To ensure the structural integrity of life-limiting component of aeroengines,Probabilistic Damage Tolerance(PDT)assessment is applied to evaluate the failure risk as required by airworthiness regulations and military ...To ensure the structural integrity of life-limiting component of aeroengines,Probabilistic Damage Tolerance(PDT)assessment is applied to evaluate the failure risk as required by airworthiness regulations and military standards.The PDT method holds the view that there exist defects such as machining scratches and service cracks in the tenon-groove structures of aeroengine disks.However,it is challenging to conduct PDT assessment due to the scarcity of effective Probability of Detection(POD)model and anomaly distribution model.Through a series of Nondestructive Testing(NDT)experiments,the POD model of real cracks in tenon-groove structures is constructed for the first time by employing the Transfer Function Method(TFM).A novel anomaly distribution model is derived through the utilization of the POD model,instead of using the infeasible field data accumulation method.Subsequently,a framework for calculating the Probability of Failure(POF)of the tenon-groove structures is established,and the aforementioned two models exert a significant influence on the results of POF.展开更多
The log-normal distribution function(LNDF)and Weibull cumulative density function(WCDF)represent two prevalent approaches for characterizing sediment grain size distributions.This study analyzes annual average suspend...The log-normal distribution function(LNDF)and Weibull cumulative density function(WCDF)represent two prevalent approaches for characterizing sediment grain size distributions.This study analyzes annual average suspended load grain size data(standardized to equivalent settling diameters)from seven hydrological stations in the lower Yellow River(LYR)spanning 1962–2020,employing various distribution functions for grain size fitting.Results demonstrate that the Weibull probability density function(WPDF)offers significant advantages over both LNDF and WCDF in terms of fitting accuracy,parameter stability,simplicity,and practical applicability for characterizing suspended load grain size distributions in the LYR.Based on these findings,universal formulas were developed for the suspended load grain size distribution across the seven stations and the entire lower reaches,yielding determination coefficients(R2)exceeding 0.9.These formulas can be applied to estimate suspended load grain size in data-scarce cross-sections.The existence of such universal formulas suggests that interannual fluctuations in suspended load grain size in the LYR are constrained within a limited range,suggesting that sediment grain size may represent an inherent property of the river channel.This limited variability may be attributed to the fact that sediments in the LYR are primarily derived from a relatively fixed source region—the Loess Plateau.The observed stability over an extended period also offers valuable insights into the fundamental properties of river systems and their long-term behavior.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
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 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
The probability distribution function （PDF） of a passive tracer, forced by a ＂mean gradient＂, is studied. First, we take two theoretical approaches, the Lagrangian and the conditional closure formalisms, to study ...The probability distribution function （PDF） of a passive tracer, forced by a ＂mean gradient＂, is studied. First, we take two theoretical approaches, the Lagrangian and the conditional closure formalisms, to study the PDFs of such an externally forced passive tracer. Then, we carry out numerical simulations for an idealized random flow on a sphere and for European Center for Medium-Range Weather Forecasts （ECMWF） stratospheric winds to test whether the mean-gradient model can be applied to studying stratospheric tracer mixing in midlatitude surf zones, in which a weak and poleward zonal-mean gradient is maintained by tracer leakage through polar and tropical mixing barriers, and whether the PDFs of tracer fluctuations in midlatitudes are consistent with the theoretical predictions. The numerical simulations show that when diffusive dissipation is balanced by the mean-gradient forcing, the PDF in the random flow and the Southern-Hemisphere PDFs in ECMWF winds show time-invariant exponential tails, consistent with theoretical predictions. In the Northern Hemisphere, the PDFs exhibit non-Gaussian tails. However, the PDF tails are not consistent with theoretical expectations. The long-term behavior of the PDF tails of the forced tracer is compared to that of a decaying tracer. It is found that the PDF tails of the decaying tracer are time-dependent, and evolve toward flatter than exponential.展开更多
Using the Feynman's path integral with topological constraints arising from the presence of one singular line, we find the homotopic probability distribution PnL for the winding number n and the partition function...Using the Feynman's path integral with topological constraints arising from the presence of one singular line, we find the homotopic probability distribution PnL for the winding number n and the partition function PL of the entangled system around a ribbon segment chain. We find that when the width of the ribbon segment chain 2a increases,the partition function exponentially decreases, whereas the free energy increases an amount, which is proportional to the square of the width. When the width tends to zero we obtain the same results as those of a single chain with one singular point.展开更多
In this paper, in terms of the technique of integration within an ordered product （IWOP） of operators and the properties of the inverses of q-deformed annihilation and creation operators, normalizable q-analogue of ...In this paper, in terms of the technique of integration within an ordered product （IWOP） of operators and the properties of the inverses of q-deformed annihilation and creation operators, normalizable q-analogue of the squeezed one-photon state, which is quite different from one introduced by Song and Fan [Int. 3. Theor. Phys. 41 （2002） 695], is constructed. Moreover, the Wigner function and phase probability distribution of q-analogue of the squeezed one-photon state are examined.展开更多
The probability distributions of small sample data are difficult to determine,while a large proportion of samples occur in the early failure period,so it is particularly important to make full use of these data in the...The probability distributions of small sample data are difficult to determine,while a large proportion of samples occur in the early failure period,so it is particularly important to make full use of these data in the statistical analysis.Based on gamma distribution,four methods of probability density function(PDF)reconstruction with early failure data are proposed,and then the mean time between failures(MTBF)evaluation expressions are concluded from the reconstructed PDFs.Both theory analysis and an example show that method 2 is the best evaluation method in dealing with early-failure-small-sample data.The reconstruction methods of PDF also have certain guiding significance for other distribution types.展开更多
In this paper we discuss a step further some convergence and continuity problems of distribution function on R^i. We give the following results: (1)distribution function F(x_1,…,x_k) on R^k is continuous if and only ...In this paper we discuss a step further some convergence and continuity problems of distribution function on R^i. We give the following results: (1)distribution function F(x_1,…,x_k) on R^k is continuous if and only if all marginal distribution functions of F is continuous on R^1. (2)If limF_n(x_1,……,x_k)=F(x_1,…,x_k) and limF_n(x_1—0,…,x_k—0)=F(x_1—0,…,x_k—0) at all non-continuity points of F, then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 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
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 distributed fusion,when one or more sensors are disturbed by faults,a common problem is that their local estimations are inconsistent with those of other fault-free sensors.Most of the existing fault-tolerant distr...In distributed fusion,when one or more sensors are disturbed by faults,a common problem is that their local estimations are inconsistent with those of other fault-free sensors.Most of the existing fault-tolerant distributed fusion algorithms,such as the Covariance Union(CU)and Faulttolerant Generalized Convex Combination(FGCC),are only used for the point estimation case where local estimates and their associated error covariances are provided.A treatment with focus on the fault-tolerant distributed fusions of arbitrary local Probability Density Functions(PDFs)is lacking.For this problem,we first propose Kullback–Leibler Divergence(KLD)and reversed KLD induced functional Fuzzy c-Means(FCM)clustering algorithms to soft cluster all local PDFs,respectively.On this basis,two fault-tolerant distributed fusion algorithms of arbitrary local PDFs are then developed.They select the representing PDF of the cluster with the largest sum of memberships as the fused PDF.Numerical examples verify the better fault tolerance of the developed two distributed fusion algorithms.展开更多
The orientation distribution function of cylindrical particle suspensions was deduced and numerically simulated, and an application was taken in a wedge-shaped flow field. The relationship between the orientation dist...The orientation distribution function of cylindrical particle suspensions was deduced and numerically simulated, and an application was taken in a wedge-shaped flow field. The relationship between the orientation distribution function and particle orientation angles was obtained. The results show that comparing with the most probable angle distribution which comes to being in short time, the distribution of the steady state doesn't vary much. in range; the main difference is the anti-clockwise rotation in the right and upper field, that is, particles rotate more at the points where the velocity gradients are larger. The most probable orientations are close to the direction of local streamlines. In the direction of streamlines, with poleradius decreasing, the most probable angles increase, but the angles between their orientations and the local streamlines decrease.展开更多
We consider the problem of approximating two, possibly unrelated probability distributions from a single complex-valued function and its Fourier transform. We show that this problem always has a solution within a spec...We consider the problem of approximating two, possibly unrelated probability distributions from a single complex-valued function and its Fourier transform. We show that this problem always has a solution within a specified degree of accuracy, provided the distributions satisfy the necessary regularity conditions. We describe the algorithm and construction of and provide examples of approximating several pairs of distributions using the algorithm.展开更多
In this work, the excitons distribution function in organic bulk hetero junction solar cells, at a depth z has been determined from solving the charge continuity equation, by exploiting the Laplace transform with appr...In this work, the excitons distribution function in organic bulk hetero junction solar cells, at a depth z has been determined from solving the charge continuity equation, by exploiting the Laplace transform with appropriate boundary conditions. Next, the influence of the electron-hole pair separation distance on the excitons dissociation probability, the internal quantum efficiency and the binding energy, has been studied. The simulated results show that the probability density of the carriers photo generated depends on the generation rate, excitons dissociation and the charge carriers in the cells. The potential improvement of the internal quantum efficiency of charge generation depends on electron-hole pair separation distance, the excitons dissociation probability into free charges and depends strongly on the optical absorption of the photons in the active layer.展开更多
For performance optimization such as placement,interconnect synthesis,and routing, an efficient and accurate interconnect delay metric is critical,even in design tools development like design for yield （DFY） and des...For performance optimization such as placement,interconnect synthesis,and routing, an efficient and accurate interconnect delay metric is critical,even in design tools development like design for yield （DFY） and design for manufacture （DFM）. In the nanometer regime, the recently proposed delay models for RLC interconnects based on statistical probability density function （PDF）interpretation such as PRIMO,H-gamma,WED and RLD bridge the gap between accuracy and efficiency. However, these models always require table look-up when operating. In this paper, a novel delay model based on the Birnbaum-Saunders distribution （BSD） is presented. BSD can accomplish interconnect delay estimation fast and accurately without table look-up operations. Furthermore, it only needs the first two moments to match. Experimental results in 90nm technology show that BSD is robust, easy to implement,efficient,and accurate.展开更多
Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh f...Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh form, involves two parameters: the average wave height H— and the state parameter γ. The role of γ in the distribution of wave heights is examined. It is found that γ may be a certain measure of sea state. A least square method for determining γ from measured data is proposed. In virtue of the method, the values of γ are determined for three sea states from the data measured in the East China Sea. The present PDF is compared with the well known Rayleigh PDF of wave height and it is shown that it much better fits the data than the Rayleigh PDF. It is expected that the present PDF would fit some other wave variables, since its derivation is not restricted only to the wave height.展开更多
The new distributions of the statistics of wave groups based on the maximum entropy principle are presented. The maximum entropy distributions appear to be superior to conventional distributions when applied to a limi...The new distributions of the statistics of wave groups based on the maximum entropy principle are presented. The maximum entropy distributions appear to be superior to conventional distributions when applied to a limited amount of information. Its applications to the wave group properties show the effectiveness of the maximum entropy distribution. FFF filtering method is employed to obtain the wave envelope fast and efficiently. Comparisons of both the maximum entropy distribution and the distribution of Longuet-Higgins （1984） with the laboratory wind-wave data show that the former gives a better fit.展开更多
基金supported by the National Major Science and Technology Project,China(No.J2019-Ⅳ-0007-0075)the Fundamental Research Funds for the Central Universities,China(No.JKF-20240036)。
文摘To ensure the structural integrity of life-limiting component of aeroengines,Probabilistic Damage Tolerance(PDT)assessment is applied to evaluate the failure risk as required by airworthiness regulations and military standards.The PDT method holds the view that there exist defects such as machining scratches and service cracks in the tenon-groove structures of aeroengine disks.However,it is challenging to conduct PDT assessment due to the scarcity of effective Probability of Detection(POD)model and anomaly distribution model.Through a series of Nondestructive Testing(NDT)experiments,the POD model of real cracks in tenon-groove structures is constructed for the first time by employing the Transfer Function Method(TFM).A novel anomaly distribution model is derived through the utilization of the POD model,instead of using the infeasible field data accumulation method.Subsequently,a framework for calculating the Probability of Failure(POF)of the tenon-groove structures is established,and the aforementioned two models exert a significant influence on the results of POF.
基金National Natural Science Foundation of China,Grant/Award Number:U2243218。
文摘The log-normal distribution function(LNDF)and Weibull cumulative density function(WCDF)represent two prevalent approaches for characterizing sediment grain size distributions.This study analyzes annual average suspended load grain size data(standardized to equivalent settling diameters)from seven hydrological stations in the lower Yellow River(LYR)spanning 1962–2020,employing various distribution functions for grain size fitting.Results demonstrate that the Weibull probability density function(WPDF)offers significant advantages over both LNDF and WCDF in terms of fitting accuracy,parameter stability,simplicity,and practical applicability for characterizing suspended load grain size distributions in the LYR.Based on these findings,universal formulas were developed for the suspended load grain size distribution across the seven stations and the entire lower reaches,yielding determination coefficients(R2)exceeding 0.9.These formulas can be applied to estimate suspended load grain size in data-scarce cross-sections.The existence of such universal formulas suggests that interannual fluctuations in suspended load grain size in the LYR are constrained within a limited range,suggesting that sediment grain size may represent an inherent property of the river channel.This limited variability may be attributed to the fact that sediments in the LYR are primarily derived from a relatively fixed source region—the Loess Plateau.The observed stability over an extended period also offers valuable insights into the fundamental properties of river systems and their long-term behavior.
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 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.
基金This work is supported by the National Natural Science Foundation of China （NSFC） under Grants Nos. 40575031 and 40533016by the Ministry of Education of China under Grant No. 106002.
文摘The probability distribution function （PDF） of a passive tracer, forced by a ＂mean gradient＂, is studied. First, we take two theoretical approaches, the Lagrangian and the conditional closure formalisms, to study the PDFs of such an externally forced passive tracer. Then, we carry out numerical simulations for an idealized random flow on a sphere and for European Center for Medium-Range Weather Forecasts （ECMWF） stratospheric winds to test whether the mean-gradient model can be applied to studying stratospheric tracer mixing in midlatitude surf zones, in which a weak and poleward zonal-mean gradient is maintained by tracer leakage through polar and tropical mixing barriers, and whether the PDFs of tracer fluctuations in midlatitudes are consistent with the theoretical predictions. The numerical simulations show that when diffusive dissipation is balanced by the mean-gradient forcing, the PDF in the random flow and the Southern-Hemisphere PDFs in ECMWF winds show time-invariant exponential tails, consistent with theoretical predictions. In the Northern Hemisphere, the PDFs exhibit non-Gaussian tails. However, the PDF tails are not consistent with theoretical expectations. The long-term behavior of the PDF tails of the forced tracer is compared to that of a decaying tracer. It is found that the PDF tails of the decaying tracer are time-dependent, and evolve toward flatter than exponential.
文摘Using the Feynman's path integral with topological constraints arising from the presence of one singular line, we find the homotopic probability distribution PnL for the winding number n and the partition function PL of the entangled system around a ribbon segment chain. We find that when the width of the ribbon segment chain 2a increases,the partition function exponentially decreases, whereas the free energy increases an amount, which is proportional to the square of the width. When the width tends to zero we obtain the same results as those of a single chain with one singular point.
基金National Natural Science Foundation of China under Grant No.10574060the Natural Science Foundation of Shandong Province of China under Grant No.Y2004A09
文摘In this paper, in terms of the technique of integration within an ordered product （IWOP） of operators and the properties of the inverses of q-deformed annihilation and creation operators, normalizable q-analogue of the squeezed one-photon state, which is quite different from one introduced by Song and Fan [Int. 3. Theor. Phys. 41 （2002） 695], is constructed. Moreover, the Wigner function and phase probability distribution of q-analogue of the squeezed one-photon state are examined.
基金National Science and Technology Major Project of China(No.2016ZX04003001)。
文摘The probability distributions of small sample data are difficult to determine,while a large proportion of samples occur in the early failure period,so it is particularly important to make full use of these data in the statistical analysis.Based on gamma distribution,four methods of probability density function(PDF)reconstruction with early failure data are proposed,and then the mean time between failures(MTBF)evaluation expressions are concluded from the reconstructed PDFs.Both theory analysis and an example show that method 2 is the best evaluation method in dealing with early-failure-small-sample data.The reconstruction methods of PDF also have certain guiding significance for other distribution types.
文摘In this paper we discuss a step further some convergence and continuity problems of distribution function on R^i. We give the following results: (1)distribution function F(x_1,…,x_k) on R^k is continuous if and only if all marginal distribution functions of F is continuous on R^1. (2)If limF_n(x_1,……,x_k)=F(x_1,…,x_k) and limF_n(x_1—0,…,x_k—0)=F(x_1—0,…,x_k—0) at all non-continuity points of F, then
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.
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 Open Fund of Intelligent Control Laboratory,China(No.ICL-2023–0202)in part by National Key R&D Program of China(Nos.2021YFC2202600,2021YFC2202603)。
文摘In distributed fusion,when one or more sensors are disturbed by faults,a common problem is that their local estimations are inconsistent with those of other fault-free sensors.Most of the existing fault-tolerant distributed fusion algorithms,such as the Covariance Union(CU)and Faulttolerant Generalized Convex Combination(FGCC),are only used for the point estimation case where local estimates and their associated error covariances are provided.A treatment with focus on the fault-tolerant distributed fusions of arbitrary local Probability Density Functions(PDFs)is lacking.For this problem,we first propose Kullback–Leibler Divergence(KLD)and reversed KLD induced functional Fuzzy c-Means(FCM)clustering algorithms to soft cluster all local PDFs,respectively.On this basis,two fault-tolerant distributed fusion algorithms of arbitrary local PDFs are then developed.They select the representing PDF of the cluster with the largest sum of memberships as the fused PDF.Numerical examples verify the better fault tolerance of the developed two distributed fusion algorithms.
文摘The orientation distribution function of cylindrical particle suspensions was deduced and numerically simulated, and an application was taken in a wedge-shaped flow field. The relationship between the orientation distribution function and particle orientation angles was obtained. The results show that comparing with the most probable angle distribution which comes to being in short time, the distribution of the steady state doesn't vary much. in range; the main difference is the anti-clockwise rotation in the right and upper field, that is, particles rotate more at the points where the velocity gradients are larger. The most probable orientations are close to the direction of local streamlines. In the direction of streamlines, with poleradius decreasing, the most probable angles increase, but the angles between their orientations and the local streamlines decrease.
文摘We consider the problem of approximating two, possibly unrelated probability distributions from a single complex-valued function and its Fourier transform. We show that this problem always has a solution within a specified degree of accuracy, provided the distributions satisfy the necessary regularity conditions. We describe the algorithm and construction of and provide examples of approximating several pairs of distributions using the algorithm.
文摘In this work, the excitons distribution function in organic bulk hetero junction solar cells, at a depth z has been determined from solving the charge continuity equation, by exploiting the Laplace transform with appropriate boundary conditions. Next, the influence of the electron-hole pair separation distance on the excitons dissociation probability, the internal quantum efficiency and the binding energy, has been studied. The simulated results show that the probability density of the carriers photo generated depends on the generation rate, excitons dissociation and the charge carriers in the cells. The potential improvement of the internal quantum efficiency of charge generation depends on electron-hole pair separation distance, the excitons dissociation probability into free charges and depends strongly on the optical absorption of the photons in the active layer.
文摘For performance optimization such as placement,interconnect synthesis,and routing, an efficient and accurate interconnect delay metric is critical,even in design tools development like design for yield （DFY） and design for manufacture （DFM）. In the nanometer regime, the recently proposed delay models for RLC interconnects based on statistical probability density function （PDF）interpretation such as PRIMO,H-gamma,WED and RLD bridge the gap between accuracy and efficiency. However, these models always require table look-up when operating. In this paper, a novel delay model based on the Birnbaum-Saunders distribution （BSD） is presented. BSD can accomplish interconnect delay estimation fast and accurately without table look-up operations. Furthermore, it only needs the first two moments to match. Experimental results in 90nm technology show that BSD is robust, easy to implement,efficient,and accurate.
文摘Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh form, involves two parameters: the average wave height H— and the state parameter γ. The role of γ in the distribution of wave heights is examined. It is found that γ may be a certain measure of sea state. A least square method for determining γ from measured data is proposed. In virtue of the method, the values of γ are determined for three sea states from the data measured in the East China Sea. The present PDF is compared with the well known Rayleigh PDF of wave height and it is shown that it much better fits the data than the Rayleigh PDF. It is expected that the present PDF would fit some other wave variables, since its derivation is not restricted only to the wave height.
基金This work was financially supported by the National Natural Science Foundation of China (Grant No50479028)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No20060423009)
文摘The new distributions of the statistics of wave groups based on the maximum entropy principle are presented. The maximum entropy distributions appear to be superior to conventional distributions when applied to a limited amount of information. Its applications to the wave group properties show the effectiveness of the maximum entropy distribution. FFF filtering method is employed to obtain the wave envelope fast and efficiently. Comparisons of both the maximum entropy distribution and the distribution of Longuet-Higgins （1984） with the laboratory wind-wave data show that the former gives a better fit.
