Quasi-relative interior-type constraint qualifications ensuring strong Lagrange duality for optimization problems with cone and affine constraints

In this article we provide weak sufficient strong duality conditions for a convex optimization problem with cone and affine constraints, stated in infinite dimensional spaces, and its Lagrange dual problem. Our results are given by using the notions of quasi-relative interior and quasi-interior for convex sets. The main strong duality theorem is accompanied by several stronger, yet easier to verify in practice, versions of it. As exemplification we treat a problem which is inspired from network equilibrium. Our results come as corrections and improvements to Daniele and Giuffré (2007) [9].     

Study of quasi two-body final states in K−n reactions at 8.25 GeV/c

Cross sections for various channels in 3 prong + V₀ final states of K^?n interactions are obtained at 8.25 GeV/c. An energy dependence study of the quasi two-body reactions Σ^?(1385) + vector meson and ΛB^? seem to imply the presence of cuts in the Regge exchange formalism, whereas the reaction Δ(1236) $\text{K}$¹ (890) does not require such cuts. Upper limits of 1 and 2 μb are found for the reactions K^?n → ΛA₁ and K^?n → ΛA₂.     

An amplitude analysis of ππ scattering from new data on the reaction π−p→π+π−n

We have carried out a partial-wave analysis of ππ scattering in the mass range 1.0 to 2.08 GeV/c². We find solutions similar to those obtained in previous analyses below 1.8 GeV/c² but, in addition, we obtain a new solution which does not suffer from violations of unitarity and is compatible with data from other channels. This solution, when continued to 2.08 GeV/c², shows a g meson with mass and width of 1.734± 0.010 GeV/c²and 0.322±0.035 GeV/c² respectively, and an h meson with mass 1.935±0.013 GeV/c²and width 0.263±0.057 GeV/c². The L = 2 partial wave contains the f meson and an additional resonance with parameters m = 1.502±0.025 Gev/c², Γ = 0.165±0.042 GeV/c²and x = 0.19±0.03. If we associate this state with the f′(1514), our ππ branching fraction is considerably higher than previous determinations. An SU(3) fit to the 2⁺ nonet yields a mixing angle of 38.4± 1.3°.     

The synthesis of multi-walled carbon nanotubes (MWNTs) by catalytic pyrolysis of the phenol-formaldehyde resins

A series of carbon nanomaterials, particularly multi-walled carbon nanotubes (MWNT), are obtained as products from catalytic pyrolysis of the cross-linked phenol-formaldehyde resins with different ferrocene under inert atmosphere. The morphology and structure of the samples were evaluated by TEM and XRD techniques. CNTs morphology is dependent on the iron nanoparticles and their forms (Fe, Fe₃C) resulted from ferrocene decomposition. The amount of nanotubes increases with iron content released from ferrocene catalyst during the pyrolysis process. Fe₃C nanoparticles drive the nucleation and the growth of carbon nanotubes during the pyrolysis process. Long (up to microns) well-defined MWNTs with small defects, ropes and disordered carbon are representatives in the pyrolyzed resins composition.     

Statistical Approach of Modulational Instability in the Class of Derivative Nonlinear Schrödinger Equations

The modulational instability (MI) in the class of NLS equations is discussed using a statistical approach (SAMI). A kinetic equation for the two-point correlation function is studied in a linear approximation, and an integral stability equation is found. The modulational instability is associated with a positive imaginary part of the frequency. The integral equation is solved for different types of initial distributions (δ-function, Lorentzian) and the results are compared with those obtained using a deterministic approach (DAMI). The differences between MI of the normal NLS equation and derivative NLS equations is emphasized. PACS: 05.45.     

Evidence for a quantum phase transition in Pr2-xCe(x)CuO4-delta from transport measurements

The doping and temperature dependences of the Hall coefficient, R(H), and ab-plane resistivity in the normal state down to 350 mK is reported for oriented films of the electron-doped high-T(c) superconductor Pr(2-x)Ce(x)CuO(4-delta). The doping dependences of beta (rho=rho(0)+ATbeta) and R(H) (at 350 mK) suggest a quantum phase transition at a critical doping near x=0.165.