Herbrand's Theorem and Equational Reasoning: Problems and Solutions

The famous Herbrand's theorem of mathematical logic plays an important role in automated theorem proving. In the first part of this article, we recall the theorem and formulate a number of natural decision problems related to it. Somewhat surprisingly, these problems happen to be equivalent. One of these problems is the so-called simultaneous rigid E-unification problem. In the second part, we survey recent result on the simultaneous rigid E-unification problem.

From XML to relational view updates: applying old solutions to solve a new problem

XML has become an important medium for data exchange, and is frequently used as an interface to - i.e. a view of - a relational database. Although lots of work have been done on querying relational databases through XML views, the problem of updating relational databases through XML views has not received much attention. In this work, we give the rst steps towards solving this problem. Using query trees to capture the notions of selection, projection, nesting, grouping, and heterogeneous sets found throughout most XML query languages, we show how XML views expressed using query trees can be mapped to a set of corresponding relational views. Thus, we transform the problem of updating relational databases through XML views into a classical problem of updating relational databases through relational views. We then show how updates on the XML view are mapped to updates on the corresponding relational views. Existing work on updating relational views can then be leveraged to determine whether or not the relational views are updatable with respect to the relational updates, and if so, to translate the updates to the underlying relational database. Since query trees are a formal characterization of view de nition queries, they are not well suited for end-users. We then investigate how a subset of XQuery can be used as a top level language, and show how query trees can be used as an intermediate representation of view de nitions expressed in this subset.

Contractual solutions to the holdup problem: a survey

In this survey, we presented the general idea and main results from what we understand that are the most important contributions to contractual solutions to the holdup problem literature. The aim of this paper is to push the previous analysis, uniform the notation and provide a snapshot on the most recent literature, as well as bring topics for future inquires on this issue.

Migration of diethylhexyl phthalate from PVC bags into intravenous cyclosporine solutions

The migration of diethylhexyl phthalate (DEHP) from PVC bags into LVPS (0.9% NaCl) and LVPS with cyclosporine at concentrations of 2.5 and 0.5 mg/ml was studied. PVC bags were placed in contact with these solutions and stored at 25 1 degrees C. They were taken for analysis each 30 min during 6 h and after this period at each 1 h until 12 h of contact. Water was used as reference, and exposed and analyzed under the same conditions. After contact, the solutions were submitted to extraction with hexane and analyzed by GC-FID. The results showed that DEHP did not migrate into water and LVPS during all the time. Also, no measurable amount of DEHP was detected during the first 3 h of contact between the PVC bag and the diluted cyclosporine solution. However, the amount of released DEHP reached a detectable level after 4 It of contact, increased until 6 h, stabilized, and increased again after 9-10 h. The 12 h of contact showed the highest DEHP levels for both cyclosporine concentrations. The DEHP migrated was 0.02-0.08% of that present in the bag. (c) 2005 Elsevier B.V. All rights reserved.

Raman and photoluminescence of Er3+-doped SnO2 obtained via the sol-gel technique from solutions with distinct pH

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Bounded solutions of fermions in the background of mixed vector-scalar inversely linear potentials

The problem of a fermion subject to a general mixing of vector and scalar potentials in a two-dimensional world is mapped into a Sturm-Liouville problem. Isolated bounded solutions are also searched. For the specific case of an inversely linear potential, which gives rise to an effective Kratzer potential in the Sturm-Liouville problem, exact bounded solutions are found in closed form. The case of a pure scalar potential with their isolated zero-energy solutions, already analyzed in a previous work, is obtained as a particular case. The behavior of the upper and lower components of the Dirac spinor is discussed in detail and some unusual results are revealed. The nonrelativistic limit of our results adds a new support to the conclusion that even-parity solutions to the nonrelativistic one-dimensional hydrogen atom do not exist. (c) 2004 Elsevier B.V. All rights reserved.

General solutions for some classes of interacting two field kinks

In this work we present some classes of models whose the corresponding two coupled first-order nonlinear equations can be put into a linear form, and consequently be solved completely. In these cases the so-called trial orbit method is completely unnecessary. We recall that some physically important models as, for instance, the problem of tiling a plane with a network of defects and polymer properties are in this class of models. (c) 2005 Elsevier B.V. All rights reserved.

Bounded solutions of fermions in the background of mixed vector-scalar Poeschl-Teller-like potentials

The problem of a fermion subject to a convenient mixing of vector and scalar potentials in a two-dimensional space-time is mapped into a Sturm-Liouville problem. For a specific case which gives rise to an exactly solvable effective modified Poschl-Teller potential in the Sturm-Liouville problem, bound-state solutions are found. The behaviour of the upper and lower components of the Dirac spinor is discussed in detail and some unusual results are revealed. The Dirac delta potential as a limit of the modified Poschl-Teller potential is also discussed. The problem is also shown to be mapped into that of massless fermions subject to classical topological scalar and pseudoscalar potentials. Copyright (C) EPLA, 2007.

Two field BPS solutions for generalized Lorentz breaking models

In this work we present nonlinear models in two-dimensional space-time of two interacting scalar fields in the Lorentz and CPT violating scenarios. We discuss the soliton solutions for these models as well as the question of stability for them. This is done by generalizing a model recently published by Barreto and collaborators and also by getting new solutions for the model introduced by them.

Some exact solutions of the Dirac equation

Exact analytic solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions.

Bounded solutions for nonconserving-parity pseudoscalar potentials

The Dirac equation is analyzed for nonconserving-parity pseudoscalar radial potentials in 3+1 dimensions. It is shown that despite the nonconservation of parity this general problem can be reduced to a Sturm-Liouville problem of nonrelativistic fermions in spherically symmetric effective potentials. The searching for bounded solutions is done for the power-law and Yukawa potentials. The use of the methodology of effective potentials allow us to conclude that the existence of bound-state solutions depends whether the potential leads to a definite effective potential-well structure or to an effective potential less singular than -1/4r(2).

Exact closed-form solutions of the Dirac equation for a class of effective Morse potentials

Exact bounded solutions for a fermion subject to exponential scalar potential in 1 + 1 dimensions are found in closed form. We discuss the existence of zero modes which are related to the ultrarelativistic limit of the Dirac equation and are responsible for the induction of a fractional fermion number on the vacuum.