Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

Characterization of a Local Renin-Angiotensin System in Rat Gingival Tissue

Background: The systemic renin-angiotensin system (RAS) promotes the plasmatic production of angiotensin (Ang) II, which acts through interaction with specific receptors. There is growing evidence that local systems in various tissues and organs are capable of generating angiotensins independently of circulating RAS. The aims of this study were to investigate the expression and localization of RAS components in rat gingival tissue and evaluate the in vitro production of Ang II and other peptides catalyzed by rat gingival tissue homogenates incubated with different Ang II precursors. Methods: Reverse transcription - polymerase chain reaction assessed mRNA expression. Immunohistochemical analysis aimed to detect and localize renin. A standardized fluorimetric method with tripeptide hippuryl-histidyl-leucine was used to measure tissue angiotensin-converting enzyme (ACE) activity, whereas high performance liquid chromatography showed products formed after the incubation of tissue homogenates with Ang I or tetradecapeptide renin substrate (TDP). Results: mRNA for renin, angiotensinogen, ACE, and Ang II receptors (AT(1a), AT(1b), and AT(2)) was detected in gingival tissue; cultured gingival fibroblasts expressed renin, angiotensinogen, and AT(1a) receptor. Renin was present in the vascular endothelium and was intensely expressed in the epithelial basal layer of periodontally affected gingival tissue. ACE activity was detected (4.95 +/- 0.89 nmol histidyl-leucine/g/minute). When Ang I was used as substrate, Ang 1-9 (0.576 +/- 0.128 nmol/mg/minute), Ang II (0.066 +/- 0.008 nmol/mg/minute), and Ang 1-7 (0.111 +/- 0.017 nmol/mg/minute) were formed, whereas these same peptides (0.139 +/- 0.031, 0.206 +/- 0.046, and 0.039 +/- 0.007 nmol/mg/minute, respectively) and Ang 1 (0.973 +/- 0.139 nmol/mg/minute) were formed when TDP was the substrate. Conclusion: Local RAS exists in rat gingival tissue and is capable of generating Ang II and other vasoactive peptides in vitro. J Periodontol 2009;80:130-139.

Smallest weak and smallest totally weak critical sets in the latin squares of order at most seven

A critical set in a latin square of order n is a set of entries in a latin square which can be embedded in precisely one latin square of order n. Also, if any element of the critical set is deleted, the remaining set can be embedded in more than one latin square of order n. In this paper we find smallest weak and smallest totally weak critical sets for all the latin squares of orders six and seven. Moreover, we computationally prove that there is no (totally) weak critical set in the back circulant latin square of order five and we find a totally weak critical set of size seven in the other main class of latin squares of order five.

Contrasting models of land use regulation: Community, government and tourism development

This paper assesses the capacity of local communities and sub-national governments to influence patterns of tourism development, within the context of a globalizing economy. Through a comparison of the contrasting examples of Hawaii and Queensland, the paper indicates the consequences of different approaches to land use regulation. It points to the importance of planning and policy processes that integrate community interests, in order to achieve long-term, sustainable tourism development. Effective regulation of development can minimize the social and environmental impacts of tourism. The paper illustrates how community organizations and sub-national governments can articulate local interests, despite the global demands of investors for more deregulated markets in land.

Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.

Supervisory control of wastewater treatment plants by combining principal component analysis and fuzzy c-means clustering

In this paper a methodology for integrated multivariate monitoring and control of biological wastewater treatment plants during extreme events is presented. To monitor the process, on-line dynamic principal component analysis (PCA) is performed on the process data to extract the principal components that represent the underlying mechanisms of the process. Fuzzy c-means (FCM) clustering is used to classify the operational state. Performing clustering on scores from PCA solves computational problems as well as increases robustness due to noise attenuation. The class-membership information from FCM is used to derive adequate control set points for the local control loops. The methodology is illustrated by a simulation study of a biological wastewater treatment plant, on which disturbances of various types are imposed. The results show that the methodology can be used to determine and co-ordinate control actions in order to shift the control objective and improve the effluent quality.

A comparison of low-storage strategies for spectral analysis in dissipative systems: filter diagonalisation in the Lanczos representation and harmonic inversion of the Chebychev-order-domain autocorrelation function

We compare the performance of two different low-storage filter diagonalisation (LSFD) strategies in the calculation of complex resonance energies of the HO2, radical. The first is carried out within a complex-symmetric Lanczos subspace representation [H. Zhang, S.C. Smith, Phys. Chem. Chem. Phys. 3 (2001) 2281]. The second involves harmonic inversion of a real autocorrelation function obtained via a damped Chebychev recursion [V.A. Mandelshtam, H.S. Taylor, J. Chem. Phys. 107 (1997) 6756]. We find that while the Chebychev approach has the advantage of utilizing real algebra in the time-consuming process of generating the vector recursion, the Lanczos, method (using complex vectors) requires fewer iterations, especially for low-energy part of the spectrum. The overall efficiency in calculating resonances for these two methods is comparable for this challenging system. (C) 2001 Elsevier Science B.V. All rights reserved.