A RANDOM FIXED POINT ITERATION FOR THREE RANDOM OPERATORS ON UNIFORMLY CONVEX BANACH SPACES

In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extersion of a known theorem in the corresponding non-random case.     

Synchronization in supply chains: implications for design and management

Supply chain management literature calls for coordination between the different members of the chain. Materials should be moved from one supplier to the next according to a just-in-time schedule. In this paper, we show that for many supply chain configurations, complete synchronization will result in some members of the chain being ‘losers’ in terms of cost. We develop an algorithm for optimal synchronization of supply chains and provide some guidelines for incentive alignment along the supply chain. In developing the model, we use the economic delivery and scheduling problem model and analyze supply chains dealing with single and multiple components. For single-component supply chains, we derive a closed-form expression for the optimal synchronized cycle time. For multi-component supply chains, we develop an algorithm for finding the optimal synchronized cycle time. We test the performance of the algorithm and show that it provides optimal solutions for a wide range of problems. We illustrate the models with numerical examples.     

Lower Bounds for the Height and Size of the Ideal Class Group in CM-Fields

 We prove that, under the assumption of the Generalized Riemann Hypothesis, the exponent of the ideal class group of a CM-field goes to infinity with its absolute discriminant. This gives a positive answer to a question raised by Louboutin and Okazaki [4]. Received September 10, 2001; in revised form April 5, 2002     

Cesàro means of double Walsh-Fourier series

We investigate approximation properties of Cesàro (C; −α, −β)-means of double Walsh-Fourier series with α, β ∈ (0, 1). As an application, we obtain a sufficient condition for the convergence of the means σ _n,m ^/−α,−β (f; x, y) to f(x,y) in the L ^p -metric, p ∈ [1, ∞]. We also show that this sufficient condition cannot be improved.     

A Branch & Cut algorithm for a four-index assignment problem

In this paper, we examine the orthogonal Latin squares (OLS) problem from an integer programming perspective. The OLS problem has a long history and its significance arises from both theoretical aspects and practical applications. The problem is formulated as a four-index assignment problem whose solutions correspond to OLS. This relationship is exploited by various routines (preliminary variable fixing, branching, etc) of the Branch & Cut algorithm we present. Clique, odd-hole and antiweb inequalities implement the ‘Cut’ component of the algorithm. For each cut type a polynomial-time separation algorithm is implemented. Extensive computational analysis examines multiple aspects concerning the design of our algorithm. The results illustrate clearly the improvement achieved over simple Branch & Bound.     

Parallel discrete event simulation algorithm for manufacturing supply chains

Parallel discrete event simulation (PDES) is concerned with the distributed execution of large-scale system models on multiple processors. It is an enabler in the implementation of the virtual enterprise concept, integrating semi-autonomous models of production cells, factories, or units of a supply chain. The key issue in PDES is to maintain causality relationships between system events, while maximizing parallelism in their execution. Events can be executed conservatively only when it is safe to do so, sacrificing the extent to which potential parallelism of the system can be exploited. Alternatively, they can be processed optimistically without guarantee of correctness, but incurring the overhead of a rollback to an earlier saved state when causality error is detected. The paper proposes a modified optimistic scheme for distributed simulation of constituent models of a supply chain in manufacturing, which exploits the inherent operating characteristics of its domain.     

Structure and reflective properties of Al-Cu-Fe quasicrystalline thin film prepared by laser induced arc method

Al-Cu-Fe thin films were prepared by laser induced arc (laser-arc) method from a single source—Al₆₃Cu₂₅Fe₁₂ alloy, which was proved to consist of quasicrystalline phase together with approximant phase. The composition of the deposited films meets the requirement for formation of icosahedral symmetry phase. Quasicrystalline phase was obtained after annealing the amorphous as-deposit film samples. The optical properties of the samples were investigated. Thin film samples of Al, Cu and Fe deposited under the same condition were employed for comparison. The results showed specific reflective properties of Al-Cu-Fe quasicrystal thin film in some wavelength range. The optical conductivity of the films exhibited a negative peak, centered about 440 nm in range of 190 to 800 nm. The Al-Cu-Fe quasicrystal thin films could absorb almost all the ray in the wavelength range from 420nm to 450 nm. The ratio of absorption was greater than 99%.     

Noncollinear optical parametric amplification in lithium triborate seeded by a cw Ti:sapphire laser

Experimental investigations of a type-I noncollinear phase-matched optical parametric amplification based on lithium triborate, which was pumped by a 5-ns second-harmonic pulses from a Q-switched Nd:YAG, seeded by a cw Ti:sapphire laser at 800 nm, was presented. The experiments generated 2-ns signal output pulses at 800 nm, the maximum signal output pulse energy reached 19 μJ, the corresponding parametric gain was 44 dB. Furthermore, the experiments demonstrate that the 65 nm-FWHM parametric fluorescence gain spectrum could also be observed. A quantitative account of the ultrabroadband parametric fluorescence gain spectrum was given with our theory. The experimental measurements are in agreement with theoretical calculations.     

<Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript> linear interpolator for missing values in time series

We propose a minimum mean absolute error linear interpolator (MMAELI), based on theL ₁ approach. A linear functional of the observed time series due to non-normal innovations is derived. The solution equation for the coefficients of this linear functional is established in terms of the innovation series. It is found that information implied in the innovation series is useful for the interpolation of missing values. The MMAELIs of the AR(1) model with innovations following mixed normal andt distributions are studied in detail. The MMAELI also approximates the minimum mean squared error linear interpolator (MMSELI) well in mean squared error but outperforms the MMSELI in mean absolute error. An application to a real series is presented. Extensions to the general ARMA model and other time series models are discussed. This research was supported by a CityU Research Grant and Natural Science Foundation of China.