TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Pibaljommee, Bundit
T1  - Clones of implicit operations
N2  - 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
Y1  - 2005
SN  - 0002-5240
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Radelecki, S.
A1  - Ratanaprasert, C.
T1  - On constantive simple and order-primal algebras
N2  - 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
Y1  - 2005
ER  - 
TY  - JOUR
A1  - Changphas, Thawhat
A1  - Denecke, Klaus-Dieter
T1  - Green's relation R on the monoid of clone endomorphisms
N2  - 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
Y1  - 2005
SN  - 1005-3867
ER  - 
TY  - BOOK
A1  - Harutjunjan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Conormal symbols of mixed elliptic problems with singular interfaces
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2005
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Janke, Thomas
A1  - Wuttke, Hans
A1  - Dietsch, Volker
A1  - Janßen, Martin
A1  - König, Gerhard
A1  - Mentzendorff, Arne
A1  - Simanowsky, Ursula
A1  - Wuttke, Joachim
T1  - Mathematik : Stochastik ; Orientierungswissen Analytische Geometrie ; Gymnasiale Oberstufe, NRW [Schülerbuch]
Y1  - 2005
SN  - 3-464-57213-7
PB  - Cornelsen
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Schmidt, Hans-Jürgen
T1  - Einsteins Arbeiten in Bezug auf die moderne Kosmologie : de Sitters Lösung der Einsteinschen Feldgleichung mit positivem kosmologischen Glied als Geometrie des inflationaeren Weltmodells
N2  - Die Arbeit von Albert Einstein von 1918 zu Willem De Sitters Loesung der Einsteinschen Feldgleichung wird unter heutigem Gesichtspunkt kommentiert. Dazu wird zunaechst die Geometrie der De Sitterschen Raum-Zeit beschrieben, sowie ihre Bedeutung fuer das inflationaere Weltmodell erlaeutert.
Y1  - 2005
UR  - http://arXiv.org/abs/gr-qc/0506121
ER  - 
TY  - BOOK
A1  - Janke, Thomas
A1  - Wuttke, Hans
A1  - Dietsch, Volker
A1  - Janßen, Martin
A1  - Koenig, Gerhard
A1  - Mentzendorff, Arne
A1  - Simanowsky, Ursula
A1  - Wuttke, Joachim
ED  - Jahnke, Thomas
T1  - Mathematik : Stochastik ; Gymnasiale Oberstufe, [Schülerbuch]
Y1  - 2005
SN  - 3-464-57218-8
PB  - Cornelsen
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Pfäffle, Frank
T1  - Eigenvalues of Dirac Operators for Hyperbolic Degenerations
N2  - We study the behaviour of the spectrum of the Dirac operator for sequences of compact hyperbolic manifolds whose limit is non-compact. If the spectrum of the limit manifold is descrete we show that the spectrum is approximated by the spectra of compact manifolds.
Y1  - 2005
UR  - http://www.springerlink.com/app/home/ contribution.asp?wasp=74877684beab42c4a04190542f838968&referrer=parent&backto=issue,1,6;journal,6,89;searchpublicationsre sults,1,2;
ER  - 
TY  - BOOK
A1  - Janke, Thomas
A1  - Wuttke, Hans
A1  - Dietsch, Volker
A1  - Janßen, Martin
A1  - König, Gerhard
A1  - Mentzendorff, Arne
A1  - Simanowsky, Ursula
A1  - Wuttke, Joachim
T1  - Mathematik : Stochastik ; Handreichungen für den Unterricht ; Gymnasiale Oberstufe [Schülerbuch]
Y1  - 2005
SN  - 3-464-57288-9
PB  - Cornelsen
CY  - Berlin
ER  - 
TY  - BOOK
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Unitary solutions of paratial differential equations
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2005
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Liu, Weian
T1  - Monotone method for nonlocal systems of first order
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2005
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Qin, Yuming
T1  - Uniform compact attractors for a nonlinear non-autonomous equation of viscoelasticity
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2005
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Zähle, Henryk
T1  - Space-time regularity of catalytic super-Brownian motion
N2  - The paper studies catalytic super-Brownian motion on the real line, where the branching rate is controlled by a catalyst. D. A. Dawson, K. Fleischmann and S. Roelly showed, for a broad class of catalysts, that, as for constant branching, the processes are absolutely continuous measures. This paper considers a class of catalysts, called moderate, which must satisfy a uniform boundedness condition and a condition controlling the degree of singularity---essentially that the mass of catalyst in small balls should (uniformly) be of order r^a, where a>0. The main result of this paper shows that for this class of catalysts there is a continuous density field for the process. Moreover the density is the unique solution (in law) of an appropriate SPDE.
Y1  - 2005
UR  - http://www.interscience.wiley.com/jpages/0025-584X/
ER  - 
TY  - THES
A1  - Rätsch, Thoralf
T1  - On the Equi-Constistency of the failure of the GAP-1 transfer property and an inaccessible cardinal
Y1  - 2005
CY  - Potsdam
ER  - 
TY  - BOOK
ED  - Brückner, Axel
T1  - Mathematik : Lehrbuch für die Klasse 10 ; Gymnasium Brandenburg
Y1  - 2005
SN  - 3-89818-142-1
PB  - Paetec
CY  - Berlin
ER  - 
TY  - BOOK
A1  - Paneah, Boris
T1  - On the general theory of the cauchy type functional equations with applications in analysis
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2005
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Böckmann, Christine
A1  - Mironova, I.
A1  - Muller, D.
T1  - Microphysical aerosol parameters from multiwavelength lidar
N2  - The hybrid regularization technique developed at the Institute of Mathematics of Potsdam University (IMP) is used to derive microphysical properties such as effective radius, surface-area concentration, and volume concentration, as well as the single-scattering albedo and a mean complex refractive index, from multiwavelength lidar measurements. We present the continuation of investigations of the IMP method. Theoretical studies of the degree of ill-posedness of the underlying model, simulation results with respect to the analysis of the retrieval error of microphysical particle properties from multiwavelength lidar data, and a comparison of results for different numbers of backscatter and extinction coefficients are presented. Our analysis shows that the backscatter operator has a smaller degree of ill- posedness than the operator for extinction. This fact underlines the importance of backscatter data. Moreover, the degree of ill-posedness increases with increasing particle absorption, i.e., depends on the imaginary part of the refractive index and does not depend significantly on the real part. Furthermore, an extensive simulation study was carried out for logarithmic-normal size distributions with different median radii, mode widths, and real and imaginary parts of refractive indices. The errors of the retrieved particle properties obtained from the inversion of three backscatter (355, 532, and 1064 nm) and two extinction (355 and 532 nm) coefficients were compared with the uncertainties for the case of six backscatter (400. 710, 800 nm. additionally) and the same two extinction coefficients. For known complex refractive index and up to 20% normally distributed noise, we found that the retrieval errors for effective radius, surface-area concentration, and volume concentration stay below approximately 15% in both cases. Simulations were also made with unknown complex refractive index. In that case the integrated parameters stay below approximately 30%, and the imaginary part of the refractive index stays below 35% for input noise up to 10% in both cases. In general, the quality of the retrieved aerosol parameters depends strongly on the imaginary part owing to the degree of ill-posedness. It is shown that under certain constraints a minimum data set of three backscatter coefficients and two extinction coefficients is sufficient for a successful inversion. The IMP algorithm was finally tested for a measurement case. (C) 2005 Optical Society of America
Y1  - 2005
SN  - 1084-7529
ER  - 
TY  - JOUR
A1  - Bovier, Anton
A1  - Gayrard, Veronique
A1  - Klein, Markus
T1  - Metastability in reversible diffusion processes : II. Precise asymptotics for small eigenvalues
N2  - We continue the analysis of the problem of metastability for reversible diffusion processes, initiated in [BEGK3], with a precise analysis of the low-lying spectrum of the generator. Recall that we are considering processes with generators of the form -epsilonDelta + delF(.) del on R-d or subsets of Rd, where F is a smooth function with finitely many local minima. Here we consider only the generic situation where the depths of all local minima are different. We show that in general the exponentially small part of the spectrum is given, up to multiplicative errors tending to one, by the eigenvalues of the classical capacity matrix of the array of capacitors made of balls of radius epsilon centered at the positions of the local minima of F. We also get very precise uniform control on the corresponding eigenfunctions. Moreover, these eigenvalues can be identified with the same precision with the inverse mean metastable exit times from each minimum. In [BEGK3] it was proven that these mean times are given, again up to multiplicative errors that tend to one, by the classical Eyring- Kramers formula
Y1  - 2005
SN  - 1435-9855
ER  - 
TY  - JOUR
A1  - Rasch, T.
A1  - Schindler, R.
T1  - A new condensation principle
N2  - We generalize del(A), which was introduced in [Schinfinity], to larger cardinals. For a regular cardinal kappa>N-0 we denote by del(kappa)(A) the statement that Asubset of or equal tokappa and for all regular theta>kappa(o), {X is an element of[L-theta[A]](<) : X &AND;  &ISIN;  &AND; otp (X &AND; Ord) &ISIN; Card (L[A&AND;X&AND;])} is stationary in [L-[A]](<). It was shown in [Sch&INFIN;] that &DEL;(N1) (A) can hold in a set-generic extension of L. We here prove that &DEL;(N2) (A) can hold in a set-generic extension of L as well. In both cases we in fact get equiconsistency theorems. This strengthens results of [Ra00] and [Ran01]. &DEL;(N3) () is equivalent with the existence of 0#
Y1  - 2005
SN  - 1432-0665
ER  - 
TY  - JOUR
A1  - Gosson, Maurice A. de
T1  - Extended Weyl calculus and application to the phase-space Schrodinger equation
N2  - We show that the Schrodinger equation in phase space proposed by Torres-Vega and Frederick is canonical in the sense that it is a natural consequence of the extended Weyl calculus obtained by letting the Heisenberg group act on functions (or half-densities) defined on phase space. This allows us, in passing, to solve rigorously the TF equation for all quadratic Hamiltonians
Y1  - 2005
ER  -