Economic Equilibrium: Optimality and Price Decentralization

Mathematical economics has a long history and covers many interdisciplinary areas between mathematics and economics. At its center lies the theory of market equilibrium. The purpose of this expository article is to introduce mathematicians to price decentralization in general equilibrium theory. In particular, it concentrates on the role of positivity in the theory of convex economic analysis and the role of normal cones in the theory of non-convex economies.     

Quinquevalent tungsten as a reducing agent in potentiometric titrations : Estimation of ceric salts,bromate and ferricyanide

Quinquevalent tungsten can be further applied as a reducing agent for the potentiometric estimation of ceric salts, ferricyanide and bromate. Reduction of these oxidants takes place easily when they are present alone or in mixtures containing them together with ferric iron, dichromate or vanadate.     

The super order dual of an ordered vector space and the Riesz-Kantorovich formula

A classical theorem of F. Riesz and L. V. Kantorovich asserts that if is a vector lattice and and are order bounded linear functionals on , then their supremum (least upper bound) exists in and for each it satisfies the so-called Riesz-Kantorovich formula:

Related to the Riesz-Kantorovich formula is the following long-standing problem: If the supremum of two order bounded linear functionals and on an ordered vector space exists, does it then satisfy the Riesz-Kantorovich formula?

In this paper, we introduce an extension of the order dual of an ordered vector space and provide some answers to this long-standing problem. The ideas regarding the Riesz-Kantorovich formula owe their origins to the study of the fundamental theorems of welfare economics and the existence of competitive equilibrium. The techniques introduced here show that the existence of decentralizing prices for efficient allocations is closely related to the above-mentioned problem and to the properties of the Riesz-Kantorovich formula.

     

On uniqueness of equilibrium in the Kyle model

A longstanding unresolved question is whether the one-period Kyle model of an informed trader and a noisily informed market maker has an equilibrium that is different from the closed-form solution derived by Kyle (Econometrica 53:1315–1335, 1985). This note advances what is known about this open problem.     

Untersuchung von Trinkwasser, Abwasser, Mineralwasser

Ohne Zusammenfassung     

Quinquevalent tungsten as a reducing agent in potentiometric titrations

Qmnquevalcnt tungsten prepared by the electrolytic reduction of tungstate in ION HC1 is sufficiently stable when kept in strong acid solutions under COg to be used as an effective reducing agent in potcntiometric titrations. It can be accurately standardised with dichromate. The formal redox potentials of the $\text{W}{}^{\mathrm{+6}}\text{W}{}^{\mathrm{+5}}$ system as determined at different acidities indicate that quinquevalent tungsten is more reducing than the corresponding molybdenum compound.Quinquevalent tungsten can be applied successfully as a volumetric reagent in the potentiometric titration of ferric iron in 8-ioN HC1 or in a mixture of HCl and H3PO4 0.5.N each and of cupric copper in 8N HCl at 80° C. It can also be applied for the estimation of iodate, provided that the latter is used as the titrant.     

Colorimetric determination of manganese

The colour developed, when freshly formed manganese dioxide dissolves in alkaline tellurate solution is found to be suitable for the colorimetric determination of manganese. The colour obeys Beer's law within the concentration range 1.886.10^-4 - 7.54.10^-4M. The colour is developed by oxidizing Mn(II) (in presence of 2.5M alkali) with the equivalent amount of H₂O₂ in the presence of 4 moles of telluric acid per mole Mn(II).