We recently introduced an extensional model of the pure λcalculus living in a cartesian closed category of sets and relations. In this paper, we provide sufficient conditions for categorical models living in arbitrary cpo-enriched cartesian closed categories to have H∗, the maximal consistent sensible λ-theory, as their equational theory. Finally, we prove that our relational model fulfils thes...

This paper presents a design and analysis of electromechanical sigma-delta modulator for MEMS gyroscope, which enables us to control the proof mass and to obtain an exact digital output without additional A/D conversion. The system structure and the circuit realization of the sigma-delta modulation are simpler than those of the analog sensing and feedback circuit. Based on the electrical sigma-...

We give closed product formulas for the irreducible characters of symmetric groups related to rectangular `almost square' Young diagrams $p \times(p+\delta)$ a fixed value an integer $\delta$ and arbitrary $p$.

‎Let $L$ be a Lie algebra‎, ‎$mathrm{Der}(L)$ be the set of all derivations of $L$ and $mathrm{Der}_c(L)$ denote the set of all derivations $alphainmathrm{Der}(L)$ for which $alpha(x)in [x,L]:={[x,y]vert yin L}$ for all $xin L$‎. ‎We obtain an upper bound for dimension of $mathrm{Der}_c(L)$ of the finite dimensional nilpotent Lie algebra $L$ over algebraically closed fields‎. ‎Also‎, ‎we classi...

We provide a constructive direct semantic proof of the completeness of the cut-free part of the hypersequent calculus HIF for the standard first-order Gödel logic (thereby proving both completeness of the calculus for its standard semantics, and the admissibility of the cut rule in the full calculus). The results also apply to derivations from assumptions (or “non-logical axioms”), showing in p...

We study the height of the delta peak at 0 in the spectrum of incidence matrices of random trees. We show that the average fraction of the spectrum occupied by the eigenvalue 0 in a large random tree is asymptotic to 2x∗−1 = 0.1342865808195677459999 · · · where x∗ is the unique real root of x = e. For finite trees, we give a closed form, a generating function, and an asymptotic estimate for the...