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81.
For the phase of vortex singular solutions of the shallow water equations we justify the Hamilton--Jacobi equation corresponding to the hydrodynamical mode of perturbation propagation. We also obtain the next correction to the Cauchy--Riemann conditions describing how the singular part of the solution affects the smooth background. 相似文献
82.
The Einstein field equations for the Friedmann universe reduce to a system of three first-order equations for the space-like
components and a constraint from the temporal component. We analyse the system from the viewpoints of symmetry and singularity
analyses. The solutions of particular relevance to Cosmology are highlighted.
相似文献
83.
指数分布场合下步进应力加速寿命试验的Bayes分析 总被引:5,自引:0,他引:5
张志华 《高校应用数学学报(A辑)》1997,(2):175-182
当寿命分布为指数分布时,本文给出了步进应力加速寿命试验的一种新的Bayes估计,为计算上的方便,本文还给出一种近似方法,数值例子表明,此方法简便可行。 相似文献
84.
LiWei Hai-liangYang 《应用数学学报(英文版)》2004,20(3):495-506
In this paper we first consider a risk process in which claim inter-arrival times and the time untilthe first claim have an Erlang (2) distribution.An explicit solution is derived for the probability of ultimateruin,given an initial reserve of u when the claim size follows a Pareto distribution.Follow Ramsay,Laplacetransforms and exponential integrals are used to derive the solution,which involves a single integral of realvalued functions along the positive real line,and the integrand is not of an oscillating kind.Then we showthat the ultimate ruin probability can be expressed as the sum of expected values of functions of two differentGamma random variables.Finally,the results are extended to the Erlang(n) case.Numerical examples aregiven to illustrate the main results. 相似文献
85.
Special Lagrangian Submanifolds with Isolated Conical Singularities. II. Moduli spaces 总被引:1,自引:1,他引:0
This is the second in a series of five papers studying special Lagrangiansubmanifolds (SLV m-folds) X in (almost) Calabi–Yau m-folds
M with singularities x
1
, ..., x
n
locally modelled on specialLagrangian cones
C
1, ..., C
n
in
m
with isolated singularities at 0.Readers are advised to begin with Paper V.This paper studies the deformation theory of compact SL m-folds X in Mwith conical singularities. We define the moduli space
X
of deformations of X in M, and construct a natural topology on it. Then we show that
X
is locally homeomorphic to the zeroes of a smooth map :
X
X between finite-dimensional vector spaces.Here the infinitesimal deformation space
X depends only on the topology of X, and the obstruction space
X only on the cones C
1, ..., C
n
at x
1, ..., x
n
. If the cones C
i
are stable then
X is zero, and
X
is a smooth manifold. We also extend our results to families of almost Calabi–Yau structures on M. 相似文献
86.
We consider the connection problem for the Heun differential equation, which is a Fuchsian differential equation that has four regular singular points. We consider the case in which the parameters in this equation satisfy a certain set of conditions coming from the eigenvalue problem of the non-commutative harmonic oscillators. As an application, we describe eigenvalues with multiplicities greater than 1 and the corresponding odd eigenfunctions of the non-commutative harmonic oscillators. The existence of a rational or a certain algebraic solution of the Heun equation implies that the corresponding eigenvalues has multiplicities greater than 1.The research of the author is supported in part by a Grant-in-Aid for Scientific Research (B) (No. 15340005) from the Ministry of Education, Culture, Sports, Science and Technology.Mathematics Subject classifications (2000). primary, 34M35, secondary, 33E20.This revised version was published online in March 2005 with corrections to the cover date. 相似文献
87.
This paper presents an analysis of the role of orientation on the rheology of discotic mesophases subjected to slow shear start-up flows, using a projection of the Landau-de Gennes equations of nematodynamics. Analysis of the shear stress surface as a function of tilt and twist orientation with respect to the shear plane shows that the stress surface is dense in well-oriented and periodically located sets of maxima and minima. Thus overshoots and undershoot stress responses to shear-start up are predicted to be the rule rather than the exception. In-plane (within the shear plane) shear start-up stress responses can exhibit multiple, single, or no overshoots, depending on the number of maxima traversed on the way to steady state. Responses originating from orientations close to the vorticity axis lead to stress undershoots. Complex stress responses, such as a weak overshoot-strong undershoot sequence, are found for intermediate tilt-twist initial states. In-plane modes lead to amplitude and strain scaling. Out-of-plane modes do not display amplitude or strain scaling. These results provide will be useful to interpret and use transient shear rheological data of carbonaceous mesophases and highly filled suspensions of disc-like particles. 相似文献
88.
Dominic D. Joyce 《Annals of Global Analysis and Geometry》2001,20(4):345-403
This is the third in a series of papers constructing explicit examples of special Lagrangian submanifolds in C
m
. The previous paper (Math. Ann.
320 (2001), 757–797), defined the idea of evolution data, which includes an (m – 1)-submanifold P in R
n
, and constructed a family of special Lagrangian m-folds N in C
m
, which are swept out by the image of P under a 1-parameter family of affine maps
t
: R
n
C
m
, satisfying a first-order o.d.e. in t. In this paper we use the same idea to construct special Lagrangian 3-folds in C3. We find a one-to-one correspondence between sets of evolution data with m = 3 and homogeneous symplectic 2-manifolds P. This enables us to write down several interesting sets of evolution data, and so to construct corresponding families of special Lagrangian 3-folds in C3.Our main results are a number of new families of special Lagrangian 3-foldsin C3, which we write very explicitly in parametric form. Generically these are nonsingular as immersed 3-submanifolds, and diffeomorphic to R3 or
1× R2. Some of the 3-folds are singular, and we describe their singularities, which we believe are of a new kind.We hope these 3-folds will be helpful in understanding singularities ofcompact special Lagrangian 3-folds in Calabi–Yau 3-folds. This will beimportant in resolving the SYZ conjecture in Mirror Symmetry. 相似文献
89.
A non-conforming finite element method with anisotropic mesh grading for the Stokes problem in domains with edges 总被引:5,自引:0,他引:5
The solution of the Stokes problem in three-dimensional domainswith edges has anisotropic singular behaviour which is treatednumerically by using anisotropic finite element meshes. Thevelocity is approximated by CrouzeixRaviart (nonconformingP1 ) elements and the pressure by piecewise constants. Thismethod is stable for general meshes (without minimal or maximalangle condition). Denoting by Ne the number of elements in themesh, the interpolation and consistency errors are of the optimalorder h Ne1/3 which is proved for tensor product meshes.As a by-product, we analyse also nonconforming prismatic elementswith P1 [oplus ] span {x32} as the local space for the velocitywhere x3 is the direction of the edge. 相似文献
90.
We propose a computational method that takes into account the dynamical influence of moving rigid walls over the pattern formation for thin films of diblock copolymers. The competition between the surface field energy and elastic stretching energy, and the effects of the molecular relaxation on pattern formation are studied. Finally, it is also observed that stretching the film enhances the ordering of patterns in it. 相似文献