Mixed Integer Linear Programming in Process Scheduling: Modeling,Algorithms, and Applications

This paper reviews the advances of mixed-integer linear programming (MILP) based approaches for the scheduling of chemical processing systems. We focus on the short-term scheduling of general network represented processes. First, the various mathematical models that have been proposed in the literature are classified mainly based on the time representation. Discrete-time and continuous-time models are presented along with their strengths and limitations. Several classes of approaches for improving the computational efficiency in the solution of MILP problems are discussed. Furthermore, a summary of computational experiences and applications is provided. The paper concludes with perspectives on future research directions for MILP based process scheduling technologies.     

An updated search of steady TeV γ-ray point sources in northern hemisphere using the Tibet air shower array

Using the data taken from Tibet Ⅱ High Density (HD) Array (1997 February--1999 September) and Tibet-Ⅲ array (1999 November--2005 November), our previous northern sky survey for TeV γ-ray point sources has now been updated by a factor of 2.8 improved statistics. From 0.0° to 60.0° in declination (Dec) range, no new TeV γ-ray point sources with sufficiently high significance were identified while the well-known Crab Nebula and Mrk421 remain to be the brightest TeV T-ray sources within the field of view of the Tibet air shower array. Based on the currently available data and at the 90% confidence level (C.L.), the flux upper limits for different power law index assumption are re-derived, which are approximately improved by 1.7 times as compared with our previous reported limits.     

A Double Infinity of Oscillator Massless Boson Resonances

In the simplest coupling of a harmonic oscillator with a massless boson field, we show that a family of coupling functions leads to resonances or bound-states of the form E _{n1 n0}()=n ₁ z ₁()+n ₀ z ₀(), where z ₁(), z ₀() are in and n ₁, n ₀ are any nonnegative integers. This holds for arbitrary values of the coupling constant.     

Periodic problems and problems with discontinuities for nonlinear parabolic equations

In this paper we study nonlinear parabolic equations using the method of upper and lower solutions. Using truncation and penalization techniques and results from the theory of operators of monotone type, we prove the existence of a periodic solution between an upper and a lower solution. Then with some monotonicity conditions we prove the existence of extremal solutions in the order interval defined by an upper and a lower solution. Finally we consider problems with discontinuities and we show that their solution set is a compact R -set in (CT, L ²(Z)).     

Existence of solutions for first order singular problems

We develop the lower and upper solutions method for first order initial value problems as well as for first order periodic problems in case the nonlinearity presents singularities. More precisely we prove that if we have a lower solution and an upper solution of these problems, which are not necessarily continuous nor ordered, we have a solution wedged between and .

     

Spectrum of Light Reflection From a Quasiperiodic Structure of a Dielectric

In the present work, we show that for quasiperiodic gratings that are described by definite functions it is possible to substantially decrease the amplitude of side peaks in the spectral dependence of the reflection factor. The results of numerical integration of a system of differential equations that describe the propagation of waves in a quasiperiodic medium indicate that with an increase in the number of first derivatives of the functions that have zero values on the grating edges the attenuation of the side peaks increases. Analysis of the spectral dependence of the reflection factor for certain functions is carried out.     

Search for GUT magnetic monopoles and nuclearites with the MACRO experiment

We present the final results obtained by the MACRO experiment in the search for GUT magnetic monopoles and nuclearites. Several searches were performed with different subdetectors, i.e. scintillation counters, limited streamer tubes and nuclear track detectors. No magnetic monopole or nuclearite candidates were found. The MACRO upper limit to the local flux of GUT magnetic monopoles is at the level of 1.4×10⁻¹⁶ cm⁻² s⁻¹ sr⁻¹.     

The admissibility of the empirical mean location for the matrix von Mises–Fisher family

In this note we consider von Mises–Fisher families of probability densities on spheres and more generally on Stiefel manifolds, which include the orthogonal groups. It addresses the estimation of the mean direction or the mean location by empirical mean location, which for the von Mises–Fisher family coincides with the maximum likelihood estimator. It is shown that (with a few exceptions) the empirical mean location of a sample is almost surely uniquely defined and that it is unbiased in the sense that its mean location coincides with the mean location of the von Mises–Fisher distribution. The main goal, however, is to show that empirical mean location is an admissible estimator for the mean location of the von Mises–Fisher distribution.     

Approximations for multivariate U-statistics

Edgeworth approximations for multivariate U-statistics hold up to the order o(n^−1/2) under moment conditions and the assumption that the projection of the U-statistic to sums of i.i.d. random vectors is strongly nonlattice.