The node-edge weighted 2-edge connected subgraph problem: Linear relaxation, facets and separation

Let G=(V,E) be a undirected k-edge connected graph with weights c_e on edges and w_v on nodes. The minimum 2-edge connected subgraph problem, 2ECSP for short, is to find a 2-edge connected subgraph of G, of minimum total weight. The 2ECSP generalizes the well-known Steiner 2-edge connected subgraph problem. In this paper we study the convex hull of the incidence vectors corresponding to feasible solutions of 2ECSP. First, a natural integer programming formulation is given and it is shown that its linear relaxation is not sufficient to describe the polytope associated with 2ECSP even when G is series-parallel. Then, we introduce two families of new valid inequalities and we give sufficient conditions for them to be facet-defining. Later, we concentrate on the separation problem. We find polynomial time algorithms to solve the separation of important subclasses of the introduced inequalities, concluding that the separation of the new inequalities, when G is series-parallel, is polynomially solvable.     

Fixed point theorems in metric spaces

In this paper, we establish two general theorems for equivalence between the Meir–Keeler type contractive conditions and the contractive definitions involving gauge functions. One of these theorems is an extension of a recent result of Lim (On characterization of Meir–Keeler contractive maps, Nonlinear Anal. 46 (2001) 113–120).     

Theories of mathematics education: European perspectives, commentaries and viable research directions

We briefly comment on different perspectives on (1) the role of mathematics education theories, (2) the issue of plurality and healthy heterogeneity versus consolidation; (3) underlying inquiry systems or the implicit role of philosophy in theories of mathematics education. This paper also outlines developments within the European research scene on theory usage in mathematics education research, which complement the discussion at the 29th PME research forum in Melbourne.     

New strong interactions: From QCD to LHC

The concept of strong interactions need not be limited to the sector of physics taken by QCD. While this domain is investigated by RHIC, LHC will be able to probe potential new strong interactions simultaneously: Finding the precise mechanism for electroweak symmetry breaking is one of the prime problems of physics. Intricately linked to this point is the question after the true nature or even the existence of the Higgs boson. Here, we present stronly interacting theories providing an explanation for the hierarchy problem and leading to a light composite Higgs boson, favoured by experimental data. Our variation of the standard model is consistent with precision data. We achieve this accordance by using technifermions in a higher representation of their gauge group. Anomaly conditions require at least one extra lepton family for some of the theories whereby they contain a natural dark matter candidate. We can accurately determine the masses of said leptons from experimental data.     

Synthesis and fungicidal activity of S-amino derivatives of O-alkyldithiocarbonic acids

S-Amino derivatives of O-alkyldithiocarbonic acid were prepared by oxidative condensation of certain alkaloids with sodium xanthates. Some of the compounds synthesized exhibit fungicidal activity.     

An improved approach for hydrogen analysis in metal samples using single laser-induced gas plasma and target plasma at helium atmospheric pressure

We report in this paper the results of an experimental study on hydrogen analysis of solid samples in high pressure helium ambient gas employing the basic scheme of laser induced breakdown spectroscopy (LIBS). It is shown that the metastable excited state of helium atom can be utilized to induce delayed excitation of the ablated hydrogen atoms, and thereby avoid the Stark broadening effect as well as overcoming the undesirable mismatch effect, which are responsible for inefficient excitation respectively. It is further demonstrated that for samples of high boiling-point materials such as zircaloy, successful hydrogen analysis can be achieved by a newly introduced double excitation technique employing single laser realized in a modified configuration of the conventional LIBS method. PACS 51-52     

On Critical Stability of Three Quantum Charges Interacting Through Delta Potentials

We consider three one-dimensional quantum, charged and spinless particles interacting through delta potentials. We derive sufficient conditions which guarantee the existence of at least one bound state.     

A Constraint Programming Approach to Extract the Maximum Number of Non-Overlapping Test Forms

This paper introduces a novel approach for extracting the maximum number of non-overlapping test forms from a large collection of overlapping test sections assembled from a given item bank. The approach involves solving maximum set packing problems (MSPs). A branch-and-bound MSP algorithm is developed along with techniques adapted from constraint programming to estimate lower and upper bounds on the optimal MSP solution. The algorithm is general and can be applied in other applications including combinatorial auctions. The results of computer simulations and experiments with an operational item bank are presented. An erratum to this article is available at .     

Magnetic anisotropy and anisotropic ballistic conductance of thin magnetic wires

The magnetocrystalline anisotropy of thin magnetic wires of iron and cobalt is quite different from the bulk phases. The spin moment of monatomic Fe wire may be as high as 3.4 μ_B, while the orbital moment as high as 0.5 μ_B. The magnetocrystalline anisotropy energy (MAE) was calculated for wires up to 0.6 nm in diameter starting from monatomic wire and adding consecutive shells for thicker wires. I observe that Fe wires exhibit the change sign with the stress applied along the wire. It means that easy axis may change from the direction along the wire to perpendicular to the wire. We find that ballistic conductance of the wire depends on the direction of the applied magnetic field, i.e. shows anisotropic ballistic magnetoresistance. This effect occurs due to the symmetry dependence of the splitting of degenerate bands in the applied field which changes the number of bands crossing the Fermi level. We find that the ballistic conductance changes with applied stress. Even for thicker wires the ballistic conductance changes by factor 2 on moderate tensile stain in our 5×4 model wire. Thus, the ballistic conductance of magnetic wires changes in the applied field due to the magnetostriction. This effect can be observed as large anisotropic BMR in the experiment.