The Gauss–Bonnet Formula for Hyperbolic Manifolds of Finite Volume

Let M denote an even-dimensional noncompact hyperbolic manifold of finite volume. We show that such manifolds are candidates for minimal volume. Generalizing H. Hopf's ideas around the Curvatura integra for compact Clifford–Klein space forms, we present an elementary combinatorial-metrical proof of the Gauss–Bonnet formula for M. In contrast to former results of G. Harder and M. Gromov, our approach doesn't make use of the arithmetical and differential geometrical machinery.     

Averaging principle for quasi-geostrophic motion under rapidly oscillating forcing

1　IntroductionandtheProblemPresentedClimateandgeophysicalflowsdefinetheenvironmentinwhichwelive ,andtheirunderstanding,beyondbeingafascinatingscientificchallenge,isoftremendouseconomicandsocialimportance.Aclassoflargescalegeophysicalfluidflows,suchastheGulfStreamandoceanicgyres,aremodelledbythequasi_geostrophicequation .Thequasi_geostrophic (QG)equationmodelsaclassoflargescalegeophysicalflows.ItisderivedasanapproximationoftherotatingNavier_StokesequationsbyanasymptoticexpansioninasmallRos…     

Two trends of sample dispersion variation with carrier flow rate in a single flow-injection manifold

Two trends of sample dispersion variation with carrier flow rate in a single flow-injection manifold are completely revealed for the first time and an inflection point in the dispersion coefficient (D) vs. flow rate (q) curve is discovered. With the increase of the flow rate, the value of D increases before the inflection point but decreases after the inflection point. The value of the carrier flow rate at the inflection point (q_m) is independent of the sample injection volume, the tube length, the tube coil radius and the tube inner diameter. It is only affected by the substance diffusion coefficient (D_m) of the analysis. The value of q_m decreases as D_m increases. Therefore, the value of D_m for a sample can be estimated according to the D_m vs. q_m curve.     

PDA－ICP－AES中光谱干扰校正的卡尔曼滤波法研究

本实验采用光电二极管阵列（ＰＤＡ）检测器消除波长定位误差、并藉平滑处理原始光谱图以减轻随机噪声影响，研究了卡尔曼滤波法在ＰＤＡ－ＩＣＰ－ＡＥＳ中光谱干扰校正方面的应用，探讨了影响滤波结果准确性的若干因素。藉此法分析了一些合成试样，回收率一般为９０％～１１０％。     

Mixed-mode solutions in an air-filled differentially heated rotating annulus

We present an analysis of the primary bifurcations that occur in a mathematical model that uses the (three-dimensional) Navier-Stokes equations in the Boussinesq approximation to describe the flows of a near unity Prandtl number fluid (i.e. air) in the differentially heated rotating annulus. In particular, we investigate the double Hopf (Hopf-Hopf) bifurcations that occur along the axisymmetric to non-axisymmetric flow transition. Parameter-dependent centre manifold reduction and normal forms are used to show that in certain regions in parameter space, stable quasiperiodic mixed-azimuthal mode solutions result as a nonlinear interaction of two bifurcating waves with different azimuthal wave numbers. These flows have been called wave dispersion and interference vacillation. The results differ from similar studies of the annulus with a higher Prandtl number fluid (i.e. water). In particular, we show that a decrease in Prandtl number can stabilize these mixed-mode solutions.     

Box dimension of Neimark–Sacker bifurcation

In this article we show how a change of a box dimension of orbits of two-dimensional discrete dynamical systems is connected to their bifurcations in a non-hyperbolic fixed point. This connection is already shown in the case of one-dimensional discrete dynamical systems and Hopf bifurcation for continuous systems. Namely, at the bifurcation point the box dimension changes from zero to a certain positive value which is connected to the appropriate bifurcation. We study a two-dimensional discrete dynamical system with only one multiplier on the unit circle, and show a result for the box dimension of an orbit on the centre manifold. We also consider a planar discrete system undergoing a Neimark–Sacker bifurcation. It is shown that box dimension depends on the order of non-degeneracy at the non-hyperbolic fixed point and on the angle–displacement map. As it was expected, we prove that the box dimension is different in the rational and irrational case.     

Some conformal and projective scalar invariants of Riemannian manifolds

It is proved that, on any closed oriented Riemannian n-manifold, the vector spaces of conformal Killing, Killing, and closed conformal Killing r-forms, where 1 ≤ r ≤ n ? 1, have finite dimensions t _r , k _r , and p _r , respectively. The numbers t _r are conformal scalar invariants of the manifold, and the numbers k _r and p _r are projective scalar invariants; they are dual in the sense that t _r = t _n?r and k _r = p _n?r . Moreover, an explicit expression for a conformal Killing r-form on a conformally flat Riemannian n-manifold is given.     

Perturbations preserving conditioned invariant subspaces

Given the set of matrix pairs keeping a subspace invariant, we obtain a miniversal deformation of a pair belonging to an open dense subset of . It generalizes the known results when S is a supplementary subspace of the unobservable one. Copyright © 2011 John Wiley & Sons, Ltd.     

On the Integration of Poisson Manifolds,Lie Algebroids,and Coisotropic Submanifolds

In recent years, methods for the integration of Poisson manifolds and of Lie algebroids have been proposed, the latter being usually presented as a generalization of the former. In this Letter it is shown that the latter method is actually related to (and may be derived from) a particular case of the former if one regards dual of Lie algebroids as special Poisson manifolds. The core of the proof is the fact, discussed in the second part of this Letter, that coisotropic submanifolds of a (twisted) Poisson manifold are in one-to-one correspondence with possibly singular Lagrangian subgroupoids of source-simply-connected (twisted) symplectic groupoids.