On the Fay identity for KdV tau functions and the identity for the Wronskian of squared solutions of Sturm-Liouville equation

We show that the well known identity for the Wronskian of squared solutions of a Sturm-Liouville equation follows from the Fay identity. We also study some odd-order (($2^n -1$)-order, $n = 2, 3, ...$) identities which are specific for tau functions, related to the KdV hierarchy.Comment: Amstex, 13 page

Magnetic moments in odd-A Cd isotopes and coupling of particles with zero-point vibrations

Background: The coupling of the last nucleon with configurations in the ground state of the even-even core is known to augment the single quasiparticle fragmentation pattern. In a recent experimental study by Yordanov \emph{et al.} the values of the magnetic dipole and electric quadrupole moments of the $11/2^-$ state in a long chain of Cd isotopes were found to follow a simple trend which we try to explain by means of incorporating long-range correlations in the ground state. Purpose: Our purpose is to study the influence of the ground-state correlations (GSC) on the magnetic moments and compare our results with the data for the odd-A Cd isotopes. Method: In order to evaluate if the additional correlations have bearing on the magnetic moments we employ an extension to the quasiparticle-phonon model (QPM) which takes into account quasiparticle$\otimes$phonon configurations in the ground state of the even-even core to the structure of the odd-A nucleus wave function. Results: It is shown that the values for the magnetic moments which the applied QPM extension yields deviate further from the Schmidt values. The latter is in agreement with the measured values for the Cd isotopes. Conclusions: The GSC exert significant influence on the magnetic dipole moments and reveal a potential for reproducing the experimental values for the studied cadmium isotopes

Decision making pattern of subsistence farmers in Bulgaria

Economic research by and large is dominated by a ‘rationality’ paradigm. Economic decision making within this paradigm is viewed as a maximising procedure. In general the latter represents the decision-making as a choice amongst a well defined set of alternatives. In this paper we question this and analyse the options of the small-scale subsistence farmers in Bulgaria in the way they see them. By applying mental accounting methodology we deduce some significant characteristics of Bulgarian subsistence agriculture.