Bounds and monotonicity for the generalized Robin problem

We consider the principal eigenvalue λ ₁^Ω(α) corresponding to Δu = λ (α) u in W, \frac?u?v = au \Omega, \frac{\partial u}{\partial v} = \alpha u on ∂Ω, with α a fixed real, and W ì Rⁿ\Omega \subset {\mathcal{R}}^n a C ^0,1 bounded domain. If α > 0 and small, we derive bounds for λ ₁^Ω(α) in terms of a Stekloff-type eigenvalue; while for α > 0 large we study the behavior of its growth in terms of maximum curvature. We analyze how domain monotonicity of the principal eigenvalue depends on the geometry of the domain, and prove that domains which exhibit domain monotonicity for every α are calibrable. We conjecture that a domain has the domain monotonicity property for some α if and only if it is calibrable.     

Genuine quantum and classical correlations in multipartite systems

Generalizing the quantifiers used to classify correlations in bipartite systems, we define genuine total, quantum, and classical correlations in multipartite systems. The measure we give is based on the use of relative entropy to quantify the distance between two density matrices. Moreover, we show that, for pure states of three qubits, both quantum and classical bipartite correlations obey a ladder ordering law fixed by two-body mutual informations, or, equivalently, by one-qubit entropies.     

New Strong MM FIR Emissions in CH2=CF2 Pumped by a Pulsed CO2 Laser

By pumping with a suitable pulsed CO₂ laser we have produced several strong MM laser lines in 1,1 difluoroethene. All the emissions are easily identified because the emission spectroscopy is simplified in pulsed optical pumping.     

The longtime behavior of a nonlinear Reissner-Mindlin plate with exponentially decreasing memory kernels

In this paper we investigate the longtime behavior of the mathematical model of a homogeneous viscoelastic plate based on Reissner-Mindlin deformation shear assumptions. According to the approximation procedure due to Lagnese for the Kirchhoff viscoelastic plate, the resulting motion equations for the vertical displacement and the angle deflection of vertical fibers are derived in the framework of the theory of linear viscoelasticity. Assuming that in general both Lame's functions, λ and μ, depend on time, the coupling terms between the equations of displacement and deflection depend on hereditary contributions. We associate to the model a nonlinear semigroup and show the behavior of the energy when time goes on. In particular, assuming that the kernels λ and μ decay exponentially, and not too weakly with respect to the physical properties considered in the model, then the energy decays uniformly with respect to the initial conditions; i.e., we prove the existence of an absorbing set for the semigroup associated to the model.     

Phase diagram of the extended hubbard model with pair hopping interaction

A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and pair-hopping interaction W is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin-density wave (SDW) and charge-density wave (CDW) phases for large U and V, respectively, we identify a bond-charge-density-wave (BCDW) phase W < 0, | U - 2V| < | 2W| and a bond-spin-density-wave (BSDW) for W > 0, | U - 2V| < W. The possibility of bond-located ordering results from the site-off-diagonal nature of the pair-hopping term and is a special feature of the half-filled band case. The BCDW phase corresponding to an enhanced Peierls instability in the system. The BdSDW is an unconventional insulating magnetic phase, characterized by a gapless spin excitation spectrum and a staggered magnetization located on bonds between sites. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the η-superconducting phase at | U - 2V| ≪ 2t?W is briefly discussed. Received 20 February 2002 / Received in final form 11 April 2002 Published online 19 July 2002     

Derivation of the Forchheimer Law Via Matched Asymptotic Expansions

Matched asymptotics are used formally in the linearized Navier–Stokes equations, the so-called Oseen approximation, to derive a nonlinear law for the flow of a single-phase, incompressible Newtonian fluid through a rigid porous medium. A suitable choice of the linear term gives, to order a Forchheimer-type law.     

Existence theorem for a minimum problem with free discontinuity set

We study the variational problem Where is an open set in ⁿ ,n2gL ^q () L (), 1q<+, O<, <+ andH _n–1 is the (n–1)-dimensional Hausdorff Measure.     

Generalized Forchheimer Equation for Two-Phase Flow Based on Hybrid Mixture Theory

In this paper, we derive a Forchheimer-type equation for two-phase flow through an isotropic porous medium using hybrid mixture theory. Hybrid mixture theory consists of classical mixture theory applied to a multiphase system with volume averaged equations. It applies to media in which the characteristic length of each phase is small relative to the extent of the mixture. The derivation of a Forchheimer equation for single phase flow has been obtained elsewhere. These results are extended to include multiphase swelling materials which have nonnegligible interfacial thermodynamic properties.     

A macrocyclic ligand as receptor and Zn(II)-complex receptor for anions in water: binding properties and crystal structures

Binding properties of 24,29-dimethyl-6,7,15,16-tetraoxotetracyclo[19.5.5.0(5,8).0(14,17)]-1,4,9,13,18,21,24,29-octaazaenatriaconta-Δ(5,8),Δ(14,17)-diene ligand L towards Zn(II) and anions, such as the halide series and inorganic oxoanions (phosphate (Pi), sulfate, pyrophosphate (PPi), and others), were investigated in aqueous solution; in addition, the Zn(II)/L system was tested as a metal-ion-based receptor for the halide series. Ligand L is a cryptand receptor incorporating two squaramide functions in an over-structured chain that connects two opposite nitrogen atoms of the Me(2)[12]aneN(4) polyaza macrocyclic base. It binds Zn(II) to form mononuclear species in which the metal ion, coordinated by the Me(2)[12]aneN(4) moiety, lodges inside the three-dimensional cavity. Zn(II)-containing species are able to bind chloride and fluoride at the physiologically important pH value of 7.4; the anion is coordinated to the metal center but the squaramide units play the key role in stabilizing the anion through a hydrogen-bonding network; two crystal structures reported here clearly show this aspect. Free L is able to bind fluoride, chloride, bromide, sulfate, Pi, and PPi in aqueous solution. The halides are bound at acidic pH, whereas the oxoanions are bound in a wide range of pH values ranging from acidic to basic. The cryptand cavity, abundant in hydrogen-bonding sites at all pH values, allows excellent selectivity towards Pi to be achieved mainly at physiological pH 7.4. By joining amine and squaramide moieties and using this preorganized topology, it was possible, with preservation of the solubility of the receptor, to achieve a very wide pH range in which oxoanions can be bound. The good selectivity towards Pi allows its discrimination in a manner not easily obtainable with nonmetallic systems in aqueous environment.