The presence of Al hydroxy species in solution during the synthesis of lepidocrocite had been previously found to influence the reaction towards goethite formation. However, under certain conditions, which are not unrealistic in terms of the natural soil environment, this influence does not occur, and Al appears to substitute for Fe(III) in the lepidocrocite structure. This substitution causes the unit-cell dimensions to decrease along the “a” direction and to increase along the “b.” From the differential line broadening of X-ray powder diffraction peaks, the incorporation of Al was found to inhibit crystal growth preferentially in the b-axis direction, the hkl peaks being more broadened the higher the value of k relative to h and l. Al-substituted lepidocrocites have been suggested to occur in soils, and although they can be synthesized under conditions approaching those expected in soils, it is considered that their formation in nature is unlikely or restricted to unusual environments.

Since the publication of Alasdair MacIntyre’s After Virtue in 1981, tensions inherent to the relationship between morally educative practices and the institutions that house them have been widely noted. We propose a taxonomy of the ways in which the pursuit of external goods by institutions undermines the pursuit of the internal goods of practices. These comprise substitution, where the institution replaces the pursuit of one type of good by another; frustration, where opportunities for practitioners to discover goods or develop new standards of excellence are frustrated by institutional priorities and resource allocation; and injustice, which undermines the integrity of relationships within the organization and/or with partners. These threats, though analytically distinct, are often mutually reinforcing. This conceptual contribution is illustrated both by the extant literature and by a novel context, the three-ring circus.

The substitution of Fe3+ in the kaolinite structure is studied by EPR spectrometry and by FTIR spectrometry on a large set of kaolins from different origins (sedimentary and primary ores, soil kaolins). The IR bands at 3598 and 875 cm−1, observed in the literature only in the case of disordered kaolins or in Fe-rich environments (synthetic, lateritic), are revealed by high-resolution IR analysis, whatever the origin and the total Fe content of the samples. The EPR bands corresponding to Fe3+ substituted in sites II of the octahedral sheet increase when the IR absorbance near 3600 cm−1 increases. Two IR absorption bands near 4465 cm−1 and 7025 cm−1 are observed for the first time, both in transmission and diffuse reflectance on all samples. These bands are assigned to the combination of the 3598 and 875 cm−1 bands and to the first harmonic of the band at 3598 cm−1, respectively. The area of the band at 4465 cm−1 in diffuse reflectance is quantitatively correlated to the abundance of Fe3+ located in centers II as measured by ESR. This directly confirms the assignment of the two IR bands at 3598 and 875 cm−1 to OH stretching and deformation vibration bands in octahedral FE3+ environment in the kaolinite structure, respectively. Effects due to the size of particles and to the main kaolins impurities on the near infrared spectra, are also discussed.

Experimental cation exchange capacities (CEC) of kaolinites were determined and compared to theoretical calculations of CEC. The comparison reveals that the exchangeable cations occur mostly on the edges and on the basal (OH) surfaces of the mineral. It also shows that permanent negative charge from isomorphous substitution of Al3+ for Si4+ is insignificant. The CEC of kaolinite strongly depends on the particle size (both thickness and diameter in the (00l plane) and pH value. Particle size is more important than crystallinity in affecting kaolinite CEC. This study shows that the hydroxyls on the exposed basal surfaces may be ionizable in aqueous solutions. The amount of negative charge on the edges and the exposed basal hydroxyls depends on pH and other ion concentrations. A higher pH value gives rise to more negative charges, which lead to a higher CEC value. This study indicates that charge from broken edges and exposed OH planes rather than charge from Al/Si substitution determines the kaolinite CEC, even at zero point charge. A high CEC in some kaolinites is found to be due to smectite layers on the surface of the kaolinite crystals.

In the classical theory of regular languages, the concept of recognition by profinite monoids is an important tool. Beyond regularity, Boolean spaces with internal monoids (BiMs) were recently proposed as a generalization. On the other hand, fragments of logic defining regular languages can be studied inductively via the so-called “Substitution Principle.” In this paper, we make the logical underpinnings of this principle explicit and extend it to arbitrary languages using Stone duality. Subsequently, we show how it can be used to obtain topo-algebraic recognizers for classes of languages defined by a wide class of first-order logic fragments. This naturally leads to a notion of semidirect product of BiMs extending the classical such construction for profinite monoids. Our main result is a generalization of Almeida and Weil’s Decomposition Theorem for semidirect products from the profinite setting to that of BiMs. This is a crucial step in a program to extend the profinite methods of regular language theory to the setting of complexity theory.

In this paper, we construct a uniformly recurrent infinite word of low complexity without uniform frequencies of letters. This shows the optimality of a bound of Boshernitzan, which gives a sufficient condition for a uniformly recurrent infinite word to admit uniform frequencies.

We provide behavioral insights into the economic substitution phenomenon among front-loaded and back-loaded tax-sheltered savings plans. We conduct three behavioral studies with adult Canadian participants to show experimentally that substitution can occur and to explain why substitution can occur. The first study shows that participants transfer savings from a front-loaded plan to a back-loaded plan when the latter becomes available, consistent with a substitution effect. The second study examines how participants trade-off two unique features of back-loaded and front-loaded savings plans. Our results indicate that participants favor the back-loaded tax feature and a variable contribution limit (offered in a front-loaded plan). As participants prefer one feature from each type of plan, this finding can help explain why substitution occurs. The third study provides participants a categorization task with various household budgeting items, including savings items. Results show that 68.1% of participants categorize multiple tax-sheltered savings plans in the same mental account, again consistent with a substitution effect under a budget constraint. As both tax-sheltered savings plans in Canada are used for different purposes, this finding shows that participants tend not to distinguish between the purpose of saving in each account, consistent with a substitution phenomenon.

Gazzari provides a mathematical theory of occurrences and of substitutions, which are a generalisation of occurrences constituting substitution functions. The dissertation focusses on term occurrences in terms of a first order language, but the methods and results obtained there can easily be carried over to arbitrary kinds of occurrences in arbitrary kinds of languages.

The aim of the dissertation is twofold: first, Gazzari intends to provide an adequate formal representation of philosophically relevant concepts (not only of occurrences and substitutions, but also of substitution functions, of calculations as well as of intuitively given properties of the discussed entities) and to improve this way our understanding of these concepts; second, he intends to provide a formal exploration of the introduced concepts including the detailed development of the methods needed for their adequate treatment.

The dissertation serves as a methodological fundament for consecutive research on topics demanding a precise treatment of occurrences and as a foundation for all scientific work dealing with occurrences only informally; the formal investigations are complemented by a brief survey of the development of the notion of occurrences in mathematics, philosophy and computer science.

The notion of occurrences. Occurrences are determined by three aspects: an occurrence is always an occurrence of a syntactic entity (its shape) in a syntactic entity (its context) at a specific position. Context and shape can be any meaningful combination of well-known syntactic entities as, in logic, terms, formulae or formula trees. Gazzari’s crucial idea is to represent the position of occurrences by nominal forms, essentially as introduced by Schütte [2]. The nominal forms are a generalisation of standard syntactic entities in which so called nominal symbols $*_k$ may occur. The position of an occurrence is obtained by eliminating the intended shape in the context, which means to replace the intended shape by suitable nominal symbols.

Standard occurrences. Central tool of the theory of nominal terms (nominal forms generalising standard terms) is the general substitution function mapping a nominal term $\mathtt {t}$ and a sequence $\vec {\mathtt {t}}$ of them to the result $\mathtt {t}[\vec {\mathtt {t}}]$ of replacing simultaneously the nominal symbols $*_k$ in the first argument by the respective entries $\mathtt {t}_k$ of the second argument.

A triple $\mathfrak {o}=\langle {t,s,\mathtt {t}} \rangle $ is a standard occurrence, if an application of the general substitution function on the position $\mathtt {t}$ and the shape s results in the context t of that occurrence. As $*_0$ can occur more than once in $\mathtt {t}$ , arbitrary many single occurrences in the context t of the common shape s can be subsumed in $\mathfrak {o}$ .1 Gazzari illustrates the appropriateness of his approach by solving typical problems (counting formally the number of specific occurrences, deciding whether an occurrence lies within another) which are not solvable without a good theory of occurrences.

Multi-shape occurrences. The multi-shape occurrences $\mathfrak {o}=\langle {t,\vec s,\mathtt {t}} \rangle $ are the generalisation of standard occurrences, where the shape $\vec s$ is a sequence of standard terms. Such occurrences subsume arbitrary non-overlapping single occurrences in the context t.

Gazzari addresses the non-trivial identity of such occurrences and their independence. The latter represents formally the idea of non-overlapping occurrences and is a far-reaching generalisation of disjointness as discussed by Huet with respect to single occurrences. Independent occurrences can be merged into one occurrence; an occurrence can be split up into independent occurrences.

Substitutions. A substitution $\mathbf s=\langle {t,\vec s,\mathtt {t},{\vec s}',t'} \rangle $ satisfies that both $\mathfrak {o}=\langle {t,\vec s,\mathtt {t}} \rangle $ and $\mathfrak {o}'=\langle {t',{\vec s}',\mathtt {t}} \rangle $ are occurrences such that the shapes have the same length. Such a substitution represents the replacement of $\vec s$ in t at $\mathtt {t}$ by $\vec s'$ resulting in $t'$ . This means that a substitution is understood as a process and not as a (specific type of a) function.

Identity and independence are addressed again, using and extending the methods developed for occurrences; as before, independent substitutions can be merged and substitutions can be split up into sequences of independent substitutions. Substitutions are used to represent formally calculations (as found in everyday mathematics) and to investigate them.

Sets of substitutions turn out to be set-theoretic functions mapping the affected occurrences $\mathfrak {o}$ and the inserted shapes ${\vec s}'$ to the result $t'$ of a substitution $\mathbf s$ . Such sets are called explicit substitution functions. In order to qualify functions which are usually understood as substitution functions (and which are not formulated in a theory of occurrences) as substitution functions, Gazzari develops the concept of an explication method transforming such functions into explicit substitution functions. The appropriateness and the (philosophical) limitations of this concept are illustrated with example functions.

Conclusion. Gazzari’s theory of occurrences is strong (not restricted to single occurrences), canonical (nominal forms are a canonical generalisation of the underlying syntactic entities) and general (presupposing the grammar for the underlying syntactic entities, suitable nominal forms are easily defined and the theory of occurrences is immediately carried over). Another advantage is a kind of methodological pureness: positions are generalised syntactic entities (and not extraneous, as sequences of natural numbers) and can be treated, in particular, with the well-known methods developed for the underlying syntactic entities.

Abstract prepared by René Gazzari.

E-mail: rene.gazzari@uni-tuebingen.de

URL: http://doi.org/10.15496/publikation-47553

How do rebels choose among available tactics during civil war? How do they substitute one tactic for another? Although previous studies address these questions, they narrowly focus on the presence or absence of substitution. Differentiating the varieties of substitution, however, is critical. How rebels respond to their tactical environment—including weather conditions—depends on the type of substitution. I formally derive three types of substitution and test them by exploiting weather-induced exogenous variation in rebels' tactical costs for ground and marine violent activities. The analysis of daily panel data in 31 coastal conflict countries indicates that rebels substitute violent ground activities for maritime piracy but not vice versa. This asymmetry cannot be explained without differentiating substitution types.