## Preprints (rote Reihe) des Fachbereich Mathematik

- 338
- Rank two Cohen-Macaulay modules over singularities of type ..... (2004)
- We describe, by matrix factoizations, all the rank two maximal Cohen-Macauly modules over singularities of type ......

- 336
- Hyperquasivarieties (2003)
- We consider the notion of hyper-quasi-identities and hyperquasivarieties, as a common generalization of the concept of quasi-identity and quasivariety invented by A.I. Mal'cev, cf. [10], cf. [5] and hypervariety invented by the authors in [6].

- 334
- Hochschild- and Cyclic-Homology of LCNT-Spaces (2003)
- We define a class of topological spaces (LCNT-spaces) which come together with a nuclear Frechet algebra. Like the algebra of smooth functions on a manifold, this algebra carries the differential structure of the object. We compute the Hochschild homology of this object and show that it is isomorphic to the space of differential forms. This is a generalization of a result obtained by Alain Connes in the framework of smooth manifolds.

- 332
- Functions preserving 2-series strict orders (2003)
- In recent years a considerable attention was paid to an investigation of finite orders relative to different properties of their isotone functions [2,3]. Strict order relations are defined as strict asymmetric and transitive binary relations. Some algebraic properties of strict orders were already studied in [6]. For the class K of so-called 2-series strict orders we describe the partially ordered set EndK of endomorphism monoids, ordered by inclusion. It is obtained that EndK possesses a least element and in most cases defines a Boolean algebra. Moreover, every 2-series strict order is determined by its n-ary isotone functions for some natural number n.

- 331
- Isotone mappings of levelled strict orders (2002)
- Strict order relations are defined as strict asymmetric and transitive binary relations. For classes of so-called levelled strict orders it is analyzed, under which conditions the endomorphism monoids of two relations coincide; in particular the case of direct sums of strict antichains is studied. Further, it is shown that these orders differ in their sets of binary order preserving functions.

- 330
- Morozov's Discrepancy Principle Under General Source Conditions (2002)
- In this paper we study linear ill-posed problems Ax = y in a Hilbert space setting where instead of exact data y noisy data y^delta are given satisfying |y - y^delta| <= delta with known noise level delta. Regularized approximations are obtained by a general regularization scheme where the regularization parameter is chosen from Morozov's discrepancy principle. Assuming the unknown solution belongs to some general source set M we prove that the regularized approximation provides order optimal error bounds on the set M. Our results cover the special case of finitely smoothing operators A and extends recent results for infinitely smoothing operators.

- 328
- On Simpson Moduli Spaces of Stable Sheaves on P_2 with Linear Hilbert Polynomial (2000)
- In this short note we prove some general results on semi-stable sheaves on P_2 and P_3 with arbitrary linear Hilbert polynomial. Using Beilinson's spectral sequence, we compute free resolutions for this class of semi-stable sheaves and deduce that the smooth moduli spaces M_{r m + s}(P_2) and M_{r m + r - s}(P_2) are birationally equivalent if r and s are coprime.

- 327
- An economic approach to discretization of nonstationary iterated Tikhonov method (2002)
- An adaptive discretization scheme of ill-posed problems is used for nonstationary iterated Tikhonov regularization. It is shown that for some classes of operator equations of the first kind the proposed algorithm is more efficient compared with standard methods.

- 324
- Derived Tameness of some Associative Algebras (2001)
- In this article we propose a new method to deal with the derived categories of some semi-perfect k-algebras. This method gives us a unifying description of the derived categories of a branch class of algebras such as gentle algebras, some lannish algebras, of the Gelfand quiver etc.