Improved approximation of maximum vertex cover

We provide a new LP relaxation of the maximum vertex cover problem and a polynomial-time algorithm that finds a solution within the approximation factor , where is the size of the smallest clique in a given clique-partition of the edge weighting of G.     

Ising wall instability in a nematic liquid crystal

A new instability for a splay-bend Ising wall was found in a 5CB nematic liquid crystal layer. This instability, which occurs in the presence of an external horizontal magnetic field, is driven by the elastic anisotropy of the liquid crystal material. Depending on the homogeneity of the magnetic field, the unstable straight interface evolves towards a new steady state or undergoes a spinodal decomposition into facets. Energy arguments are given in order to explain these physical phenomena.     

Selective oxidation of sulfides to sulfoxides and sulfones using 30% aqueous hydrogen peroxide and silica-vanadia catalyst

A green, efficient and selective approach for the oxidation of sulfides to sulfoxides and sulfones with stoichiometric amount of 30% aq. H₂O₂ is reported. The reaction is performed in methanol with silica-vanadia as heterogeneous and reusable catalyst.     

Helically modulated electroclinical effects in twist grain boundary liquid crystals

We report the first observation of an electroclinical effect at the TGB-TGB transition induced by an external DC electric field applied perpendicular to the pitch direction. Upon increasing the field, the smectic layers rather than the director field tilt over relative to the helical axis, allowing to detect the effect by X-ray scattering from well aligned samples. The observations are qualitatively interpreted in the frame of a mean field phenomenological model of a helically modulated electroclinical effect. Received: 24 April 1998 / Revised: 22 June 1998 / Accepted: 31 July 1998     

A hard ferromagnetic and elastic beam-plate sandwich structure

In this paper, the deformation of a composite hard ferromagnetic-elastic beam-plate structure is investigated. A sandwich structure, composed of two thin hard ferromagnetic layers, with a linear elastic layer in between, is considered. The deformation is due to the self generated magnetic field (magnetostriction). The aim is to assess the interaction forces among the perfectly bonded layers, through a consistent application of the classical nonlinear magneto-elastic theory. Once the general mechanical model is stated, the analysis is specialized to study longitudinal elongation, given its great relevance in technical applications. Owing to the non-local character of the magnetic action, a nonlinear integro-differential equation is derived. Some qualitative properties of the solution are pointed out and the asymptotic behavior near the end sections is examined in detail. A finite differences approach allows writing an approximating nonlinear system of equations in the non asymptotic part of the solution, which is solved through a Newton’s iterative scheme. The numerical results are discussed and it is shown how the asymptotic part of the solution well approximates the full behavior of the structure. Furthermore, the longitudinal interaction force density is found to be singular at the end cross-sections, regardless of the assumed bonding type.     

Finite homogeneous deformations of symmetrically loaded compressible membranes

The equilibrium problem of nonlinear, isotropic and hyperelastic square membranes, stretched by a double symmetric system of dead loads, is investigated. Depending on the form of the stored energy function, the problem considered may admit asymmetric solutions in addition to the expected symmetric solutions. For compressible materials, the mathematical condition allowing the computation of these asymmetric solutions is given. Moreover, explicit expressions for evaluating critical loads and bifurcation points are derived. Results and basic relations obtained for general isotropic materials are then specialized for a compressible Mooney–Rivlin material and a broad numerical analysis is performed. The qualitatively more interesting branches of asymmetric equilibrium are shown and the influence of the material parameters is discussed. Finally, using the energy criterion, some stability considerations are made.     

On the stability loss for an Euler beam resting on a tensionless Pasternak foundation

In the present work, the tensionless contact problem of an Euler–Bernoulli beam of finite length resting on a two-parameter Pasternak-type foundation is investigated. Owing to the tensionless character of the contact, the beam may lift-off the foundation and the point where contact ceases and detachment begins, named contact locus, needs be assessed. In this situation, a one-dimensional free boundary problem is dealt with. An extra condition, in the form of a homogeneous second-order equation in the displacement and its derivatives, is demanded to set the contact locus and it gives the problem its nonlinear feature. Conversely, the loading and the beam length may be such that the beam rests entirely supported on the foundation, which situation is governed by a classical linear boundary value problem. In this work, contact evolution is discussed for a continuously varying loading condition, starting from a symmetric layout and at a given beam length, until overturning is eventually reached. In particular, stability is numerically assessed through the energy criterion, which is shown to stand for the free boundary situation as well. At overturning, a descending pathway in the system energy appears and stability loss is confirmed.     

Experimental measurement of the azimuthal anchoring energy function at a SiO-nematic interface

The functional form of the azimuthal anchoring energy, i.e. the anisotropic part of the interfacial free energy, at the interface between the nematic liquid crystal 4-n-pentyl-4'-cyanobiphenyl and an obliquely evaporated SiO substrate is measured for the first time by using a reflectometric method. The anchoring energy function is obtained by measuring the director rotation on the interface caused by an external magnetic field ranging from 0 to 2·3 T. The dependence of the anchoring energy on the director azimuthal angle is found to be well fitted by the function W_a(ϕ) = W_asin² ϕ in agreement with the predictions of the Berreman model for the anchoring at a grooved interface.     

Facets and lifting procedures for the set covering polytope

Given a family of subsets of an arbitrary groundsetE, acover of is any setC E having non-empty intersection with every subset in. In this paper we deal with thecovering polytope, i.e., the convex hull of the incidence vectors of all the covers of. In Section 2 we review all the known properties of the covering polytope. In Sections 3 and 4 we introduce two new classes of non-Boolean facets of such a polytope. In Sections 5 and 6 we describe some non-sequential lifting procedures. In Section 7 a generalization of the notion ofweb introduced by L.E. Trotter is presented together with the facets of the covering polytope produced by such a structure.Moreover, the strong connections between several combinatorial problems and the covering problem are pointed out and, exploiting those connections, some examples are presented of new facets for the Knapsack and Acyclic Subdigraph polytopes.