带有奇异项的临界增长p-Laplace方程的非平凡解

本文研究了一种带有奇异项的临界增长p-Laplace方程在N维空间中的有界集上非平凡解的问题,利用山路引理和集中紧性原理,得出方程在非线性项满足一定条件下有非平凡解的结果.     

Dynamic Nonlinear Modelization of Operational Supply Chain Systems

Supply Chain Management (SCM) is an important activity in all producing facilities and in many organizations to enable vendors, manufacturers and suppliers to interact gainfully and plan optimally their flow of goods and services. To realize this, a dynamic modelling approach for characterizing supply chain activities is opportune, so as to plan efficiently the set of activities over a distributed network in a formal and scientific way. The dynamical system will result so complex that it is not generally possible to specify the functional forms and the parameters of interest, relating outputs to inputs, states and stochastic terms by experiential specification methods. Thus the algorithm that will presented is Data Driven, determining simultaneously the functional forms, the parameters and the optimal control policy from the data available for the supply chain. The aim of this paper is to present this methodology, by considering dynamical aspects of the system, the presence of nonlinear relationships and unbiased estimation procedures to quantify these relations, leading to a nonlinear and stochastic dynamical system representation of the SCM problem. Moreover, the convergence of the algorithm will be proved and the satisfaction of the required statistical conditions demonstrated. Thus SCM problems may be formulated as formal scientific procedures, with well defined algorithms and a precise calculation sequence to determine the best alternative to enact. A “Certainty equivalent principle” will be indicated to ensure that the effects of the inevitable uncertainties will not lead to indeterminate results, allowing the formulation of demonstrably asymptotically optimal management plans.     

Complete systems, elementary submodels and the tightness of upper hyperspaces

We introduce and study some completeness properties for systems of open coverings of a given topological space. A Hausdorff space admitting a system of cardinality κ satisfying one of these properties is of type Gκ. Hence, we define several new variants of the ?ech number and use elementary submodels to determine further results. We introduce M-hulls and M-networks, for M elementary submodel. As an application, we give estimates for both the tightness and the Lindelöf number of a generic upper hyperspace. Two recent results of Costantini, Holá and Vitolo on the tightness of co-compact hyperspaces follow from ours as corollaries.     

Chemically controlled pattern formation in phase-separating materials

Summary The role of chemical reactions in the selection of patterns in phase-separating mixtures is presented. Linearized theory and computer simulation show that the initial long-wavelength instability characteristic of spinodal decomposition is suppressed by chemical reactions, which restrict domain growth to intermediate length scales even in the late stages of phase separation. Our findings suggest that chemical reactions may provide a novel way to stabilize and tune the steady-state morphology of phase-separating materials. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Normal Vietoris Implies Compactness: A Short Proof

One of the most celebrated results in the theory of hyperspaces says that if the Vietoris topology on the family of all nonempty closed subsets of a given space is normal, then the space is compact (Ivanova-Keesling-Velichko). The known proofs use cardinality arguments and are long. In this paper we present a short proof using known results concerning Hausdorff uniformities.     

Inorganic Sol-Gel Preparation of Medium Sized Microparticles of Li2TiO3 from TiCl4 as Tritium Breeding Material for Fusion Reactors

Microspheres of Li₂TiO₃ were fabricated by a classical, inorganic sol-gel process from commercially available TiCl₄. Elaborated process consists of the following main steps: (1) dissolving of TiCl₄ in concentrated aqueous HCl and addition of LiOH; (2) formation of sol emulsion in 2-ethylhexanol-1 containing the surfactant SPAN-80 (EH); (3) gelation of emulsion drops by extraction of water with partially dehydrated EH; (4) impregnation of gel to Li:Ti molar ratio MR = 2; (5) thermal treatment at 1200°C in order to receive chloride free product. This temperature can be significantly lowered (to 750°C) by dechlorination starting solution TiCl₄ by chemical treatment of the with nitric acid to form of nitrate-stabilized titania sols. Tritium release from sol-gel made Li₂TiO₃ microspheres were found very close to that observed for other traditional materials, however for the first sample process starts slightly earlier.     

A purely algebraic characterization of the hyperreal numbers

The hyperreal numbers of nonstandard analysis are characterized in purely algebraic terms as homomorphic images of a suitable class of rings of functions.

     

Assignments of methanol laser lines by frequency measurements and Fourier transform spectroscopy

We have measured the frequencies of four CH₃OH far-infrared laser lines that were previously known only by wavelength measurement. Two of these lines turned out to be doublets, bringing the total number of measured lines to six. We can now confirm the assignments of five of them and definitely disprove the assignments proposed for the sixth.In particular we confirm the assignments for the four strong laser lines at 205 and 208 µm pumped by the 9-P(34) CO₂ laser line. These lines share a common upper level in the first excited CO-stretch state, and terminate in the upper and lower levels of a hybrid state with J=5. Heterodyne frequency measurements and conventional microwave spectroscopy show that both lines are split into two components approximately 3.5 MHz apart. The origin of this further splitting is interpreted as a perturbed K-splitting.Work supported by Consiglio Nazionale delle Ricerche -Italia     

Growth of single-crystal magnetite nanowires from Fe3O4 nanoparticles in a surfactant-free hydrothermal process

Single-crystal magnetite nanowires with average diameter of ca. 20 nm and length of up to several micrometers were prepared by a simple alkaline surfactant-free hydrothermal process. The crystallinity, purity, morphology, and structural features of the as-prepared magnetite nanowires were investigated by powder X-ray diffraction, transmission electron microscopy (TEM) and selected area electron diffraction. The composition and length of nanowires depends on the pH, with higher pH favoring longer nanowires composed entirely of Fe₃O₄. A mechanism for nanowire growth is proposed.