Shift,Rotation and Limited Scale Invariant Pattern Recognition Using Synthetic Discriminant Functions

Making use of the idea of synthetic discriminant functions (SDF), a simple way to synthesize a shift, rotation and limited size correlation filter is proposed. The SDF is synthesized by superimposing four 2nd order circular harmonics of a training reference pattern in 4 different sizes. Computer simulation experiments have shown that the filter is indeed shift, full rotation and limited size invariant over a size range from 1 to 1.82. The invariant range can be increased if more training patterns are used.     

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.     

Amphoteric refraction exhibited by anisotropic crystals

Amphoteric refraction of light ray at the interface between isotropic materials and anisotropic materials is analyzed. Depending on the incident angle, the refractive light ray can either refract positively or negatively. This amphoteric refraction phenomenon can be quite prevalent when the difference of the two principal refractive indices is large. The reflectance under various incident angles has also been calculated, and an experimental demonstration with a calcite crystal in air is presented.     

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-switch and mode-locking modulators for Nd:hosted lasers

Four kinds of currently available Nd:hosted laser passive Q-switch and mode-locking modulators: plastic dye sheet, LiF:F₂⁻ color center crystal, Cr⁺⁴ :YAG crystal and RG1000 colored glass filter were investigated in detail and summarized for comparison for the first time. The LiF:F₂⁻ crystal with outstanding annealability, long lifetime, low cost and operability at high repetition rates is highly recommended.     

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.     

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.     

Mode selection of slowly opened Q-switch operation

The beam divergence angle is measured of the Q-switched laser pulse resulting from a resonator switched with a Pockels cell which is driven with a slowly opened circuit using a transformer. The rise time of the output voltage of this transformer type circuit is controllable. After optimization, the beam divergence of the present laser system is decreased by 30% compared with the conventional system using a Krytron. A model concerning the mode selection in the resonator is proposed.