This study utilized the MM5 mesoscale model to simulate the landfalling process of Typhoon Talim.The simulated typhoon track,weather patterns,and rainfall process are consistent with the observation.Using the simulati...This study utilized the MM5 mesoscale model to simulate the landfalling process of Typhoon Talim.The simulated typhoon track,weather patterns,and rainfall process are consistent with the observation.Using the simulation results,the relation of the second type thermal helicity(H2) to rainfall caused by the landfalling typhoon Talim was analyzed.The results show that H2 could well indicate the heavy inland rainfall but it did not perform as well as the helicity in predicting rainfall during the beginning stage of the typhoon landfall.In particular,H2 was highly correlated with rainfall of Talim at 1-h lead time.For 1-5-h lead time,it also had a higher correlation with rainfall than the helicity did,and thus showing a better potential in forecasting rainfall intensification.Further analyses have shown that when Talim was in the beginning stage of landfall,1) the 850-200-hPa vertical wind shear around the Talim center was quite small(about 5 m s-1);2) the highest rainfall was to the right of the Talim track and in the area with a 300-km radius around the Talim center,exhibiting no obvious relation to low-level temperature advection,low-level air convergence,and upper-level divergence;3) the low-level relative vorticity reflected the rainfall change quite well,which was the main reason why helicity had a better performance than H2 in this period.However,after Talim moved inland further,1) it weakened gradually and was increasingly affected by the northern trough;2) the vertical wind shear was enhanced as well;3) the left side of the down vertical wind shear lay in the Lushan and Dabieshan mountain area,which could have contributed to triggering a secondary vertical circulation,helping to produce the heavy rainfall over there;hence,H2 showed a better capacity to reflect the rainfall change during this stage.展开更多
In this paper, convex solutions for the second type of Feigenbaum's equation f (x) = λ1 f (f (λx)), 0 < λ < 1, f (0) = 1, 0 f (x) 1, x ∈ [0, 1] are investigated. Using constructive methods, we discuss th...In this paper, convex solutions for the second type of Feigenbaum's equation f (x) = λ1 f (f (λx)), 0 < λ < 1, f (0) = 1, 0 f (x) 1, x ∈ [0, 1] are investigated. Using constructive methods, we discuss the existence and uniqueness of continuous convex solutions, C1-convex solutions and C2-convex solutions of the above equation.展开更多
In this paper,the oscillation criteria for the solutions of the nonlinear differential equations of neutral type of the forms:[x(t)+p(t)x(σ(t))]″+q(t)f(x(τ(t)))g(x′(t))=0and[x(t)+p(t)x(σ(t))]″+q(t)f(x(t),x(τ(t)...In this paper,the oscillation criteria for the solutions of the nonlinear differential equations of neutral type of the forms:[x(t)+p(t)x(σ(t))]″+q(t)f(x(τ(t)))g(x′(t))=0and[x(t)+p(t)x(σ(t))]″+q(t)f(x(t),x(τ(t)))g(x′(t))=0are obtained.展开更多
We introduce the higher-order type 2 Bernoulli numbers and polynomials of the second kind.In this paper,we investigate some identities and properties for them in connection with central factorial numbers of the second...We introduce the higher-order type 2 Bernoulli numbers and polynomials of the second kind.In this paper,we investigate some identities and properties for them in connection with central factorial numbers of the second kind and the higher-order type 2 Bernoulli polynomials.We give some relations between the higher-order type 2 Bernoulli numbers of the second kind and their conjugates.展开更多
In this paper we establish Levin type comparison theorems for certain second order differential equations. The results obtained here generalize and extend some of the earlier ones related to the Levin's comparison...In this paper we establish Levin type comparison theorems for certain second order differential equations. The results obtained here generalize and extend some of the earlier ones related to the Levin's comparison theorems.展开更多
A simplified fragility analysis of fan type cable stayed bridges usingProbabilistic Risk Analysis (PRA) procedure is presented for determining their failure probabilityunder random ground motion. Seismic input to the ...A simplified fragility analysis of fan type cable stayed bridges usingProbabilistic Risk Analysis (PRA) procedure is presented for determining their failure probabilityunder random ground motion. Seismic input to the bridge support is considered to be a riskconsistent response spectrum which is obtained from a separate analysis. For the response analysis,the bridge deck is modeled as a beam supported on springs at different points. The stiffnesses ofthe springs are determined by a separate 2D static analysis of cable-tower-deck system. The analysisprovides a coupled stiffness matrix for the spring system. A continuum method of analysis usingdynamic stiffness is Used to determine the dynamic properties of the bridges .The response of thebridge deck is obtained by the response spectrum method of analysis as applied to multi-degree offreedom system which duly takes into account the quasi - static component of bridge deck vibration.The fragility analysis includes uncertainties arising due to the variation in ground motion,material property, modeling, method of analysis, ductility factor and damage concentration effect.Probability of failure of the bridge deck is determined by the First Order Second Moment (FOSM)method of reliability. A three span double plane symmetrical fan type cable stayed bridge of totalspan 689 m, is used as an illustrative example. The fragility curves for the bridge deck failure areobtained under a number of parametric variations. Some of the important conclusions of the studyindicate that (ⅰ) not only vertical component but also the horizontal component of ground motionhas considerable effect on the probability of failure; (ⅱ) ground motion with no time lag betweensupport excitations provides a smaller probability of failure as compared to ground motion with verylarge time lag between support excitation; and (ⅲ) probability of failure may considerablyincrease for soft soil condition.展开更多
This work presents the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2<sup>nd</sup>-CASAM)” for the efficient and exact computation of 1<sup>st</sup>- and 2<sup>...This work presents the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2<sup>nd</sup>-CASAM)” for the efficient and exact computation of 1<sup>st</sup>- and 2<sup>nd</sup>-order response sensitivities to uncertain parameters and domain boundaries of linear systems. The model’s response (<em>i.e.</em>, model result of interest) is a generic nonlinear function of the model’s forward and adjoint state functions, and also depends on the imprecisely known boundaries and model parameters. In the practically important particular case when the response is a scalar-valued functional of the forward and adjoint state functions characterizing a model comprising N parameters, the 2<sup>nd</sup>-CASAM requires a single large-scale computation using the First-Level Adjoint Sensitivity System (1<sup>st</sup>-LASS) for obtaining all of the first-order response sensitivities, and at most N large-scale computations using the Second-Level Adjoint Sensitivity System (2<sup>nd</sup>-LASS) for obtaining exactly all of the second-order response sensitivities. In contradistinction, forward other methods would require (<em>N</em>2/2 + 3 <em>N</em>/2) large-scale computations for obtaining all of the first- and second-order sensitivities. This work also shows that constructing and solving the 2<sup>nd</sup>-LASS requires very little additional effort beyond the construction of the 1<sup>st</sup>-LASS needed for computing the first-order sensitivities. Solving the equations underlying the 1<sup>st</sup>-LASS and 2<sup>nd</sup>-LASS requires the same computational solvers as needed for solving (<em>i.e.</em>, “inverting”) either the forward or the adjoint linear operators underlying the initial model. Therefore, the same computer software and “solvers” used for solving the original system of equations can also be used for solving the 1<sup>st</sup>-LASS and the 2<sup>nd</sup>-LASS. Since neither the 1<sup>st</sup>-LASS nor the 2<sup>nd</sup>-LASS involves any differentials of the operators underlying the original system, the 1<sup>st</sup>-LASS is designated as a “<u>first-level</u>” (as opposed to a “first-order”) adjoint sensitivity system, while the 2<sup>nd</sup>-LASS is designated as a “<u>second-level</u>” (rather than a “second-order”) adjoint sensitivity system. Mixed second-order response sensitivities involving boundary parameters may arise from all source terms of the 2<sup>nd</sup>-LASS that involve the imprecisely known boundary parameters. Notably, the 2<sup>nd</sup>-LASS encompasses an automatic, inherent, and independent “solution verification” mechanism of the correctness and accuracy of the 2nd-level adjoint functions needed for the efficient and exact computation of the second-order sensitivities.展开更多
The computational problems of two special determinants are investigated. Those determinants appear in the construction of the function-valued Pade-type approximation for computing Fredholm integral equation of the sec...The computational problems of two special determinants are investigated. Those determinants appear in the construction of the function-valued Pade-type approximation for computing Fredholm integral equation of the second kind. The main tool to be used in this paper is the well-known Schur complement theorem.展开更多
基金Supported by the "973" Program of China (2009CB421505)National Natural Science Foundation of China (40405012,40830958, 40705024, and 40875039)Shanghai Meteorological Bureau (2009ST11)
文摘This study utilized the MM5 mesoscale model to simulate the landfalling process of Typhoon Talim.The simulated typhoon track,weather patterns,and rainfall process are consistent with the observation.Using the simulation results,the relation of the second type thermal helicity(H2) to rainfall caused by the landfalling typhoon Talim was analyzed.The results show that H2 could well indicate the heavy inland rainfall but it did not perform as well as the helicity in predicting rainfall during the beginning stage of the typhoon landfall.In particular,H2 was highly correlated with rainfall of Talim at 1-h lead time.For 1-5-h lead time,it also had a higher correlation with rainfall than the helicity did,and thus showing a better potential in forecasting rainfall intensification.Further analyses have shown that when Talim was in the beginning stage of landfall,1) the 850-200-hPa vertical wind shear around the Talim center was quite small(about 5 m s-1);2) the highest rainfall was to the right of the Talim track and in the area with a 300-km radius around the Talim center,exhibiting no obvious relation to low-level temperature advection,low-level air convergence,and upper-level divergence;3) the low-level relative vorticity reflected the rainfall change quite well,which was the main reason why helicity had a better performance than H2 in this period.However,after Talim moved inland further,1) it weakened gradually and was increasingly affected by the northern trough;2) the vertical wind shear was enhanced as well;3) the left side of the down vertical wind shear lay in the Lushan and Dabieshan mountain area,which could have contributed to triggering a secondary vertical circulation,helping to produce the heavy rainfall over there;hence,H2 showed a better capacity to reflect the rainfall change during this stage.
基金supported by National Natural Science Foundation of China (Grant No. 10871117)Natural Science Foundation of Shandong Province (Grant No. Y2006A07)
文摘In this paper, convex solutions for the second type of Feigenbaum's equation f (x) = λ1 f (f (λx)), 0 < λ < 1, f (0) = 1, 0 f (x) 1, x ∈ [0, 1] are investigated. Using constructive methods, we discuss the existence and uniqueness of continuous convex solutions, C1-convex solutions and C2-convex solutions of the above equation.
文摘In this paper,the oscillation criteria for the solutions of the nonlinear differential equations of neutral type of the forms:[x(t)+p(t)x(σ(t))]″+q(t)f(x(τ(t)))g(x′(t))=0and[x(t)+p(t)x(σ(t))]″+q(t)f(x(t),x(τ(t)))g(x′(t))=0are obtained.
基金This work was supported by the National Research Foundation of Korea(NRF)Grant Funded by the Korea Government(No.2020R1F1A1A01071564).
文摘We introduce the higher-order type 2 Bernoulli numbers and polynomials of the second kind.In this paper,we investigate some identities and properties for them in connection with central factorial numbers of the second kind and the higher-order type 2 Bernoulli polynomials.We give some relations between the higher-order type 2 Bernoulli numbers of the second kind and their conjugates.
文摘In this paper we establish Levin type comparison theorems for certain second order differential equations. The results obtained here generalize and extend some of the earlier ones related to the Levin's comparison theorems.
文摘A simplified fragility analysis of fan type cable stayed bridges usingProbabilistic Risk Analysis (PRA) procedure is presented for determining their failure probabilityunder random ground motion. Seismic input to the bridge support is considered to be a riskconsistent response spectrum which is obtained from a separate analysis. For the response analysis,the bridge deck is modeled as a beam supported on springs at different points. The stiffnesses ofthe springs are determined by a separate 2D static analysis of cable-tower-deck system. The analysisprovides a coupled stiffness matrix for the spring system. A continuum method of analysis usingdynamic stiffness is Used to determine the dynamic properties of the bridges .The response of thebridge deck is obtained by the response spectrum method of analysis as applied to multi-degree offreedom system which duly takes into account the quasi - static component of bridge deck vibration.The fragility analysis includes uncertainties arising due to the variation in ground motion,material property, modeling, method of analysis, ductility factor and damage concentration effect.Probability of failure of the bridge deck is determined by the First Order Second Moment (FOSM)method of reliability. A three span double plane symmetrical fan type cable stayed bridge of totalspan 689 m, is used as an illustrative example. The fragility curves for the bridge deck failure areobtained under a number of parametric variations. Some of the important conclusions of the studyindicate that (ⅰ) not only vertical component but also the horizontal component of ground motionhas considerable effect on the probability of failure; (ⅱ) ground motion with no time lag betweensupport excitations provides a smaller probability of failure as compared to ground motion with verylarge time lag between support excitation; and (ⅲ) probability of failure may considerablyincrease for soft soil condition.
文摘This work presents the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2<sup>nd</sup>-CASAM)” for the efficient and exact computation of 1<sup>st</sup>- and 2<sup>nd</sup>-order response sensitivities to uncertain parameters and domain boundaries of linear systems. The model’s response (<em>i.e.</em>, model result of interest) is a generic nonlinear function of the model’s forward and adjoint state functions, and also depends on the imprecisely known boundaries and model parameters. In the practically important particular case when the response is a scalar-valued functional of the forward and adjoint state functions characterizing a model comprising N parameters, the 2<sup>nd</sup>-CASAM requires a single large-scale computation using the First-Level Adjoint Sensitivity System (1<sup>st</sup>-LASS) for obtaining all of the first-order response sensitivities, and at most N large-scale computations using the Second-Level Adjoint Sensitivity System (2<sup>nd</sup>-LASS) for obtaining exactly all of the second-order response sensitivities. In contradistinction, forward other methods would require (<em>N</em>2/2 + 3 <em>N</em>/2) large-scale computations for obtaining all of the first- and second-order sensitivities. This work also shows that constructing and solving the 2<sup>nd</sup>-LASS requires very little additional effort beyond the construction of the 1<sup>st</sup>-LASS needed for computing the first-order sensitivities. Solving the equations underlying the 1<sup>st</sup>-LASS and 2<sup>nd</sup>-LASS requires the same computational solvers as needed for solving (<em>i.e.</em>, “inverting”) either the forward or the adjoint linear operators underlying the initial model. Therefore, the same computer software and “solvers” used for solving the original system of equations can also be used for solving the 1<sup>st</sup>-LASS and the 2<sup>nd</sup>-LASS. Since neither the 1<sup>st</sup>-LASS nor the 2<sup>nd</sup>-LASS involves any differentials of the operators underlying the original system, the 1<sup>st</sup>-LASS is designated as a “<u>first-level</u>” (as opposed to a “first-order”) adjoint sensitivity system, while the 2<sup>nd</sup>-LASS is designated as a “<u>second-level</u>” (rather than a “second-order”) adjoint sensitivity system. Mixed second-order response sensitivities involving boundary parameters may arise from all source terms of the 2<sup>nd</sup>-LASS that involve the imprecisely known boundary parameters. Notably, the 2<sup>nd</sup>-LASS encompasses an automatic, inherent, and independent “solution verification” mechanism of the correctness and accuracy of the 2nd-level adjoint functions needed for the efficient and exact computation of the second-order sensitivities.
基金The work is supported by the National Natural Science Foundation of China (10271074)by the Special Funds for Major Specialities of Shanghai Education Committee.
文摘The computational problems of two special determinants are investigated. Those determinants appear in the construction of the function-valued Pade-type approximation for computing Fredholm integral equation of the second kind. The main tool to be used in this paper is the well-known Schur complement theorem.