General Response Surface Reliability Analysis for Fuzzy-Random Uncertainty both in Basic Variables and in State Variables

A general response surface（RS） method is presented for reliability analysis of complex structure/mechanism with fuzzy-random uncertainty both in basic variables and in failure state variables. On the basis of equivalent transformation from fuzzy basic variable to random basic variable, the fuzziness and randomness in the basic variables are considered simultaneously in the presented general RS method. Once the fuzzy basic variables are transformed into the random basic variables, the conventional RS method is employed to establish the general RS for the complex structure/mechanism with implicit limit state equation by finite element numerical simulation. Furthermore, the general failure probability is defined according to the probability formula for fuzzy-random event by taking the fuzziness and randomness in the failure-safety state into consideration, and an appropriate fuzzy operator is adopted to calculate the general failure probability for the complex structure/mechanism with multiple implicit failure modes. Finally, a general reliability analysis of an elastic linkage mechanism is introduced to illustrate the present method.

Geometrical design of blade's surface and boundary control of Navier-Stokes equations

In this article a new principle of geometric design for blade's surface of an impeller is provided.This is an optimal control problem for the boundary geometric shape of flow and the control variable is the surface of the blade.We give a minimal functional depending on the geometry of the blade's surface and such that the flow's loss achieves minimum.The existence of the solution of the optimal control problem is proved and the Euler-Lagrange equations for the surface of the blade are derived.In addition,under a new curvilinear coordinate system,the flow domain between the two blades becomes a fixed hexahedron,and the surface as a mapping from a bounded domain in R2 into R3,is explicitly appearing in the objective functional.The Navier-Stokes equations,which include the mapping in their coefficients,can be computed by using operator splitting algorithm.Furthermore,derivatives of the solution of Navier-Stokes equations with respect to the mapping satisfy linearized Navier-Stokes equations which can be solved by using operator splitting algorithms too.Hence,a conjugate gradient method can be used to solve the optimal control problem.

On the canonical map of surfaces with q≥6

We carry out an analysis of the canonical system of a minimal complex surface S of general type with irregularity q > 0.Using this analysis,we are able to sharpen in the case q > 0 the well-known Castelnuovo inequality KS2≥3pg(S) + q(S)-7.Then we turn to the study of surfaces with pg=2q-3 and no fibration onto a curve of genus > 1.We prove that for q≥6 the canonical map is birational.Combining this result with the analysis of the canonical system,we also prove the inequality:KS2≥7χ(S) + 2.This improves an earlier result of Mendes Lopes and Pardini (2010).

On a non-abelian invariant on complex surfaces of general type Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In this paper,we give certain homotopy and diffeomorphism versions as a generalization to an earlier result due to W.S.Cheung,Bun Wong and Stephen S.T.Yau concerning a local rigidity problem of the tangent bundle over compact surfaces of general type.

A characterization of Burniat surfaces with K^2 = 4 and of non nodal type

Let S be a minimal surface of general type with pg(S) = 0 and K_S^2= 4. Assume the bicanonical map ψ of S is a morphism of degree 4 such that the image of ψ is smooth. Then we prove that the surface S is a Burniat surface with K^2= 4 and of non nodal type.

Boundary Shape Control of the Navier-Stokes Equations and Applications

In this paper, the geometrical design for the blade's surface in an impeller or for the profile of an aircraft, is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations. The objective function is the sum of a global dissipative function and the power of the fluid. The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations. The Euler-Lagrange equations of the optimal control problem are derived, which are an elliptic boundary value system of fourth order, coupled with the Navier-Stokes equations. The authors also prove the existence of the solution of the optimal control problem, the existence of the solution of the Navier-Stokes equations with mixed boundary conditions, the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the Gateaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary.

Propagation and Mechanisms of the Quasi-Biweekly Oscillation over the Asian Summer Monsoon Region

The propagation and underlying mechanisms of the boreal summer quasi-biweekly oscillation（QBWO）over the entire Asian monsoon region are investigated,based on ECMWF Interim reanalysis（ERA-Interim）data,GPCP precipitation data,and an atmospheric general circulation model（AGCM）.Statistical analyses indicate that the QBWO over the Asian monsoon region derives its main origin from the equatorial western Pacific and moves northwestward to the Bay of Bengal and northern India,and then northward to the Tibetan Plateau（TP）area,with a baroclinic vertical structure.Northward propagation of the QBWO is promoted by three main mechanisms：barotropic vorticity,boundary moisture advection,and surface sensible heating（SSH）.It is dominated by the barotropic vorticity effect when the QBWO signals are situated to the south of 20°N.During the propagation taking place farther north toward the TP,the boundary moisture advection and SSH are the leading mechanisms.We use an AGCM to verify the importance of SSH on the northward propagation of the QBWO.Numerical simulations confirm the diagnostic conclusion that the equatorial western Pacific is the source of the QBWO.Importantly,the model can accurately simulate the propagation pathway of the QBWO signals over the Asian monsoon region.Simultaneously,sensitivity experiments demonstrate that the SSH over northern India and the southern slope of the TP greatly contributes to the northward propagation of the QBWO as far as the TP area.

Simulation of the Effects of the Preceding SST Anomalies over the Tropical Eastern Pacific on Precipitation to the South of the Yangtze River in June

Numerical experiments are performed to simulate the response of the atmospheric circulation and pre-cipitation over East China in June to the sea surface temperature（SST）anomalies over the tropical eastern Pacific（TEP）from preceding September to June by using an atmospheric general circulation model （AGCM）.We constructed composite positive/negative SST anomalies（P-SSTAs/N-SSTAs）based on the observational SST anomalies over the TEP from September 1997 to June 1998.The results show that：（1） the response of the precipitation in the Yangtze River basin and its southern area（YRBS）to El Nino with different durations varies with the maximum amplitude of the precipitation anomalies appearing when the imposed duration is from November to next June,and the minimum appearing when the SST anomalies is only imposed in June.The anomalies of the precipitation are reduced when the duration of the forcing SST anomalies over the TEP is shortened and the positive SST anomalies in the preceding autumn tend to cause significantly more rainfall in the YRBS.This is in agreement with previous diagnostic analysis results.（2）The simulated precipitation anomalies over the YRBS are always obviously positive under strong or weak positive SST anomalies over the TEP.The intensity of the precipitation anomalies increases with increasing intensity of the SST anomalies in the experiments.The simulation results are consistent with the observations during the warm SST events,suggesting reasonable modeling results.（3）When negative SST anomalies in the TEP are put into the model,the results are different from those of the diagnostic analysis of La Nina events.Negative precipitation anomalies in YRBS could be reproduced only when the negative SST anomalies are strong enough.