In this paper we study the behavior of trajectories of the Lotka-Volterra competition system with periodic coefficients under telegraph noise. We give sufficient conditions for the average permanence. Furthermore, we determine the $\omega$-limit sets of the system.

We introduce the concepts of rounding and flattening of a smooth map $g$ of an $m$-dimensional manifold $M$ to the euclidean space $\R^n$ with $m<n$, as those points in $M$ such that the image $g(M)$ has contact of type $\Sigma^{m,\dots,m}$ with a hypersphere or a hyperplane of $\R^n$, respectively. This includes several known special points such as vertices or flattenings of a curve in $\R^n$, umbilics of a surface in $\R^3$, or inflections of a surface in $\R^4$.

We study when the pull-back of an eigenform of the Laplacian on the base of a compact Riemannian $V$-submersion is an eigenform of the Laplacian on the total space of the submersion, and when the associated eigenvalue can change.

The non totally geodesic parallel $2n$-dimensional Kähler submanifolds of the $n$-dimensional quaternionic projective space were classified by K. Tsukada. Here we give the complete classification of non totally geodesic immersions of parallel $2m$-dimensional Kähler submanifolds in a quaternionic Kähler symmetric space of non zero scalar curvature, i.e., in a Wolf space or in its non compact dual. They are exhausted by parallel Kähler submanifolds of a totally geodesic submanifold which is either an Hermitian symmetric space or a quaternionic projective space.

The aim of this paper is to give, for any real cyclotomic field, elements of the group ring of the Galois group which annihilate the ideal class group. Our annihilators are constructed by using the prime decomposition of an element which is an analogy of the Gaussian sum. This method is essentially due to Thaine.

We prove an integral maximum principle for random walks on graphs, and give several applications to pointwise estimates of their transition probabilities, including the time-dependent case.

R. Nevanlinna showed, in 1926, that for two nonconstant meromorphic functions on the complex plane, if they have the same inverse images counting multiplicities for four distinct complex values, then they coincide up to a Möbius transformation, and if they have the same inverse images counting multiplicities for five distinct complex values, then they are identical. H. Fujimoto, in 1975, extended Nevanlinna’s result to nondegenerate holomorphic curves. This paper extends Fujimoto’s uniqueness theorem to the case of moving hyperplanes in pointwise general position.

We give a sufficient condition for a collection of two-point sets to have the uniqueness property for meromorphic functions.

Functions which are monotone close to boundary are defined. Some oscillation estimates are given for these functions in Orlicz classes. Criteria for monotonicity close to boundary are obtained.