The nonexistence of spurious solutions to discrete, two-point boundary value problems

We investigate difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations. We formulate conditions under which all solutions to the discrete problem satisfy certain a priori bounds which axe independent of the step-size. As a result, the nonexistence of spurious solutions are guaranteed. Some existence and convergence theorems for solutions to the discrete problem are also presented. (C) 2002 Elsevier Science Ltd. All rights reserved.

Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.

On continuous selection problems for multivalued mappings with the local intersection property in hyperconvex metric spaces

In the paper we present two continuous selection theorems in hyperconvex metric spaces and apply these to study xed point and coincidence point problems as well as variational inequality problems in hyperconvex metric spaces.

Investigation of candidate division TM7, a recently recognized major lineage of the domain bacteria with no known pure-culture representatives

A molecular approach was used to investigate a recently described candidate division of the domain Bacteria, TM7, currently known only from environmental 16S ribosomal DNA sequence data, A number of TM7-specific primers and probes were designed and evaluated. Fluorescence in situ hybridization (FISH) of a laboratory scale bioreactor using two independent TM7-specific probes revealed a conspicuous sheathed-filament morphotype, fortuitously enriched in the reactor. Morphologically, the filament matched the description of the Eikelboom morphotype 0041-0675 widely associated with bulking problems in activated-sludge wastewater treatment systems. Transmission electron microscopy of the bioreactor sludge demonstrated that the sheathed-filament morphotype had a typical gram-positive cell envelope ultrastructure. Therefore, TM7 is only the third bacterial lineage recognized to have gram-positive representatives. TM7-specific FISH analysis of two full-scale wastewater treatment plant sludges, including the one used to seed the laboratory scale reactor, indicated the presence of a number of morphotypes, including sheathed filaments. TM7-specific PCR clone libraries prepared from the two full-scale sludges yielded 23 novel TM7 sequences. Three subdivisions could be defined based on these data and publicly available sequences. Environmental sequence data and TM7-specific FISH analysis indicate that members of the TM7 division are present in a variety of terrestrial, aquatic, and clinical habitats. A highly atypical base substitution (Escherichia coli position 912; C to U) for bacterial 16S rRNAs was present in almost all TM7 sequences, suggesting that TM7 bacteria, like Archaea, may be streptomycin resistant at the ribosome level.

The uniqueness of solutions to discrete, victor, two-point boundary value problems

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented.

Water table waves in an unconfined aquifer: Experiments and modeling

[1] Comprehensive measurements are presented of the piezometric head in an unconfined aquifer during steady, simple harmonic oscillations driven by a hydrostatic clear water reservoir through a vertical interface. The results are analyzed and used to test existing hydrostatic and nonhydrostatic, small-amplitude theories along with capillary fringe effects. As expected, the amplitude of the water table wave decays exponentially. However, the decay rates and phase lags indicate the influence of both vertical flow and capillary effects. The capillary effects are reconciled with observations of water table oscillations in a sand column with the same sand. The effects of vertical flows and the corresponding nonhydrostatic pressure are reasonably well described by small-amplitude theory for water table waves in finite depth aquifers. That includes the oscillation amplitudes being greater at the bottom than at the top and the phase lead of the bottom compared with the top. The main problems with respect to interpreting the measurements through existing theory relate to the complicated boundary condition at the interface between the driving head reservoir and the aquifer. That is, the small-amplitude, finite depth expansion solution, which matches a hydrostatic boundary condition between the bottom and the mean driving head level, is unrealistic with respect to the pressure variation above this level. Hence it cannot describe the finer details of the multiple mode behavior close to the driving head boundary. The mean water table height initially increases with distance from the forcing boundary but then decreases again, and its asymptotic value is considerably smaller than that previously predicted for finite depth aquifers without capillary effects. Just as the mean water table over-height is smaller than predicted by capillarity-free shallow aquifer models, so is the amplitude of the second harmonic. In fact, there is no indication of extra second harmonics ( in addition to that contained in the driving head) being generated at the interface or in the interior.

Unknown Radial Distortion Centers in Multiple View Geometry Problems

The radial undistortion model proposed by Fitzgibbon and the radial fundamental matrix were early steps to extend classical epipolar geometry to distorted cameras. Later minimal solvers have been proposed to find relative pose and radial distortion, given point correspondences between images. However, a big drawback of all these approaches is that they require the distortion center to be exactly known. In this paper we show how the distortion center can be absorbed into a new radial fundamental matrix. This new formulation is much more practical in reality as it allows also digital zoom, cropped images and camera-lens systems where the distortion center does not exactly coincide with the image center. In particular we start from the setting where only one of the two images contains radial distortion, analyze the structure of the particular radial fundamental matrix and show that the technique also generalizes to other linear multi-view relationships like trifocal tensor and homography. For the new radial fundamental matrix we propose different estimation algorithms from 9,10 and 11 points. We show how to extract the epipoles and prove the practical applicability on several epipolar geometry image pairs with strong distortion that - to the best of our knowledge - no other existing algorithm can handle properly.

Annotation taken, in the perspective of criminal and constitutional law, as well as in criminology, to the decision of the portuguese constitutional court, of January 13, 2011 – with respect to the problems of “consent” and “medical act”

1 – Summary of the decision taken by the Portuguese Constitutional Court, of January 13, 2011; 2 – Complete text of the decision of the Portuguese Constitutional Court, of January 13, 2011, Judge Maria João ANTUNES (Reporter), Judge Carlos Pamplona de OLIVEIRA, Judge José Borges SOEIRO, Judge Gil GALVÃO, Judge Rui Manuel Moura RAMOS (President) –in terms of the tribunalconstitucional.pt, August 1, 2011; 3 – Brief annotation to the problem of the “medical act”; 3.1 – Plus some conclusions on the brief annotation to the problem of the “medical act”; 3.2 – Brief annotation to the problem of “consent”– continuation of the previous comments; 4 – Conclusions. It must never be forgotten that “consent” does not stand as the only cause of exclusion of unlawfulness.