Graphical Abstract “My favorite science outreach activity is meeting with young people at fairs to answer the questions they have about world around them (not always easy but often inspiring) … I chose chemistry as a career because you transform and model matter scale of molecule, imperceptible human beings until very recently in our history. …” Find out more Morgan Donnard his Introducing Prof...

The main purpose of this paper is to axiomatize the join of the variety DPCSHC of dually pseudocomplemented semi-Heyting algebras generated by chains and the variety generated by D2, the De Morgan expansion of the four element Boolean Heyting algebra. Toward this end, we first introduce the variety DQDLNSH of dually quasi-De Morgan linear semi-Heyting algebras defined by the linearity axiom and...

In this paper we show that an algebra Ω(m,n) is functionally free for the Berman class Km,n of Ockham algebras, that is, for any two polynomials f and g, they are identically equal in Km,n if and only if f = g holds in Ω(m,n). This result can be applied to the well-known algebras, e.g., Boolean, de Morgan, Kleene, Stone, Bunge algebras, and so on.

We solve the following problem of Z. Füredi, J. C. Lagarias and F. Morgan [FLM]: Is there an upper bound polynomial in n for the largest cardinality of a set S of unit vectors in an n-dimensional Minkowski space (or Banach space) such that the sum of any subset has norm less than 1? We prove that |S| ≤ 2n and that equality holds iff the space is linearly isometric to l ∞ , the space with an n-c...

In (Mennle and Seuken, 2017), we have introduced partial strategyproofness, a new, relaxed notion of strategyproofness, to study the incentive properties of nonstrategyproof assignment mechanisms. In this paper, we present results pertaining to local sufficiency for partial strategyproofness: We show that, for any r P r0, 1s, r-local partial strategyproofness implies r2-partial strategyproofnes...

Inspired by the paper of Simplifying Decision Trees by J.R. Quinlan and the book C4.5: programs for machine learning by J.R. Quinlan and Morgan Kaufmann where they test the very traditional pruned decision tree models on credit approval data set, we want to re-exam the data set used in Simplifying Decision Trees and build advanced models to increase the accuracy. No surprise that all of the mod...

In this paper we overview basic known results about the varieties generated by De Morgan triples and about the problem to find equations defining the variety generated by a concrete De Morgan triple. We also provide some alternative proofs and some new results, specially for the case of Łukasiewicz De Morgan triples.