Parametric linear programming techniques for the indefnite quadratic programming problem

In this paper, we discuss a multiparametric technique for findinga global minimum for an indefinite quadratic programming problembased on the spectral decomposition of the matrix of the quadraticform. Special attention is given to the case where this matrixhas only rank 1, where the multiparametric linear program turnsout to be a single-parameter linear program. An extension ofthe traditional linear parametric procedure is introduced whichin general solves this problem efficiently. However, an exampleis presented showing that this technique may take an exponentialnumber of steps.     

Determination of Densities of Liquids and Solids Using a Gas

An experiment for the determination of densities of solids and liquids is described. It uses Archimedes Principle with air as the fluid. It can be used in general and introductory physical chemistry courses as a regular laboratory experiment or as a demonstration. A typical calibration curve and the values of some densities measured using this method are given as examples.     

On the low temperature anomalies in the properties of the electrochemical interface. A non-local free-energy density functional approach

The restricted primitive model has proved to be a useful system to describe the behaviour of electrical double layers. In this model, ions are represented by charged hard spheres of equal diameter and the solvent is represented by a uniform dielectric constant. Classical Gouy-Chapman's theory, and its modification by Stern, always predicts a monotonically decreasing capacitance for this system when the fluid's temperature is increased. Similar results are given by the mean spherical approximation. These predictions are in qualitative agreement with experiment for dissolved electrolytes, but disagree with molten salt experiments where capacitance increases with temperature. Additionally, recent Monte Carlo (MC) simulations for this model show that at very low temperatures, the capacitance of the interface, near its point of zero charge, increases with increasing temperature for both diluted and highly concentrated salts. In this work we apply a particular model of a non-local free-energy density functional theory to study the capacitance of the electrical interface. In our calculations we considered symmetrical 1:1 systems for both diluted electrolytes and highly concentrated salts at very low electrode surface charge. Density functional theory agrees very well with MC results for capacitance at high temperature, but fails to predict a positive slope for this property at low temperatures. Comparison of theoretical density profiles with MC results allows the exploration of possible causes of failure.     

The pseudo-Jahn—Teller effect: a CASSCF diagnostic

A simple test for the pseudo-Jahn-Teller effect is proposed, based on the behaviour of a CASSCF frequency calculation when symmetry is restricted. The test suggests that the pseudo-Jahn-Teller effect operates at the D_2h transition structure of S₀ pentalene and the D_8h transition structure of S₀ cyclooctatetraene. The D_4h transition structure of S₀ cyclooctatetraene is not subject to a pseudo-Jahn-Teller distortion according to this test. Our interpretation of the pseudo-Jahn-Teller effect differs from the conventional one based on a single-transition (CIS-like) approximation.     

Quasi diabatic CASSCF state functions

A new method to determine quasi diabatic (QD) CASSCF states is presented. The adiabatic states are subjected to a unitary transformation resulting from diagonalization of a state-selection operator. The latter is constructed from the overlap of the adiabatic states with a suitable set of reference states. The multi-state (MS) CASPT2 method is used to account for the dynamical correlation effects in an approach where the QD-CASSCF wave functions are used as reference states. The procedure is applied to avoided crossings in excited states of BeH, LiO and ozone. The advantages of the proposed formulation are discussed.     

Vapour—liquid equilibrium of the square-well fluid of variable range via a hybrid simulation approach

The equilibrium between vapour and liquid in a square-well system has been determined by a hybrid simulation approach combining chemical potentials calculated via the Gibbs ensemble Monte Carlo technique with pressures calculated by the standard NVT Monte Carlo method. The phase equilibrium was determined from the thermodynamic conditions of equality of pressure and chemical potential between the two phases. The results of this hybrid approach were tested by independent NPT and μPT calculations and are shown to be of much higher accuracy than those of conventional GEMC simulations. The coexistence curves, vapour pressures and critical points were determined for SW systems of interaction ranges λ = 1.25, 1.5, 1.75 and 2. The new results show a systematic dependence on the range λ, in agreement with results from perturbation theory where previous work had shown more erratic behaviour.     

THE EFFECTS OF REDUCING MATING LIKELIHOOD ON POPULATION VIABILITY

Abstract The success a species may have invading a patch previously unoccupied is of considerable interest for pest managers and conservation ecologists. The purpose here is to present a mechanistic approach to analyze reproductive Allee effects appearing through the failure in the process of fertilization in a two‐sex population and observe how the survival in an invaded patch is affected. This is in contrast to the usually employed stochastic models with a deterministic skeleton that describe the presence of Allee effects. A Poisson–Ricker model, which includes stochastic demography and sex determination with females classified as successfully fertilized or not fertilized, is used. Numerical approximations to the probabilities of extinction and the mean time to extinction are presented, for fixed parameter values, suggesting how stochasticity in the mating process combined with random fluctuations in the male and female densities, at each generation, contribute to the risk of extinction of a population which started an invasion at a low density.     

An Ergodic Control Problem for Reflected Diffusion with Jump

The control of the drift of a stochastic differential equationwith jump term is considered for the long-run average cost.The convergence of the discounted problem is studied, as wellas the corresponding dynamic programming condition. This research was supported in part by U.S. Army Research Officeunder contract DAAG29-83-K-0014 and completed during a visitto INRIA.     

DEVELOPMENT AND EVALUATION OF A SYSTEM DYNAMICS MODEL FOR INVESTIGATING AGRICULTURALLY DRIVEN LAND TRANSFORMATION IN THE NORTH CENTRAL UNITED STATES

Land transformation from grassland to cropland in the Northern Great Plains (NGP) has become a growing concern among many stakeholders. A growing body of work has sought to determine the amount and rate of land use change with less emphasis on the systemic structures or feedback processes of land use decisions. This paper presents the development of a system dynamics simulation model to integrate ecological, economic, and social components influencing land use decisions, including cattle ranching, cropland production, rural communities, land quality, and public policies. Evaluation indicated that the model satisfactorily predicted historical land, agricultural commodity, and rural community data from the model structure. Reference modes for key variables, including the farmland area, were characterized by a bias correction of 0.999, root mean squared error of prediction of 0.053, R² of 0.921, and concordance correlation coefficient of 0.0959. The model was robust under extreme and varying sensitivity tests, as well as adequately predicting land use under changing system context. The model's major contributions were the inclusion of decision‐making feedbacks from economic and social signals with connectivity to land quality and elasticity values that drive land transformation. Limitations include lack of spatial input and output capabilities useful for visual interfacing.