The K(a)hler-Einstein metric for some Hartogs domains over symmetric domains

We study the complete K(a)hler-Einstein metric of a Hartogs domain (Ω) built on an irreducible bounded symmetric domain Ω, using a power Nμ of the generic norm of Ω. The a boundary condition. The domain (Ω) is in general not homogeneous, but it has a subgroup of automorphisms, the orbits of which are parameterized by X ∈ [0, 1[. This allows us to reduce the can be explicitly solved for a special valueμ0 ofμ. We work out the details for the two exceptional symmetric domains. The special value μ0 seems also to be significant for the properties of other invariant metrics like the Bergman metric; a conjecture is stated, which is proved for the exceptional domains.     

从一道微积分题到三个拓扑定理

借助于一般化方法,将一道微积分题推广为L-预拓扑空间中的三个定理,并详细揭示了一般化的步骤,对高校的数学教育工作有一定的启发意义.     

Regularized variable metric method versus the conjugate gradient method in solution of radiative boundary design problem

In this paper, an appropriate distribution of the heating elements’ strengths in a radiation furnace is estimated using inverse methods so that a pre-specified temperature and heat flux distribution is attained on the design surface. Minimization of the sum of the squares of the error function is performed using the variable metric method (VMM), and the results are compared with those obtained by the conjugate gradient method (CGM) established previously in the literature. It is shown via test cases and a well-founded validation procedure that the VMM, when using a “regularized” estimator, is more accurate and is able to reach at a higher quality final solution as compared to the CGM. The test cases used in this study were two-dimensional furnaces filled with an absorbing, emitting, and scattering gas.     

Time,gravity and the exterior angle of parallelism

Applying calculus to the horizontal and vertical unit hyperbolas we derive the obtuse exterior and the acute angle of parallelism formulas for the arc length of a unit circle. When the analogous arc length of a hyperbola is figured, we further define metric distance with radian measure. Employing a non-conventional velocity of light formula, we explain several aspects of physics with a logical geometry. The hyperbolic geometry Lobacevskii angle of parallelism is mathematically measured to agree with the physical measure, without using the gravitational constant, but rather the electromagnetic spectrum and geodesics. Space is hereby measured with units of radians and time. Half-angle formulas for slopes and boosts pertain to spinor algebra. The new light velocity is justified when its derivative results in Einstein's mass–energy formula. Relativity is reformulated with these half-angle formulas.     

Einstein-Kahler Metric with Explicit Formula on Super-Cartan Domain of the Fourth Type

Let YIV be the Super-Cartan domain of the fourth type, We reduce the Monge-Ampere equation for the metric to an ordinary differential equation in the auxiliary function X = X（Z, W）. This differential equation can be solved to give an implicit function in X. We give the generating function of the Einstein Kahler metric on YIV. We obtain the explicit form of the complete Einstein-Kahler metric on YIV for a special case.     

Controlled Geometry via Smoothing

We prove that Riemannian metrics with a uniform weak norm can be smoothed to having arbitrarily high regularity. This generalizes all previous smoothing results. As a consequence we obtain a generalization of Gromov's almost flat manifold theorem. A uniform Betti number estimate is also obtained. Received: August 31, 1995.     

On the metrical properties of the configuration space

We study some topological and metrical properties of configuration spaces. In particular, we introduce a family of metrics on the configuration space Γ, which makes it a Polish space. Compact functions on Γ are also considered. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Limit sets for maps of the circle

A trick which reduces some questions concerning the dynamics of self-maps of the circle to similar questions about self-maps of the interval is suggested and applied to answer two questions of Block and Coppel.     

Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings

In this paper, the famous Banach contraction principle and Caristi's fixed point theorem are generalized to the case of multi-valued mappings. Our results are extensions of the well-known Nadler's fixed point theorem [S.B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969) 475-487], as well as of some Caristi type theorems for multi-valued operators, see [N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989) 177-188; J.P. Aubin, Optima and Equilibria. An Introduction to Nonlinear Analysis, Grad. Texts in Math., Springer-Verlag, Berlin, 1998, p. 17; S.S. Zhang, Q. Luo, Set-valued Caristi fixed point theorem and Ekeland's variational principle, Appl. Math. Mech. 10 (2) (1989) 111-113 (in Chinese), English translation: Appl. Math. Mech. (English Ed.) 10 (2) (1989) 119-121], etc.