On Bogovski\u{\i} and regularized Poincar\'e integral operators for de Rham complexes on Lipschitz domains

We study integral operators related to a regularized version of the classical Poincar\'e path integral and the adjoint class generalizing Bogovski\u{\i}'s integral operator, acting on differential forms in $R^n$. We prove that these operators are pseudodifferential operators of order -1. The Poincar\'e-type operators map polynomials to polynomials and can have applications in finite element analysis. For a domain starlike with respect to a ball, the special support properties of the operators imply regularity for the de Rham complex without boundary conditions (using Poincar\'e-type operators) and with full Dirichlet boundary conditions (using Bogovski\u{\i}-type operators). For bounded Lipschitz domains, the same regularity results hold, and in addition we show that the cohomology spaces can always be represented by $C^\infty$ functions.Comment: 23 page

CSR as a Strategic Management Tool: Expectations and Realities of Two MNCs in Nigeria

Corporate social responsibility (CSR) as a concept has been a subject of debate in the management cycle for decades. However, the incorporation of CSR, competitive advantage and strategic management into top management decision making processes, forms a set of new alliances that are beginning to gain attention. This paper examined the strategic alliances of these highly volatile but significantly critical components in order to determine the extent to which these three seemingly incongruous factors can be achieved in reality within a developing country such as Nigeria. Using a comparative case study approach, the activities of two multinationals - Shell Plc and Coca Cola – were examined. The critical success factors were explained based on the strategies adopted in order to determine the impact on the society and whether they were in line with stakeholders’ expectations. Findings however indicate that there has been an interplay of high level forces which has resulted in the unsavoury news emanating from the oil producing communities in Nigeria, unfortunately, the activities of Coca cola in both the content and context of their operations have received little or no attention. This paper contributes to the scarce literature of this discourse within the African continent in general and Nigerian state in particular as well as sets a precedent for future research

BRST Hamiltonian for Bulk-Quantized Gauge Theory

By treating the bulk-quantized Yang-Mills theory as a constrained system we obtain a consistent gauge-fixed BRST hamiltonian in the minimal sector. This provides an independent derivation of the 5-d lagrangian bulk action. The ground state is independent of the (anti)ghosts and is interpreted as the solution of the Fokker-Planck equation, thus establishing a direct connection to the Fokker-Planck hamiltonian. The vacuum state correlators are shown to be in agreement with correlators in lagrangian 5-d formulation. It is verified that the complete propagators remain parabolic in one-loop dimensional regularization.Comment: 23 pages, AMS-LaTeX, 1 feynmf diagram, added 2 refs email addres

Generalized Korn's inequality and conformal Killing vectors

Korn's inequality plays an important role in linear elasticity theory. This inequality bounds the norm of the derivatives of the displacement vector by the norm of the linearized strain tensor. The kernel of the linearized strain tensor are the infinitesimal rigid-body translations and rotations (Killing vectors). We generalize this inequality by replacing the linearized strain tensor by its trace free part. That is, we obtain a stronger inequality in which the kernel of the relevant operator are the conformal Killing vectors. The new inequality has applications in General Relativity.Comment: 8 page

Strichartz estimates for the water-wave problem with surface tension

Strichartz-type estimates for one-dimensional surface water-waves under surface tension are studied, based on the formulation of the problem as a nonlinear dispersive equation. We establish a family of dispersion estimates on time scales depending on the size of the frequencies. We infer that a solution $u$ of the dispersive equation we introduce satisfies local-in-time Strichartz estimates with loss in derivative: $$\| u \|_{L^p([0,T]) W^{s-1/p,q}(\mathbb{R})} \leq C, \qquad \frac{2}{p} + \frac{1}{q} = {1/2},$$ where $C$ depends on $T$ and on the norms of the initial data in $H^s \times H^{s-3/2}$. The proof uses the frequency analysis and semiclassical Strichartz estimates for the linealized water-wave operator.Comment: Fixed typos and mistakes. Merged with arXiv:0809.451

Product Differentiation Costs and Global Competition

The growing competitive intensity on the markets determines the emergence of competition costs that are expressed at a corporate level and have implicit repercussions for the supply system. This type of costs makes it possible to identify a close link between competition costs and supply differentiation costs. Classification by competitive intensity presupposes that the analysis performed identifies the classification of company costs as the discriminating element, in terms of the competitive pressure of the context in which the firm operates. The emergence of competition costs is linked to an attempt to squeeze them as an aspect of vertical, or more specifically, horizontal cooperation strategies.Product Differentiation; Differentiation Costs; Over-Supply; Global Competition; Marketing; Market-Driven Management; Global Corporations; Global Markets DOI:http://dx.doi.org/10.4468/2005.1.06garbelli