Weber-Fechner's Law, Demand Function and Related Topics

In our previous paper, we derive the demand function in the form p=du(x)/dx and we apply the Weber-Fechner's law to the utility function and we obtain the demand function in the familiar form p=A/x. We compare our derivation of the demand function with the standard one. The differences are i) different functional form of the utility function, ii) different objective function to aximize, iii) different treatment of the budget condition. We also study how much quantity of goods we should distribute to N persons in n kinds of goods. By adding each person's demand function, we obtain the total demand function. By the market equilibrium, we obtain the only unique solution of how much quantity of goods we should distribute to each person. The quantity of goods is distributed according to each person's preference.Weber-Fechner's law, utility function, demand function, Pareto optimum

Various Logistic Curves in SIS and SIR Models

In our previous paper, the logistic curve of the removed number was derived from SIR and SEIR models in the case of the small basic reproduction number. In this paper, we derive various logistic curves of the removed, unsusceptible and infectious numbers respectively from SIS and SIR models in the case of small and large basic reproduction numbers.Comment: 9 pages, 6 fugure

Relation between Yang-Baxter and Pair Propagation Equations in 16-Vertex Models

We study a relation between two integrability conditions, namely the Yang-Baxter and the pair propagation equations, in 2D lattice models. While the two are equivalent in the 8-vertex models, discrepancies appear in the 16-vertex models. As explicit examples, we find the exactly solvable 16-vertex models which do not satisfy the Yang-Baxter equations.Comment: 11 pages, TEZU-F-059 and EWHA-TH-00