The Michaelis-Menten-Stueckelberg Theorem

We study chemical reactions with complex mechanisms under two assumptions: (i) intermediates are present in small amounts (this is the quasi-steady-state hypothesis or QSS) and (ii) they are in equilibrium relations with substrates (this is the quasiequilibrium hypothesis or QE). Under these assumptions, we prove the generalized mass action law together with the basic relations between kinetic factors, which are sufficient for the positivity of the entropy production but hold even without microreversibility, when the detailed balance is not applicable. Even though QE and QSS produce useful approximations by themselves, only the combination of these assumptions can render the possibility beyond the "rarefied gas" limit or the "molecular chaos" hypotheses. We do not use any a priori form of the kinetic law for the chemical reactions and describe their equilibria by thermodynamic relations. The transformations of the intermediate compounds can be described by the Markov kinetics because of their low density ({\em low density of elementary events}). This combination of assumptions was introduced by Michaelis and Menten in 1913. In 1952, Stueckelberg used the same assumptions for the gas kinetics and produced the remarkable semi-detailed balance relations between collision rates in the Boltzmann equation that are weaker than the detailed balance conditions but are still sufficient for the Boltzmann $H$-theorem to be valid. Our results are obtained within the Michaelis-Menten-Stueckelbeg conceptual framework.Comment: 54 pages, the final version; correction of a misprint in Attachment

Proximal Point Algorithms for Finding a Zero of a Finite Sum of Monotone Mappings in Banach Spaces

We introduce an iterative process which converges strongly to a zero of a finite sum of monotone mappings under certain conditions. Applications to a convex minimization problem are included. Our theorems improve and unify most of the results that have been proved in this direction for this important class of nonlinear mappings

Text me! New consumer practices and change in organizational fields

While scholars have provided increasingly well-developed theoretical frameworks for understanding the role of institutional entrepreneurs and other purposeful actors in bringing about change in organizational fields, much less attention has been paid to the role of unorganized, nonstrategic actors in catalyzing change. In particular, the role of consumers remains largely uninvestigated. In this article, we draw on a case of the introduction of text messaging in the United Kingdom to explore the role of consumers in catalyzing change in organizational fields. Text messaging has become a widely diffused and institutionalized communication practice, in part changing mobile telephony from a voice-based, aural, and synchronous experience to a text-based, visual, and asynchronous experience. As consumers innovated and diffused new practices around this product, their actions led to significant changes in the field. We suggest how and under what conditions consumers are likely to innovate at the micro level and, with the subsequent involvement of other actors, catalyze change at the field level. Our primary contribution is to show how the cumulative effect of the spontaneous activities of one important and particularly dispersed and unorganized group can lead to changes in a field. By showing how change can result from the uncoordinated actions of consumers accumulating and converging over time, we provide an alternative explanation of change in organizational fields that does not privilege purposeful actors such as institutional entrepreneurs

Some notes on fixed points of quasi-contraction maps

AbstractIn this paper, we shall give some results about fixed points of quasi-contraction maps on cone metric spaces. These results generalize some recent results

Boundedness character of a max-type system of difference equations of second order

The boundedness character of positive solutions of the next max-type system of difference equations $$x_{n+1}=\max\left\{A,\frac{y_n^p}{x_{n-1}^q}\right\},\quad y_{n+1}=\max\left\{A,\frac{x_n^p}{y_{n-1}^q}\right\},\quad n\in\mathbb{N}_0,$$ with $\min\{A, p, q\}>0$, is characterized

On a higher-order system of difference equations

Here we study the following system of difference equations xn = f −1 cnf(xn−2k) ∏k an + bn i=1 g(y) n−(2i−1))f(xn−2i) yn = g −1 γng(yn−2k) ∏k αn + βn i=1 f(x) n−(2i−1))g(yn−2i) n ∈ N0, where f and g are increasing real functions such that f(0) = g(0) = 0, and coefficients an, bn, cn, αn, βn, γn, n ∈ N0, and initial values x−i, y−i, i ∈ {1, 2,..., 2k} are real numbers. We show that the system is solvable in closed form, and study asymptotic behavior of its solutions

A review on removal of pharmaceuticals from water by adsorption

Pharmaceuticals and personal care products are recognized as emerging pollutants in water resources. Various treatment options have been investigated for the removal of pharmaceuticals that include both conventional (e.g., biodegradation, adsorption, activated sludge) and advanced (e.g., membrane, microfiltration, ozonation) processes. This article reviews literature for adsorptive removal of pharmaceuticals from water sources. Adsorbents from various origins were reviewed for their capacity to remove pharmaceuticals from water. These adsorbents include carbonaceous materials, clay minerals, siliceous adsorbents, and polymeric materials. The adsorption capacity of adsorbents to adsorb pharmaceuticals from water is discussed in this study. The review discusses the mechanism for adsorption of pharmaceuticals onto adsorbents as well. Finally, effectiveness of processing parameters during adsorption processes is presented