TY  - JOUR
A1  - Böckmann, Christine
A1  - Brückner, Axel
T1  - 100 years of the Runge-Kutta method : a brief editing for schools
BT  - Hundred years of the Runge-Kutta method : a brief editing for schools
N2  - This paper reports on the historical development of the Runge-Kutta methods beginning with the simple Euler method up to an embedded 13-stage method. Moreover, the design and the use of those methods under error order, stability and computation time conditions is edited for students of numerical analysis at undergraduate level. The second part presents applications in natural sciences, compares different methods and illustrates some of the difficulties of numerical solutions.
Y1  - 2001
SN  - 0268-3679
ER  - 
TY  - JOUR
A1  - Dzhunushaliev, Vladimir
A1  - Schmidt, Hans-Jürgen
T1  - 2+2-decomposable solutions of weyl gravity
BT  - Zwei plus zwei-decomposable solutions of wey gravity
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Gonzáles-Diaz, P. F.
A1  - Kasper, Uwe
A1  - Rainer, Martin
T1  - 2-Dimensional dilatonic gravity from multidimensional Einstein gravity
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Schmidt, Hans-Jürgen
T1  - 2-dimensional representations of 4-dimensional gravitational waves
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Hoehnke, Hans-Jürgen
A1  - Johnson, K. W.
T1  - 3-characters are sufficient for the group determinant
BT  - Three-characters are sufficient for the group determinant
Y1  - 1995
ER  - 
TY  - JOUR
A1  - Boldrighini, Carlo
A1  - Frigio, Sandro
A1  - Maponi, Pierluigi
A1  - Pellegrinotti, Alessandro
A1  - Sinai, Yakov G.
T1  - 3-D incompressible Navier-Stokes equations: Complex blow-up and related real flows
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472201
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 185
EP  - 194
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Dzhunushaliev, Vladimir
A1  - Schmidt, Hans-Jürgen
T1  - 4D wormhole with signature change in the presence of extra dimensions
BT  - VierD wormhole with signature change in the presence of extra dimensions
JF  - General relativity and quantum cosmology : preprints gr-qc
Y1  - 1999
UR  - http://xxx.soton.ac.uk/form/gr-qc?
VL  - 9908076
ER  - 
TY  - JOUR
A1  - Mariucci, Ester
A1  - Ray, Kolyan
A1  - Szabo, Botond
T1  - A Bayesian nonparametric approach to log-concave density estimation
JF  - Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability
N2  - The estimation of a log-concave density on R is a canonical problem in the area of shape-constrained nonparametric inference. We present a Bayesian nonparametric approach to this problem based on an exponentiated Dirichlet process mixture prior and show that the posterior distribution converges to the log-concave truth at the (near-) minimax rate in Hellinger distance. Our proof proceeds by establishing a general contraction result based on the log-concave maximum likelihood estimator that prevents the need for further metric entropy calculations. We further present computationally more feasible approximations and both an empirical and hierarchical Bayes approach. All priors are illustrated numerically via simulations.
KW  - convergence rate
KW  - density estimation
KW  - Dirichlet mixture
KW  - log-concavity
KW  - nonparametric hypothesis testing
KW  - posterior distribution
Y1  - 2020
U6  - https://doi.org/10.3150/19-BEJ1139
SN  - 1350-7265
SN  - 1573-9759
VL  - 26
IS  - 2
SP  - 1070
EP  - 1097
PB  - International Statistical Institute
CY  - The Hague
ER  - 
TY  - JOUR
A1  - Hoehnke, Hans-Jürgen
T1  - A Birkhoff theorem for partial algebras via completion
Y1  - 1996
ER  - 
TY  - JOUR
A1  - Ly, Ibrahim
T1  - A Cauchy problem for the Cauchy-Riemann operator
JF  - Afrika Matematika
N2  - We study the Cauchy problem for a nonlinear elliptic equation with data on a piece S of the boundary surface partial derivative X. By the Cauchy problem is meant any boundary value problem for an unknown function u in a domain X with the property that the data on S, if combined with the differential equations in X, allows one to determine all derivatives of u on S by means of functional equations. In the case of real analytic data of the Cauchy problem, the existence of a local solution near S is guaranteed by the Cauchy-Kovalevskaya theorem. We discuss a variational setting of the Cauchy problem which always possesses a generalized solution.
KW  - nonlinear PDI
KW  - Cauchy problem
KW  - Zaremba problem
Y1  - 2020
U6  - https://doi.org/10.1007/s13370-020-00810-4
SN  - 1012-9405
SN  - 2190-7668
VL  - 32
IS  - 1-2
SP  - 69
EP  - 76
PB  - Springer
CY  - Heidelberg
ER  -