Stability results for Mountain Pass and Linking type solutions of semilinear problems involving Dirichlet forms

Some stability results for Mountain Pass and Linking type solutions of semilinear problems involving a very general class of Dirichlet forms are stated. The non linear terms are supposed to have a suitable superlinear growth and the family of Dirichlet forms is required to be dominated from below and from above by a fixed diffusion type form. Some concrete examples are also given.     

Semigroups Generated by Ordinary Differential Operators in L 1(I)*

In this paper we give necessary and sufficient conditions for the existence of a C> ₀-semigroup in L ¹(I) (I real interval) generated by a second-order differential operator when suitable boundary conditions at the endpoints are imposed.     

Stable determination of an inhomogeneous inclusion by local boundary measurements

We deal with the problem of determining an inclusion within an electrostatic conductor from boundary measurements. Under mild a priori assumptions we establish optimal stability estimates. Measurements are performed on a portion of the boundary of the conductor.     

Packing into the smallest square: Worst-case analysis of lower bounds

We address the problem of packing a given set of rectangles into the minimum size square. We consider three versions of the problem, arising when the rectangles (i) are squares; (ii) have a fixed orientation; (iii) can be rotated by 90. For each case we study lower bounds, and analyze their worst-case performance ratio. In addition, we evaluate through computational experiments their average performance on instances from the literature.     

A remark on Serrin’s Theorem

An approximation theorem for families of weakly coercive convex functions by means of countably many smooth families of convex functions is proved. As a consequence, the classical “three-fold” lower semicontinuity theorem for integral functionals of the Calculus of Variations by James Serrin is unified in one single statement.     

NMRON studies of ferromagnetic hcp and fcc Co

The high resolution hyperfine spectroscopy, modulated adiabatic passage of oriented nuclei (MAPON), has been applied for the first time to high purity, elemental systems. Detailed comparisons between the electric quadrupole hyperfine interactions (EQI’s) and, in particular, their distributions, are obtained for⁶⁰CoCo where the hosts are a single crystal of hcp cobalt and a polycrystalline cobalt foil of predominantly fcc character. For hcp Co, with the electronic magnetization, M, parallel to the c-axis, the mode value P/h=3e²qQ/4I(2I−1)h=−48.5(5) kHz. This fractional distribution implies the sharpest electric field gradient (efg) measured in a metal to date, using MAPON spectroscopy, in excess of two times sharper than that of the most dilute impurity efg in a crystallographically cubic ferromagnetic host. The mode efg is V_zz=−27.3(32)×10¹⁹ Vm⁻². For the polycrystalline, predominantly fcc foil, prepared by quenching, the EQI mode value is P/h=−6.2(4) kHz with a FWHM of 12.0(7) kHz yielding a mode efg of V_zz=−3.5(5)×10¹⁹ Vm⁻².     

Ab initio path-integral molecular dynamics

A path-integral molecular dynamics technique for strongly interacting atoms using ab initio potentials derived from density functional theory is implemented. This allows the efficient inclusion of nuclear quantum dispersion in ab initio simulations at finite temperatures. We present an application to the quantum cluster H ₅ ⁺ .     

General theorems and fundamental solutions in the dynamical theory of mixtures

This paper is concerned with the dynamic theory of a binary mixture consisting of a gas and an elastic solid. First, we derive general theorems (reciprocal theorem, uniqueness theorem, minimum principle). The, we establish a Galerkin representation and the fundamental solutions in the case of steady vibrations.Work performed under the auspices of G.N.F.M. of the Italian Research Council (C.N.R.), with the grant 60% M.U.R.S.T. (ITALY).