A few remarks on "On certain Vandermonde determinants whose variables separate"

In the recent paper \u201cOn certain Vandermonde determinants whose variables separate\u201d [Linear Algebra and its Applications 449 (2014) pp. 17\u201327], there was established a factorized formula for some bivariate Vandermonde determinants (associated to almost square grids) whose basis functions are formed by Hadamard products of some univariate polynomials. That formula was crucial for proving a conjecture on the Vandermonde determinant associated to Padua-like points. In this note we show that the same formula holds when those polynomials are replaced by arbitrary functions and we extend this formula to general rectangular grids. We also show that the Vandermonde determinants associated to Padua-like points are nonvanishing

Glass-ionomer Adhesives in Orthodontics: Clinical Implications and Future Research Directions

During the past ten years significant advances have been made in the development of glass-ionomer bonding adhesives. The beneficial effects of fluoride are well documented and an agent which reduces or prevents a white spot lesion that commonly occurs clinically, is desirable. There has been a notable lack of randomized clinical trials to determine the prevalence of white spot lesions after orthodontic treatment although it is often reported in the literature. White spot lesions pose health and esthetic problems and their proper clinical management has yet to be resolved. The objective of this paper Is to review the literature in this area and suggest a rationale for a clinical trial to assess the efficiency of glass-ionomer adhesives in facing the problem of decalcification and study the bond strength of these materials

Learning-by-employing: the value of commitment

We analyze a dynamic principal–agent model where an infinitely-lived principal faces asequence of finitely-lived agents who differ in their ability to produce output. The ability of anagent is initially unknown to both him and the principal. An agent’s effort affects the informationon ability that is conveyed by performance. We characterize the equilibrium contracts andshow that they display short–term commitment to employment when the impact of effort onoutput is persistent but delayed. By providing insurance against early termination, commitmentencourages agents to exert effort, and thus improves on the principal’s ability to identify theirtalent. We argue that this helps explain the use of probationary appointments in environmentsin which there exists uncertainty about individual ability.Keywords: dynamic principal–agent model, learning, commitment.

Limited memory and the essentiality of money

This paper investigates the relationship between memory and the essentiality ofmoney. We consider a random matching economy with a large finite population inwhich commitment is not possible and memory is limited in the sense that only afraction m E(0; 1) of the population has publicly observable histories. We show thatno matter how limited memory is, there exists a social norm that achieves the firstbest regardless of the population size. In other words, money can fail to be essentialirrespective of the amount of memory in the economy. This suggests that the emphasison limited memory as a fundamental friction for money to be essential deserves a deeperexamination.

Money versus memory

A well–established fact in monetary theory is that a key ingredient for the essentialityof money is its role as a form of memory. In this paper we study a notion ofmemory that includes information about an agent’s past actions and trading opportunitiesbut, in contrast to Kocherlakota (1998), does not include information aboutthe past actions and trading opportunities of an agent’s past partners. We first showthat the first–best can be achieved with memory even if it only includes informationabout an agent’s very recent past. Thus, money can fail to be essential even if memoryis minimal. We then establish, more interestingly, that if information about tradingopportunities is not part of an agent’s record, then money can be better than memory.This shows that the societal benefit of money lies not only on being a record of pastactions, but also on being a record of past trading opportunities, a fact that has beenoverlooked by the monetary literature.

Essence and Cause: Making Something Be What It Is

Aristotle frequently describes essence as a “cause” or “explanation”, thus ascribing to essence some sort of causal or explanatory role. This explanatory role is often explicated by scholars in terms of essence “making the thing be what it is” or “making it the very thing that it is”. I argue that this is problematic, at least on the assumption that “making” expresses an explanatory relation, since it violates certain formal features of explanation. I then consider whether Aristotle is vulnerable to this problem by examining the explanatory role of essence in Posterior Analytics and Metaphysics Z 17