Testing for additivity with B-splines

Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey's one degree of freedom test and a nonparametric version of Rao's score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance.     

Moderate deviation for super-Brownian motion with immigration

We prove a moderate deviation principle for a super-Brownian motion with im-migration of all dimensions, and consequently fill the gap between the central limit theoremand large deviation principle.     

Uniform Boundedness for Neutral Equations with Unbouned Delay

We consider a system of neutral equations with unbounded delay, and derive conditions on Liapunov functionals to ensure that the solutions are uniformly bounded and uniformly ultimately bounded.     

Vortex-lines motion for the Ginzburg-Landau equation with impurity

In this paper,we study the asymptotic behavior of solutions of the Ginzburg-Landau equation with impurity.We prove that,asymptotically,the vortex-lines evolve according to the mean curvature flow with a forcing term in the sense of the weak formulation.     

Spectral Asymptotics for Laplacian with Mixed Boundary-value Condition

Let Ω be a non-empty bounded open set in Rn(n ≥1) with boundary (?)Ω=Γ1∪Γ2. WedefineIn this paper, we consider the following variational eigenvalue problem:where △ denotes the Laplacian in Ω. We say that the scalar λ is an eigenvalue of (P) if     

Rigidity for rational maps with Cantor Julia sets

In this paper, we prove that two rational maps with the Cantor Julia sets are quasicon- formally conjugate if they are topologically conjugate.     

Existence for Semilinear Wave Equations with Low Regularity

In this paper, we study how much regularity of initial data is needed to ensure existence of a local solution to the following semilinear wave equations utt-Δu=F(u, Du), u(0, x)=f(x)∈HS,(?)tu(0, x)=g(x)∈HS-1, where F is quadratic in Du with D = ((?)t,(?)x1,…,(?)xn). We proved that the range of s is s≥n 1/2 δ, respectively, withδ>1/4 if n = 2, andδ>0 if n = 3, andδ≥0 if n≥4. Which is consistent with Lindblad's counterexamples [3] for n = 3, and the main ingredient is the use of the Strichartz estimates and the refinement of these.     

Blaschke's rolling theorem for manifolds¶with boundary

For a complete Riemannian manifold M with compact boundary ∂M denote by $\Cut$ the cut locus of $\f M$ in M. The rolling radius of M is roll(M)≔ dist(∂M, ?_{∂ M} ). Let Focal(∂M) be the focal distance of ∂M in M. Then conditions are given that imply the equality roll(M)= Focal(∂M). This generalizes Blaschke's rolling theorem from bounded convex domains in Euclidean space to more general Euclidean domains and to Riemannian manifolds with boundary. Received: 28 August 1998 / Revised version: 8 February 1999     

L~P Estimate for Klein-Gordon Equation with a Perturbed Potential

Ｌ~Ｐ　Ｅｓｔｉｍａｔｅ　ｆｏｒ　Ｋｌｅｉｎ－Ｇｏｒｄｏｎ　Ｅｑｕａｔｉｏｎ　ｗｉｔｈ　ａ　Ｐｅｒｔｕｒｂｅｄ　ＰｏｔｅｎｔｉａｌＭｕＣｈｕｎｌａｉ（穆春来）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｄａｎＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈ?..     

Distributional chaos for operators with full scrambled sets

In this article we answer in the negative the question of whether hypercyclicity is sufficient for distributional chaos for a continuous linear operator (we even prove that the mixing property does not suffice). Moreover, we show that an extremal situation is possible: There are (hypercyclic and non-hypercyclic) operators such that the whole space consists, except zero, of distributionally irregular vectors.     

Regularization method with two parameters for nonlinear ill-posed problems

This paper is devoted to the regularization of a class of nonlinear ill-posed problems in Banach spaces. The operators involved are multi-valued and the data are assumed to be known approximately. Under the assumption that the original problem is solvable, a strongly convergent approximation procedure is designed by means of the Tikhonov regularization method with two pa- rameters.     

Möbius inversion formula for monoids with zero

The Möbius inversion formula, introduced during the 19th century in number theory, was generalized to a wide class of monoids called locally finite such as the free partially commutative, plactic and hypoplactic monoids for instance. In this contribution are developed and used some topological and algebraic notions for monoids with zero, similar to ordinary objects such as the (total) algebra of a monoid, the augmentation ideal or the star operation on proper series. The main concern is to extend the study of the Möbius function to some monoids with zero, i.e., with an absorbing element, in particular the so-called Rees quotients of locally finite monoids. Some relations between the Möbius functions of a monoid and its Rees quotient are also provided.     

Large Deviations for Two-Time-Scale Diffusions, with Delays

We consider the problem of large deviations for a two-time-scale reflected diffusion process, possibly with delays in the dynamical terms. The Dupuis-Ellis weak convergence approach is used. It is perhaps the most intuitive and simplest for the problems of concern. The results have applications to the problem of approximating optimal controls for two-time-scale systems via use of the averaged equation.     

An Algorithm for l∞ Regression with Quadratic Complexity

Using a few very basic observations, we proposed recently a direct and finite algorithm for the computation of the l regression line on a discrete set under the assumption that In this paper, we extend the algorithm to the case with at least one, possibly multiple y-values for each distinct x_i. Our algorithm finds all the regression lines in O(n ²) operations in the worst-case scenario and improves the existing best-known computational complexity result for this problem. Numerical results on random problems are included.     

Interpolation for weak Orlicz spaces with M_Δ condition

An interpolation theorem for weak Orlicz spaces generalized by N-functions satisfying MΔ condition is given. It is proved to be true for weak Orlicz martingale spaces by weak atomic decomposition of weak Hardy martingale spaces. And applying the interpolation theorem, we obtain some embedding relationships among weak Orlicz martingale spaces.     

Conditions for the existence of quasi-stationary distributions for birth–death processes with killing

We consider birth–death processes on the nonnegative integers, where {1,2,…}$\{1,2,\dots \}$ is an irreducible class and 0 an absorbing state, with the additional feature that a transition to state 0 (killing) may occur from any state. Assuming that absorption at 0 is certain we are interested in additional conditions on the transition rates for the existence of a quasi-stationary distribution. Inspired by results of Kolb and Steinsaltz [M. Kolb, D. Steinsaltz, Quasilimiting behavior for one-dimensional diffusions with killing, Ann. Probab. 40 (2012) 162–212] we show that a quasi-stationary distribution exists if the decay rate of the process is positive and exceeds at most finitely many killing rates. If the decay rate is positive and smaller than at most finitely many killing rates then a quasi-stationary distribution exists if and only if the process one obtains by setting all killing rates equal to zero is recurrent.     

Large-time asymptotics for one-dimensional Dirichlet problems for Hamilton–Jacobi equations with noncoercive Hamiltonians

We study large-time asymptotics for a class of noncoercive Hamilton–Jacobi equations with Dirichlet boundary condition in one space dimension. We prove that the average growth rate of a solution is constant only in a subset of the whole domain and give the asymptotic profile in the subset. We show that the large-time behavior for noncoercive problems may depend on the space variable in general, which is different from the usual results under the coercivity condition. This work is an extension with more rigorous analysis of a recent paper by E. Yokoyama, Y. Giga and P. Rybka, in which a growing crystal model is established and the asymptotic behavior described above is first discovered.     

Cartan-Grauert theorem for tuboids with “curvilinear” edge

Tuboids are tube type domains with totally real edge that are asymptotically approximated near the edge points by local tubes over convex cones. For these domains we prove an analog of the Cartan-Grauert theorem on holomorphic convexity of domains in ^{n n} .Translated fromMatematicheskie Zametki, Vol. 64, No. 6, pp. 888–901, December, 1998.The author wishes to express his gratitude to Professor A. G. Sergeev for setting the problem and for constant attention to this work.This research was supported by the Russian Foundation for Basic Research under grant No. 98-01-00640 and by the program Leading Scientific Schools under grant No. 96-15-96131.     

Maslov P-Index Theory for a Symplectic Path with Applications

The Maslov P-index theory for a symplectic path is defined. Various properties of this index theory such as homotopy invariant, symplectic additivity and the relations with other Morse indices are studied. As an application, the non-periodic problem for some asymptotically linear Hamiltonian systems is considered.