The Hidden Structural Rules of the Discontinuous Lambek Calculus

The sequent calculus sL for the Lambek calculus L (lambek 58) has no structural rules. Interestingly, sL is equivalent to a multimodal calculus mL, which consists of the nonassociative Lambek calculus with the structural rule of associativity. This paper proves that the sequent calculus or hypersequent calculus hD of the discontinuous Lambek calculus (Morrill and Valent\'in), which like sL has no structural rules, is also equivalent to an omega-sorted multimodal calculus mD. More concretely, we present a faithful embedding translation between mD and hD in such a way that it can be said that hD absorbs the structural rules of mD.Comment: Submitted to Lambek Festschrift volum

Application of Transition Metal Catalysis to Small Molecule Synthesis

Over the past decade, transition metal catalysis has developed into a new field in organic synthesis, enabling numerous synthetic transformations that were previously not feasible. This thesis describes the application of both ruthenium and rhenium catalysis to the synthesis of several classes of small molecules. Ruthenium-catalyzed ring-opening cross-metathesis of five- through eight-membered ring cycloolefins was investigated for the synthesis of functionalized dienes (Chapter 1). Unsubstituted, trisubstituted, and allyl-substituted cycloolefins were studied. Regioselective reactions could be achieved with the use of unsymmetrical cycloolefins. Ruthenium-catalyzed cross-metathesis was explored for the synthesis of both di- and trisubstituted vinyl boronates (Chapter 2). These reactions proceeded efficiently for a wide variety of functionalized alkenes and generally exhibited high E-stereoselectivity. The resultant vinyl boronate products were stereoselectively converted into both Z-vinyl bromides and E-vinyl iodides. The rhenium-catalyzed 1,3-isomerization of allylic alcohols was employed in the synthesis of various allylic alcohols (Chapter 3). Two different strategies were developed to promote high product selectivity in these reactions: conjugated product synthesis and N,O-bis(trimethylsilyl)acetamide-promoted product trapping. These reactions enabled the synthesis of allylic alcohols with conjugated or non-conjugated, di- or trisubstituted, and electron-rich or electron-deficient alkene components. Partial chirality transfer was observed during the 1,3-isomerization of certain enantioenriched allylic alcohols. The fundamental reaction properties observed during these studies were all consistent with the operation of a mechanism involving a chair-like transition state, which contains a partially cationic allyl moiety, as the primary reaction pathway

Higher-order Linear Logic Programming of Categorial Deduction

We show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing problem of Lambek categorial grammar applicable to a variety of its extensions.Comment: 8 pages LaTeX, uses eaclap.sty, to appear EACL9

Geometry of language and linguistic circuitry

We illustrate the potential for geometry of language and linguistic circuitry under the rendering of the syntactic structures of Lambek categorial grammar as proof nets. This empirical application sees sentences as proof nets and words as partial proof nets, and well-formedness/meaningfulness as a global harmony of categorial syntactic connection. The global cohesion coincides with a dynamic connectivity remaniscent of circuits, but whereas circuits are just generalisations of formulas, our syntactic structures are much more sublime objects: proofs.Postprint (published version

Availability and Accuracy of Accounting and Financial Data in Emerging Markets: The Case of Malaysia

As investor and researcher interest in emerging markets increases, the question of the availability and reliability of financial information pertinent to these markets becomes more and more important. This paper examines the availability and quality of accounting information on Malaysian firms contained in three different, widely available databases: Disclosure, Infostat and PACAP. An analysis of the firm coverage and and transcription policies of these databases reveals systematic differences that could give rise to a database effect on research findings. The paper identifies these differences and demonstrates, where possible, ways to adjust for them. L'intérêt croissant des investisseurs et des chercheurs envers les marchés émergents pose avec acuité la question de la fiabilité et de la disponibilité de l'information financière et comptable relative aux entreprises de ces pays. Cet article analyse la fiabilité de l'information comptable disponible sur les entreprises de Malaisie dans trois bases de données largement utilisées : Disclosure, Infostat et PACAP. L'analyse de l'ensemble des entreprises couvertes, des données et des pratiques de transcription révèle d'importantes différences qui peuvent influencer de façon importante les résultats des travaux empiriques. L'article identifie ces différences et indique de quelle façon il est possible d'en tenir compte.Emerging markets, accounting data, Malaysia, databases, Marchés émergents, données comptables, Malaisie, banques de données

Robin's inequality for 20-free integers

In 1984, Robin showed that the Riemann Hypothesis for $\zeta$ is equivalent to demonstrating $\sigma(n) 5040$. Robin's inequality has since been proven for various infinite families of power-free integers: $5$-free integers, $7$-free integers, and $11$-free integers. We extend these results to cover $20$-free integers

Multiplicative-Additive Focusing for Parsing as Deduction

Spurious ambiguity is the phenomenon whereby distinct derivations in grammar may assign the same structural reading, resulting in redundancy in the parse search space and inefficiency in parsing. Understanding the problem depends on identifying the essential mathematical structure of derivations. This is trivial in the case of context free grammar, where the parse structures are ordered trees; in the case of categorial grammar, the parse structures are proof nets. However, with respect to multiplicatives intrinsic proof nets have not yet been given for displacement calculus, and proof nets for additives, which have applications to polymorphism, are involved. Here we approach multiplicative-additive spurious ambiguity by means of the proof-theoretic technique of focalisation.Comment: In Proceedings WoF'15, arXiv:1511.0252