Extension of the Virasoro and Neveu-Schwarz Algebras and Generalized Sturm-Liouville Operators

We consider the universal central extension of the Lie algebra Vect(S ¹) C(S ¹). The coadjoint representation of thisLie algebra has a natural geometric interpretation by matrix analogues ofthe Sturm –Liouville operators. This approach leads to new Liesuperalgebras generalizing the well-known Neveu –Schwarz algebra.     

Optimal smoothing of accounting earnings

Accountants seeking to estimate the profitability of a firmvia the calculation of earnings utilize information about thenumber and current lifespan of unfinished activities by incorporatinga smoothing device—depreciation—into their calculations.This paper considers a firm in steady state, carrying out alarge number of similar activities with random starts and completiondates. By developing a stochastic model for the firm's activities,a difference equation for the minimum-variance smoothing functionis obtained. This can be solved explicitly in the case of aperiodic Poisson process of start times and independent exponentialdurations and is a variant of declining-balance depreciation.     

The statistical analysis of standard-cost deviations

Very little is known about the theoretical statistical propertiesof accounting numbers. In this papera probability modellingtechnique is used to analyse the volume, efficiency, and pricedeviation—more usually known in the accounting literatureas ‘variances’—of standard costing. Standard-costdeviations are defined asdifferences between certain types ofconditional and unconditional expected costs. The basic statisticsrequired to construct theoretical confidence intervals for thesedifferences are identified, and it is shown how the formulaenormally used in their calculation may sometimes be correlated.The modelling technique adopted is based on a theory of accountingmeasurement which interprets accounting numbers as specializedtypes of statistics. It illustrates the potential of the theoryfor the development of a better understanding of the statisticalproperties of accounting numbers.