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.     

The Effect of Wall Material Type on the Encapsulation Efficiency and Oxidative Stability of Fish Oils

Fish oil is the primary source of long-chain omega-3 fatty acids, which are important nutrients that assist in the prevention and treatment of heart disease and have many health benefits. It also contains vitamins that are lipid-soluble, such as vitamins A and D. This work aimed to determine how the wall material composition influenced the encapsulation efficiency and oxidative stability of omega fish oils in spray-dried microcapsules. In this study, mackerel, sardine waste oil, and sand smelt fish oil were encapsulated in three different wall materials (whey protein, gum Arabic (AG), and maltodextrin) by conventional spray-drying. The effect of the different wall materials on the encapsulation efficiency (EE), flowability, and oxidative stability of encapsulated oils during storage at 4 °C was investigated. All three encapsulating agents provided a highly protective effect against the oxidative deterioration of the encapsulated oils. Whey protein was found to be the most effective encapsulated agent comparing to gum Arabic and maltodextrin. The results indicated that whey protein recorded the highest encapsulation efficiency compared to the gum Arabic and maltodextrin in all encapsulated samples with EE of 71.71%, 68.61%, and 64.71% for sand smelt, mackerel, and sardine oil, respectively. Unencapsulated fish oil samples (control) recorded peroxide values (PV) of 33.19, 40.64, and 47.76 meq/kg oil for sand smelt, mackerel, and sardine oils after 35 days of storage, while all the encapsulated samples showed PV less than 10 in the same storage period. It could be concluded that all the encapsulating agents provided a protective effect to the encapsulated fish oil and elongated the shelf life of it comparing to the untreated oil sample (control). The results suggest that encapsulation of fish oil is beneficial for its oxidative stability and its uses in the production of functional foods.     

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.     

MgO‐ZrO2 Mixed Oxides as Effective and Reusable Base Catalysts for Glucose Isomerization into Fructose in Aqueous Media

MgO‐ZrO₂ mixed oxides prepared with different Mg/Zr atomic ratios (denoted as xMZ: where x is the atomic ratio of Mg/Zr) are investigated for the glucose isomerization to fructose in water at 95 °C. The highest fructose yield of 33 % is obtained over 0.76MZ with ≈74 % selectivity after 3 h. To gain insight into the structure–activity relationships, the prepared catalysts are characterized by N₂ physisorption, XRD, FTIR and CO₂‐TPD. The results indicate that the addition of MgO drastically changed the textual property of ZrO₂ and increased the number of basic sites. The kinetic studies revealed that the Lewis basic sites (cus‐O^2?) generated from the highly dispersed MgO are the active sites responsible for the enhanced isomerization activity. Notably, MZ is reusable for four runs without a significant decrease in catalyst activity. Accordingly, this study provides an easily prepared, cheap, and recyclable catalyst that may hold great potential for fructose production.     

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.     

Pathwise accuracy and ergodicity of metropolized integrators for SDEs

Metropolized integrators for ergodic stochastic differential equations (SDEs) are proposed that (1) are ergodic with respect to the (known) equilibrium distribution of the SDEs and (2) approximate pathwise the solutions of the SDEs on finite‐time intervals. Both these properties are demonstrated in the paper, and precise strong error estimates are obtained. It is also shown that the Metropolized integrator retains these properties even in situations where the drift in the SDE is nonglobally Lipschitz, and vanilla explicit integrators for SDEs typically become unstable and fail to be ergodic. © 2009 Wiley Periodicals, Inc.     

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.