Reactions of ketones on oxide surfaces. I. Reaction sequence of cyclohexanone on alumina

The reaction of cyclohexanone on alumina is investigated at various temperatures and contact times. The poisoning of the surface of pure alumina as well as of alumina impregnated with different amounts of sodium is also studied. The main reaction products are a dimeric aldol condensation product and cyclohexene. The reaction sequence of cyclohexanone on alumina involves first a rapid polymerisation of cyclohexanone on the surface. At low temperatures, hydrogen transfer from the polymer to cyclohexanone is responsible for the formation of cyclohexene, the polymer itself being converted to coke which poisons the surface. At higher temperatures the disproportionation of cyclohexanone is the dominant mechanism for the formation of cyclohexene. Cyclohexanol itself is not formed under the reaction conditions employed. Conditions of low acidity and temperature favour the formation of the dimer.     

Moving towards a feminist epistemology of mathematics

There is, now, an extensive critical literature on gender and the nature of science, three aspects of which, philosophy, pedagogy and epistemology, seem to be pertinent to a discussion of gender and mathematics. Although untangling the inter-relationships between these three is no simple matter, they make effective starting points in order to ask similar questions of mathematics to those asked by our colleagues in science. In the process of asking such questions, a major difference between the empirical approach of the sciences, and the analytic nature of mathematics, is exposed and leads towards the definition of a new epistemological position in mathematics.     

Wave simulations of Gray‐Scott reaction‐diffusion system

In this work, we study the numerical simulation of the one‐dimensional reaction‐diffusion system known as the Gray‐Scott model. This model is responsible for the spatial pattern formation, which we often meet in nature as the result of some chemical reactions. We have used the trigonometric quartic B‐spline (T4B) functions for space discretization with the Crank‐Nicolson method for time integration to integrate the nonlinear reaction‐diffusion equation into a system of algebraic equations. The solutions of the Gray‐Scott model are presented with different wave simulations. Test problems are chosen from the literature to illustrate the stationary waves, pulse‐splitting waves, and self‐replicating waves.     

Oxidation studies

The results on the kinetics of oxidation of HCHO and some alcohols,viz.,n-propanol, allyl alcohol, cyclohexanol and benzyl alcohol by ceric nitrate in nitric acid medium in the temperature range of 10–35° C. are presented. The active form of Ce⁴⁺ during the oxidation of the above organic substrates was assumed to be the neutral Ce(NO₃)₄. The mechanism of oxidation and thermodynamic parameters for the above compounds are also given.     

Modelling and information systems for senior management in local government: problems and prospects

The paper considers the role of modelling systems at senior levels in democratically accountable multi-service public sector organisations such as local government.The main basis for the arguments proposed is three years of project work terminating in mid-1977. During this period the writer acted as a consultant to the IBM (UK) Scientific Centre and was responsible for the day-to-day co-ordination of a major project undertaken in the first tier Welsh local authority, Clwyd County Council.The project, which involved substantial resource inputs from both IBM and the local authority, led to definitive conclusions as to the nature and potential value of the modelling system developed.The main purpose of this paper is to consider the extent to which multi-service modelling systems in general are of relevance to local government. The system developed in the Welsh local authority may be described as affording means oriented resource planning facilities. Further it was designed to generate short and medium term (up to five years) information.It is concluded that although at first sight the implementation of an extensive modelling system may seem to involve intervention on a narrow front the reality is that it impinges upon all the main organisational variables. Because of this the prospect for realising the potential of the system will vary considerably from organisation to organisation. It is important that this should be appreciated by senior management before they approve the commitment of resources to developments of this nature.     

A dynamical systems approach based on averaging to model the macroscopic flow of freeway traffic

The flow of traffic exhibits distinct characteristics under different conditions, reflecting the congestion during peak hours and relatively free motion during off-peak hours. This requires one to use different mathematical equations to describe the diverse traffic characteristics. Thus, the flow of traffic is best described by a hybrid system, namely different governing equations for the different regimes of response, and it is such a hybrid approach that is investigated in this paper. Existing models for the flow of traffic treat traffic as a continuum or employ techniques similar to those used in the kinetic theory of gases, neither of these approaches gainfully exploit the hybrid nature of the problem. Spurious two-way propagation of disturbances that are physically unacceptable are predicted by continuum models for the flow of traffic. The number of vehicles in a typical section of the highway does not justify its being modeled as a continuum. It is also important to recognize that the basic premises of kinetic theory are not appropriate for the flow of traffic (see [S. Darbha, K.R. Rajagopal, Limit of a collection of dynamical systems: an application to modeling the flow of traffic, Mathematical Models and Methods in Applied Sciences 12 (10) (2002) 1381–1399] for a rationale for the same). A model for the flow of traffic that does not treat traffic as a continuum or use notions from kinetic theory is developed here and corroborated with real-time data collected on US 183 in Austin, Texas. Predictions based on the hybrid system model seem to agree reasonably well with the data collected on US 183.     

Hydrolysis of elemental sulphur in a homogeneous medium

Elemental sulphur dissolved in organic solvents (such as chloroform, carbon tetrachloride and benzene) reacts rapidly and quantitatively, with aqueous alkali at room temperature, when this immiscible liquid mixture is homogenized by the addition of ethyl alcohol. The products of reaction under these experimental conditions are sulphide, thiosulphate and a small quantity of sulphite. A mechanism involving the intermediate formation and decomposition of dihydrogen sulphoxide, HSOH, is suggested for the reaction.     

Qualitative model of the atom,its components and origin in the early universe

This paper is the first qualitative model of the atom and its components as well as its origin in our early universe. The atom’s components–proton, neutron (with its neutrino) and electron–are built on the prima, units of visible matter. Their qualitative models are obtained using some laws of nature. They yield new information such as the mass of the neutrino and how heavy isotopes of an atom form as well as the arrangement of the nucleons. It clarifies some presently unresolved issues such as what happens in thermonuclear explosion and whether it can be controlled to generate energy. It also explains the wave-particle duality of the primum and photon, metal fatigue, matter-anti-matter interaction and brittle and malleable materials and reviews the early phase of the development of our universe beyond the formation of the first atom up to its rapid formation at the present time in the Cosmos and tissues of living organisms.     

Asymptotic expansions for central limit theorems for general linear stochastic processes. I: General theorems on rates of convergence

This paper deals with so-called general linear stochastic processes (GLSP), defined by T. Kawata in 1972 in generalization of work of R. Lugannani and J. B. Thomas of 1967/71. These second order processes (which are not necessarily stationary nor have independent increments) are described by rather weak requirements, so that several processes such as some random noise and pulse train processes are specific models of these GLSP. Part I is concerned with two general theorems giving asymptotic expansions (including those for the density function) in the central limit theorem for such GLSP, together with error rates. The assumptions for the corresponding θ– and o–error estimates seem rather natural: in the former, apart from assumptions on the inherent structure of such GLSP, the existence of certain moments of higher order as well as a Cramer-type condition are assumed, in the latter in addition a Lindeberg-type condition of higher order. Fourier analytic machinery is used for the proofs.     

General two-place information functions

This paper deals with a functional equation and its application in information theory to the characterization of semisymmetric recursive deviations of degree (1, β) (β≠ 0). Those of degrees (a, β) (α≠ 0,1) and (1,0) (directed divergences and inaccuracies being the most important such deviations) have recently been characterized under the same conditions and on the same domains. These domains seem to be simpler and/or better adjusted, for instance to directed divergences and inaccuracies, than those in previous similar characterizations.     

On quantitative versions of theorems due to F.E. Browder and R. Wittmann

This paper is another case study in the program of logically analyzing proofs to extract new (typically effective) information (‘proof mining’). We extract explicit uniform rates of metastability (in the sense of T. Tao) from two ineffective proofs of a classical theorem of F.E. Browder on the convergence of approximants to fixed points of nonexpansive mappings as well as from a proof of a theorem of R. Wittmann which can be viewed as a nonlinear extension of the mean ergodic theorem. The first rate is extracted from Browder's original proof that is based on an application of weak sequential compactness (in addition to a projection argument). Wittmann's proof follows a similar line of reasoning and we adapt our analysis of Browder's proof to get a quantitative version of Wittmann's theorem as well. In both cases one also obtains totally elementary proofs (even for the strengthened quantitative forms) of these theorems that neither use weak compactness nor the existence of projections anymore. In this way, the present article also discusses general features of extracting effective information from proofs based on weak compactness. We then extract another rate of metastability (of similar nature) from an alternative proof of Browder's theorem essentially due to Halpern that already avoids any use of weak compactness. The paper is concluded by general remarks concerning the logical analysis of proofs based on weak compactness as well as a quantitative form of the so-called demiclosedness principle. In a subsequent paper these results will be utilized in a quantitative analysis of Baillon's nonlinear ergodic theorem.     

A generalized Hungarian method for solving minimum weight perfect matching problems with algebraic objective

The well known blossom-algorithm for solving minimum weight perfect matching problems makes use of the optimality criteria arising from LP-duality and complementary slackness. But these instruments seem to fail when such a matching problem is considered with a different objective function as for instance the bottleneck objective which is also relevant in practice. Such a dilemma occurs for all those combinatorial optimization problems with algorithms based on Linear Programming. Therefore we present a rarely combinatorially motivated approach in this paper.     

Observations on the nuclear interactions of cosmic ray pions and nucleons at energies ≳ 20 GeV

Detailed features of extremely collimated nuclear interactions induced by cosmic ray particles in carbon and brass (belonging to group I as classified in Part I of this series of papers) are presented. These extremely collimated nuclear interactions seem to be preferentially induced by pions rather than by nucleons; also the relative frequency of these seems to be less when brass is used as target compared to the case with carbon as target. The distribution of multiplicities of secondary particles emitted in the forward direction show certain regularities in the case of interactions induced by charged primaries. Observations on the γ-rays associated with these events give support to the interpretation that in these inelastic collisions pions are produced in pairs in the forward direction with low transverse momentum. It is suggested that such a low energy di-pion system could be the same as found in the so-called ABC effect.     

Surface Reaction Near a Stagnation Point

To measure rate constants while performing biomolecular interaction analysis (BIA), scientists often use resonant mirror devices such as the IAsys^TM. A full mathematical model of the IAsys^TM consists of a convection–diffusion equation in a closed well with a reacting surface at the bottom. The flow in the well is complex, but near the sensor, the qualitative nature of the reaction can be analyzed by reducing to stagnation point flow. The concentration of the reacting species in several cases is analyzed using singular perturbation techniques. Linear and nonlinear integral equations result from the analysis; explicit and series solutions are constructed for physically realizable cases. These solutions, which include the effects of transport on the reaction, provide improved estimates for the rate constants from raw IAsys^TM binding data.     

GROWTH WITH EXHAUSTIBLE RESOURCES AND A MATERIALS - BALANCE PRODUCTION FUNCTION

The materials-balance production function proposed in this paper is a modified Cobb-Douglas-type function which is as neoclassical in nature as materials-balance considerations would seem to permit. Incorporation of such a production function in a neoclassical growth model severely limits the growth potential of an economy with exhaustible resources.     

Frontier analysis in air pollution

Carbon containing aerosol is the most abundant particulate air pollutant species. It causes poor visibility and can be toxic. Tracing its origins is an important step in environmental management and control. This study analyses the carbon concentrations at Duarte, CA (a suburban site near Los Angeles) and in Lennox, CA (a site next to a Los Angeles freeway). Concentrations inside a tunnel are also available and used to derive a motor vehicle emission profile. A new approach is proposed for calculating the motor vehicle contribution to organic carbon and the amount of background carbon found at these two sites. Regression analysis provides insight in the formation of organic carbon and frontier analysis is used to calculate the motor vehicle contribution to organic carbon and the amount of background carbon in the atmosphere. The information obtained from this analysis can be used in the regulation of motor vehicle emissions and in air pollution control.     

Zahlenmythen im öffentlichen Leben —Aufgabe für den Mathematikunterricht

When administrative bodies publish figures we are often stunned by the precision with which they seem to render various situations and consequently tend to rely on their correctness. These figures, however, frequently do not describe a situation as accurately as they suggest. Thus working and drawing conclusions from such “precise figures” soon turns out to be highly problematic. Mathematics taught in school today encourages the pupils’ belief in the validity of such seemingly “precise figures”. This article promotes a deeper consciousness of this widely neglected problem and gives first suggestions of how to use the term “precision” in relation to figures in school mathematics in a reasonable and responsible way.     

Action research to improve methods of delivery and feedback in an Access Grid Room environment

This article describes a qualitative study which was undertaken to improve the delivery methods and feedback opportunity in honours mathematics lectures which are delivered through Access Grid Rooms. Access Grid Rooms are facilities that provide two-way video and audio interactivity across multiple sites, with the inclusion of smart boards. The principal aim was to improve the student learning experience, given the new environment. The specific aspects of the course delivery that the study focused on included presentation of materials and provision of opportunities for interaction between the students and between students and lecturers. The practical considerations in the delivery of distance learning are well documented in the literature, and similar problems arise in the Access Grid Room environment; in particular, those of limited access to face-to-face interaction and the reduction in peer support. The nature of the Access Grid Room classes implies that students studying the same course can be physically situated in different cities, and possibly in different countries. When studying, it is important that students have opportunity to discuss new concepts with others; particularly their peers and their lecturer. The Access Grid Room environment also presents new challenges for the lecturer, who must learn new skills in the delivery of materials. The unique nature of Access Grid Room technology offers unprecedented opportunity for effective course delivery and positive outcomes for students, and was developed in response to a need to be able to interact with complex data, other students and the instructor, in real-time, at a distance and from multiple sites. This is a relatively new technology and as yet there has been little or no studies specifically addressing the use and misuse of the technology. The study found that the correct placement of cameras and the use of printed material and smart boards were all crucial to the student experience. In addition, the inclusion of special tutorial type sessions were necessary to provide opportunities to students for one-on-one discussion with both lecturer and other students. This study contributes to the broader understanding of distance education in general and future Access Grid Room course delivery in particular.     

Energetic modelling for carbon fibre reinforced carbon

In this contribution an energetic model for multi-phase materials is developed describing the influence of microstructure on different length scales as well as the evolution of phase changes. Restrictions on the energy functional are discussed. In such a non-convex framework, interfacial contributions serve for relaxing the total energy. Such models can be applied to describe the macroscopic material properties of carbon fibre reinforced carbon where phase transitions between regions of different texture of the carbon matrix are observed on nanoscale as well as columnar microstructures on microscale [2]. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)