Demand variability and incentives in inventory-based contracts

We present some results on the impact of demand variability on stocking policies and incentives to forecast, in the context of single period inventory-based contracts in a manufacturer-retailer channel.     

Minimizing makespan on a single machine subject to random breakdowns

We investigate optimal sequencing policies for the expected makespan problem with an unreliable machine, where jobs have to be reprocessed in their entirety if preemptions occur because of breakdowns. We identify a class of uptime distributions under which LPT minimizes expected makespan.     

Nonnegative curvature and cobordism type

We show that in each dimension n = 4k, k≥ 2, there exist infinite sequences of closed simply connected Riemannian n-manifolds with nonnegative sectional curvature and mutually distinct oriented cobordism type. W. Tuschmann’s research was supported in part by a DFG Heisenberg Fellowship.     

Polyadic codes of prime power length

Polyadic codes constitute a special class of cyclic codes and are generalizations of quadratic residue codes, duadic codes, triadic codes, m-adic residue codes and split group codes, which have good error-correcting properties. In this paper, we give necessary and sufficient conditions for the existence of polyadic codes of prime power length. Examples of some good codes arising from the family of polyadic codes of prime power length are also given.     

Solving large-scale semidefinite programs in parallel

We describe an approach to the parallel and distributed solution of large-scale, block structured semidefinite programs using the spectral bundle method. Various elements of this approach (such as data distribution, an implicitly restarted Lanczos method tailored to handle block diagonal structure, a mixed polyhedral-semidefinite subdifferential model, and other aspects related to parallelism) are combined in an implementation called LAMBDA, which delivers faster solution times than previously possible, and acceptable parallel scalability on sufficiently large problems. This work was supported in part by NSF grants DMS-0215373 and DMS-0238008.     

Robust locally testable codes and products of codes

We continue the investigation of locally testable codes, i.e., error‐correcting codes for which membership of a given word in the code can be tested probabilistically by examining it in very few locations. We give two general results on local testability: First, motivated by the recently proposed notion of robust probabilistically checkable proofs, we introduce the notion of robust local testability of codes. We relate this notion to a product of codes introduced by Tanner and show a very simple composition lemma for this notion. Next, we show that codes built by tensor products can be tested robustly and somewhat locally by applying a variant of a test and proof technique introduced by Raz and Safra in the context of testing low‐degree multivariate polynomials (which are a special case of tensor codes). Combining these two results gives us a generic construction of codes of inverse polynomial rate that are testable with poly‐logarithmically many queries. We note that these locally testable tensor codes can be obtained from any linear error correcting code with good distance. Previous results on local testability, albeit much stronger quantitatively, rely heavily on algebraic properties of the underlying codes. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

Photonic crystals--a step towards integrated circuits for photonics.

The field of photonic crystals has, over the past few years, received dramatically increased attention. Photonic crystals are artificially engineered structures that exhibit a periodic variation in one, two, or three dimensions of the dielectric constant, with a period of the order of the pertinent light wavelength. Such structures in three dimensions should exhibit properties similar to solid-state electronic crystals, such as bandgaps, in other words wavelength regions where light cannot propagate in any direction. By introducing defects into the periodic arrangement, the photonic crystals exhibit properties analogous to those of solid-state crystals. The basic feature of a photonic bandgap was indeed experimentally demonstrated in the beginning of the 1990s, and sparked a large interest in, and in many ways revitalized, photonics research. There are several reasons for this attention. One is that photonic crystals, in their own right, offer a proliferation of challenging research tasks, involving a multitude of disciplines, such as electromagnetic theory, nanofabrication, semi-conductor technology, materials science, biotechnology, to name a few. Another reason is given by the somewhat more down-to-earth expectations that photonics crystals will create unique opportunities for novel devices and applications, and contribute to solving some of the issues that have plagued photonics such as large physical sizes, comparatively low functionality, and high costs. Herein, we will treat some basics of photonic crystal structures and discuss the state-of-the-art in fabrication as well give some examples of devices with unique properties, due to the use of photonic crystals. We will also point out some of the problems that still remain to be solved, and give a view on where photonic crystals currently stand.     

Julia sets of permutable Holomorphic maps

Let f and g be two permutable transcendental holomorphic maps in the plane. We shall discuss the dynamical properties of f, g and f o g and prove, among other things, that if either f has no wandering domains or f is of bounded type, then the Julia sets of f and f(g) coincide. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

Tracing of interference fringes using average gray value and simultaneous row and column scan

An algorithm for computer tracing of interference fringes is reported. The method uses the average gray-level value for thresholding, row and column scans for determining the type of the scan and simultaneous row and column scan for tracing. The proposed method yield good result even for low-contrast and high-noise images. The program for the interferogram tracing was written using MATLAB6.