Total Positivity Properties of Generalized Hypergeometric Functions of Matrix Argument

In multivariate statistical analysis, several authors have studied the total positivity properties of the generalized (₀ F ₁) hypergeometric function of two real symmetric matrix arguments. In this paper, we make use of zonal polynomial expansions to obtain a new proof of a result that these ₀ F ₁functions fail to satisfy certain pairwise total positivity properties; this proof extends both to arbitrary generalized ( _r F _s ) functions of two matrix arguments and to the generalized hypergeometric functions of Hermitian matrix arguments. In the case of the generalized hypergeometric functions of two Hermitian matrix arguments, we prove that these functions satisfy certain modified pairwise TP₂properties; the proofs of these results are based on Sylvester's formula for compound determinants and the condensation formula of C. L. Dodgson [Lewis Carroll] (1866).     

Reducing system of parameters and the Cohen-Macaulay property

Let R be a local ring and let (x ₁, …, x _r) be part of a system of parameters of a finitely generated R-module M, where r < dim_R M. We will show that if (y ₁, …, y _r) is part of a reducing system of parameters of M with (y ₁, …, y _r) M = (x ₁, …, x _r) M then (x ₁, …, x _r) is already reducing. Moreover, there is such a part of a reducing system of parameters of M iff for all primes P ε Supp M ∩ V _R(x ₁, …, x _r) with dim_R R/P = dim_R M − r the localization M _P of M at P is an r-dimensional Cohen-Macaulay module over R _P. Furthermore, we will show that M is a Cohen-Macaulay module iff y _d is a non zero divisor on M/(y ₁, …, y _d−1) M, where (y ₁, …, y _d) is a reducing system of parameters of M (d:= dim_R M).     

The location of median paths on grid graphs

In this paper we consider the location of a path shaped facility on a grid graph. In the literature this problem was extensively studied on particular classes of graphs as trees or series-parallel graphs. We consider here the problem of finding a path which minimizes the sum of the (shortest) distances from it to the other vertices of the grid, where the path is also subject to an additional constraint that takes the form either of the length of the path or of the cardinality. We study the complexity of these problems and we find two polynomial time algorithms for two special cases, with time complexity of O(n) and O(nℓ) respectively, where n is the number of vertices of the grid and ℓ is the cardinality of the path to be located. The literature about locating dimensional facilities distinguishes between the location of extensive facilities in continuous spaces and network facility location. We will show that the problems presented here have a close connection with continuous dimensional facility problems, so that the procedures provided can also be useful for solving some open problems of dimensional facilities location in the continuous case.     

Laser-induced breakdown of soda-lime glass microspheres using Nd:YAG laser

The Nd:YAG laser-induced breakdown of 20 μm glass microspheres was investigated using time-resolved optical shadow and Schlieren images. Time-resolved imaging showed the location of the initial breakdown and the shockwave motion over its first 400 μm of expansion. Measured shockwave velocities were in the range of 1–10 km/s and showed a linear dependency on laser fluence within 30 ns.     

Low-energy fission investigated in reactions of 750 AMeV 238U-ions on 208Pb. II: Isotopic distributions

Projectile fission of 750 AMeV ²³⁸U-ions interacting with a Pb target was studied by means of the spectrometer FRS, GSI-Darmstadt. One of the two fission fragments was detected with a transmission of few percent and identified in mass and charge. Low-energy fission (E^* < 25 MeV) events were selected by their magnetic rigidity. Whereas the production of asymmetric fission events is dominated by the GDR excitation, very asymmetric fission and symmetric fission take place after a GQR or DGDR excitation or after a nuclear interaction. Cross sections of more than 250 isotopes were measured. Isotopic distributions of low-energy fission were reconstructed for elements from Se to Te. The fission modes SI, SII and SL were clearly shown in these distributions and in the mass and TKE distributions. Charge polarization and mass dispersion were deduced for each fission mode. Finally, the characteristics of the low-energy fission process explain the production rates of neutron-rich species. Received: 14 July 1997 / Revised version: 6 October 1997     

On local optima in multiobjective combinatorial optimization problems

In this article, local optimality in multiobjective combinatorial optimization is used as a baseline for the design and analysis of two iterative improvement algorithms. Both algorithms search in a neighborhood that is defined on a collection of sets of feasible solutions and their acceptance criterion is based on outperformance relations. Proofs of the soundness and completeness of these algorithms are given.     

Moisture sorption, transport, and hydrolytic degradation in polylactide

Management of moisture penetration and hydrolytic degradation of polylactide (PLA) is extremely important during the manufacturing, shipping, storage, and end-use of PLA products. Moisture transport, crystallization, and degradation, in PLA have been measured through a variety of experimental techniques including size-exclusion chromatography, differential scanning calorimetry, and X-ray diffraction. Quartz crystal microbalance and dynamic vapor sorption experiments have also been used to measure moisture sorption isotherms in PLA films with varying crystallinity. A surprising result is that, within the accuracy of the experiments, crystalline and amorphous PLA films exhibit identical sorption isotherms.     

CONFLICT AND COOPERATION IN UTILIZING A COMMON PROPERTY RESOURCE

Noncooperative games are used to demonstrate that, while free riding is always an option, the “tragedy of the commons” is not inevitable. When the decision to cooperate or free ride is considered in a dynamic setting, there is no intermediate case where some cooperate and others free ride. The game is only stabilized in either full cooperation or full defection. The important factor in obtaining a cooperative outcome is the critical number of players that decide to cooperate. The concept of commitment is used to demonstrate the necessary and sufficient conditions for full cooperation. Although the analysis is based on a shared water resource, it can be extended to other natural resources with common costs and private benefits, especially in the cases where there are no international authorities or treaties that internalize the externalities involved in privatizing the resource.