The exploration of Mars would heavily rely on Martian rocks mechanics and engineering technology.As the mechanical property of Martian rocks is uncertain,it is of utmost importance to predict the probability distribut...The exploration of Mars would heavily rely on Martian rocks mechanics and engineering technology.As the mechanical property of Martian rocks is uncertain,it is of utmost importance to predict the probability distribution of Martian rocks mechanical property for the success of Mars exploration.In this paper,a fast and accurate probability distribution method for predicting the macroscale elastic modulus of Martian rocks was proposed by integrating the microscale rock mechanical experiments(micro-RME),accurate grain-based modeling(AGBM)and upscaling methods based on reliability principles.Firstly,the microstructure of NWA12564 Martian sample and elastic modulus of each mineral were obtained by micro-RME with TESCAN integrated mineral analyzer(TIMA)and nanoindentation.The best probability distribution function of the minerals was determined by Kolmogorov-Smirnov(K-S)test.Secondly,based on best distribution function of each mineral,the Monte Carlo simulations(MCS)and upscaling methods were implemented to obtain the probability distribution of upscaled elastic modulus.Thirdly,the correlation between the upscaled elastic modulus and macroscale elastic modulus obtained by AGBM was established.The accurate probability distribution of the macroscale elastic modulus was obtained by this correlation relationship.The proposed method can predict the probability distribution of Martian rocks mechanical property with any size and shape samples.展开更多
The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields ...The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields under extreme sea states. The model, integrating the ST6 source term, is validated against observed data, demonstrating its credibility. The spatial distribution of the occurrence probability of strong nonlinear waves during typhoons is shown, and the waves in the straits and the northeastern part of the South China Sea show strong nonlinear characteristics. The high-order spectral model HOS-ocean is employed to simulate the random wave surface series beneath five different platform areas. The waves during the typhoon exhibit strong nonlinear characteristics, and freak waves exist. The space-varying probability model is established to describe the short-term probability distribution of nonlinear wave series. The exceedance probability distributions of the wave surface beneath different platform areas are compared and analyzed. The results show that with an increase in the platform area, the probability of a strong nonlinear wave beneath the platform increases.展开更多
The secure and normal operation of distributed networks is crucial for accurate parameter estimation.However,distributed networks are frequently susceptible to Byzantine attacks.Considering real-life scenarios,this pa...The secure and normal operation of distributed networks is crucial for accurate parameter estimation.However,distributed networks are frequently susceptible to Byzantine attacks.Considering real-life scenarios,this paper investigates a probability Byzantine(PB)attack,utilizing a Bernoulli distribution to simulate the attack probability.Historically,additional detection mechanisms are used to mitigate such attacks,leading to increased energy consumption and burdens on distributed nodes,consequently diminishing operational efficiency.Differing from these approaches,an adaptive updating distributed estimation algorithm is proposed to mitigate the impact of PB attacks.In the proposed algorithm,a penalty strategy is initially incorporated during data updates to weaken the influence of the attack.Subsequently,an adaptive fusion weight is employed during data fusion to merge the estimations.Additionally,the reason why this penalty term weakens the attack has been analyzed,and the performance of the proposed algorithm is validated through simulation experiments.展开更多
In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of ratio of China aviation network edge vertices degree were s...In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of ratio of China aviation network edge vertices degree were studied based on the statistics data of China civil aviation network in 1988, 1994, 2001, 2008 and 2015. According to the theory and method of complex network, the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network. Based on the statistical data, the ratio of edge vertices degree in China aviation network in 1988, 1994, 2001, 2008 and 2015 were calculated. Using the probability statistical analysis method and regression analysis approach, it was found that the ratio of edge vertices degree had linear probability distribution and the two parameters of the probability distribution had linear evolution trace.展开更多
The earthquake magnitude probability distribution is one of the underlying input data for certain earthquake analyses, such as probabilistic seismic hazard analysis. Nowadays, the method proposed by McGuire and Arabas...The earthquake magnitude probability distribution is one of the underlying input data for certain earthquake analyses, such as probabilistic seismic hazard analysis. Nowadays, the method proposed by McGuire and Arabasz (1990) is commonly used for obtaining the (simulated) earthquake magnitude probability distributions. However, based on the observed earthquake data in 5 regions (Taiwan, Japan, California, Turkey, and Greece), the model did not fit the observation well. Instead, all of the case studies show that using the newly proposed gamma distribution can improve the simulation significantly compared to the conventional method.展开更多
In order to reveal the complex network characteristics and evolution principle of China aviation network,the probability distribution and evolution trace of node nearest neighbor average degree of China aviation netwo...In order to reveal the complex network characteristics and evolution principle of China aviation network,the probability distribution and evolution trace of node nearest neighbor average degree of China aviation network were studied based on the statistics data of China civil aviation network in 1988,1994,2001,2008 and 2015.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network.Based on the statistical data,the nearest neighbor average degrees of nodes in China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Using the probability statistical analysis method,it was found that the nearest neighbor average degree had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.展开更多
The well-known multi-dimensional reconciliation is an effective method used in the continuous-variable quantum key distribution in the long-distance and the low signal-to-noise-ratio scenarios.The virtual channel empl...The well-known multi-dimensional reconciliation is an effective method used in the continuous-variable quantum key distribution in the long-distance and the low signal-to-noise-ratio scenarios.The virtual channel employed to exchange data is generally established by using a finite-dimensional rotation in the reconciliation procedure.In this paper,we found that the finite dimension of the multi-dimensional reconciliation inevitably leads to the mismatch of the signal-to-noise-ratio between the quantum channel and the virtual channel,which may be called the finite-dimension effect.Such an effect results in an overestimation on the secret key rate,and subsequently induces vital practical security loopholes.展开更多
In this paper, we conduct analysis on the development and optimization of financial management and the benefit distribution pattern from perspective of multi-dimensional cooperation enterprise. Financial management is...In this paper, we conduct analysis on the development and optimization of financial management and the benefit distribution pattern from perspective of multi-dimensional cooperation enterprise. Financial management is the whole process of capital operation of the modern enterprise decision-making, planning and control of the management activities. Financial management is an important part of enterprise management, enterprise' s sustainable development requires the financial management in the central position in the management of the enterprise, according to the present our country enterprise financial management of a series of problems, in this paper, starting from the connotation of the enterprise financial management, we analyses the center of the enterprise financial management status and further puts forward some countermeasures to solve from the perspectives of the multi-dimensional cooperation which obtains the satisfactory performance.展开更多
A new idea was proposed to find out the stability and root location of multi-dimensional linear time invariant discrete system (LTIDS) for real coefficient polynomials. For determining stability the sign criterion is ...A new idea was proposed to find out the stability and root location of multi-dimensional linear time invariant discrete system (LTIDS) for real coefficient polynomials. For determining stability the sign criterion is synthesized from the Jury’s method for stability which is derived from the characteristic polynomial coefficients of the discrete system. The number of roots lying inside or outside the unit circle and hence on the unit circle is directly determined from the proposed single modified Jury tabulation and the sign criterion. The proposed scheme is simple and the examples are given to bring out the merits of the proposed scheme which is also applicable for the singular and non-singular cases.展开更多
The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard (GH) copula function, and the Clayton copul...The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard (GH) copula function, and the Clayton copula function. Twenty years of wind data from 1989 to 2008 were collected from the European Centre for Medium-Range Weather Forecasts (ECMWF) database and the blended wind data of the Quick Scatterometer (QSCAT) satellite data set and re-analysis data from the United States National Centers for Environmental Prediction (NCEP). Several typhoons were taken into account and merged with the background wind fields from the ECMWF or QSCAT/NCEP database. The 20-year data of significant wave height were calculated with the unstructured-grid version of the third-generation wind wave model Simulating WAves Nearshore (SWAN) under extreme wind process conditions. The Gumbel distribution was used for univariate and marginal distributions. The distribution parameters were estimated with the method of L-moments. Based on the marginal distributions, the joint probability distributions, the associated return periods, and the conditional probability distributions were obtained. The GH copula function was found to be optimal according to the ordinary least squares (OLS) test. The results show that wind waves are the prevailing type of wave in the Bohai Bay.展开更多
The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameteri...The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameterization within the overall cumulus parameterization scheme.In this study,an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculateλof cumulus clouds in a large-eddy simulation.The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method,becauseλ,as calculated from the improved method,falls within the range ofλvalues obtained from the traditional method using different conserved variables.The probability density functions ofλfor all data,different times,and different heights can be well-fitted by a log-normal distribution,which supports the assumed stochastic entrainment process in previous studies.Further analysis demonstrate that the relationship betweenλand the vertical velocity is better than other thermodynamic/dynamical properties;thus,the vertical velocity is recommended as the primary influencing factor for the parameterization ofλin the future.The results of this study enhance the theoretical understanding ofλand its influencing factors and shed new light on the development ofλparameterization.展开更多
The equation of two-dimensional fiber direction vector was solved theoretically to give the fiber orientation distri- bution in simple shear flow, flow with two direction shears, extensional flow and arbitrary planar ...The equation of two-dimensional fiber direction vector was solved theoretically to give the fiber orientation distri- bution in simple shear flow, flow with two direction shears, extensional flow and arbitrary planar incompressible flow. The Fok- ker-Planck equation was solved numerically to validify the theoretical solutions. The stable orientation and orientation period of fiber were obtained. The results showed that the fiber orientation distribution is dependent on the relative not absolute magnitude of the matrix rate-of-strain of flow. The effect of fiber aspect ratio on the orientation distribution of fiber is insignificant in most conditions except the simple shear case. It was proved that the results for a planar flow could be generalized to the case of 3-D fiber direction vector.展开更多
In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by w<sub>i</sub> ≥ 0 and . These mixed distributions are used in various discip...In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by w<sub>i</sub> ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by w<sub>i</sub> ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.展开更多
By large eddy simulation (LES), turbulent databases of channel flows at different Reynolds numbers were established. Then, the probability distribution functions of the streamwise and wall-normal velocity fluctuatio...By large eddy simulation (LES), turbulent databases of channel flows at different Reynolds numbers were established. Then, the probability distribution functions of the streamwise and wall-normal velocity fluctuations were obtained and compared with the corresponding normal distributions. By hypothesis test, the deviation from the normal distribution was analyzed quantitatively. The skewness and flatness factors were also calculated. And the variations of these two factors in the viscous sublayer, buffer layer and log-law layer were discussed. Still illustrated were the relations between the probability distribution functions and the burst events-sweep of high-speed fluids and ejection of low-speed fluidsIin the viscous sub-layer, buffer layer and loglaw layer. Finally the variations of the probability distribution functions with Reynolds number were examined.展开更多
The famous de Moivre’s Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre’s Laplace approach is cumbe...The famous de Moivre’s Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre’s Laplace approach is cumbersome as it relies heavily on many lemmas and theorems. This paper invented an alternative and less rigorous method of deriving Gaussian distribution from basic random experiment conditional on some assumptions.展开更多
A quantum image searching method is proposed based on the probability distributions of the readouts from the quantum measurements. It is achieved by using low computational resources which are only a single Hadamard g...A quantum image searching method is proposed based on the probability distributions of the readouts from the quantum measurements. It is achieved by using low computational resources which are only a single Hadamard gate combined with m + 1 quantum measurement operations. To validate the proposed method, a simulation experiment is used where the image with the highest similarity value of 0.93 to the particular test image is retrieved as the search result from 4 × 4 binary image database. The proposal provides a basic step for designing a search engine on quantum computing devices where the image in the database is retrieved based on its similarity to the test image.展开更多
The gamma function is a good approximation to the luminosity function of astrophysical objects, and a truncated gamma distribution would permit a more rigorous analysis. This paper examines the generalized gamma distr...The gamma function is a good approximation to the luminosity function of astrophysical objects, and a truncated gamma distribution would permit a more rigorous analysis. This paper examines the generalized gamma distribution (GG) and then introduces the scale and the new double truncation. The magnitude version of the truncated GG distribution with scale is adopted in order to fit the luminosity function (LF) for galaxies or quasars. The new truncated GG LF is applied to the five bands of SDSS galaxies, to the 2dF QSO Redshift Survey in the range of redshifts between 0.3 and 0.5, and to the COSMOS QSOs in the range of redshifts between 3.7 and 4.7. The average absolute magnitude versus redshifts for SDSS galaxies and QSOs of 2dF was modeled adopting a redshift dependence for the lower and upper absolute magnitude of the new truncated GG LF.展开更多
The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, <img src="Edit_699140d3-f569-463e-b835-7ccdab822717.png" width="290" height="22" ...The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, <img src="Edit_699140d3-f569-463e-b835-7ccdab822717.png" width="290" height="22" alt="" /><img src="Edit_bdd10470-9b63-4b2d-9cec-636969547ca5.png" width="90" height="22" alt="" /><span style="white-space:normal;">and <img src="Edit_e9cd6876-e2b8-45cf-ba17-391f054679b4.png" width="90" height="21" alt="" /></span>where <span style="white-space:nowrap;"><em>α</em>,<span style="white-space:nowrap;"><em>η</em></span><em></em></span> and <span style="white-space:nowrap;"><em>β</em></span> are real or complex constants are evaluated in terms of the confluent hypergeometric function <sub>1</sub><em>F</em><sub>1</sub> and the hypergeometric function <sub>1</sub><em>F</em><sub>2</sub>. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">1</sub> and <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">2</sub>. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (<span style="white-space:nowrap;"><em>x</em><sup>2</sup></span>) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.展开更多
Starting with the Aalen (1989) version of Cox (1972) 'regression model' we show the method for construction of "any" joint survival function given marginal survival functions. Basically, however, we restrict o...Starting with the Aalen (1989) version of Cox (1972) 'regression model' we show the method for construction of "any" joint survival function given marginal survival functions. Basically, however, we restrict ourselves to model positive stochastic dependences only with the general assumption that the underlying two marginal random variables are centered on the set of nonnegative real values. With only these assumptions we obtain nice general characterization of bivariate probability distributions that may play similar role as the copula methodology. Examples of reliability and biomedical applications are given.展开更多
In this paper, we consider the optimal problem of channels sharing with het-erogeneous traffic (real-time service and non-real-time service) to reduce the data conflict probability of users. Moreover, a multi-dimens...In this paper, we consider the optimal problem of channels sharing with het-erogeneous traffic (real-time service and non-real-time service) to reduce the data conflict probability of users. Moreover, a multi-dimensional Markov chain model is developed to analyze the performance of the proposed scheme. Meanwhile, performance metrics are derived. Numerical results show that the proposed scheme can effectively reduce the forced termination probability, blocking probability and spectrum utilization.展开更多
文摘The exploration of Mars would heavily rely on Martian rocks mechanics and engineering technology.As the mechanical property of Martian rocks is uncertain,it is of utmost importance to predict the probability distribution of Martian rocks mechanical property for the success of Mars exploration.In this paper,a fast and accurate probability distribution method for predicting the macroscale elastic modulus of Martian rocks was proposed by integrating the microscale rock mechanical experiments(micro-RME),accurate grain-based modeling(AGBM)and upscaling methods based on reliability principles.Firstly,the microstructure of NWA12564 Martian sample and elastic modulus of each mineral were obtained by micro-RME with TESCAN integrated mineral analyzer(TIMA)and nanoindentation.The best probability distribution function of the minerals was determined by Kolmogorov-Smirnov(K-S)test.Secondly,based on best distribution function of each mineral,the Monte Carlo simulations(MCS)and upscaling methods were implemented to obtain the probability distribution of upscaled elastic modulus.Thirdly,the correlation between the upscaled elastic modulus and macroscale elastic modulus obtained by AGBM was established.The accurate probability distribution of the macroscale elastic modulus was obtained by this correlation relationship.The proposed method can predict the probability distribution of Martian rocks mechanical property with any size and shape samples.
基金financially supported by the National Key R&D Program of China(No.2022YFC3104205)the National Natural Science Foundation of China(No.42377457).
文摘The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields under extreme sea states. The model, integrating the ST6 source term, is validated against observed data, demonstrating its credibility. The spatial distribution of the occurrence probability of strong nonlinear waves during typhoons is shown, and the waves in the straits and the northeastern part of the South China Sea show strong nonlinear characteristics. The high-order spectral model HOS-ocean is employed to simulate the random wave surface series beneath five different platform areas. The waves during the typhoon exhibit strong nonlinear characteristics, and freak waves exist. The space-varying probability model is established to describe the short-term probability distribution of nonlinear wave series. The exceedance probability distributions of the wave surface beneath different platform areas are compared and analyzed. The results show that with an increase in the platform area, the probability of a strong nonlinear wave beneath the platform increases.
文摘The secure and normal operation of distributed networks is crucial for accurate parameter estimation.However,distributed networks are frequently susceptible to Byzantine attacks.Considering real-life scenarios,this paper investigates a probability Byzantine(PB)attack,utilizing a Bernoulli distribution to simulate the attack probability.Historically,additional detection mechanisms are used to mitigate such attacks,leading to increased energy consumption and burdens on distributed nodes,consequently diminishing operational efficiency.Differing from these approaches,an adaptive updating distributed estimation algorithm is proposed to mitigate the impact of PB attacks.In the proposed algorithm,a penalty strategy is initially incorporated during data updates to weaken the influence of the attack.Subsequently,an adaptive fusion weight is employed during data fusion to merge the estimations.Additionally,the reason why this penalty term weakens the attack has been analyzed,and the performance of the proposed algorithm is validated through simulation experiments.
文摘In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of ratio of China aviation network edge vertices degree were studied based on the statistics data of China civil aviation network in 1988, 1994, 2001, 2008 and 2015. According to the theory and method of complex network, the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network. Based on the statistical data, the ratio of edge vertices degree in China aviation network in 1988, 1994, 2001, 2008 and 2015 were calculated. Using the probability statistical analysis method and regression analysis approach, it was found that the ratio of edge vertices degree had linear probability distribution and the two parameters of the probability distribution had linear evolution trace.
文摘The earthquake magnitude probability distribution is one of the underlying input data for certain earthquake analyses, such as probabilistic seismic hazard analysis. Nowadays, the method proposed by McGuire and Arabasz (1990) is commonly used for obtaining the (simulated) earthquake magnitude probability distributions. However, based on the observed earthquake data in 5 regions (Taiwan, Japan, California, Turkey, and Greece), the model did not fit the observation well. Instead, all of the case studies show that using the newly proposed gamma distribution can improve the simulation significantly compared to the conventional method.
文摘In order to reveal the complex network characteristics and evolution principle of China aviation network,the probability distribution and evolution trace of node nearest neighbor average degree of China aviation network were studied based on the statistics data of China civil aviation network in 1988,1994,2001,2008 and 2015.According to the theory and method of complex network,the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network.Based on the statistical data,the nearest neighbor average degrees of nodes in China aviation network in 1988,1994,2001,2008 and 2015 were calculated.Using the probability statistical analysis method,it was found that the nearest neighbor average degree had the probability distribution of normal function and the position parameters and scale parameters of the probability distribution had linear evolution trace.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61332019,61671287,and 61631014)the National Key Research and Development Program of China(Grant No.2016YFA0302600)
文摘The well-known multi-dimensional reconciliation is an effective method used in the continuous-variable quantum key distribution in the long-distance and the low signal-to-noise-ratio scenarios.The virtual channel employed to exchange data is generally established by using a finite-dimensional rotation in the reconciliation procedure.In this paper,we found that the finite dimension of the multi-dimensional reconciliation inevitably leads to the mismatch of the signal-to-noise-ratio between the quantum channel and the virtual channel,which may be called the finite-dimension effect.Such an effect results in an overestimation on the secret key rate,and subsequently induces vital practical security loopholes.
文摘In this paper, we conduct analysis on the development and optimization of financial management and the benefit distribution pattern from perspective of multi-dimensional cooperation enterprise. Financial management is the whole process of capital operation of the modern enterprise decision-making, planning and control of the management activities. Financial management is an important part of enterprise management, enterprise' s sustainable development requires the financial management in the central position in the management of the enterprise, according to the present our country enterprise financial management of a series of problems, in this paper, starting from the connotation of the enterprise financial management, we analyses the center of the enterprise financial management status and further puts forward some countermeasures to solve from the perspectives of the multi-dimensional cooperation which obtains the satisfactory performance.
文摘A new idea was proposed to find out the stability and root location of multi-dimensional linear time invariant discrete system (LTIDS) for real coefficient polynomials. For determining stability the sign criterion is synthesized from the Jury’s method for stability which is derived from the characteristic polynomial coefficients of the discrete system. The number of roots lying inside or outside the unit circle and hence on the unit circle is directly determined from the proposed single modified Jury tabulation and the sign criterion. The proposed scheme is simple and the examples are given to bring out the merits of the proposed scheme which is also applicable for the singular and non-singular cases.
基金supported by the Science Fund for Creative Research Groups of the National Natural ScienceFoundation of China (Grant No. 51021004)the National High Technology Research and DevelopmentProgram of China (863 Program, Grants No. 2012AA112509 and 2012AA051702)
文摘The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard (GH) copula function, and the Clayton copula function. Twenty years of wind data from 1989 to 2008 were collected from the European Centre for Medium-Range Weather Forecasts (ECMWF) database and the blended wind data of the Quick Scatterometer (QSCAT) satellite data set and re-analysis data from the United States National Centers for Environmental Prediction (NCEP). Several typhoons were taken into account and merged with the background wind fields from the ECMWF or QSCAT/NCEP database. The 20-year data of significant wave height were calculated with the unstructured-grid version of the third-generation wind wave model Simulating WAves Nearshore (SWAN) under extreme wind process conditions. The Gumbel distribution was used for univariate and marginal distributions. The distribution parameters were estimated with the method of L-moments. Based on the marginal distributions, the joint probability distributions, the associated return periods, and the conditional probability distributions were obtained. The GH copula function was found to be optimal according to the ordinary least squares (OLS) test. The results show that wind waves are the prevailing type of wave in the Bohai Bay.
基金supported by the National Natural Science Foundation of China(Grant Nos.42175099,42027804,42075073)the Innovative Project of Postgraduates in Jiangsu Province in 2023(Grant No.KYCX23_1319)+3 种基金supported by the National Natural Science Foundation of China(Grant No.42205080)the Natural Science Foundation of Sichuan(Grant No.2023YFS0442)the Research Fund of Civil Aviation Flight University of China(Grant No.J2022-037)supported by the National Key Scientific and Technological Infrastructure project“Earth System Science Numerical Simulator Facility”(Earth Lab)。
文摘The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameterization within the overall cumulus parameterization scheme.In this study,an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculateλof cumulus clouds in a large-eddy simulation.The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method,becauseλ,as calculated from the improved method,falls within the range ofλvalues obtained from the traditional method using different conserved variables.The probability density functions ofλfor all data,different times,and different heights can be well-fitted by a log-normal distribution,which supports the assumed stochastic entrainment process in previous studies.Further analysis demonstrate that the relationship betweenλand the vertical velocity is better than other thermodynamic/dynamical properties;thus,the vertical velocity is recommended as the primary influencing factor for the parameterization ofλin the future.The results of this study enhance the theoretical understanding ofλand its influencing factors and shed new light on the development ofλparameterization.
基金Project (No. 10372090) supported by the National Natural Science Foundation of China
文摘The equation of two-dimensional fiber direction vector was solved theoretically to give the fiber orientation distri- bution in simple shear flow, flow with two direction shears, extensional flow and arbitrary planar incompressible flow. The Fok- ker-Planck equation was solved numerically to validify the theoretical solutions. The stable orientation and orientation period of fiber were obtained. The results showed that the fiber orientation distribution is dependent on the relative not absolute magnitude of the matrix rate-of-strain of flow. The effect of fiber aspect ratio on the orientation distribution of fiber is insignificant in most conditions except the simple shear case. It was proved that the results for a planar flow could be generalized to the case of 3-D fiber direction vector.
文摘In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by w<sub>i</sub> ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by w<sub>i</sub> ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.
文摘By large eddy simulation (LES), turbulent databases of channel flows at different Reynolds numbers were established. Then, the probability distribution functions of the streamwise and wall-normal velocity fluctuations were obtained and compared with the corresponding normal distributions. By hypothesis test, the deviation from the normal distribution was analyzed quantitatively. The skewness and flatness factors were also calculated. And the variations of these two factors in the viscous sublayer, buffer layer and log-law layer were discussed. Still illustrated were the relations between the probability distribution functions and the burst events-sweep of high-speed fluids and ejection of low-speed fluidsIin the viscous sub-layer, buffer layer and loglaw layer. Finally the variations of the probability distribution functions with Reynolds number were examined.
文摘The famous de Moivre’s Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre’s Laplace approach is cumbersome as it relies heavily on many lemmas and theorems. This paper invented an alternative and less rigorous method of deriving Gaussian distribution from basic random experiment conditional on some assumptions.
文摘A quantum image searching method is proposed based on the probability distributions of the readouts from the quantum measurements. It is achieved by using low computational resources which are only a single Hadamard gate combined with m + 1 quantum measurement operations. To validate the proposed method, a simulation experiment is used where the image with the highest similarity value of 0.93 to the particular test image is retrieved as the search result from 4 × 4 binary image database. The proposal provides a basic step for designing a search engine on quantum computing devices where the image in the database is retrieved based on its similarity to the test image.
文摘The gamma function is a good approximation to the luminosity function of astrophysical objects, and a truncated gamma distribution would permit a more rigorous analysis. This paper examines the generalized gamma distribution (GG) and then introduces the scale and the new double truncation. The magnitude version of the truncated GG distribution with scale is adopted in order to fit the luminosity function (LF) for galaxies or quasars. The new truncated GG LF is applied to the five bands of SDSS galaxies, to the 2dF QSO Redshift Survey in the range of redshifts between 0.3 and 0.5, and to the COSMOS QSOs in the range of redshifts between 3.7 and 4.7. The average absolute magnitude versus redshifts for SDSS galaxies and QSOs of 2dF was modeled adopting a redshift dependence for the lower and upper absolute magnitude of the new truncated GG LF.
文摘The non-elementary integrals involving elementary exponential, hyperbolic and trigonometric functions, <img src="Edit_699140d3-f569-463e-b835-7ccdab822717.png" width="290" height="22" alt="" /><img src="Edit_bdd10470-9b63-4b2d-9cec-636969547ca5.png" width="90" height="22" alt="" /><span style="white-space:normal;">and <img src="Edit_e9cd6876-e2b8-45cf-ba17-391f054679b4.png" width="90" height="21" alt="" /></span>where <span style="white-space:nowrap;"><em>α</em>,<span style="white-space:nowrap;"><em>η</em></span><em></em></span> and <span style="white-space:nowrap;"><em>β</em></span> are real or complex constants are evaluated in terms of the confluent hypergeometric function <sub>1</sub><em>F</em><sub>1</sub> and the hypergeometric function <sub>1</sub><em>F</em><sub>2</sub>. The hyperbolic and Euler identities are used to derive some identities involving exponential, hyperbolic, trigonometric functions and the hypergeometric functions <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">1</sub> and <sub style="white-space:normal;">1</sub><em style="white-space:normal;">F</em><sub style="white-space:normal;">2</sub>. Having evaluated, these non-elementary integrals, some new probability measures generalizing the gamma-type and Gaussian distributions are also obtained. The obtained generalized probability distributions may, for example, allow to perform better statistical tests than those already known (e.g. chi-square (<span style="white-space:nowrap;"><em>x</em><sup>2</sup></span>) statistical tests and other statistical tests constructed based on the central limit theorem (CLT)), while avoiding the use of computational approximations (or methods) which are in general expensive and associated with numerical errors.
文摘Starting with the Aalen (1989) version of Cox (1972) 'regression model' we show the method for construction of "any" joint survival function given marginal survival functions. Basically, however, we restrict ourselves to model positive stochastic dependences only with the general assumption that the underlying two marginal random variables are centered on the set of nonnegative real values. With only these assumptions we obtain nice general characterization of bivariate probability distributions that may play similar role as the copula methodology. Examples of reliability and biomedical applications are given.
基金supported in part by the National Natural Science Foundation of China(60972016,61231010)the Funds of Distinguished Young Scientists(2009CDA150)+1 种基金China-Finnish Cooperation Project(2010DFB10570)Specialized Research Fund for the Doctoral Program of Higher Education(20120142110015)
文摘In this paper, we consider the optimal problem of channels sharing with het-erogeneous traffic (real-time service and non-real-time service) to reduce the data conflict probability of users. Moreover, a multi-dimensional Markov chain model is developed to analyze the performance of the proposed scheme. Meanwhile, performance metrics are derived. Numerical results show that the proposed scheme can effectively reduce the forced termination probability, blocking probability and spectrum utilization.