Stability of certain one-dimensional unsteady gas motions

This paper studies the stability of the adiabatic unsteady motions of a perfect gas for which the velocity is proportional to the distance to the center of symmetry. The solutions of the gas dynamic equations of such a form and their physical interpretation are considered in [1]. The stability of one of the solutions, which corresponds to the pulsations of uniform gravitating spheres, was studied in paper [2]. The stability of the other solutions (gas motions in the absence of Newtonian gravitation, nonperiodic motions of gravitating gas) has not previously been investigated. The stability of such solutions is investigated in this paper and it is shown that the motions in which gas compression occurs are, as a rule, unstable.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 120–127, November–December, 1985.     

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.