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There is a close connection between a variety and its clone. The clone of a variety is a multibased algebra, where the different universes are the sets of n-ary terms over this variety for every natural number n and where the operations describe the superposition of terms of different arities. All projections are added as nullary operations. Subvarieties correspond to homomorphic images of clones. Subclones can be described by reducts of varieties, isomorphic clones by equivalent varieties. Clone identities correspond to hyperidentities and varieties of clones to hypervarieties. Pseudovarieties are classes of finite algebras which are closed under taking of subalgebras, homomorphic images and finite direct products. Pseudovarieties are important in the theories of finite state automata, rational languages, finite semigroups and their connections. In a very natural way, there arises the question for the clone of a pseudovariety. In the present paper, we will describe this algebraic structure
A finite algebra A = (A; F-A) is said to be order-primal if its clone of all term operations is the set of all operations defined on A which preserve a given partial order <= on A. In this paper we study algebraic properties of order-primal algebras for connected ordered sets (A; <=). Such order-primal algebras are constantive, simple and have no non-identical automorphisms. We show that in this case F-A cannot have only unary fundamental operations or only one at least binary fundamental operation. We prove several properties of the varieties and the quasi-varieties generated by constantive and simple algebras and apply these properties to order-primal algebras. Further, we use the properties of order-primal algebras to formulate new primality criteria for finite algebras
A hypersubstitution is a map which takes n-ary operation symbols to n-ary terms. Any such map can be uniquely extended to a map defined on the set W-tau(X) of all terms of type tau, and any two such extensions can be composed in a natural way. Thus, the set Hyp(tau) of all hypersubstitutions of type tau forms a monoid. In this paper, we characterize Green's relation R on the monoid Hyp(tau) for the type tau = (n, n). In this case, the monoid of all hypersubstitutions is isomorphic with the monoid of all Clone endomorphisms. The results can be applied to mutually derived varieties
Intrinsic fluorescence quenching of humic substances (HS) and the sensitization of Ln(3+) luminescence (Ln3+ Tb3+, Eu3+) in HS complexes were investigated. Both measurements yielded complementary information on the complexation of metals by HS. Large differences between fulvic acids(FA)and humic acids (HA) were found. From time-resolved luminescence measurements it is concluded that a combination of energy transfer and energy back transfer between HS and Ln(3+) is responsible for the observed luminescence decay characteristics. In the case of Eu3+, an additional participation of charge-transfer states is suggested. A new concept for the evaluation of the sensitized luminescence decays of Ln(3+) was adapted
The spectrum of the quasar PHL 1226 is known to have a strong Mg II and sub-damped Lymanalpha (sub-DLA) absorption line system with N(H I) = (5 +/- 2) x 10(19) cm(-2) at z = 0.1602. Using integral field spectra from the Potsdam Multi Aperture Spectrophotometer (PMAS) we investigate a galaxy at an impact parameter of 6".4 which is most probably responsible for the absorption lines. A fainter galaxy at a similar redshift and a slightly larger distance from the QSO is known to exist, but we assume that the absorption is caused by the more nearby galaxy. From optical Balmer lines we estimate an intrinsic reddening consistent with 0, and a moderate star formation rate of 0.5 M-circle dot yr(-1) is inferred from the Ha luminosity. Using nebular emission line ratios we find a solar oxygen abundance 12 + log (O/H) = 8.7 +/- 0.1 and a solar nitrogen to oxygen abundance ratio log (N/O) = -1.0 +/- 0.2. This abundance is larger than those of all known sub-DLA systems derived from analyses of metal absorption lines in quasar spectra. On the other hand, the properties are compatible with the most metal rich galaxies responsible for strong Mg II absorption systems. These two categories can be reconciled if we assume an abundance gradient similar to local galaxies. Under that assumption we predict abundances 12 + log (O/H) = 7.1 and log (N/O) = -1.9 for the sub-DLA cloud, which is similar to high redshift DLA and sub-DLA systems. We find evidence for a rotational velocity of similar to200 km s(-1) over a length of similar to7 kpc. From the geometry and kinematics of the galaxy we estimate that the absorbing cloud does not belong to a rotating disk, but could originate in a rotating halo
The Hengshan complex forms part of the central zone of the North China Craton and consists predominantly of ductilely-deformed late Archaean to Palaeoproterozoic high-grade, partly migmatitic, granitoid orthogneisses, intruded by mafic dykes of gabbroic composition. Many highly strained rocks were previously misinterpreted as supracrustal sequences and represent mylonitized granitoids and sheared dykes. Our single zircon dating documents magmatic granitoid emplacement ages between 2.52 Ga and 2.48 Ga, with rare occurrences of 2.7 Ga gneisses, possibly reflecting an older basement. A few granitic gneisses have emplacement ages between 2.35 and 2.1 Ga and show the same structural features as the older rocks, indicating that the main deformation occurred after similar to 2.1 Ga. Intrusion of gabbroic dykes occurred at similar to 1920 Ma, and all Hengshan rocks underwent granulite-facies metamorphism at 1.88-1.85 Ga, followed by retrogression, shearing and uplift. We interpret the Hengshan and adjacent Fuping granitoid gneisses as the lower, plutonic, part of a late Archaean to early Palaeoproterozoic Japan-type magmatic arc, with the upper, volcanic part represented by the nearby Wutai complex. Components of this arc may have evolved at a continental margin as indicated by the 2.7 Ga zircons. Major deformation and HP metamorphism occurred in the late Palaeoproterozoic during the Luliang orogeny when the Eastern and Western blocks of the North China Craton collided to form the Trans-North China orogen. Shear zones in the Hengshan are interpreted as major lower crustal discontinuities post-dating the peak of HP metamorphism, and we suggest that they formed during orogenic collapse and uplift of the Hengshan complex in the late Palaeoproterozoic (< 1.85 Ga)