The assignment of credit limits with a behaviour-scoring system

Received on 1 July 1991. Behaviour-scoring systems for authorizations enable the riskof a customer defaulting to be quantified. These risks mustbe incorporated into a credit strategy which assigns creditlimits and makes authorization decisions in the most effectivemanner. This paper introduces the concept of marginal risk whichhas proved a useful tool in defining credit limit strategiesfor a mail-order company. Behaviour scores for authorizations are similar to credit applicationscores in that they predict the overall risk of a customer defaulting.If a cut-off risk can be established, then the optimal strategywould appear to be to withhold credit for customers exceedingthis risk and to grant unlimited credit for the remainder (thisis analogous to application strategies). The notion of grantingunlimited credit is often commercially unacceptable (particularlyif customers are to be informed of their credit limits!) andso strategies which give all or nothing are of limited valueand need further refinement. In order to overcome this problem, the concept of marginal riskhas been devised. The marginal risk is the risk of the ‘last£’ of an account being defaulted. This reflectsthe fact that small-balance customers may well pay off theircurrent balance only to default on larger subsequent purchases.Although the overall risk of customers with a given behaviourscore defaulting is relatively constant, their marginal riskwill vary according to their outstanding balance. This paperexplores the relationships between marginal risk and overallrisk and between marginal risk and outstanding balance. A modelwhich summarizes these relationships is proposed, and contoursof equal marginal risk are built on the basis of this model.These contours provide strategies for allocating credit limitswhich are both practical and optimal for a well formulated cut-offrisk and which suggest that the probability of defaulting isnot the best criterion for allocating credit limits. The results of the application of this approach will be demonstrated.Some of the problems that have been overcome are discussed,as are some of the outstanding problems.     

Quantum-chemical gas-phase calculations on the protonation forms oftrans- andcis-urocanic acid

The neutral, cationic, and anionic structures of both prototropic tautomers oftrans- andcis-urocanic acid [(E)- and (Z)-3-(1H-imidazol-4(5)-yl)propenoic acid, respectively] were studied by using semiempirical andab initio gas-phase calculations. Potential energy surfaces of the structures were calculated by using the semiempirical AM1 method, and the geometries corresponding to global minima on these surfaces were optimized up to the MP2/6-31G^* level of theory. The calculated protonation forms of each urocanic acid isomer have a planar molecular structure due to a delocalized -electron system, and all of them prefer thes-trans conformation with respect to the bond between the imidazole and the propenoic acid moieties. Thecis-urocanic acid structures are stabilized by an intramolecular hydrogen bond. The chargedcis-urocanic acid isomers have a lower molecular energy than the correspondingtrans-isomers, whereas the neutral molecules have, after inclusion of thermodynamic corrections, approximately the same energy. The cationic urocanic acid structures have about 2500 kJ mol^–1 lower energy than the anionic ones and about 1000 kJ mol^–1 lower energy than the neutral ones. The nonzwitterionic forms of the neutral urocanic acid isomers have about 200 kJ mol^–1 lower energy than the zwitterionic ones. These energy differences are explained by the proton affinities of the imidazole and the propenoic acid moieties of the urocanic acid structures.     

Zur Theorie der dielektrischen Relaxation der amorphen Polymeren

Zusammenfassung In der Arbeit wird im Rahmen der theoretischen Deutung der dielektrischen Eigenschaften der amorphen Polymeren ein einfaches Modell diskutiert, das erstmalig auf zwei Relaxationsgebiete führt. Die berechneten Relaxationsspektren sind zwar gegenüber den experimentellen Gr?\en noch zu schmal, in bezug auf das Frequenz- und Intensit?tsverh?ltnis der beiden Relaxationsgebiete ergeben sich jedoch sinnvolle Werte. Das Modell gehorcht nicht dem Reduktionsverfahren vonTobolsky undFerry, es erm?glicht deshalb prinzipiell eine Deutung der Temperaturabh?ngigkeit des Frequenzverh?ltnisses.     

Purification and partial characterization ofRhizomucor miehei lipase for ester synthesis

A commercialRhizomucor miehei lipase was purified by ammonium sulfate precipitation. Phenyl Sepharose 6 Fast Row hydrophobic interaction chromatography, and DEAE Sepharose Fast Flow anion-exchange chromatography. The recovery of lipase activity was 32% with a 42-fold purification. The molecular size of the purified enzyme was 31,600 Dalton and the pI 3.8. The enzyme was stable for at least 24 h within a pH range of 7.0-10.0, and 96.8% of the enzyme activity remained when kept at 30‡C for 24 h. Further, about 10–30% of the lipase activity was inhibited by K⁺, Li⁺, Ni⁺, Co²⁺, Zn²⁺, Mg²⁺, Sn²⁺, Cu²⁺, Ba²⁺, Ca²⁺, and Fe²⁺ ions and by SDS, but EDTA had no effect. Under the experimental conditions, the optimum temperature for the hydrolysis of olive oil was 50‡C (pH 8.0), and for the synthesis of 1-butyl oleate, 37‡C. It was concluded that hydrolytic activity of lipase alone is not a sufficient criterion for its synthetic potential. The optimal molar ratio of oleic acid and 1-butanol was 2:1 for 1-butyl oleate synthesis. The 1-butyl oleate yield was unaffected by purification of the enzyme after 12 h.     

Fractal dimension,attractors, and the boussinesq approximation in three dimensions

The Boussinesq approximation, where the viscosity depends polynomially on the shear rate, finds more and more frequent use in geological practice. In the paper, this modified Boussinesq approximation is investigated as a dynamical system for which the existence of a global attractor is proved. Finally, a new criterion for estimating the fractal dimension of invariant sets is formulated and its application to the problem under consideration is illustrated.     

Alpha decay of the new isotopes207, 208Ac

Two new neutron-deficient isotopes^207,208Ac have been produced in fusion reactions with 5.2–5.6 MeV/nucleon⁴⁰Ar ions on¹⁷⁵Lu and identified on the basis of genetic correlations. The fusion evaporation products were separated on-line using a gas-filled magnetic recoil separator. The alpha energy and half-life of²⁰⁸Ac were determined to be (7572±15) keV and (95 _?16 ⁺²⁴ ) ms, respectively. A new alpha line with a half-life of (25 _?5 ⁺⁹ ) ms and an energy of (7758±20) keV is assigned to the decay of an isomeric state in²⁰⁸Ac. Another new activity with a half-life of (22 _?9 ⁺⁴⁰ ) ms and an alpha energy of (7712±25) keV is assigned to²⁰⁷Ac.     

ABSENCE OF OXYGEN-EVOLVING CAPACITY IN DARK-GROWN CHLORELLA: THE PHOTO ACTIVATION OF OXYGEN-EVOLVING CENTERS*

Abstract— Chlorella cells were cultured in darkness on glucose and examined for pigment composition, capacity to evolve oxygen, and capacity to photo-oxidize artificial electron donors to Photosystems II and I. Evidence was obtained which indicated that such cells lack oxygen-evolving centers and the Mn pool associated with such centers but possess fully active System II and I trapping centers. Brief illumination ( t _1/2˜ 2–3 min) of dark-grown cells resulted in incorporation of Mn into the O₂-evolving centers and the capacity to evolve O₂ (photo-activation). Kinetic data from flashing or continuous light showed that the photoactivation is a multi-quantum process involving several rate limitations and a photosensitive state of limited stability. Measurements of oxygen-yield oscillations indicated that throughout the photoactivation process each newly formed oxygen-yielding center was independent of its neighbors. It is concluded that photoactivation of the Mn-containing oxygen-yielding catalyst is a fundamental process in all photosynthetic oxygen-evolving tissue.