Eigenvalue estimates for the Dirac operator depending on the Weyl curvature tensor

We prove new lower bounds for the first eigenvalue of the Dirac operator on compact manifolds whose Weyl tensor or curvature tensor, respectively, is divergence free. In the special case of Einstein manifolds, we obtain estimates depending on the Weyl tensor.Comment: Latex2.09, 9 page

Carcass and meat quality of different pig genotypes in an organic extensive outdoor fatting system

Carcass, meat, and fat quality were evaluated of 37 castrates of 4 different genotypes [Pi*Du*GLR (10), Pi*AS (7), Du (10), Du*GLR (10)] kept on grass clover and fed with coarse meal made up of farm grown cereal and grain legumes without optimising the amount of amino acids and their relation to the energy content. Due to the energy surplus in the diet and in relation to the diminishing muscularity of the genotypes (corresponding to the above-mentioned sequence) lean meat contents were on a low level whereas intramuscular fat contents increased distinctly. Sensory meat quality was only at a medium level and did not differ noticeably between the genotypes. It is concluded that adipose carcasses associated with increased intramuscular fat contents do not lead automatically to higher sensory meat qualities. Therefore the system boundaries of organic pig fattening cannot be used without further efforts supplying market niches for pork of high eating quality

European Integration and Changing Trade Patterns: The Case of the Baltic States

The analysis of Baltic regional trade patterns reveals that during the nineties the Baltic states made significant progress to integrate into the Western European division of labour although a significant share of (transit) trade with Russia remained. In view of this development, history seems to matter with respect to the interwar period and the period of Soviet occupation. In addition, a trade entropy analysis and gravity model estimates show that European integration of the Baltic states has a regional centre of gravity located in the Baltic Sea region. The Baltic trade flows increasingly follow the gravitational forces that generally shape trade relations, while regional integration is still much more important than it is normally the case.Eastern enlargement, regional integration, gravity model, Baltic trade patterns

LEAST COST EFFICIENCY OF AGRICULTURAL PROGRAMS: AN EMPIRICAL INVESTIGATION

The study evaluates the efficiency of government intervention using a vertical structured model including imperfectly competitive agricultural input markets, the bread grains market, and the imperfectly competitive food industry. The actually observed policy is compared to a hypothetical optimal policy of the same policy instruments to test for policy efficiency.Agricultural and Food Policy, Research Methods/ Statistical Methods,

Wellposedness of NLS in modulation spaces

We prove new local and global well-posedness results for the cubic one-dimensional Nonlinear Schrödinger Equation in Modulation Spaces. Local results are obtained via multilinear interpolation. Global results are proven using conserved quantities from the integrability of the equation, persistence of regularity and by separating off the time evolution of finitely many Picard iterates

Wellposedness of NLS in Modulation Spaces

We prove new local and global well-posedness results for the cubic one-dimensional nonlinear Schrödinger equation in modulation spaces. Local results are obtained via multilinear interpolation. Global results are proven using conserved quantities based on the complete integrability of the equation, persistence of regularity, and by separating off the time evolution of finitely many Picard iterates

A Strichartz estimate for quasiperiodic functions

In this work we prove a Strichartz estimate for the Schrödinger equation in the quasiperiodic setting. We also show a lower bound on the number of resonant frequency interactions in this situation

A priori estimates for a quadratic dNLS

In this work we consider integrable PDE with higher dimensional Lax pairs. Our main example is a quadratic dNLS equation with a $3\times3$ Lax pair. For this equation we show a-priori estimates in Sobolev spaces of negative regularity $H^s(\mathbb{R})$, $s> −\frac{1}{2}$. We also prove that for general $N\times N$ Lax operators $L$, the transmission coefficient coincides with the $2$-renormalized perturbation determinant

Nonlinear Schrödinger Equations with Rough Data

In this thesis we consider nonlinear Schrödinger equations with rough initial data. Roughness of the initial data in nonlinear Schrödinger equations can be understood as being of low regularity and as a lack of decay at infinity. Firstly we prove low regularity a priori estimates for the derivative nonlinear Schrödinger equation in Besov spaces with positive regularity index. These a priori estimates are sharp at the level of regularity but are conditional upon small mass. The proof uses the operator determinant characterization of the transmission coefficient introduced by Killip-Visan-Zhang. Secondly we show global wellposedness for the tooth problem of defocusing nonlinear Schrödinger equations, that is the Cauchy problem with initial data in the space $H^{s_1}(\mathbb{R}) + H^{s_2}(\mathbb{T})$. This result can be seen as an intermediate step between the wellposedness theory in the $L^2(\mathbb{T})$-based setting and more generic non-decaying behavior at infinity. In the case $s_1 = 1$ we obtain an at most exponentially growing energy, based on the Hamiltonian of the perturbed equation. For the cubic nonlinearity we may choose $s_2 > 3/2$ whereas for higher power nonlinearities our assumption is $s_2 > 5/2$. Finally we investigate the question of wellposedness of nonlinear Schrödinger equations with initial data in modulation spaces. Modulation spaces $M^s_{p,q}(\mathbb{R}^n)$ encode both regularity ($s$ and $q$) and decay ($p$) in their indices. By making use of multilinear interpolation we prove new local wellposedness results. The local wellposedness results we obtain are proven to be sharp with respect to the regularity index. Moreover we complement the local results by showing global wellposedness in several cases, including low regularity and very slow decay. This is done on the one hand by an extension of techniques developed by Oh-Wang to a broader range of modulation spaces, and on the other hand by applying calculations from Dodson-Soffer-Spencer to the modulation space setting