Lazer-McKenna conjecture: The critical case

We consider an elliptic problem of Ambrosetti-Prodi type involving critical Sobolev exponent on a bounded smooth domain of dimension six or higher. By constructing solutions with many sharp peaks near the boundary of the domain, but not on the boundary, we prove that the number of solutions for this problem is unbounded as the parameter tends to infinity, thereby proving the Lazer-McKenna conjecture in the critical case.     

Two-body threshold spectral analysis, the critical case

We study in dimension d?2 low-energy spectral and scattering asymptotics for two-body d-dimensional Schrödinger operators with a radially symmetric potential falling off like −γr−2, γ>0. We consider angular momentum sectors, labelled by l=0,1,…, for which γ>²(l+d/2−1). In each such sector the reduced Schrödinger operator has infinitely many negative eigenvalues accumulating at zero. We show that the resolvent has a non-trivial oscillatory behaviour as the spectral parameter approaches zero in cones bounded away from the negative half-axis, and we derive an asymptotic formula for the phase shift.     

Topological and analytical properties of Sobolev bundles,I: The critical case

We study the interrelationship between topological and analytical properties of Sobolev bundles and describe some of their applications to variational problems on principal bundles. We in particular show that the category of Sobolev principal G-bundles of class W ^2,m/2 defined over M ^m is equivalent to the category of smooth principal G-bundles on M and give a characterization of the weak sequential closure of smooth principal G-bundles with prescribed isomorphism class. We also prove a topological compactness result for minimizing sequences of a conformally invariant Yang-Mills functional.      

Analysis and visualization tools in CFD, part II: A case study in grid adaptivity

The objective of the present paper is to show, in the context of a configurable resolution and analysis environment, how grid adaptivity methodology can be made configurable and rapidly applied to various problems. In order to reach this objective, our error estimation and grid adaptation tools were configured to integrate Zienkiewicz and Zhu's local error estimator. The environment was then applied to the simulation of incompressible isothermal flow and natural convection problems.     

Operations management of new project development: innovation,efficient, effective aspects

The integration of distribution management systems (DMS) and feeder management systems (FMS) in China has become a trend in recent years, in addition to upgrading and rebuilding the existing energy management system and DMS. However, some management methods are different and contradictory, thus result in obstacles to innovation and effectiveness. Thus, firms still struggle to find effective process management that is associated with innovative project operations. In addition, there is no standard method to evaluate information technology (IT) projects, and at least 40% of IT projects realize no benefits. It is astonishing that none of the above-mentioned issues have been addressed or solved by previous literatures. In order to fill the vacancy, this paper first briefly introduces FMS and determines its critical success criteria, and then proposes suitable forms of organization for knowledge management. It also applies process management methods according to knowledge creation mode and maturity of the project. Finally, an analytic network process associated with benefits, opportunities, costs, and risks is constructed to compare the performance of different FMS projects with and without adopting the proposed methodology.     

Linear parabolic problem: High-frequency asymptotics in the critical case

A second-order linear parabolic problem with high-frequency terms is considered. The elliptic operator of the corresponding limiting (averaged) problem is assumed to be degenerate. A complete formal asymptotic expansion of a time-periodic solution of the perturbed problem is constructed.     

Process-oriented knowledge management: a case study

Most knowledge repositories store documents organized by subject areas. In process-oriented knowledge management, each knowledge management project is developed around an organizational process and the mission, rationale and objectives of the process define the scope of the project. At the heart of the process-oriented knowledge management strategy is a knowledge management system called KMS. KMS has a workflow management subsystem that enables it to capture knowledge in context as it is created and present knowledge to the user at the right step of the process. Its repository contains not only knowledge created and manipulated in an organizational process, but also the knowledge of the process itself in the form of process designs, case histories and lessons learned from past experiences. This paper describes the process-oriented knowledge management strategy and its implementation in the real estate organization of a real-life global company.     

Sharp sobolev embeddings and related hardy inequalities: The critical case

The paper deals with sharp embeddings of the Sobolev spaces H^s_p(IRⁿ) and the Besov spaces B^s_p,p(IRⁿ) into rearrangement—invariant spaces and related Hardy inequalities. Here 1 < p < ∞ and s = n/p.     

A critical case for Brownian slow points

Summary LetX _t be a Brownian motion and letS(c) be the set of realsr0 such that üX _r+t –X _r üct, 0th, for someh=h(r)>0. It is known thatS(c) is empty ifc<1 and nonempty ifc>1, a.s. In this paper we prove thatS(1) is empty a.s.This research was partially supported by NSF Grant 9322689.     

The critical case for a Berestycki-Lions theorem

We consider the existence of the ground states solutions to the following Schrdinger equation:△u+V(x)u=f(u),u∈H1(RN),where N 3 and f has critical growth.We generalize an earlier theorem due to Berestycki and Lions about the subcritical case to the current critical case.     

Orange harvesting scheduling management: a case study

The competitiveness of Brazil's citrus sector is a function of quality control in the transformation of fruit into juice. The transformation process commences with the harvest, the timing of which significantly affects fruit quality. In this paper, a mathematical model is formulated that links pertinent chemical, biologic, and logistic restrictions to the quality of the fruit to be harvested, applying linear programming theory. The modelling structure was verified and validated with real data from 320 Brazilian farms involved with an annual production of approximately 7?200?000 boxes of oranges. It could be attested that the maximization of the number of boxes of oranges to be harvested (strategy that is still adopted by a representative number of Brazilian citrus farmers, based on the industry advice) does not necessarily correspond to the maximum quantity of total soluble solids (TSS). In many cases, citrus harvested at the optimum TSS point offered higher concentrated juice productivity. The estimated potential benefits ($) from using the proposed model reached figures over 6%.     

Elliptic equations with critical exponent on S3: new non-minimising solutions

Consider the problem:

$\{\begin{array}{cc}?{\Delta }_{S^3}U=\lambda U+U^5\text{,}U>0\hfill & \text{on?}{B}^{\prime }\text{,}\hfill \\ U=0\hfill & \text{on?}?B^{\prime }\text{,}\hfill \end{array}$

where $B^{\prime }$ is a ball on ${\mathbf{S}}^3$ with geodesic radius ${\theta }_1$, and ${\Delta }_{S^3}$ is the Laplace–Beltrami operator on ${\mathbf{S}}^3$. We prove that for any ${\theta }_1\in (\pi /2\text{,}\pi )$ and any $k>1$, there exist at least 2k solutions of this problem for λ sufficiently large negative. To cite this article: H. Brezis, L.A. Peletier, C. R. Acad. Sci. Paris, Ser. I 339 (2004).