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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