Corrections to Sirlin's Theorem in O(p6)O(p^6) Chiral Perturbation Theory

We present the results of the first two-loop calculation of a form factor in full $SU(3) \times SU(3)$ Chiral Perturbation Theory. We choose a specific linear combination of $\pi^+, K^+, K^0$ and $K\pi$ form factors (the one appearing in Sirlin's theorem) which does not get contributions from order $p^6$ operators with unknown constants. For the charge radii, the correction to the previous one-loop result turns out to be significant, but still there is no agreement with the present data due to large experimental uncertainties in the kaon charge radii.Comment: 6 pages, Latex, 2 LaTeX figure

Merging fragments of classical logic

We investigate the possibility of extending the non-functionally complete logic of a collection of Boolean connectives by the addition of further Boolean connectives that make the resulting set of connectives functionally complete. More precisely, we will be interested in checking whether an axiomatization for Classical Propositional Logic may be produced by merging Hilbert-style calculi for two disjoint incomplete fragments of it. We will prove that the answer to that problem is a negative one, unless one of the components includes only top-like connectives.Comment: submitted to FroCoS 201

METAL-FORMING STUDIES BY MOIRÉ INTERFEROMETRY

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75097/1/j.1747-1567.1989.tb01032.x.pd

Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis

Obtaining lower bounds for NP-hard problems has for a long time been an active area of research. Recent algebraic techniques introduced by Jonsson et al. (SODA 2013) show that the time complexity of the parameterized SAT($\cdot$) problem correlates to the lattice of strong partial clones. With this ordering they isolated a relation $R$ such that SAT($R$) can be solved at least as fast as any other NP-hard SAT($\cdot$) problem. In this paper we extend this method and show that such languages also exist for the max ones problem (MaxOnes($\Gamma$)) and the Boolean valued constraint satisfaction problem over finite-valued constraint languages (VCSP($\Delta$)). With the help of these languages we relate MaxOnes and VCSP to the exponential time hypothesis in several different ways.Comment: This is an extended version of Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis, appearing in Proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science MFCS 2014 Budapest, August 25-29, 201

A general approximation of quantum graph vertex couplings by scaled Schroedinger operators on thin branched manifolds

We demonstrate that any self-adjoint coupling in a quantum graph vertex can be approximated by a family of magnetic Schroedinger operators on a tubular network built over the graph. If such a manifold has a boundary, Neumann conditions are imposed at it. The procedure involves a local change of graph topology in the vicinity of the vertex; the approximation scheme constructed on the graph is subsequently `lifted' to the manifold. For the corresponding operator a norm-resolvent convergence is proved, with the natural identification map, as the tube diameters tend to zero.Comment: 19 pages, one figure; introduction amended and some references added, to appear in CM

Soliton surfaces associated with symmetries of ODEs written in Lax representation

The main aim of this paper is to discuss recent results on the adaptation of the Fokas-Gel'fand procedure for constructing soliton surfaces in Lie algebras, which was originally derived for PDEs [Grundland, Post 2011], to the case of integrable ODEs admitting Lax representations. We give explicit forms of the \g-valued immersion functions based on conformal symmetries involving the spectral parameter, a gauge transformation of the wave function and generalized symmetries of the linear spectral problem. The procedure is applied to a symmetry reduction of the static $\phi^4$-field equations leading to the Jacobian elliptic equation. As examples, we obtain diverse types of surfaces for different choices of Jacobian elliptic functions for a range of values of parameters.Comment: 14 Pages, 2 figures Conference Proceedings for QST7 Pragu