Characterization of isolated homogeneous hypersurface singularities in C~4 Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

Let V be a hypersurface with an isolated singularity at the origin in Cn 1. It is a natural question to ask when V is defined by weighted homogeneous polynomial or homogeneous polynomial up to biholomorphic change of coordinates. In 1971, a beautiful theorem of Saito gives a necessary and sufficient condition for V to be defined by a weighted homogeneous polynomial. For a two-dimensional isolated hypersurface singularity V, Xu and Yau found a coordinate free characterization for V to be defined by a homogeneous polynomial. Recently Lin and Yau gave necessary and sufficient conditions for a 3-dimensional isolated hypersurface singularity with geometric genus bigger than zero to be defined by a homogeneous polynomial. The purpose of this paper is to prove that Lin-Yau's theorem remains true for singularities with geometric genus equal to zero.     

On variance of exponents for isolated surface singularities with modality ≤ 2 In Memory of Professor Philip Wagreich

Using the theory of the mixed Hodge structure one can define a notion of exponents of a singularity.In 2000,Hertling proposed a conjecture about the variance of the exponents of a singularity.Here,we prove that the Hertling conjecture is true for isolated surface singularities with modality ≤ 2.     

Passive Q-switches for Nd:hosted Solid State Lasers

The currently available Nd:hosted lasers utilizing passive Q-switches: a plastic dye sheet, a LiF:F₂- color center crystal, a Cr⁴⁺:YAG crystal or a RG1000 colored glass filter have been investigated in detail and the results summarized for comparison purposes for the first time. We first briefly summarize our own and others’ past studies, and report on recent new results concerning the use of Cr⁴⁺:YAG crystals and RG1000 colored glass filters as Nd:hosted laser passive Q-switchings. We then investigate in detail solid state laser system design using the above four passive modulators. Typical interpretations are given based on characteristic features of the materials, such as their saturation intensity and relaxation times. The results are then explained via adequate equations derived with respect to the relevant physical parameters of the materials. The optical dersity selection of plastic dye sheet passive Q-switching for the Nd:YAG laser system design is verified quantitatively, and the slope efficiencies from plastic dye sheet passive Q-switched operation by single pulse and multiple pulse bursts are investigated. The multi-peak Q-switched pulse timing phenomena are presented as well. The outstanding annealability, long lifetime, inexpensiveness and high repetition rate operation of LiF:F₂- crystals are highly recommended.     

Optical Image Combination and Logic AND Operation Using Beam Fanning Effect

Using the beam fanning effect in a BaTiO₃ crystal, we propose two simple set-ups to perform the function of an optical image combiner and an optical AND gate respectively. The optical image combiner combines two mutually coherent as well as mutually incoherent patterns transmitted to it separately into a single coherent pattern. This set-up can also be used as an optical OR gate. For the AND gate, the two input signals may also be mutually coherent or incoherent. Experimental results showed the response time of these two devices to range from 0.01 second to 2.5 seconds.     

Metrics on complex manifolds

In this note we discuss various canonical metrics on complex manifolds. A generalization of the Bergman metric is proposed and the relations of metrics on moduli spaces are commented. At last, we review some existence theorems of solutions to the Strominger system.     

The second pluri-genus of smoothable Gorenstein surface singularities

For complete intersection isolated surface singularities, Okuma gave a formula for the second plurigenus relating geometry genus, Milnor number and Tjurina number. We generalize Okuma’s theorem to Gorenstein smoothable surface singularities.     

The diffeomorphic types of the complements of arrangements in CP~3Ⅱ

For any arrangement of hyperplanes in CP~3,we introduce the soul of this arrangement. The soul,which is a pseudo-complex,is determined by the combinatorics of the arrangement of hyper- planes.In this paper,we give a sufficient combinatoric condition for two arrangements of hyperplanes to be diffeomorphic to each other.In particular we have found sufficient conditions on combinatorics for the arrangement of hyperplanes whose moduli space is connected.This generalizes our previous result on hyperplane point arrangements in CP~3.     

Spherical extension property no longer true for domains in algebraic variety with isolated singularity Dedicated to Professor YANG Lo on the occasion of his 70th birthday

Let D be a domain in Cn. It is known that if D is a simply connected bounded domain in C with spherical real analytic boundary D, then every local biholomorphic map at boundary as above extends to a biholomorphic map from D onto the unit ball in Cn. As a consequence, a local biholomorphic map between D1 and D2 where D1 and D2 are simply connected domains in Cn with spherical real analytic boundaries can extend to a global biholomorphic map from D1 onto D2. If the boundary is algebraic, the simply connected condition in the above result can be dropped. In this note, we show that the above phenomenon is no longer true if domains are in algebraic varieties with isolated singularities.     

ACTION SPECTRA FOR THE ABSORBANCE CHANGE AT 880 nm AND FOR P870 FLUORESCENCE FROM A PHOTOSYNTHETIC REACTION CENTER*

Abstract— Photosynthetic reaction centers isolated from blue-green mutant strain R-26 of Rhodopseudomonas spheroides were used to study the action spectra for the light-induced absorption changes at 880 nm, and for the P870 fluorescence. These spectra indicated that a pigment, possibly bacteriopheophytin, with an absorption maximum at 757 nm is an intrinsic component of the reaction center and transfers energy to P870 with relatively high efficiency.