ISSN 1439-8516 CN 11-2039/O1
![$$\operatorname{Re} (a + d^ * ) \in \left\{ {\begin{array}{*{20}c} {( - 2,2),if g(x) is f.p.f. or elliptic,} \\ {\left[ { - 2,2} \right], if g(x) is parabolic,} \\ {( - \infty ,\infty ), if g(x) is loxodromic.} \\ \end{array} } \right.$$](http://www.springerlink.com/content/f3185r489r87010k/10114_2007_Article_BF02560041_TeX2GIFE1.gif) |
is a Clifford matrix of dimensionn, g(x)=(ax+b)(cx+d) −1. We study the invariant balls and the more careful classifications of the loxodromic and parabolic elements inM(R n ), prove that the loxodromic elements inM(R 2k+1 ) certainly have an invariant ball, expound the geometric meaning of Ahlfors' hyperbolic elements, and introduce the uniformly hyperbolic and parabolic elements and give their identifications. We prove that
![$$\operatorname{Re} (a + d^ * ) \in \left\{ {\begin{array}{*{20}c} {( - 2,2),if g(x) is f.p.f. or elliptic,} \\ {\left[ { - 2,2} \right], if g(x) is parabolic,} \\ {( - \infty ,\infty ), if g(x) is loxodromic.} \\ \end{array} } \right.$$](http://www.springerlink.com/content/f3185r489r87010k/10114_2007_Article_BF02560041_TeX2GIFE2.gif) |
These results are fundamental in the higher dimensional Möbius groups, especially in Fuchs groups.
In this paper, we use the variational method to study the existence of periodic and generalized periodic solutions of planar second order Hamiltonian systems when a singular potential is present. The results obtained are applied to the study of generalized periodic solutions of the Restricted Three-Body Problem and the Planarn-Body Problem.
From a coincidence theorem in [1] there are derived some interesting applications to many respects such as minimax inequality, fixed point theory, existence of minimizable quasiconvex functions, etc..
In this article, we prove that the repetitive algebra of an iterated tilted algebra can be realized by the repetitive algebra of some tilted algebra. In particular, an iterated tilted algebra can be obtained by a series of reflections from some tilted algebra.
In this paper, we consider an initial value problem for nonlinear integro-differential equations in a Banach space. First, we give a comparison result between the under and over functions and some comparison principles. Then, using these results and the Kuratowski measure of noncompactness, we establish the existence theorem of extremal solutions between the under and over functions, and prove that there exists a unique solution between the lower and upper solutions under an additional Lipschitz's condition.
It is a general problem to study the measure of Julia sets. There are a lot of results for rational and entire functions. In this note, we describe the measure of Julia set for some holomorphic self-maps onC *. We'll prove thatJ(f) has positive area, wheref:C *→C *,f(z)=z m c P(z)+Q(1/z) ,P(z) andQ(z) are monic polynomials of degreed, andm is an integer.
The main purpose of this paper is to study the existence of nonoscillatory solutions of the second order non-linear differential equation (1). The author first generalizes a Wintner's lemma [1,8] to nonlinear equations (i.e. the following Theorem 1 and 4), and then obtains the necessary and sufficient conditions for the existence of nonoscillatory solutions of (1). These theorems generalize the corresponding results of [1] to include nonlinear equations. Using the above results, the author further obtains a series of criterion theorems for the existence of nonoscillatory solutions and comparison theorems for the oscillation and nonoscillation of nonlinear equations.
ConsiderD n the maximum Kolmogorov distance betweenP n andP among all possible one-dimensional projections, whereP n is an empirical measure based ond-dimensional i.i.d vectors with spherically symmetric probability measureP. We show in this paper that
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for large λ,d≥2 and an appropriate constantc 1. From this, when dimensiond is fixed, we give a negative answer to Huber's conjecture,P(D n >ε)≤N exp(−2n? 2), whereN is a constant depending only on dimensiond.
In this paper, we give an explicit expression of the fundamental solutions and the global solvability for a class of LPDO's consisting of left invariant vector fields on the nilpotent Lie groupG d 1+d 2.
This paper discusses the Keldys-Fichera boundary value problem for a kind of degenerate quasilinear elliptic equations in divergence form. The existence theorem, comparison principle and uniqueness theorem are proved.
In this paper Ruelle's inequality for the entropy of diffusion processes and, more generally, for the entropy of random diffeomorphisms is proved.
to be zero, compact, normal, hyponormal, subnormal, essential normal,k-quasihyponormal, etc.