The auction algorithm for the transportation problem

The auction algorithm is a parallel relaxation method for solving the classical assignment problem. It resembles a competitive bidding process whereby unassigned persons bid simultaneously for objects, thereby raising their prices. Once all bids are in, objects are awarded to the highest bidder. This paper generalizes the auction algorithm to solve linear transportation problems. The idea is to convert the transportation problem into an assignment problem, and then to modify the auction algorithm to exploit the special structure of this problem. Computational results show that this modified version of the auction algorithm is very efficient for certain types of transportation problems.     

Fiberings with Fiber RP（κ）

Let κ be non-negative integer. The unoriented bordism classes, which can be represented as [RP（ξ^κ）] where ξ^κ is a k-plane bundle, form an ideal of the unoriented bordism ring MO.. A group of generators of this ideal expressed by a base of MO. and a necessary and sufficient condition for a bordism class to belong to this ideal are given.     

Representations of Positive Projections II

In this paper we obtain a number of Maharam-type slice integral representations, with respect to scalar measures, for positive projections in Dedekind complete vector lattices and f-algebras. AMS Classification: 47B65, 46A40, 06F25     

Propriétés statistiques des entiers friables

Let Ψ(x,y) (resp. Ψ_m(x,y)) denote the number of integers not exceeding x that are y-friable, i.e. have no prime factor exceeding y (resp. and are coprime to m). Evaluating the ratio Ψ_m(x/d,y)/Ψ(x,y) for 1≤slantd≤slantx, m≥slant 1, x≥slant y≥slant 2, turns out to be a crucial step for estimating arithmetic sums over friable integers. Here, it is crucial to obtain formulae with a very wide range of validity. In this paper, several uniform estimates are provided for the aforementioned ratio, which supersede all previously known results. Applications are given to averages of various arithmetic functions over friable integers which in turn improve corresponding results from the literature. The technique employed rests mainly on the saddle-point method, which is an efficient and specific tool for the required design.2000 Mathematics Subject Classification: Primary—11N25; Secondary—11K65, 11N37     

Avalanche multiplication in a compact bipolar transistor model forcircuit simulation

A simple weak avalanche model valid in a wide range of voltages and currents, is presented. The proposed model is derived by using the base-collector depletion capacitance for predicting the avalanche current. The model needs only one additional transistor parameter; the extraction method and temperature dependence of this parameter are discussed. The decrease in avalanche current for high collector current densities may originate from internal device heating, a voltage drop in the epilayer, or mobile carriers in the depleted part. From experimental results it is concluded that, below a critical hot-carrier current, the decrease in avalanche current due to mobile carriers is negligible     

Séries trigonométriques à coefficients arithmétiques

Journal d'Analyse Mathématique -     

The preparation of 2-iodoamides from glucals and their further transformations into oxazolines

2-Deoxy-2-iodo-glycosylamides have been prepared from a variety of protected d-glucals by their reaction with N-iodosuccinimide and amides. Benzyl protected 2-iodoamides, when treated with sodium hydride and 15-crown-5, gave stable C1 N-linked 2-glycooxazolines as the major products. Silyl protected 2-iodoamides afforded the C1 O-linked 2-glycooxazolines; presumably by the rearrangement of unstable N-acylaziridine intermediates.     

Evaluation of Digitally Encoded Layer‐by‐layer Coated Microparticles as Cell Carriers

To obtain more biologically relevant data there is a growing interest in the use of living cells for assaying the biological activity of unknown chemical compounds. Density ‘multiplex’ cell‐based assays, where different cell types are mixed in one well and simultaneously investigated upon exposure to a certain compound are beginning to emerge. To be able to identify the cells they should be attached to microscopic carriers that are encoded. This paper investigates how digitally encoded microparticles can be loaded with cells while keeping the digital code in the microcarriers readable. It turns out that coating the surface of the encoded microcarriers with polyelectrolytes using the layer‐by‐layer (LbL) approach provides the microcarriers with a ‘highly functional’ surface. The polyelectrolyte layer allows the growth of the cells, allows the orientation of the cell loaded microcarriers in a magnetic field, and does not hamper the reading of the code. It has further been shown that the cells growing on the polyelectrolyte layer can become transduced by adenoviral particles hosted by the polyelectrolyte layer. It is concluded that the digitally encoded microparticles are promising materials for use in biomedical and pharmaceutical in‐vitro research where cells are used as tools.     

From Long Infrared to Very Long Infrared Wavelength Focal Plane Arrays Made with HgCdTe n + n ?/ p Ion Implantation Technology

This paper aims at studying the feasibility of very long infrared wavelength (VLWIR) (12–18 μm) focal plane arrays using n-on-p planar ion-implanted technology. To explore and analyze the feasibility of such VLWIR detectors, a set of four Cd _x Hg_1−x Te LPE layers with an 18 μ cutoff at 50 K has been processed at Defir (LETI/LIR–Sofradir joint laboratory), using both our “standard” n-on-p process and our improved low dark current process. Several 320 × 256 arrays, 30-μm pitch, have been hybridized on standard Sofradir readout circuits and tested. Small dimension test arrays characterization is also presented. Measured photonic currents with a 20°C black body suggest an internal quantum efficiency above 50%. Typical I(V) curves and thermal evolution of the saturation current are discussed, showing that standard photodiodes remain diffusion limited at low biases for temperatures down to 30 K. Moreover, the dark current gain brought by the improved process is clearly visible for temperatures higher than 40 K. Noise measurements are also discussed showing that a very large majority of detectors appeared background limited under usual illumination and biases. In our opinion, such results demonstrate the feasibility of high-performance complex focal plane arrays in the VLWIR range at medium term.