Proof compressions with circuit-structured substitutions

It is well known that the size of propositional classical proofs can be huge. Proof-theoretical studies discovered exponential gaps between cut-free (or normal) proofs and the corresponding (non-normal) proofs with cuts (or modus ponens). The task of automatic theorem proving is, on the other hand, usually based on the construction of cut-free or only atomic-cuts proofs, since this procedure produces less alternative choices. There are familiar tautologies whose cut-free proofs are huge while the non-cut-free ones are small. The aim of this paper is to discuss basic methods of weight and/or size reduction of deductions by switching from traditional tree-structured deductions to circuit-structured deductions. A desired efficiency is achieved by adding the standard weakening rule of inference upgraded by adding suitable (propositional) unifications modulo variable substitutions. We show examples where such a unification provides strong (in fact, exponential) compression of cut-free deductions. Bibliography: 10 titles. Published in Zapiski Nauchnykh Seminarov POMI, Vol. 358, 2008, pp. 77–99.     

Domain walls in a generalized Chern–Simons model

In this paper we study the structure of one dimensional topological solitons in a generalized Abelian-Higgs Chern–Simons model where the kinetic term is non-canonical. We present an example of an analytical self-dual electrically charged soliton solution which has a finite momentum per unit length along its direction. We compared the physical properties of our soliton with those for wall of Jackiw–Lee–Weinberg wall presented in Jackiw et al. (Phys. Rev. D 42:3488, 1990) to conclude that the non-canonical kinetic term can make the wall “thicker” redistributing uniformly the momentum flow along it.     

Junction of ferromagnetic thin films

In this paper, starting from the classical 3D micromagnetic energy, we determine, via an asymptotic analysis, the free energy of two joined ferromagnetic thin films. We distinguish different regimes depending on the limit of the ratio between the small thicknesses of the two films.     

Induced polarization forward modelling using finite element method and the fractal model

The modeling of induced polarization data from 2D and 3D geological medium was developed. We applied the finite element method and the fractal model to complex resistivity of rocks as an intrinsic electrical property of geological medium. The LU factorization and pre-conditioned complex bi-conjugated gradient method were applied to solve the complex linear equation system. The modeling implemented in this work was efficient and prompt. In addition, the induced polarization survey using the fractal model as intrinsic property of the medium is a promising method for environmental investigation.     

The concept of proof in the light of mathematical work

ZDM – Mathematics Education - Our article aims to show how illuminating mathematical work as a concept from didactics of mathematics is useful in understanding issues relating to proving and...     

Improvement of permanent memory effect in PDLC films using TX-100 as an additive

A number of polymer dispersed liquid crystal (PDLC) films based on dimethacrylate monomers were synthesised by polymer-induced phase separation (PIPS) using polyethylene glycol p-(1,1,3,3-tetramethylbutyl)-phenyl ether (TX-100) as an additive up to total solution weight of 10% aiming to modify the initial anchorage force of the liquid crystal (LC) molecules to the polymeric matrix. The effects of the addition of this additive to the PDLC films were studied resorting to electro-optical studies. Using a fitting model, several parameters were correlated such as the permanent memory effect (PME), the voltage required to achieve 90% of maximum transmittance (E90), the average elastic constant (K) and the rotational viscosity of the director (γ). The use of TX-100 results on an increase on the PME and γ, and decrease on the E90 and K.     

First report of the nutritional profile and antioxidant potential of Holothuria arguinensis,a new resource for aquaculture in Europe

This work reports for the first time the nutritional profile and antioxidant potential of the edible sea cucumber Holothuria arguinensis from the North-eastern Atlantic. H. arguinensis has high levels of protein, with the amino acids profile dominated by alanine, glycine and proline and low lysine/arginine ratios. Its carbohydrate and energetic contents are also low as well as the total lipid levels, although its lipid profile is rich in polyunsaturated fatty acids (PUFA), especially arachidonic, eicosapentaenoic and docosahexaenoic acids. In addition, H. arguinensis has high levels of calcium. The water and ethanol extracts show ability to scavenge free radicals and to chelate copper and iron ions. Our results indicate that H. arguinensis has a balanced nutritional quality suitable for human consumption. In addition, it contains compounds with antioxidant potential; thus its intake can contribute for a healthy and well-balanced diet.