Chiral effective field theories of the strong interactions

Effective field theories of the strong interactions based on the approximate chiral symmetry of QCD provide a model-independent approach to low-energy hadron physics. We give a brief introduction to mesonic and baryonic chiral perturbation theory and discuss a number of applications. We also consider the effective field theory including vector and axial-vector mesons.Comment: 22 pages, 9 figures, proceedings of "Many-Body Structure of Strongly Interacting Systems", Mainz, Germany, Feb. 23-25 201

A convex polynomial that is not sos-convex

A multivariate polynomial $p(x)=p(x_1,...,x_n)$ is sos-convex if its Hessian $H(x)$ can be factored as $H(x)= M^T(x) M(x)$ with a possibly nonsquare polynomial matrix $M(x)$. It is easy to see that sos-convexity is a sufficient condition for convexity of $p(x)$. Moreover, the problem of deciding sos-convexity of a polynomial can be cast as the feasibility of a semidefinite program, which can be solved efficiently. Motivated by this computational tractability, it has been recently speculated whether sos-convexity is also a necessary condition for convexity of polynomials. In this paper, we give a negative answer to this question by presenting an explicit example of a trivariate homogeneous polynomial of degree eight that is convex but not sos-convex. Interestingly, our example is found with software using sum of squares programming techniques and the duality theory of semidefinite optimization. As a byproduct of our numerical procedure, we obtain a simple method for searching over a restricted family of nonnegative polynomials that are not sums of squares.Comment: 15 page

The Synthesis of [{n-Bu2Sn(S2N2)}2] and its use in the preparation of Organometallic Iridium Sulfur Nitrogen Complexes

The addition of [n-Bu2SnCl2] to a solution of [S4N3][Cl] in liquid ammonia gave after extraction of the dry reaction mixture the new tin disulfur dinitrido compound [{n-Bu2Sn(S2N2)}(2)] (1). Reaction of [{n-Bu2Sn(S2N2)}(2)] (1) with the pentamethylcyclopentadienyl (Cp*) iridium derivatives [{IrCl(mu-Cl)(eta(5)-C5Me5)}(2)] or [(eta(5)-C5Me5)IrCl2(PPh3)] gave different products, which were dependent on the reactant ratios. A 1:1 reaction between 1 and [{IrCl(mu-Cl)(eta(5)-C5Me5)}(2)] gave only [(eta(5)-C5Me5)Ir(S2N2)] (2) in moderate yield; the same product in higher yield was obtained from a 2:1 reaction between 1 and [(eta(5)-C5Me5)IrCl2(PPh3)]. Reaction of 1 and [(eta(5)-C5Me5)(2)IrCl2(PPh3)] (1:1 molar ratio) in the presence of NH4[PF6] gave the unusual bimetallic species [(eta(5)-C5Me5)IrCl(PPh3)(S2N2)Ir(eta(5)-C5Me5)][PF6] (3). The X-ray crystal structures of 1, 2, and 3 are reported.PostprintPeer reviewe

Co-limitation towards lower latitudes shapes global forest diversity gradients

The latitudinal diversity gradient (LDG) is one of the most recognized global patterns of species richness exhibited across a wide range of taxa. Numerous hypotheses have been proposed in the past two centuries to explain LDG, but rigorous tests of the drivers of LDGs have been limited by a lack of high-quality global species richness data. Here we produce a high-resolution (0.025° × 0.025°) map of local tree species richness using a global forest inventory database with individual tree information and local biophysical characteristics from ~1.3 million sample plots. We then quantify drivers of local tree species richness patterns across latitudes. Generally, annual mean temperature was a dominant predictor of tree species richness, which is most consistent with the metabolic theory of biodiversity (MTB). However, MTB underestimated LDG in the tropics, where high species richness was also moderated by topographic, soil and anthropogenic factors operating at local scales. Given that local landscape variables operate synergistically with bioclimatic factors in shaping the global LDG pattern, we suggest that MTB be extended to account for co-limitation by subordinate drivers