Computation of Weng's rank 2 zeta function over an algebraic number field

In this paper, we study the zeta function, named non-abelian zeta function, defined by Lin Weng. We can represent Weng's rank r zeta function of an algebraic number field F as the integration of the Eisenstein series over the moduli space of the semi-stable OF-lattices with rank r. For r=2, in the case of F=Q, Weng proved that it can be written by the Riemann zeta function, and Lagarias and Suzuki proved that it satisfies the Riemann hypothesis. These results were generalized by the author to imaginary quadratic fields and by Lin Weng to general number fields. This paper presents proofs of both these results. It derives a formula (first found by Weng) for Weng's rank 2 zeta functions for general number fields, and then proves the Riemann hypothesis holds for such zeta functions.     

Hyperbolicity, heterodimensional cycles and Lyapunov exponents for partially hyperbolic dynamics

We prove a dichotomy of C² partially hyperbolic sets with one-dimensional center direction admitting no zero Lyapunov exponents, either hyperbolicity over the supports of ergodic measures or approximation by a heterodimensional cycle. This provides a partial result to the C¹ Palis Conjecture that claims a dichotomy, hyperbolicity or homoclinic bifurcations in a dense subset of the space of C¹ diffeomorphisms. Moreover, a theorem of Ma?é applied in the proof is modified to have an additional property concerning the Hausdorff distance between a periodic orbit and the support of a hyperbolic ergodic measure.     

Charge-induced self-feedback optical bistable device: switchingtime and spatial resolution

We report extensive experimental and theoretical studies on the properties of an optical bistable device called the charge-induced self-feedback device (CSFD) which is a variation of a self electro-optic effect device (SEED). In the mechanism, a novelty: of the CSFD consists of the feedback due to field-screening, resulting in independent switchings of optical beams focused at different spots on the CSFD without the help of pixellated structures. We experimentally demonstrate independent switchings without pixellation. In addition, a spatial resolution of the CSFD on such a device operation is found to be limited by an in-plane spreading of photoexcited carriers enhanced by a lateral electric-field induced by photoexcitation. Also, it is experimentally demonstrated that shortening carrier escape times leads to an improvement on the spatial resolution in terms of the suppression of the in-plane carrier spreading. Furthermore, an investigation on dynamics of the photoexcited carriers in the device reveals that the switching time of the CSPD is on the order of nanosecond, limited mainly by the hole escape time     

An ultra-high-speed optoelectronic integrated receiver forfiber-optic communications

An ultra-high-speed optoelectronic integrated receiver consisting of a GaInAs p-i-n photodiode and a transimpedance AlInAs-GaInAs high-electron-mobility-transistor amplifier was successfully fabricated on an InP substrate. A 3-dB bandwidth of 6 GHz with a transimpedance of 50 dBΩ was achieved for the receiver with a feedback resistance of 750 Ω. Measured noise currents of the receiver were analyzed and found to be dominated by the low-frequency noise and the induced gate noise. A sensitivity of -21.2 dBm for 8.0-Gb/s NRZ signals was deduced from the noise current characteristics     

Microfabrication of gold dots in SiO2/TiO2 glass films by two-photon absorption

Photogeneration of Au nanoparticles in SiO₂/TiO₂ glass films was carried out by two-photon absorption with a femtosecond pulse laser. Exquisite microdot-arrays of Au with micrometer spatial resolution were achieved by scanning of the focused laser beam. These structures were constructed in SiO₂/TiO₂ glass films by a sol–gel method. The sol–gel method demonstrated that Au dots microarray are fabricated at any position by two-photon absorption in the glass. The results show the utility of a two-photon absorption technique in the fabrication of complicated patterns with metal particles.     

Radical reactions initiated by the photochemical cleavage of carbon-indium bonds of organoindium compounds

Intra- and intermolecular reactions of carbon-centered radicals generated by photolysis of organoindium compounds were examined. The photolysis of vinylindium compounds and indium acetylides provided vinyl and alkynyl radicals, respectively, which were trapped with ethyl iodoacetate giving the corresponding β,γ-unsaturated esters. Allylic indium compounds, prepared from 8-bromo- or 8-iodooct-1,6-dienes and powdered indium metal, underwent an intramolecular radical cyclization to afford the 5-exo-trig product.     

A new manufacturing control system using Mahalanobis distance for maximizing productivity

Primary productivity in the semiconductor manufacturing industry, which includes cycle time, cost, and production, depends to a great extent on the capability of manufacturing administrators (MA), particularly with regards to the critical tradeoff between cycle time and tool utilization. The Mahalanobis distance (MD) has significance in pattern recognition, and the authors have found a method to make use of the MD as the core of a manufacturing control system. By using this system, one can easily distinguish deviations from normality in respect to productivity, specify the root cause of the abnormality, and decide how to prioritize the problem. As a result, one can efficiently concentrate limited resources on the root cause in the absence of a capable MA and restore productivity on a minimum timescale.     

System failure-frequency analysis using a differential operator

A method for obtaining the failure frequency of any system whose structure function is coherent is introduced. The relationship of the availability to the failure frequency can be expressed as a unique differential operator. In this way, regardless of the form of expression, the failure frequency can be obtained by applying the differential operator to the availability expression. Some reduction techniques are shown to be useful in evaluating failure frequency by means of this differential operator. If the reduction formulas are approximate rather than exact, it is generally difficult to apply the operator. This operator is tested on a special type of approximate reduction (the quadrilateral-star transformation). A numerical example for this reduction is presented