TY  - JOUR
A1  - Kalousek, Martin
A1  - Mitra, Sourav
A1  - Schlömerkemper, Anja
T1  - Existence of weak solutions of diffuse interface models for magnetic fluids
JF  - Proceedings in Applied Mathematics and Mechanics
N2  - In this article we collect some recent results on the global existence of weak solutions for diffuse interface models involving incompressible magnetic fluids. We consider both the cases of matched and unmatched specific densities. For the model involving fluids with identical densities we consider the free energy density to be a double well potential whereas for the unmatched density case it is crucial to work with a singular free energy density.
KW  - mathematics
KW  - magnetic fluids
KW  - diffuse interface models
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-257642
VL  - 21
IS  - 1
ER  - 
TY  - JOUR
A1  - Ludwig, K. U.
A1  - Sämann, P.
A1  - Alexander, M.
A1  - Becker, J.
A1  - Bruder, J.
A1  - Moll, K.
A1  - Spieler, D.
A1  - Czisch, M.
A1  - Warnke, A.
A1  - Docherty, S. J.
A1  - Davis, O. S. P.
A1  - Plomin, R.
A1  - Nöthen, M. M.
A1  - Landerl, K.
A1  - Müller-Myhsok, B.
A1  - Hoffmann, P.
A1  - Schumacher, J.
A1  - Schulte-Körne, G.
A1  - Czamara, D.
T1  - A common variant in Myosin-18B contributes to mathematical abilities in children with dyslexia and intraparietal sulcus variability in adults
JF  - Translational Psychiatry
N2  - The ability to perform mathematical tasks is required in everyday life. Although heritability estimates suggest a genetic contribution, no previous study has conclusively identified a genetic risk variant for mathematical performance. Research has shown that the prevalence of mathematical disabilities is increased in children with dyslexia. We therefore correlated genome-wide data of 200 German children with spelling disability, with available quantitative data on mathematic ability. Replication of the top findings in additional dyslexia samples revealed that rs133885 was a genome-wide significant marker for mathematical abilities\((P_{comb}=7.71 x 10^{-10}, n=699)\), with an effect size of 4.87%. This association was also found in a sample from the general population (P=0.048, n=1080), albeit with a lower effect size. The identified variant encodes an amino-acid substitution in MYO18B, a protein with as yet unknown functions in the brain. As areas of the parietal cortex, in particular the intraparietal sulcus (IPS), are involved in numerical processing in humans, we investigated whether rs133885 was associated with IPS morphology using structural magnetic resonance imaging data from 79 neuropsychiatrically healthy adults. Carriers of the MYO18B risk-genotype displayed a significantly lower depth of the right IPS. This validates the identified association between rs133885 and mathematical disability at the level of a specific intermediate phenotype.
KW  - disability
KW  - sulcal morphology
KW  - prelevance
KW  - identification
KW  - brain
KW  - cancer
KW  - association
KW  - developmental dyscalculia
KW  - tumor-suppressor gene
KW  - correlate
KW  - disorders
KW  - dyscalculia
KW  - dyslexia
KW  - genomic imaging
KW  - mathematics
KW  - quantitative trait
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-131513
N1  - Supplementary Information accompanies the paper on the Translational Psychiatry website (http://www.nature.com/tp).
VL  - 3
IS  - e229
ER  - 
TY  - JOUR
A1  - Schönlein, Michael
T1  - Ensemble reachability of homogenous parameter‐depedent systems
JF  - Proceedings in Applied Mathematics and Mechanics
N2  - In this paper we consider the class (θA, B) of parameter-dependent linear systems given by matrices A ∈ ℂ\(^{nxn}\) and B ∈ ℂ\(^{nxm}\). This class is of interest for several applications and the frequently met task for such systems is to steer the origin toward a given target family f(θ) by using an input that is independent from the parameter. This paper provides a collection of necessary and sufficient conditions for ensemble reachability for these systems.
KW  - ensemble reachability
KW  - homogenous parameter-depedent systems
KW  - mathematics
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-257637
VL  - 20
IS  - 1
ER  -