Solution of a system of functional-differential equations arising from an optimization problem

In connection with an optimization problem, all functions ?: Iⁿ → $\text{R}$ with continuous nonzero partial derivatives and satisfying

$\text{??}\text{?x,}{}_{\mathrm{i}}\text{??}\text{?x}{}_{\mathrm{j}}$

for all x_i, x_j ≠ I, i, j = 1,2,…, n (n > 2) are determined (I is an interval of positive real numbers).     

Adsorption of metal halides from ethanol solutions by a 3-n-propylpyridiniumsilsesquioxane chloride-coated silica gel surface

3-n-propylpyridiniumsilsesquioxane chloride polymer, abbreviated as SiPy+Cl-, was used to coat a porous silica gel, SiO2, surface to form the chemically modified solid SiO2/SiPy+Cl-. The resulting polymer film was well adhered to the surface and presented an ion exchange capacity of 0.74 mmol g(-1). Metal halides, MClz [M=Fe(III), Cu(II), and Zn(II)], were adsorbed by the modified solid from ethanol solutions as neutral species by forming the surface anionic complexes described by the equation: mSiO2/SiPy+Cl-+ MClz <=> (SiO2/SiPy+)m[MCl(z+m)]m-, where the [MCl(z+m)]m- species adsorbed on the surface are FeCl4-, ZnCl4(2-), and CuCl4(2-). Accurate estimates of the specific sorption capacities and the heterogeneous stability constants of the immobilized metal complexes were determined with the aid of computational procedures.     

Anderson localization for multi-dimensional systems at large disorder or large energy

We prove that discrete Schrödinger operators on ^d with a random-potential have almost-surely only pure point spectrum and exponentially decaying eigenfunctions for large disorder or large energy. This is the first proof of localization for multi-dimensional Anderson models.Groupe de recherche 048 du CNRS     

Finiteness of Ricci flat supersymmetric non-linear σ-models

Combining the constraints of Kähler differential geometry with the universality of the normal coordinate expansion in the background field method, we study the ultraviolet behavior of 2-dimensional supersymmetric non-linear -models with target space an arbitrary riemannian manifoldM. We show that the constraint ofN=2 supersymmetry requires that all counterterms to the metric beyond one-loop order be cohomologically trivial. It follows that such supersymmetric non-linear -models defined on locally symmetric spaces are super-renormalizable and thatN=4 models are on-shell ultraviolet finite to all orders of perturbation theory.     

Posets isomorphic to their extensions

A standard extension for a poset P is a system Q of lower ends (descending subsets) of P containing all principal ideals of P. An isomorphism between P and Q is called recycling if [Y]Q for all YQ. The existence of such an isomorphism has rather restrictive consequences for the system Q in question. For example, if Q contains all lower ends generated by chains then a recycling isomorphism between P and Q forces Q to be precisely the system of all principal ideals. For certain standard extensions Q, it turns out that every isomorphism between P and Q (if there is any) must be recycling. Our results include the well-known fact that a poset cannot be isomorphic to the system of all lower ends, as well as the fact that a poset is isomorphic to the system of all ideals (i.e., directed lower ends) only if every ideal is principal.     

Nondynamical calculation of polarization observables in d+d reactions at low energies

The parametrization of polarization observables in terms of (l, s, J) matrix elements is given for²H(d, p)³H and²H(d, n)³He reactions at low energies. It is shown that transverse polarizations of outgoing nucleons are to be measured in order to obtain a complete set of cross-section, analysing powers, spin-correlation and polarization transfer experiments.