In this paper, the notion of structural completeness is explored in the context of a generalized class of superintuitionistic logics that also involve systems that are not closed under uniform substitution. We just require that each logic must be closed under $D$-substitutions assigning to atomic formulas only $\vee$-free formulas. For these systems, we introduce four different notions of structural completeness and study how they are related. We focus on superintuitionistic inquisitive logics that validate a schema called Split and have the disjunction property. In these logics, disjunction can be interpreted in the sense of inquisitive semantics as a question-forming operator. It is shown that a logic is structurally complete with respect to $D$-substitutions if and only if it validates Split. Various consequences of this result are explored. For example, it is shown that every superintuitionistic inquisitive logic can be characterized by a Kripke model built from $D$-substitutions. We also formulate an algebraic counterpart of this result that says that the Lindenbaum–Tarski algebra ${\mathscr{H}}$ of any inquisitive logic can be embedded into the Heyting algebra formed from left ideals of endomorphisms on ${\mathscr{H}}$. Additionally, we resolve a conjecture concerning superintuitionistic inquisitive logics due to Miglioli et al. and show that a false conjecture about superintuitionistic logics due to Minari and Wroński becomes true in the broader space of regular generalized superintuitionistic logics.

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.