Chains of Infinite Order, Chains with Memory of Variable Length, and Maps of the Interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we characterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval.

Non-lacunary Gibbs Measures for Certain Fractal Repellers

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A creature of statute: Copyright law and legal formalism

This article argues that copyright law is not just a creature of statute, but it is also a social and imaginative contruct. It evaluates a number of critiques of legal formalism. Part 1 examines whether the positive rules and principles of copyright law are the product of historical contingency and political expediency. Part 2 considers the social operation of copyright law in terms of its material effects and cultural significance. Part 3 investigates the future of copyright law, in light of the politics of globalisation and the impact of new information technologies.

Phase Equilibria in the System $Al_{2}O_{3}-CaO-CoO$ and Gibbs Energy of Formation of $Ca_{3}CoAl_{4}O_{10}$

The floating-zone method with different growth ambiences has been used to selectively obtain hexagonal or orthorhombic DyMnO3 single crystals. The crystals were characterized by x-ray powder diffraction of ground specimens and a structure refinement as well as electron diffraction. We report magnetic susceptibility, magnetization and specific heat studies of this multiferroic compound in both the hexagonal and the orthorhombic structure. The hexagonal DyMnO3 shows magnetic ordering of Mn3+ (S = 2) spins on a triangular Mn lattice at T-N(Mn) = 57 K characterized by a cusp in the specific heat. This transition is not apparent in the magnetic susceptibility due to the frustration on the Mn triangular lattice and the dominating paramagnetic susceptibility of the Dy3+ (S = 9/2) spins. At T-N(Dy) = 3 K, a partial antiferromagnetic order of Dy moments has been observed. In comparison, the magnetic data for orthorhombic DyMnO3 display three transitions. The data broadly agree with results from earlier neutron diffraction experiments, which allows for the following assignment: a transition from an incommensurate antiferromagnetic ordering of Mn3+ spins at T-N(Mn) = 39 K, a lock-in transition at Tlock-in = 16 K and a second antiferromagnetic transition at T-N(Dy) = 5 K due to the ordering of Dy moments. Both the hexagonal and the orthorhombic crystals show magnetic anisotropy and complex magnetic properties due to 4f-4f and 4f-3d couplings.

Gibbs Energy of Formation of Cobalt Divanadium Tetroxide

The Gibbs energy of formation of V2O3-saturated spinel CoV2O4 has been measured in the temperature range 900–1700 K using a solid state galvanic cell, which can be represented as Pt, Co + CoV2O4 + V2O3/(CaO) ZrO2/Co + CoO, Pt. The standard free energy of formation of cobalt vanadite from component oxides can be represented as CoO (rs) + V2O3 (cor) → CoV2O4 (sp), ΔG° = −30,125 − 5.06T (± 150) J mole−1. Cation mixing on crystallographically nonequivalent sites of the spinel is responsible for the decrease in free energy with increasing temperature. A correlation between “second law” entropies of formation of cubic 2–3 spinels from component oxides with rock salt and corundum structures and cation distribution is presented. Based on the information obtained in this study and trends in the stability of aluminate and chromite spinels, it can be deduced that copper vanadite is unstable.

Scheme of squares: Part I. Systems formalism for potentiostatic studies

The so-called “Scheme of Squares”, displaying an interconnectivity of heterogeneous electron transfer and homogeneous (e.g., proton transfer) reactions, is analysed. Explicit expressions for the various partial currents under potentiostatic conditions are given. The formalism is applicable to several electrode geometries and models (e.g., semi-infinite linear diffusion, rotating disk electrodes, spherical or cylindrical systems) and the analysis is exact. The steady-state (t→∞) expressions for the current are directly given in terms of constant matrices whereas the transients are obtained as Laplace transforms that need to be inverted by approximation of numerical methods. The methodology employs a systems approach which replaces a system of partial differential equations (governing the concentrations of the several electroactive species) by an equivalent set of difference equations obeyed by the various partial currents.

Scheme of squares: Part II. Systems formalism for sinusoidal perturbations

We extend here the formalism developed in Part I (for the potentiostatic response) to the admittance analysis of the scheme of squares. The results are applicable, as before, to several configurations of the electrode such as the rotating disk or the planar. All that one has to do is “to plug in” the appropriate matrices relating the interfacial concentrations to the fluxes.

Many-body effects in electrochemisorption : Part IV. Multi-boson formalism

Several boson subsystems may be involved in electrosorption phenomena. To accommodate this possibility, the one-boson formalism described in Parts I–III is extended to this case. The hierarchy in the superoperator scheme, the evaluation of operator averages for closure and several special cases are indicated. As an illustration, some calculations are presented to indicate the trends of many-body corrections in chemisorption.

Fluctuation phenomena in electrochemistry part I. The formalism

A unified approach to the problem of electrochemical fluctuations is presented. On the basis of the Langevin procedure, primary noise sources are introduced in the basic phenomenological equations and a discussion of the secondary noise sources arising in the expressions for the power spectra of currents is given.

Gibbs energies of formation of rare earth oxysulfides

The standard Gibbs energy change accompanying the conversion of rare earth oxides to oxysulfides by reaction of rare earth oxides with diatomic sulfur gas has been measured in the temperature range 870 to 1300 K using the solid state cell: Pt/Cu+Cu2S/R2O2S+R2O3‖(CaO)ZrO2‖Ni+NiO, Pt where R=La, Nd, Sm, Gd, Tb, and Dy. The partial pressure of diatomic sulfur over a mixture of rare earth oxide (R2O3) and oxysulfide (R2O2S) is fixed by the dissociation of Cu2S to Cu in a closed system. The buffer mixture of Cu+Cu2S is physically separated from the rare earth oxide and oxysulfide to avoid complications arising from interaction between them. The corresponding equilibrium oxygen partial pressure is measured with an oxide solid electrolyte cell. Gibbs energy change for the conversion of oxide to the corresponding oxysulfide increases monotonically with atomic number of the rare earth element. Second law enthalpy of formation also shows a similar trend. Based on this empirical trend Gibbs energies of formation of oxysulfides of Pr, Eu, Ho, and Er are estimated as a function of temperature.

A new formalism for representation of binary thermodynamic data

The applicability of a formalism involving an exponential function of composition x1 in interpreting the thermodynamic properties of alloys has been studied. The excess integral and partial molar free energies of mixing are expressed as: $$\begin{gathered} \Delta F^{xs} = a_o x_1 (1 - x_1 )e^{bx_1 } \hfill \\ RTln\gamma _1 = a_o (1 - x_1 )^2 (1 + bx_1 )e^{bx_1 } \hfill \\ RTln\gamma _2 = a_o x_1^2 (1 - b + bx_1 )e^{bx_1 } \hfill \\ \end{gathered} $$ The equations are used in interpreting experimental data for several relatively weakly interacting binary systems. For the purpose of comparison, activity coefficients obtained by the subregular model and Krupkowski’s formalism have also been computed. The present equations may be considered to be convenient in describing the thermodynamic behavior of metallic solutions.

Enterprise education: Revisiting Whitehead to satisfy Gibbs

Purpose – This paper seeks to demonstrate that a truly learner-centred enterprise education programme can be developed within a traditional business school environment. Design/methodology/approach – This paper unites the broad teaching philosophy of Alfred Whitehead with that of Allan Gibbs’s enterprise specific teaching philosophies to consider the fitness of the recently developed hic et nunc enterprise framework. This is largely achieved by testing the framework for constructive alignment. Findings – It is argued that the hic et nunc framework is consistent with the philosophies of both Whitehead and Gibb. Further, the framework illustrates a process through which enterprise education programmes can be developed independently of any pressures to conform to more traditional pedagogy. Practical implications – Through careful consideration of the process of constructive alignment, an analytical approach to developing and/or refining an enterprise education program exists. Importantly, it represents an approach that is explicitly learner-centred, and therefore free from the constraints of the environment within which the programme is delivered. Originality/value – This paper brings to life the wonderful ideas of the great philosopher, Alfred Whitehead, combining them with the contemporary ideas of Allan Gibb. In doing so, the complementary nature of their thoughts helps to illustrate the minimal requirements of a learner-centred approach to enterprise education

Tannakian Formalism Applied to the Category of Mixed Hodge Structures

Many problems in analysis have been solved using the theory of Hodge structures. P. Deligne started to treat these structures in a categorical way. Following him, we introduce the categories of mixed real and complex Hodge structures. Category of mixed Hodge structures over the field of real or complex numbers is a rigid abelian tensor category, and in fact, a neutral Tannakian category. Therefore it is equivalent to the category of representations of an affine group scheme. The direct sums of pure Hodge structures of different weights over real or complex numbers can be realized as a representation of the torus group, whose complex points is the Cartesian product of two punctured complex planes. Mixed Hodge structures turn out to consist of information of a direct sum of pure Hodge structures of different weights and a nilpotent automorphism. Therefore mixed Hodge structures correspond to the representations of certain semidirect product of a nilpotent group and the torus group acting on it.

Socialist Realism instead of Formalism : the Formation and Development of the Soviet Music Control System 1932-1950

Whereas it has been widely assumed in the public that the Soviet music policy system had a “top-down” structure of control and command that directly affected musical creativity, in fact my research shows that the relations between the different levels of the music policy system were vague, and the viewpoints of its representatives differed from each other. Because the representatives of the party and government organs controlling operas could not define which kind of music represented Socialist Realism, the system as it developed during the 1930s and 1940s did not function effectively enough in order to create such a centralised control of Soviet music, still less could Soviet operas fulfil the highly ambiguous aesthetics of Socialist Realism. I show that musical discussions developed as bureaucratic ritualistic arenas, where it became more important to reveal the heretical composers, making scapegoats of them, and requiring them to perform self-criticism, than to give directions on how to reach the artistic goals of Socialist Realism. When one opera was found to be unacceptable, this lead to a strengthening of control by the party leadership, which lead to more operas, one after the other, to be revealed as failures. I have studied the control of the composition, staging and reception of the opera case-studies, which remain obscure in the West despite a growing scholarly interest in them, and have created a detailed picture of the foundation and development of the Soviet music control system in 1932-1950. My detailed discussion of such case-studies as Ivan Dzerzhinskii’s The Quiet Don, Dmitrii Shostakovich’s Lady Macbeth of Mtsensk District, Vano Muradeli’s The Great Friendship, Sergei Prokofiev’s Story of a Real Man, Tikhon Khrennikov’s Frol Skobeev and Evgenii Zhukovskii’s From All One’s Heart backs with documentary precision the historically revisionist model of the development of Soviet music. In February 1948, composers belonging to the elite of the Union of Soviet Composers, e.g. Dmitri Shostakovich and Sergei Prokofiev, were accused in a Central Committee Resolution of formalism, as been under the influence of western modernism. Accusations of formalism were connected to the criticism of the conciderable financial, material and social privileges these composers enjoyed in the leadership of the Union. With my new archival findings I give a more detailed picture of the financial background for the 1948 campaign. The independent position of the music funding organization of the Union of Soviet Composers (Muzfond) to decide on its finances was an exceptional phenomenon in the Soviet Union and contradicted the strivings to strengthen the control of Soviet music. The financial audits of the Union of Soviet Composers did not, however, change the elite status of some of its composers, except for maybe a short duration in some cases. At the same time the independence of the significal financial authorities of Soviet theatres was restricted. The cuts in the governmental funding allocated to Soviet theatres contradicted the intensified ideological demands for Soviet operas.