On $\mu $-singular and $\mu $-extending modules

On the possible volume of $mu$-$(v,k,t)$ trades

‎A $mu$-way $(v,k,t)$ $trade$ of volume $m$ consists of $mu$‎ ‎disjoint collections $T_1$‎, ‎$T_2‎, ‎dots T_{mu}$‎, ‎each of $m$‎ ‎blocks‎, ‎such that for every $t$-subset of $v$-set $V$ the number of‎ ‎blocks containing this t-subset is the same in each $T_i (1leq‎ ‎i leq mu)$‎. ‎In other words any pair of collections ${T_i,T_j}$‎, ‎$1leq i< j leq mu‎$ is a $(v,k,t)$ trade of volume $m$. In th...

Superdeduction in Lambda-Bar-Mu-Mu-Tilde

Superdeduction is a method specially designed to ease the use of first-order theories in predicate logic. The theory is used to enrich the deduction system with new deduction rules in a systematic, correct and complete way. A proof-term language and a cut-elimination reduction already exist for superdeduction, both based on Christian Urban’s work on classical sequent calculus. However the compu...

Hopf algebroids and the structure of MU∗(MU)

$\mu$-calculus on data words

We study the decidability and expressiveness issues of µ-calculus on data words and data ω-words. It is shown that the full logic as well as the fragment which uses only the least fixpoints are undecidable, while the fragment containing only greatest fixpoints is decidable. Two subclasses, namely BMA and BR, obtained by limiting the compositions of formulas and their automata characterizations ...

Lambda and mu-symmetries

Symmetry analysis is a standard and powerful method in the analysis of differential equations, and in the determination of explicit solutions of nonlinear ones. It was remarked by Muriel and Romero [10] (see also the work by Pucci and Saccomandi [14]) that for ODEs the notion of symmetry can be somehow relaxed to that of lambda-symmetry (see below), still retaining the relevant properties for s...