Representation of differential operators in wavelet basis

AbstractExisting work on the representation of operators in one-dimensional, compactly-supported, orthonormal wavelet bases is extended to two dimensions. The nonstandard form of the representation of operators is given in separable two-dimensional, periodic, orthonormal wavelet bases. The matrix representation of the partial-differential operators ∂x and ∂y are constructed and a closed form formula for the matrix representation of a general partial-differential operator g(∂x, ∂y) is derived, where g is an analytic function

State Trading Companies, Time Inconsistency, Imperfect Enforceability and Reputation

Strategic trade in international markets is important for agricultural and other basic commodities. State trading companies (STCs) and large private firms control most of the trade volume. In this study the authors use concepts of modern game theory to treat time inconsistency issues associated with strategic trade. The results are particularly applicable to trade in commodities with lengthy production periods, such as agriculture. The model considered here provides an important context for exploring impacts of signaling, reputation, and third party interventions that approximate the institutions and authorities that govern international trade

Shared features and reciprocal complementation of the Chlamydomonas and Arabidopsis microbiota

Microscopic algae release organic compounds to the region immediately surrounding their cells, known as the phycosphere, constituting a niche for colonization by heterotrophic bacteria. These bacteria take up algal photoassimilates and provide beneficial functions to their host, in a process that resembles the establishment of microbial communities associated with the roots and rhizospheres of land plants. Here, we characterize the microbiota of the model alga Chlamydomonas reinhardtii and reveal extensive taxonomic and functional overlap with the root microbiota of land plants. Using synthetic communities derived from C. reinhardtii and Arabidopsis thaliana, we show that phycosphere and root bacteria assemble into taxonomically similar communities on either host. We show that provision of diffusible metabolites is not sufficient for phycosphere community establishment, which additionally requires physical proximity to the host. Our data suggest the existence of shared ecological principles driving the assembly of the A. thaliana root and C. reinhardtii phycosphere microbiota, despite the vast evolutionary distance between these two photosynthetic organisms

Psi-series solutions of the cubic H\'{e}non-Heiles system and their convergence

The cubic H\'enon-Heiles system contains parameters, for most values of which, the system is not integrable. In such parameter regimes, the general solution is expressible in formal expansions about arbitrary movable branch points, the so-called psi-series expansions. In this paper, the convergence of known, as well as new, psi-series solutions on real time intervals is proved, thereby establishing that the formal solutions are actual solutions

Construction of Special Solutions for Nonintegrable Systems

The Painleve test is very useful to construct not only the Laurent series solutions of systems of nonlinear ordinary differential equations but also the elliptic and trigonometric ones. The standard methods for constructing the elliptic solutions consist of two independent steps: transformation of a nonlinear polynomial differential equation into a nonlinear algebraic system and a search for solutions of the obtained system. It has been demonstrated by the example of the generalized Henon-Heiles system that the use of the Laurent series solutions of the initial differential equation assists to solve the obtained algebraic system. This procedure has been automatized and generalized on some type of multivalued solutions. To find solutions of the initial differential equation in the form of the Laurent or Puiseux series we use the Painleve test. This test can also assist to solve the inverse problem: to find the form of a polynomial potential, which corresponds to the required type of solutions. We consider the five-dimensional gravitational model with a scalar field to demonstrate this.Comment: LaTeX, 14 pages, the paper has been published in the Journal of Nonlinear Mathematical Physics (http://www.sm.luth.se/math/JNMP/

Constraints on new interactions from neutron scattering experiments

Constraints for the constants of hypothetical Yukawa-type corrections to the Newtonian gravitational potential are obtained from analysis of neutron scattering experiments. Restrictions are obtained for the interaction range between 10^{-12} and 10^{-7} cm, where Casimir force experiments and atomic force microscopy are not sensitive. Experimental limits are obtained also for non-electromagnetic inverse power law neutron-nucleus potential. Some possibilities are discussed to strengthen these constraints.Comment: 18 pages, 3 figure