Object Sharing in Mbya Guarani: A Case of Asymmetrical Verbal Serialization?

In this paper, we intend to describe and discuss the grammatical status of the V1-V2 (Cy/vy) constructions found in Mbya Guarani which can express simultaneous events, among other meanings, and which involve a single clause. We suggest here that this verbal complex can be treated as a case of asymmetrical verbal serialization because it contains verbs from a major lexical class, occupying the V1 slot, followed by a more restricted intransitive verbal class, such as movement, postural, or stative verbs, which stands in the V2 position. The curious property of these constructions is that V2 can be transitivized through the attachment of applicative or causative morphemes and “share” its object with transitive V1. “Object sharing” is another property attributed to serialization, as suggested by Baker and Baker and Stewart, which may be seen as a strong argument in favor of the present hypothesis. We will also provide evidence to distinguish Mbya Guarani V1-V2 (Cy/vy) complex from other constructions, such as temporal and purpose subordinate clauses, involving the particle vy.

A Curious Property of Octagons

The famous theorem of Van Aubel for quadrilaterals postulates that if squares are built externally on the sides of any quadrilateral, then the two segments that join the opposing centers of these squares are congruent and orthogonal. Inspired by this result and also by the results of Krishna, in this article we will prove the following result of plane geometry: each octagon is associated with a parallelogram, in some cases the parallelogram in question can be degenerate at a point or a segment. This is possible because of complex numbers and basics of analytical geometry.

A note on iterated galileo sequences

Galileo sequences are generalizations of a simple sequence of integers that Galileo used in early 17th century for describing his law of falling bodies. The curious property he noted happens to be exactly what is needed to quantify his observation that the acceleration of falling bodies is uniform. Among the generalizations and extensions later given are iterated Galileo sequences. We show that these are closely related to polynomials that arise in enumerating integers by their Hamming weight.

A Square Root Map on Sturmian Words

We introduce a square root map on Sturmian words and study its properties. Given a Sturmian word of slope $\alpha$, there exists exactly six minimal squares in its language (a minimal square does not have a square as a proper prefix). A Sturmian word $s$ of slope $\alpha$ can be written as a product of these six minimal squares: $s = X_1^2 X_2^2 X_3^2 \cdots$. The square root of $s$ is defined to be the word $\sqrt{s} = X_1 X_2 X_3 \cdots$. The main result of this paper is that $\sqrt{s}$ is also a Sturmian word of slope $\alpha$. Further, we characterize the Sturmian fixed points of the square root map, and we describe how to find the intercept of $\sqrt{s}$ and an occurrence of any prefix of $\sqrt{s}$ in $s$. Related to the square root map, we characterize the solutions of the word equation $X_1^2 X_2^2 \cdots X_n^2 = (X_1 X_2 \cdots X_n)^2$ in the language of Sturmian words of slope $\alpha$ where the words $X_i^2$ are minimal squares of slope $\alpha$.We also study the square root map in a more general setting. We explicitly construct an infinite set of non-Sturmian fixed points of the square root map. We show that the subshifts $\Omega$ generated by these words have a curious property: for all $w \in \Omega$ either $\sqrt{w} \in \Omega$ or $\sqrt{w}$ is periodic. In particular, the square root map can map an aperiodic word to a periodic word.

The library as heterotopia: Michel Foucault and the experience of library space

Purpose – Using Michel Foucault’s notion of heterotopia as a guide, the purpose of this paper is to explore the implications of considering the library as place, and specifically as a place that has the “curious property of being in relation with all the other sites, but in such a way as to suspect, neutralize, or invent the set of relations that they happen to designate, mirror, or reflect” (Foucault, 1986a, p. 24). Design/methodology/approach – The paper draws upon a range of literary examples and from biographical accounts of authors such as Alan Bennett, Michel Foucault, and Umberto Eco to show how the library space operates as a heterotopia. Findings – The paper finds that drawing together the constructs of heterotopia and serendipity can enrich the understanding of how libraries are experienced as sites of play, creativity, and adventure. Originality/value – Foucault’s concept of heterotopia is offered as an original and useful frame that can account for the range of experiences and associations uniquely attached to the library.

Dissipation-Induced Self-Recovery in Systems on Principal Bundles

The “self-recovery” phenomenon is a seemingly curious property of certain underactuated dissipative systems in which dissipative forces always push the system to a pre-determined equilibrium state dependent on the initial conditions. The systems for which this has been studied are Abelian, with all system velocity interactions due entirely to inertial effects. In this paper we also consider Abelian systems, but in the context of principal bundles, and introduce drag in addition to inertial interactions, allowing us to show that the same conservation that induces self-recovery now depends on the trajectories of the system inputs in addition to initial conditions. We conclude by demonstrating an example illustrating the conditions derived from our proof, along with an observation that the present analysis is insufficient for self-recovery in non-Abelian systems.

SUPERNILPOTENCE PREVENTS DUALIZABILITY

We address the question of the dualizability of nilpotent Mal’cev algebras, showing that nilpotent finite Mal’cev algebras with a nonabelian supernilpotent congruence are inherently nondualizable. In particular, finite nilpotent nonabelian Mal’cev algebras of finite type are nondualizable if they are direct products of algebras of prime power order. We show that these results cannot be generalized to nilpotent algebras by giving an example of a group expansion of infinite type that is nilpotent and nonabelian, but dualizable. To our knowledge this is the first construction of a nonabelian nilpotent dualizable algebra. It has the curious property that all its nonabelian finitary reducts with group operation are nondualizable. We were able to prove dualizability by utilizing a new clone theoretic approach developed by Davey, Pitkethly, and Willard. Our results suggest that supernilpotence plays an important role in characterizing dualizability among Mal’cev algebras.

ON A CURIOUS PROPERTY OF BELL NUMBERS

In this paper we derive congruences expressing Bell numbers and derangement numbers in terms of each other modulo any prime.