Gumbel distributions,respectively.The joint distribution of the horizontal and uplifting wave forces is analyzed using different probabilistic distributions,including the bivariate logistic Gumbel distribution,the bivariate lognormal distribution,and three bivariate Archimedean copulas functions constructed with different marginal distributions simultaneously.We use the fully nested copulas to construct multivariate distributions taking into account related variables.Different goodness fitting tests are carried out to determine the best bivariate copula model for wave forces on a vertical breakwater.We show that a bivariate model constructed by Frank copula gives the best reliability analysis,using marginal distributions of Gumbel and lognormal to account for uplifting pressure and horizontal wave force on a vertical breakwater,respectively.The results show that failure probability of the vertical breakwater calculated by multivariate density function is comparable to those by the Joint Committee on Structural Safety methods.As copulas are suitable for constructing a bivariate or multivariate joint distribution,they have great potential in reliability analysis for other coastal structures.
基金supported by Public Science and Technology Research Funds Projects of Ocean(201405036-4)the National Natural Science Foundation of China(Grant Nos.11404406,51179034,41072176 and 11204109)+1 种基金Defense Technology Research(JSJC2013604C012)Postdoctoral Science Foundation of China(Grant No.2013 M531015)
文摘In order to solve the problem of depth classification of the underwater target in a very low frequency acoustic field, the active component of cross spectra of particle pressure and horizontal velocity (ACCSPPHV) is adopted to distinguish the surface vessel and the underwater target. According to the effective depth of a Pekeris waveguide, the placing depth forecasting equations of passive vertical double vector hydrophones are proposed. Numerical examples show that when the sum of depths of two hydro- phones is the effective depth, the sign distribution of ACCSPPHV has nothing to do with horizontal distance; in addition, the sum of the first critical surface and the second critical surface is equal to the effective depth. By setting the first critical surface less than the difference between the effective water depth and the actual water depth, that is, the second critical surface is greater than the actual depth, the three positive and negative regions of the whole ocean volume are equivalent to two positive and negative regions and therefore the depth classification of the underwater target is obtained. Besides, when the 20 m water depth is taken as the first critical surface in the simulation of underwater targets (40 Hz, 50 Hz, and 60 Hz respectively), the effectiveness of the algorithm and the cor- reemess of relevant conclusions are verified, and the analysis of the corresponding forecasting performance is conducted.
文摘In this paper, a mathematical model about the optimal booking level problem in airline overbooking rnanageanent is proposed. Firstly, the normal distribution is employed to approximate Poisson requests and binomial goshows. By calculating the mean loss, a model to describe the relationship between booking level and flight revenue is established. Then, an equation is deduced to decide the optimal booking level. Finally, a numerical example is utilized to illustrate the proposed model and discuss the impact of refund rate on the optimal booking level and the mean loss.
文摘The statistical characteristics of a hydrological data for the purposes of decision making in water resource planning and management is only justifiable if the data has the right attributes. This requires that the data being analysed are consistent, free of trend and being part of a stochastic process whose random characteristics is described by an appropriate distribution hypothesis. The data available for statistical analysis had a lot of missing values which could not be ordinarily filled but required a more comprehensive approach to fill these missing values. The KSOM (Kohonen Self-organising Map) was used to fill the missing runoff data from the Jidere-Bonde, Lokoja and Makundi river sites in the Niger basin. Results from the studies have shown that KSOM is the best tool for filling hydrological data with high number of missing values. After the data had been processed, some statistical applications were used to establish the runoff time-series characteristics of the three river sites of the Niger River basin. The results showed good attributes for all three river sites, except that Jidere River's data exhibited inconsistency. The presence of trend was also established for all three river sites; Jidere River was modelled based on 3-pararneter lognormal, the other two river sites were modelled based on normal distribution probability. The presence of trend and other attributes require that a more stochastic modelling process be carried out. However, the results established give reference for water resource planning and management.
文摘The selectivity of gillnets for Oreochromis niloticus in Amerti reservoir (9°63′ N, 37°23′ E) was determined from gillnets with four mesh sizes (60, 80, 100 and 120 mm). Four selectivity models (a normal model assuming fixed spread, a normal model assuming that spread is proportional to mesh size, a lognormal model and a gamma model) were fitted to the data by using the share each length's catch total (SELECT) method. A total of 657 specimens of Oreochromis niloticus were caught (12.0-35.5 cm total length, TD. The sizes at first sexual maturity were 21.5 cm TL and 18.9 cm TL, respectively, for male and female Oreochromis niloticus. The lognormal selectivity curve provided the best fit to the data according to model deviance estimates with optimum selectivity of 16.66, 22.26, 27.78 and 33.38 cm TL for the 60, 80, 100 and 120 mm mesh sizes, respectively.