We develop the general theory of RMV-algebras, which are essentially unit intervals in Riesz spaces with strong unit. Since the variety of RMV-algebras is generated by [0, 1], we get an equational characterization of the real product on [0,1] interpreted as scalar multiplication.

The reproducibility over temperature and time of the pull-in voltage of micromechanical structures has been analyzed and verified using fabricated devices in silicon. The pull-in structures are intended for use as an on-chip voltage reference. Microbeams of 100m length, 3m width, and 11m thickness are electrostatically actuated with a very reproducible pull-in voltage at 9.1 V. Devices demonstr...

Effect basic algebras (which correspond to lattice ordered effect algebras) are studied. Their ideals are characterized (in the language of basic algebras) and one-to-one correspondence between ideals and congruences is shown. Conditions under which the quotients are OMLs or MV-algebras are found.

Proof. Suppose Mv = λv. We want to show that λ has imaginary value 0. For a complex number x = a + ib, the conjugate of x, is defined as follows: x∗ = a − ib. So, all we need to show is that λ = λ∗. The conjugate of a vector is the conjugate of all of its coordinate. Taking the conjugate transpose of both sides of the above equality, we have v∗M = λ∗v∗, (8.1) where we used that M = M . So, on o...

In this note we prove that it is impossible to extend the natural equivalence between the category of MV-algebras and the category of Abelian `-groups with strong unit described by C. C. Chang, 1958, and Cignoli & Mundici, 1997, to a natural equivalence between the category of m-zeroids and some category containing the category of Abelian `-groups with strong unit.

We prove that RS-BL-algebras are MV-algebras.

Coalition games are generalized to semisimple MV-algebras. Coalitions are viewed as [0,1]-valued functions on a set of players, which enables to express a degree of membership of a player in a coalition. Every game is a real-valued mapping on a semisimple MV-algebra. The goal is to recover the so-called core: a set of final distributions of payoffs, which are represented by measures on the MV-a...

This paper summarizes Kormendy et al. (2009, ApJS, in press, arXiv:0810.1681). We confirm that spheroidal galaxies have fundamental plane correlations that are almost perpendicular to those for bulges and ellipticals. Spheroidals are not dwarf ellipticals. They are structurally similar to late-type galaxies. We suggest that they are defunct (“red and dead”) late-type galaxies transformed by a v...

HST observations show that the surface brightness profiles of early-type galaxies have central cusps, I ∝ r−γ. Two characteristic profile types are observed: ‘core’ profiles have a break at a resolved radius and γ ≤ 0.3 inside that radius; ‘power-law’ profiles have no clear break and γ > 0.3. With few exceptions, galaxies with MV < −22 have core profiles, and galaxies with MV > −20.5 have power...

Lukasiewicz implication algebras are the {→, 1}-subreducts of MV algebras. They are the algebraic counterpart of SuperLukasiewicz Implicational Logics. We give a description of free Lukasiewicz implication algebras in the context of McNaughton functions. More precisely, we show that the |X|-free Lukasiewicz implication algebra is isomorphic to ⋃ x∈X [xθ) for a certain congruence θ over the |X|-...