TY  - INPR
A1  - Makhmudov, K. O.
A1  - Makhmudov, O. I.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A nonstandard Cauchy problem for the heat equation
N2  - We consider a Cauchy problem for the heat equation in a cylinder X x (0,T) over a domain X in the n-dimensional space with data on a strip lying on the lateral surface. The strip is of the form 
S x (0,T), where S is an open subset of the boundary of X. The problem is ill-posed. Under natural restrictions on the configuration of S we derive an explicit formula for solutions of this problem.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015)11 
KW  - heat equation
KW  - Cauchy problem
KW  - Carleman formulas
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-83830
SN  - 2193-6943
VL  - 4
IS  - 11
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Maergoiz, L.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Optimal recovery from a finite set in Banach spaces of entire functions
N2  - We develop an approach to the problem of optimal recovery of continuous linear functionals in Banach spaces through information on a finite number of given functionals. The results obtained are applied to the problem of the best analytic continuation from a finite set in the complex space Cn, n ≥ 1, for classes of entire functions of exponential type which belong to the space Lp, 1 < p < 1, on the real subspace of Cn. These latter are known as Wiener classes.
T3  - Preprint - (2006) 19 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30199
ER  - 
TY  - INPR
A1  - Maaß, Peter
A1  - Rieder, Andreas
T1  - Wavelet-accelerated Tikhonov-Phillips regularization with applications
N2  - Contents: 1 Introduction 1.1 Tikhanov-Phillips Regularization of Ill-Posed Problems 1.2 A Compact Course to Wavelets 2 A Multilevel Iteration for Tikhonov-Phillips Regularization 2.1 Multilevel Splitting 2.2 The Multilevel Iteration 2.3 Multilevel Approach to Cone Beam Reconstuction 3 The use of approximating operators 3.1 Computing approximating families {Ah}
T3  - NLD Preprints - 30 
Y1  - 1996
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14104
ER  - 
TY  - INPR
A1  - Maaß, Peter
A1  - Pereverzev, Sergei V.
A1  - Ramlau, Ronny
A1  - Solodky, Sergei G.
T1  - An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection
N2  - The aim of this paper is to describe an efficient strategy for descritizing ill-posed linear operator equations of the first kind: we consider Tikhonov-Phillips-regularization χ^δ α = (a * a + α I)^-1 A * y ^δ with a finite dimensional approximation A n instead of A. We propose a sparse matrix structure which still leads to optimal convergences rates but requires substantially less scalar products for computing A n compared with standard methods.
T3  - NLD Preprints - 48 
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14739
ER  - 
TY  - INPR
A1  - Ma, Li
A1  - Xu, Xingwang
T1  - Positive solutions of a logistic equation on unbounded intervals
N2  - In this paper, we study the existence of positive solutions of a one-parameter family of logistic equations on R+ or on R. These equations are stationary versions of the Fisher equations and the KPP equations. We also study the blow up region of a sequence of the solutions when the parameter approachs a critical value and the nonexistence of positive solutions beyond the critical value. We use the direct method and the sub and super solution method.
T3  - Preprint - (2001) 17 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26015
ER  - 
TY  - INPR
A1  - Ma, L.
A1  - Schulze, Bert-Wolfgang
T1  - Operators on manifolds with conical singularities
N2  - We construct elliptic elements in the algebra of (classical pseudo-differential) operators on a manifold M with conical singularities. The ellipticity of any such operator A refers to a pair of principal symbols (σ0, σ1) where σ0 is the standard (degenerate) homogeneous principal symbol, and σ1 is the so-called conormal symbol, depending on the complex Mellin covariable z. The conormal symbol, responsible for the conical singularity, is operator-valued and acts in Sobolev spaces on the base X of the cone. The σ1-ellipticity is a bijectivity condition for all z of real part (n + 1)/2 − γ, n = dimX, for some weight γ. In general, we have to rule out a discrete set of exceptional weights that depends on A. We show that for every operator A which is elliptic with respect to σ0, and for any real weight γ there is a smoothing Mellin operator F in the cone algebra such that A + F is elliptic including σ1. Moreover, we apply the results to ellipticity and index of (operator-valued) edge symbols from the calculus on manifolds with edges.
T3  - Preprint - (2009) 07 
KW  - Operators on manifolds with conical singularities
KW  - conormal symbols
KW  - ellipticity of cone operators
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-36608
ER  - 
TY  - INPR
A1  - Léonard, Christian
A1  - Roelly, Sylvie
A1  - Zambrini, Jean-Claude
T1  - Temporal symmetry of some classes of stochastic processes
N2  - In this article we analyse the structure of Markov processes and reciprocal processes to underline their time symmetrical properties, and to compare them. Our originality consists in adopting a unifying approach of reciprocal processes, independently of special frameworks in which the theory was developped till now (diffusions, or pure jump processes). This leads to some new results, too.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 7 
KW  - Markov processes
KW  - reciprocal processes
KW  - time symmetry
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-64599
SN  - 2193-6943
ER  - 
TY  - INPR
A1  - Läuter, Henning
A1  - Ramadan, Ayad
T1  - Statistical Scaling of Categorical Data
N2  - Estimation and testing of distributions in metric spaces are well known. R.A. Fisher, J. Neyman, W. Cochran and M. Bartlett achieved essential results on the statistical analysis of categorical data. In the last 40 years many other statisticians found important results in this field. Often data sets contain categorical data, e.g. levels of factors or names. There does not exist any ordering or any distance between these categories. At each level there are measured some metric or categorical values. We introduce a new method of scaling based on statistical decisions. For this we define empirical probabilities for the original observations and find a class of distributions in a metric space where these empirical probabilities can be found as approximations for equivalently defined probabilities. With this method we identify probabilities connected with the categorical data and probabilities in metric spaces. Here we get a mapping from the levels of factors or names into points of a metric space. This mapping yields the scale for the categorical data. From the statistical point of view we use multivariate statistical methods, we calculate maximum likelihood estimations and compare different approaches for scaling.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 01 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49566
ER  - 
TY  - INPR
A1  - Läuter, Henning
A1  - Ramadan, Ayad
T1  - Modeling and Scaling of Categorical Data
N2  - Estimation and testing of distributions in metric spaces are well known. R.A. Fisher, J. Neyman, W. Cochran and M. Bartlett achieved essential results on the statistical analysis of categorical data. In the last 40 years many other statisticians found important results in this field. Often data sets contain categorical data, e.g. levels of factors or names. There does not exist any ordering or any distance between these categories. At each level there are measured some metric or categorical values. We introduce a new method of scaling based on statistical decisions. For this we define empirical probabilities for the original observations and find a class of distributions in a metric space where these empirical probabilities can be found as approximations for equivalently defined probabilities. With this method we identify probabilities connected with the categorical data and probabilities in metric spaces. Here we get a mapping from the levels of factors or names into points of a metric space. This mapping yields the scale for the categorical data. From the statistical point of view we use multivariate statistical methods, we calculate maximum likelihood estimations and compare different approaches for scaling.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 03 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49572
ER  - 
TY  - INPR
A1  - Läuter, Henning
A1  - Liero, Hannelore
T1  - Nonparametric estimation and testing in survival models
N2  - The aim of this paper is to demonstrate that nonparametric smoothing methods for estimating functions can be an useful tool in the analysis of life time data. After stating some basic notations we will present a data example. Applying standard parametric methods to these data we will see that this approach fails - basic features of the underlying functions are not reflected by their estimates. Our proposal is to use nonparametric estimation methods. These methods are explained in section 2. Nonparametric approaches are better in the sense that they are more flexible, and misspecifications of the model are avoided. But, parametric models have the advantage that the parameters can be interpreted. So, finally, we will formulate a test procedure to check whether a parametric or a nonparametric model is appropriate.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2004, 05 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51586
ER  - 
TY  - INPR
A1  - Läuter, Henning
T1  - On approximate likelihood in survival models
N2  - We give a common frame for different estimates in survival models. For models with nuisance parameters we approximate the profile likelihood and find estimates especially for the proportional hazard model.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2006, 04 
KW  - Approximate likelihood
KW  - profile likelihood
KW  - propor-tional hazard mode
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51615
ER  - 
TY  - INPR
A1  - Läuter, Henning
T1  - Estimation in partly parametric additive Cox models
N2  - The dependence between survival times and covariates is described e.g. by proportional hazard models. We consider partly parametric Cox models and discuss here the estimation of interesting parameters. We represent the ma- ximum likelihood approach and extend the results of Huang (1999) from linear to nonlinear parameters. Then we investigate the least squares esti- mation and formulate conditions for the a.s. boundedness and consistency of these estimators.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2003, 16 
KW  - Survival models with covariates
KW  - estimation of regression
KW  - maximum likelihood estimator
KW  - least squares estimator
KW  - boun- dedness
KW  - consistency
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51509
ER  - 
TY  - INPR
A1  - Läuter, Henning
T1  - Empirical Minimax Linear Estimates
N2  - We give the explicit solution for the minimax linear estimate. For scale dependent models an empirical minimax linear estimates is de¯ned and we prove that these estimates are Stein's estimates.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2008, 06 
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49483
ER  - 
TY  - INPR
A1  - Ly, Ibrahim
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Generalised Beltrami equations
N2  - We enlarge the class of Beltrami equations by developping a stability theory for the sheaf of solutions of an overdetermined elliptic system of first order homogeneous partial differential equations with constant coefficients in the Euclidean space.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)14 
KW  - Quasiconformal mapping
KW  - Beltrami equation
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-67416
ER  - 
TY  - INPR
A1  - Ly, Ibrahim
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Radó theorem for p-harmonic functions
N2  - Let A be a nonlinear differential operator on an open set X in R^n and S a closed subset of X. Given a class F of functions in X, the set S is said to be removable for F relative to A if any weak solution of A (u) = 0 in the complement of S of class F satisfies this equation weakly in all of X. For the most extensively studied classes F we show conditions on S which guarantee that S is removable for F relative to A.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 3 
KW  - Quasilinear equations
KW  - removable sets
KW  - p-Laplace Operator
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-71492
SN  - 2193-6943
VL  - 4
IS  - 3
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Ly, Ibrahim
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Asymptotic expansions at nonsymmetric cuspidal points
N2  - We study asymptotics of solutions to the Dirichlet problem in a domain whose boundary contains a nonsymmetric conical point. We establish a complete asymptotic expansion of solutions near the singular point.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 7 
KW  - the Dirichlet problem
KW  - singular point
KW  - asymptotic expansion
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-78199
SN  - 2193-6943
VL  - 4
IS  - 7
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Ly, I.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - The cauchy problem for nonlinear elliptic equations
N2  - This paper is devoted to investigation of the Cauchy problem for nonlinear elliptic equations with a small parameter.
T3  - Preprint - (2007) 01 
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30228
ER  - 
TY  - INPR
A1  - Lukaschewitsch, Michael
T1  - Geoelectrical conductivity problems on unbounded domains
N2  - This paper deals with the electrical conductivity problem in geophysics. It is formulated as an elliptic boundary value problem of second order for a large class of bounded and unbounded domains. A special boundary condition, the so called "Complete Electrode Model", is used. Poincaré inequalities are formulated and proved in the context of weighted Sobolev spaces, leading to existence and uniqueness statements for the boundary value problem. In addition, a parameter-to-solution operator arising from the inverse conductivity problem in medicine (EIT) and geophysics is investigated mathematically and is shown to be smooth and analytic.
T3  - NLD Preprints - 45 
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14704
ER  - 
TY  - INPR
A1  - Lucke, Ulrike
A1  - Steinmetz, Ralf
T1  - Special issue on "Pervasive Education"
T2  - Pervasive and mobile computing
Y1  - 2014
U6  - https://doi.org/10.1016/j.pmcj.2014.08.001
SN  - 1574-1192
SN  - 1873-1589
VL  - 14
SP  - 1
EP  - 2
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - INPR
A1  - Louis, Pierre-Yves
A1  - Rouquier, Jean-Baptiste
T1  - Time-to-Coalescence for interacting particle systems : parallel versus sequential updating
N2  - Studying the influence of the updating scheme for MCMC algorithm on spatially extended models is a well known problem. For discrete-time interacting particle systems we study through simulations the effectiveness of a synchronous updating scheme versus the usual sequential one. We compare the speed of convergence of the associated Markov chains from the point of view of the time-to-coalescence arising in the coupling-from-the-past algorithm. Unlike the intuition, the synchronous updating scheme is not always the best one. The distribution of the time-to-coalescence for these spatially extended models is studied too.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2009, 03 
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49454
ER  -