共查询到20条相似文献,搜索用时 31 毫秒
1.
A. V. Kochergin 《Proceedings of the Steklov Institute of Mathematics》2007,256(1):238-252
A detailed proof of the absence of mixing is presented for a special flow constructed by an arbitrary rotation of the circle and by a symmetric function with logarithmic singularities (i.e., a function for which the sums of the coefficients of logarithms for “right” and “left” singularities are equal). 相似文献
2.
O. S. Rozanova 《Journal of Mathematical Sciences》2007,143(4):3355-3376
One considers a class of solutions with finite total energy and moment of inertia for the equations of motion of compressible
fluids. It is shown that for a wide class of right-hand sides, including the viscosity term, initially smooth solutions may
acquire singularities on a finite time interval. A sufficient condition for the appearance of singularities is found. This
condition may be called “the best possible sufficient condition” in the sense that one can explicitly construct a time-global
smooth solution for which this condition does not hold to within arbitrary infinitely small quantities. For a nontrivial constant
state, perturbations with compact support are considered. A generalization is proved for the known theorem on the initial
conditions for which the solution acquires singularities on a finite time interval. The effect of dry friction and rotation
on the formation of singularities of smooth solutions is examined.
__________
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 26, pp. 274–308, 2007. 相似文献
3.
We prove that under certain regularity conditions imposed on the renormalizations of two circle diffeomorphisms with singularities,
their C
1-smooth equivalence follows from exponential convergence of those renormalizations. As an easy corollary, any two analytical
critical circle maps with the same order of critical points and the same irrational rotation number are C
1-smoothly conjugate. 相似文献
4.
Keisuke Uchikoshi 《偏微分方程通讯》2013,38(5):689-700
We consider linear Cauchy problems of order two in a complex domain. We assume that the initial values have singularities along a family of hypersurfaces, which cross pairwise transversally along a single intersection. We study the propagation of the singularities of the solution. We show that the solution may have anomalous singularities, and study the monodromy of the solution. 相似文献
5.
Aviva Szpirglas 《manuscripta mathematica》2001,104(1):71-95
We describe the general homological framework (the variation arrays and variation homological diagrams) in which can be studied hypersurface isolated singularities as well as boundary singularities and corner singularities from
the point of view of duality. We then show that any corner singularity is extension, in a sense which is defined, of the corner
singularities of less dimension on which it is built. This framework is also used to rewrite Thom–Sebastiani type properties
for isolated singularities and to establish them for boundary singularities.
Received: 27 June 2000 / Revised version: 18 October 2000 相似文献
6.
I. G. Shcherbak 《Journal of Mathematical Sciences》1992,60(5):1681-1693
We define the decomposition of a boundary singularity as a pair (a singularity in the ambient space together with a singularity of the restriction to the boundary). We prove that the Lagrange transform is an involution on the set of boundary singularities that interchanges the singularities that occur in the decomposition of a boundary singularity. We classify the boundary singularities for which both of these singularities are simple. Bibliography: 8 titles.Translated fromTrudy Seminara imeni I. G. Petrovskogo, No. 15, pp. 55–69, 1991. 相似文献
7.
We use integrable systems techniques to study the singularities of timelike non-minimal constant mean curvature (CMC) surfaces in the Lorentz–Minkowski 3-space. The singularities arise at the boundary of the Birkhoff big cell of the loop group involved. We examine the behavior of the surfaces at the big cell boundary, generalize the definition of CMC surfaces to include those with finite, generic singularities, and show how to construct surfaces with prescribed singularities by solving a singular geometric Cauchy problem. The solution shows that the generic singularities of the generalized surfaces are cuspidal edges, swallowtails, and cuspidal cross caps. 相似文献
8.
《Journal de Mathématiques Pures et Appliquées》2006,85(2):295-312
We consider 2-dimensional quasilinear Cauchy problems for singular initial values in a complex domain. We study the singularities of the solution, in terms of monoidal transformation. We study whether the singularities propagate toward characteristic directions, and whether the singularities branch. 相似文献
9.
We describe discrete maximal surfaces with singularities in 3-dimensional Minkowski space and give a Weierstrass type representation for them. In the smooth case, maximal surfaces (spacelike surfaces with mean curvature identically 0) in Minkowski 3-space generally have certain singularities. We give a criterion that naturally describes the “singular set” for discrete maximal surfaces, including a classification of the various types of singularities that are possible in the discrete case. 相似文献
10.
Dmitry S. Kaliuzhnyi-Verbovetskyi 《Linear algebra and its applications》2009,430(4):869-3417
We show that the singularities of a matrix-valued noncommutative rational function which is regular at zero coincide with the singularities of the resolvent in its minimal state space realization. The proof uses a new notion of noncommutative backward shifts. As an application, we establish the commutative counterpart of the singularities theorem: the singularities of a matrix-valued commutative rational function which is regular at zero coincide with the singularities of the resolvent in any of its Fornasini-Marchesini realizations with the minimal possible state space dimension. The singularities results imply the absence of zero-pole cancellations in a minimal factorization, both in the noncommutative and in the commutative setting. 相似文献
11.
Using the structure of the jet schemes of rational double point singularities, we construct “minimal embedded toric resolutions” of these singularities. We also establish, for these singularities, a correspondence between a natural class of irreducible components of the jet schemes centered at the singular locus and the set of divisors which appear on every “minimal embedded toric resolution”. We prove that this correspondence is bijective except for the E8 singulartiy. This can be thought as an embedded Nash correspondence for rational double point singularities. 相似文献
12.
A. Giacobbe 《Regular and Chaotic Dynamics》2007,12(6):717-731
In this article we give a list of 10 rank zero and 6 rank one singularities of 2-degrees of freedom completely integrable
systems. Among such singularities, 14 are the singularities that satisfy a non-vanishing condition on the quadratic part,
the remaining 2 are rank 1 singularities that play a role in the geometry of completely integrable systems with fractional
monodromy. We describe which of them are stable and which are unstable under infinitesimal completely integrable deformations
of the system.
相似文献
13.
Summary We study particular singularities of complex analytic spaces that we call weakly rational and that contain rational singularities. In fact, a weakly rational singularity is rational if and only if it is Cohen-Macauley. Invariance under morphisms and deformations of weakly rational singularities is also studied.Partially supported by C.N.R. 相似文献
14.
Wolfgang Ebeling 《Proceedings of the Steklov Institute of Mathematics》2009,267(1):50-58
A boundary singularity is a singularity of a function on a manifold with boundary. The simple and unimodal boundary singularities
were classified by V.I. Arnold and V.I. Matov. The McKay correspondence can be generalized to the simple boundary singularities.
We consider the monodromy of the simple, parabolic, and exceptional unimodal boundary singularities. We show that the characteristic
polynomial of the monodromy is related to the Poincaré series of the coordinate algebra of the ambient singularity. 相似文献
15.
16.
The philosophy of this article is that the desingularization invariant together with natural geometric information can be used to compute local normal forms of singularities. The idea is used in two related problems: (1) We give a proof of resolution of singularities of a variety or a divisor, except for simple normal crossings (i.e., which avoids blowing up simple normal crossings, and ends up with a variety or a divisor having only simple normal crossings singularities). (2) For more general normal crossings (in a local analytic or formal sense), such a result does not hold. We find the smallest class of singularities (in low dimension or low codimension) with which we necessarily end up if we avoid blowing up normal crossings singularities. Several of the questions studied were raised by Kollár. 相似文献
17.
Abbas Nasrollah Nejad 《代数通讯》2018,46(8):3553-3562
The Alu? algebra is an algebraic definition of a characteristic cycle of a hypersurface in intersection theory. In this paper, we study the Alu? algebra of quasi-homogeneous and locally Eulerian hypersurfaces with only isolated singularities. We prove that the Jacobian ideal of an a?ne hypersurface with isolated singularities is of linear type if and only if it is locally Eulerian. We show that the gradient ideal of a projective hypersurface with only isolated singularities is of linear type if and only if the a?ne curve in each a?ne chart associated to singular points is locally Eulerian. We show that the gradient ideal of Nodal and Cuspidal projective plane curves are of linear type. 相似文献
18.
We study the variational convergence of a family of twodimensional Ginzburg-Landau functionals arising in the study of superfluidity
or thin-film superconductivity as the Ginzburg-Landau parameter ε tends to 0. In this regime and for large enough applied rotations (for superfluids) or magnetic fields (for superconductors),
the minimizers acquire quantized point singularities (vortices). We focus on situations in which an unbounded number of vortices
accumulate along a prescribed Jordan curve or a simple arc in the domain. This is known to occur in a circular annulus under
uniform rotation, or in a simply connected domain with an appropriately chosen rotational vector field. We prove that if suitably
normalized, the energy functionals Γ-converge to a classical energy from potential theory. Applied to global minimizers, our
results describe the limiting distribution of vortices along the curve in terms of Green equilibrium measures. 相似文献
19.
《偏微分方程通讯》2013,38(9-10):1721-1738
We study the inverse scattering problem for Schroedinger equation. We prove that for non-smooth potential the main singularities of the potential are contained in the Born approximation which can be obtained from measurement of the scattering amplitude in a single outgoing direction. We measure singularities in the scale of Sobolev spaces. 相似文献
20.
Trond Stølen Gustavsen 《Compositio Mathematica》2003,138(2):199-231
We relate the equisingular deformation theory of plane curve singularities and sandwiched surface singularities. We show the existence of a smooth map between the two corresponding deformation functors and study the kernel of this map. In particular we show that the map is an isomorphism when a certain invariant is large enough. 相似文献