Analysis of a Duopoly Supply Chain and its Application in Electricity Spot Markets

This paper studies a supply chain consisting of two suppliers and one retailer in a spot market, where the retailer uses the newsvendor solution as its purchase policy, and suppliers compete for the retailer’s purchase. Since each supplier’s bidding strategy affects the other’s profit, a game theory approach is used to identify optimal bidding strategies. We prove the existence and uniqueness of a Nash solution. It is also shown that the competition between the supplier leads to a lower market clearing price, and as a result, the retailer benefits from it. Finally, we demonstrate the applicability of the obtained results by deriving optimal bidding strategies for power generator plants in the deregulated California energy market. Supported in part by RGC (Hong Kong) Competitive Earmarked Research Grants (CUHK4167/04E and CUHK4239/03E), a Distinguished Young Investigator Grant from the National Natural Sciences Foundation of China, and a grant from Hundred Talents Program of the Chinese Academy of Sciences.     

Hyperbolic Schrödinger equation

Clifford algebra corresponds to Minkwoski space. The coupling between real object particles and light quantums can be discussed by Minkowski space’s directional strangeness. We introduce Galilei transfomation and Schr?dinger equation into Minkowski space and give a geometrical explanation for classical quantum theory.     

Branch and win: OR tree search algorithms for solving combinatorial optimisation problems

Currently, most combinatorial optimisation problems have to be solved, if the optimum solution is sought, using general techniques to explore the space of feasible solutions and, more specifically, through exploratory enumerative procedures in trees and search graphs. We propose Branch and Win, a general formulation for understanding and synthesising the different tree search procedures that have been presented in the literature of operations research as well as in that of artificial intelligence. Several general ideas are also presented, whose application allows designing new hybrid search algorithms, in order to implement the procedure.     

Power scaling of printed-circuit-board preionized TEA CO2 laser up to 3.6 kW

A high average power, high-repetition-rate TEA CO₂ laser employing printed-circuit-board preionizer is described. The power scaling of this preionization configuration has been demonstrated. The average output power reaches 3.6 kW at pulse repetition rate of 180 pps. Furthermore, the scaling-up ability of the rotating spark gap as high-voltage switch for high-average-power gas laser has been validated.     

Planting in his Neighbor's Garden: David Hilbert and Early Göttingen Quantum Physics

David Hilbert (1862-1943) played an important role in establishing quantum physics in Göttingen. I analyze the ways in which his influence was decisive by comparison with Woldemar Voigt (1850-1919). Voigt was the leading Göttingen theoretical physicist before the arrival of Peter Debye (1884-1966), who was appointed to a new professorship in 1914 at Hilbert's instigation. I portray the Göttingen mathematicians, above all Hermann Minkowski (1864-1909) and David Hilbert, as planting the seeds for the blossoming of quantum physics under their student Max Born (1882-1970) in the 1920s.     

10-GHz Optical Comb in L-Band Region With Brillouin/Erbium-Doped Fibre Laser

A multiwavelength Brillouin/erbium fibre laser (BEFL) which operates in the long wavelength (L-band) region is demonstrated for potential applications in an L-band wavelength division multiplexing (WDM) communication system. The laser configuration consists of a long erbium-doped fibre to enable L-band amplification where two 3-dB couplers take a portion of the generated BEFL signal and re-inject it into the single mode fibre to seed a cascaded BEFL line in the same direction as the first BEFL line. A stable and strong laser comb of up to five lines with 10-GHz spacing has been obtained with a Brillouin pump (BP) of 9.2 mW and a 980 nm pump of 92 mW. The BEFL has shown a broad tuning range with a tuning characteristic for line #1 which is flat over a range greater than 9.9 nm.     

Wiener path integrals and the fundamental solution for the Heisenberg Laplacian

In this paper, we present an explicit calculation of the heat kernel, fundamental solution and Schwartz kernel of the resolvent for the Heisenberg Laplacian using Wiener path integrals and their realizations via the Trotter product formula. This also gives another derivation of mehler’s formula.     

Experimental 511 W Composite Nd：YAG Ceramic Laser

We demonstrate a 511 W laser diode pumped composite Nd：YAG ceramic laser. The optical pumping system is consisted of five laser diode stacked arrays arranged in a pentagonal shape around the ceramic rod whose size is φ6.35×144mm. When the pumping power is 1600 W, the cw laser output up to 511 W at 1064nm can be obtained with a linear piano-piano cavity, and the optical-to-optical efficiency is 31.9%. To our knowledge, this is the highest value of laser output by using a newly invented composite Nd：YAG ceramic rod as the gain medium.     

A modified Silver–Meal heuristic for dynamic lot sizing under incremental quantity discounts

This note presents a variation of the well-known Silver–Meal heuristic to deal with lot sizing under a combination of a known, but time-varying, demand pattern along with an incremental quantity discount structure. The heuristic is shown to perform very well on a set of experiments presented in a recent paper in this journal. Additional experiments are performed to further explore the time horizon effects on the relative performance of the newly proposed heuristic compared to the two best performing ones from the previous paper.     

A Crowning Moment for Wiener Indices

The Wiener (Sum of All Distances) Index for three out of the four classes of hexagonal models or regular planar hex-patterns used to model graphite and similar structures have been known for a few years. In this paper we find the Wiener Index for the Crown or Beehive hexagonal model.