A Type Calculus for Executable Modelling Languages

There is considerable current interest in the design and constructionof directly executable modelling languages for mathematicalprogramming. The present research extends contemporary modellinglanguages by specifying a type calculus for an extended dimensionalsystem that determines if the model is well formed in the sensethat the objective function and constraints consist of homogeneouscomponents. Each variable, coefficient, constant, function,constraint, input, and output of the model is assigned a typethat consists of its concepts, quantities, and units of measurementwith optional scale factors. In checking the composition offunctions and constraints, the system can do automatic unitconversions and apply user-supplied conversions. The systemallows a hierarchy of concepts that provides inheritance ofquantities and automatic concept conversion. In addition, eachset in a model is typed so the system can check the validityof operations on indices.     

An Essay Assignment for Organic Chemistry Courses

An essay assignment suitable for large introductory organic chemistry courses is described. Students were asked to write four-to five-page essays about any organic compound of their choosing that was in the news recently, was used widely, or had some social significance. The assignment was designed to stimulate student interest in the role of organic chemistry in their lives, to help them make connections between classroom information and the real world, to have them practice their writing skills, to teach them to use the library and other sources of scientific information, and to help them improve their grades by evaluating them with an instrument other than an exam. Techniques used by the instructor to manage the burden of grading a large number of essays are described.     

The flat-maximum effect and generic linear scoring models: a test

Received on 1 July 1991. Predicting human behaviour patterns with linear correlationmodels has absorbed researchers for the past five decades. Althoughmost observers generally concede that humans are inferior tosuch models in combining information, linear scoring modelsare unfortunately, plagued by the flat-maximum effect or the‘curse of insensitivity’. As Lovie & Lovie(1986)observe: ‘The predictive ability of linear models is insensitiveto large variations in the size of regression weights and tothe number of predictors.’ In essence, seemingly differentscoringmodels tend to produce indistinguishable predictive outcomes. Since its demonstration by Dawes & Corrigan (1974), observershave cast the flat maximum in a decidedly negative light. Incontrast, Lovie & Lovie (1986) present a provocatively contrarianview of the flat maximum‘s positive potential. In thissame vein, we examine the predictive power of a generic credit-scoringmodel versus individual empirically derived systems. If, asWainer (1976) noted in regard to the flat maximum, ’itdon‘t make no nevermind’, generic credit-scoringmodels could provide cheaper alternatives to individual empiricallyderived models. During the period 1984–8, a series of linear credit-scoringmodels were developed for ten Southeastern U.S. credit unions.For each credit union, stepwise multiple regression was employedto select a subset of explanatory variables to be used in adiscriminant analysis. A generic credit-scoring equation wasdeveloped from the resulting discriminant analyses using weightedaverage coefficients from five systems. The predictive powerof the generic model was compared to the predictive power ofholdout sample of the five remaining credit-scoring models. In all cases, the generic model's performance was very closeto that of the empirically derived models. Thus, our findingssupport Lovie & Lovie's (1986) challenge to the conventionalwisdom that the flat maximum casts a pall on the successfulmodelling of judgement processes. Indeed, the flat maximum impliesa positive role for simpler, and hence cheaper, generic models.Although further research is needed, it should be possible todevelop hybrid models with generic cores that perform as wellas empirically derived linear models.     

Electrostatic interactions between molecules from relaxed one-electron density matrices of the coupled cluster singles and doubles model

The influence of electron correlation on the electrostatic interaction between closed shell molecules is studied using the relaxed electron densities of the coupled cluster singles and doubles (CCSD) model. The corresponding CCSD one-electron density matrices are efficiently computed without full four-index transformation by employing the generalized exchange and Coulomb operator technique. Using several representative van der Waals and hydrogen bonded complexes it was found that in most cases the convergence of the M?ller-Plesset expansion of the electrostatic energy, restricted to single, double and quadruple excitations, is satisfactory and the fourth-order triple excitation term is more important than the sum of the fifth- and higher-order contributions from CCSD theory. The importance of the CCSD correlation correction to the electrostatic energy was gauged by comparison of the total interaction energy computed by symmetry-adapted perturbation theory (SAPT) and by the super-molecular CCSD(T) approach (coupled cluster singles and doubles model with a non-iterative inclusion of triple excitations). Except for the CO and N₂ dimers, very good agreement between the two sets of results is observed. For the difficult case of the CO dimer the difference between the SAPT and CCSD(T) results can be explained by the truncation of the SAPT expansion for the dispersion energy at second order in the intramonomer correlation operator.     

Adiabatic-diabatic transformations for molecular systems: a model study of two interacting conical intersections

A model is presented for studying the interaction between two conical intersections (e.g. a dimer of two bound molecules each characterized by a conical intersection). The model is an extension of a previous model for a single conical intersection formed by an electron housed in a vibrating molecule (Baer, M. and Englman, R., 1992, Molec. Phys., 75, 293). We distinguish between two situations: when the coupling is weak (for instance when it takes place in the asymptotic region) and when it is strong. The study is accomplished by calculating the adiabatic—diabatic transformation (ADT) matrix. Whereas the features of the ADT matrix for weak coupling seem reasonable (and to a certain extent expected), we find some unexpected features in the case of strong coupling. In particular, the two characteristic ADT angles of the uncoupled systems namely (?_1/2) and (?_2/2) are replaced by two new ADT angles, namely, (?₁ + ?₂)/2 and (?₁—?₂)/2. This implies that the corresponding nuclear wavefunctions, which originally were multi-valued, become single-valued in cases of strong interaction.     

Rotational spectrum,structure and internal motions of the ethylene-OCS weakly bound dimer

The rotational spectra of five isotopomers of the ethylene-OCS dimer have been observed by Fourier transform microwave spectroscopy and its structure was determined. The dipole moment components and rotational constants for this complex are consistent with a stacked geometry in which the OCS lies above the ethylene molecular plane, approximately parallel to the C=C bond. Two internal motions of the monomer subunits split each rotational transition into four components. The larger tunneling splittings have been analysed to give a twofold barrier for the internal motion of the ethylene subunit about its c inertial axis of 16(3) cm^?1. The results are compared with calculations with a semi-empirical model employing electrostatic, dispersion and repulsion interactions.     

Long-lived diatomic dications: potential curves and radiative lifetimes for CaBr2+ and CaI2+ including relativistic effects

Relativistic effective core potential calculations have been employed in the framework of a spin–orbit configuration interaction to compute the lowest-lying electronic states of the CaBr²⁺ and CaI²⁺ dications, and the results are compared with the data for the isovalent CaCl²⁺ system studied earlier. The ground X²Π state in all three dications arises from a strong polarization of X(²P°)(X= Cl, Br or I) by the Ca²⁺(¹S) ion and is bound by 0·96–1·55eV with respect to the corresponding diabatic dissociation limits. It is split by the spinorbit interaction into the X₁ ²Π_3/2 and X₂ ²Π_1/2 components, with the energy splittings calculated to be 647 cm^-1(CaCl²⁺), 2115 cm^-1(CaBr²⁺) and 3544 cm^-1(CaI²⁺). The X₁ and X₂ states are found to be thermodynamically stable in CaCl²⁺ and CaBr²⁺, while in CaI²⁺ the lowest dissociation limit, Ca⁺+(²S)+ I^{+ 3}P₂), lies 1700 and 5200 cm^-1 lower than the X₁ and X₂ minima respectively. The X₁ and X₂ states in CaI²⁺ are extremely long-lived, however, owing to the high and very broad potential barriers to dissociation. The first electronic excited state, A²σ⁺, is also bound in all the above systems, although it is pre-dissociated in CaBr²⁺and CaI²⁺ at large internuclear distances. All other low-lying electronic states of CaX²⁺ are repulsive. Electric-dipole moments are calculated for the A→ X₁, X₂ transitions. The corresponding radiative lifetimes are found to be very long in CaCl²⁺ : τ(A→X₁) = 19·3 ms and τ(A→X₂) = 9·9 ms (the values are given for ν' = 0), and become very significantly shorter for CaBr²⁺ and CaI²⁺ because of the stronger spin-orbit interaction in the heavier systems. This effect is especially noticeable for the A →X₂ transitions, for which the values are computed to be 364 μs in CaBr²⁺ and 50·3 μs in CaI²⁺. The theoretical data obtained should aid in the future spectroscopic detection of these species. To data no experiment of this type has been successfully carried out for any of the thermodynamically stable diatomic dications.     

DYNAMICS OF AN AGE‐STRUCTURED METAPOPULATION MODEL

ABSTRACT. We introduce a metapopulation model that includes both landscape changes (patch destruction and recreation) and age‐dependent metapopulation dynamics. A threshold quantity is derived and related to the existence of an ecologically nontrivial equilibrium, to the stability of the species‐free equilibrium, and to weak and strong persistence of the species. We provide examples to illustrate how age‐related changes in patch colonization and extinction rates can alter metapopulation persistence. Future field studies may need to address the temporal dynamics that characterize local populations in fragmented landscapes.