The Moduli Space of Complex Geodesics in the Complex Hyperbolic Plane

We consider the space M\mathcal{M} of ordered m-tuples of distinct complex geodesics in complex hyperbolic 2-space, H_\mathbbC²{\rm\bf H}_{\mathbb{C}}^{2}, up to its holomorphic isometry group PU(2,1). One of the important problems in complex hyperbolic geometry is to construct and describe the moduli space for M\mathcal{M}. This is motivated by the study of the deformation space of groups generated by reflections in complex geodesics. In the present paper, we give the complete solution to this problem.     

On the Cohomology of the Invariant Euler–Lagrange Complex

Given a Lie group action G we show, using the method of equivariant moving frames, that the local cohomology of the invariant Euler–Lagrange complex is isomorphic to the Lie algebra cohomology of G.     

Auslander–Reiten Quivers and the Coxeter Complex

Let Q be a quiver of type ADE. We construct the corresponding Auslander–Reiten quiver as a topological complex inside the Coxeter complex associated with the underlying Dynkin diagram. In A_n case, we recover special wiring diagrams. Presented by R. RentschlerMathematics Subject Classifications (2000) 16G70, 17B10, 20F55.     

Inviscid Limits of the Complex Generalized Ginzburg—Landau Equations

1 IntroductionDerivative Ginzburg-Landau equation appeared in many physical problem. It was derivedfor instability waves in hydrodynamic such as the nonlinear growth of Rayleigh-Benard convectiverolls, the appearance of Taylor Vortices in the couette flow between counter-rotating cylinders.This paper is concerning with the generalized derivative Ginzburg-Landau equations given by     

Attractors of the Derivative Complex Ginzburg-Landau Equation in Unbounded Domains

We consider the following initial boundary problem of derivative complex Ginzburg-Landau （DCGL） equation     

Order of Approximation by Hermite-Fejer Interpolating Polynomials in the Complex Plane

Suppose that either the outer mapping function of a domain D has continuous second derivatives or D is a strictly star domain. In this paper we first establish two inequalities concerning polynomials at Fejer's points with multiplicity (3 + 1). Using these two inequalities, we obtain the order of approximation in Lp(dD), 0相似文献   

Possible World Semantics and the Complex Mechanism of Reference Fixing

Possible world semantics considers not only what an expression actually refers to but also what it might have referred to in counterfactual circumstances. This has proven exceptionally useful both inside and outside philosophy. The way this is achieved is by using intensions. An intension of an expression is a function that assigns to each possible world the reference of the expression in that world. However, the specific intension of terms has been subject to frequent disputes. How is one to determine the intension of a term? Carnap has shown how the intension of a term depends on the type of that term. Two-dimensional semantics has shown how intensions also depend on the actual state of affairs. I will show how, in addition, intensions are no less dependent on metaphysical criteria of identity. Furthermore, I will reveal how these three factors interact to fix the exact intension of a term. In other words, I propose an outline of the overall mechanism by which intensions are being fixed.     

Extension of the Set of Complex Hadamard Matrices of Size 8

A complex Hadamard matrix is defined as a matrix H which fulfills two conditions, \(|H_{j,k}|=1\) for all j and k and \(HH^{*}=N \mathbb {I}_N\) where \(\mathbb {I}_N\) is an identity matrix of size N. We explore the set of complex Hadamard matrices \(\mathcal {H}_N\) of size \(N=8\) and present two previously unknown structures: a one-parametric, non-affine family \(T_8^{(1)}\) of complex Hadamard matrices and a single symmetric and isolated matrix \(A_8^{(0)}\).     

Symplectic Reduction and the Homogeneous Complex Monge–Ampère Equation

A Riemannian manifold ( ⁿ , g) is said to be the center of thecomplex manifold ⁿ if is the zero set of a smooth strictly plurisubharmonic exhaustion function ² on such that is plurisubharmonic and solves theMonge–Ampère equation ( ) ⁿ = 0 off , and g is induced by the canonical Kähler metric withfundamental two-form ². Insisting that be unbounded puts severe restrictions on as acomplex manifold as well as on ( , g). It is an open problemto determine the class Riemannian manifolds that are centers of complexmanifolds with unbounded . Before the present work, the list of knownexamples of manifolds in that class was small. In the main result of thispaper we show, by means of the moment map corresponding to isometric actionsand the associated bundle construction, that such class is larger than originally thought and contains many metrically and diffeomorphically`exotic' examples.     

On the Bloch Constant for Κ-Quasiconformal Mappings in Several Complex Variables

We study the Bloch constant for Κ-quasiconformal holomorphic mappings of the unit ball B of C ⁿ . The final result we prove in this paper is: If f is a Κ-quasiconformal holomorphic mappig of B into C ⁿ such that det(f′(0)) = 1, then f(B) contains a schlicht ball of radius at least where C _n > 1 is a constant depending on n only, and as n→∞. Received June 24, 1998, Accepted January 14, 1999     

Group Foliation Approach to the Complex Monge–Ampère Equation

We apply the group foliation method to find noninvariant solutions of the complex Monge–Ampère equation (CMA₂). We use the infinite symmetry subgroup of the CMA₂ to foliate the solution space into orbits of solutions with respect to this group and correspondingly split the CMA₂ into an automorphic system and a resolvent system. We propose a new approach to group foliation based on the commutator algebra of operators of invariant differentiation. This algebra together with Jacobi identities provides the commutator representation of the resolvent system. For solving the resolvent system, we propose symmetry reduction, which allows deriving reduced resolving equations.     

Approximation by the Complex form of a Link Operator Between the Phillips and the Szász–Mirakjan Operators

Results in Mathematics - The link operator $${P_{\alpha}^\rho(f,x)=\sum_{k=1}^\infty s_{\alpha,k}(x)\int_0^\infty \theta_{\alpha,k}^\rho(t)f(t)dt+e^{-\alpha x}f(0)}$$ , $${\alpha, \rho >...     

Sectional Curvatures and the Separation Set of the Complex Projective Space in Its Plücker Model

The Plücker embedding of the complex projective space in the Grassmannian of bivectors is used for proving several theorems on the relationship between the complex structure of and its Riemannian geometry. It is shown that the separation set of in the Plücker model is the face of for a certain calibration. Bibliography: 11 titles.     

Complex dynamics of a discrete predator–prey model with the prey subject to the Allee effect

In this paper, complex dynamics of the discrete predator–prey model with the prey subject to the Allee effect are investigated in detail. Firstly, when the prey intrinsic growth rate is not large, the basins of attraction of the equilibrium points of the single population model are given. Secondly, rigorous results on the existence and stability of the equilibrium points of the model are derived, especially, by analyzing the higher order terms, we obtain that the non-hyperbolic extinction equilibrium point is locally asymptotically stable. The existences and bifurcation directions for the flip bifurcation, the Neimark–Sacker bifurcation and codimension-two bifurcations with 1:2 resonance are derived by using the center manifold theorem and the bifurcation theory. We derive that the model only exhibits a supercritical flip bifurcation and it is possible for the model to exhibit a supercritical or subcritical Neimark–Sacker bifurcation at the larger positive equilibrium point. Chaos in the sense of Marotto is proved by analytical methods. Finally, numerical simulations including bifurcation diagrams, phase portraits, sensitivity dependence on the initial values, Lyapunov exponents display new and rich dynamical behaviour. The analytic results and numerical simulations demonstrate that the Allee effect plays a very important role for dynamical behaviour.     

The Hilbert Problem for the First Order Elliptic Complex Equation With Discontinuous Coefficients

本文研究一阶带间断系数的椭圆型复方程的Ｈｉｌｂｅｒｔ边值问题，在一定条件下给出了上述问题解的存在性、可解条件以及解的积分表示式．     

The Moduli Space of Points in the Boundary of Complex Hyperbolic Space

We consider the space M(n,m)\mathcal{M}(n,m) of ordered m-tuples of distinct points in the boundary of complex hyperbolic n-space, H_\mathbbCⁿ\mathbf{H}_{\mathbb{C}}^{n}, up to its holomorphic isometry group PU(n,1). An important problem in complex hyperbolic geometry is to construct and describe the moduli space for M(n,m)\mathcal{M}(n,m). In particular, this is motivated by the study of the deformation space of complex hyperbolic groups generated by loxodromic elements. In the present paper, we give the complete solution to this problem.     

Complex powers of the Schrödinger operator with a regularly growing potential

A meromorphic extension to the entire plane is obtained for the -function of a Schrödinger operator with a potential that increases at infinity in a power-like manner.Translated from Problemy Matematicheskogo Analiza, No. 11, pp. 176–187, 1990.     

When do the Recession Cones of a Polyhedral Complex Form a Fan?

We study the problem of when the collection of the recession cones of a polyhedral complex also forms a complex. We exhibit an example showing that this is no always the case. We also show that if the support of the given polyhedral complex satisfies a Minkowski–Weyl-type condition, then the answer is positive. As a consequence, we obtain a classification theorem for proper toric schemes over a discrete valuation ring in terms of complete strongly convex rational polyhedral complexes.