Algebraic analysis of offsets to hypersurfaces

In this paper, we present a complete algebraic analysis of degeneration and existence of simple and special components of generalized offsets to irreducible hypersurfaces over algebraically closed fields of characteristic zero. More precisely, we analyze the degeneration situations when offseting, and we state that there exist, at most, a finite set of distances for which the offset of a hypersurface may degenerate. As a consequence of this analysis, an algorithmic method to determine such distances is derived. Furthermore, as an application of these results, a complete degeneration analysis of the generalized offset to the sphere is developed. In addition, we study the existence of simple and special components of the offset. In this context we prove that, in the case of classical offsets, there always exists at least one simple component and, in the case of generalized offsets, we prove that for almost every distance and for almost every isometry, all components of the offset are simple. Received November 9, 1998; in final form March 5, 1999 / Published online May 8, 2000     

Degree formulae for offset curves

In this paper, we present three different formulae for computing the degree of the offset of a real irreducible affine plane curve C given implicitly, and we see how these formulae particularize to the case of rational curves. The first formula is based on an auxiliary curve, called S, that is defined depending on a non-empty Zariski open subset of R². The second formula is based on the resultant of the defining polynomial of C, and the polynomial defining generically S. The third formula expresses the offset degree by means of the degree of C and the multiplicity of intersection of C and the hodograph H to C, at their intersection points.     

Analysis of t-butylphenol acetylene condensed resin with methyl-methine linkages in vulcanized rubber by pyrolysis-gas chromatography/mass spectrometry

Methyl-methine linkages of Novolac, a commercially available t-butylphenol acetylene condensed (TBPA) resin, have been identified by recognition of pyrolysis pathways using pyrolysis-gas chromatography/mass spectrometry (Py-GC/mS) in vulcanized rubber. The diagnostic mass spectrum of t-butylphenol with methyl-methine linkages between phenolic rings was observed at m/z 192, corresponding to 4-t-butyl-2-ethyl-6-methylphenol. Other molecular ions were observed at m/z 178, 164, and 150 in the characteristic pyrolyzates. The ion at m/z 192 in the TBPA resin was observed to be characteristic for methyl-methine linkages between the phenolic groups, and the analytical pyrolysis-GC/mS method was thus able to identify the resin at low levels in vulcanized rubber. Copyright 1999 John Wiley & Sons, Ltd.     

DBI models for the unification of dark matter and dark energy

We propose a model based on a DBI action for the unification of dark matter and dark energy. This is supported by the results of the study of its background behavior at early and late times, and reinforced by the analysis of the evolution of perturbations. We also perform a Bayesian analysis to set observational constraints on the parameters of the model using type Ia SN, CMB shift and BAO data. Finally, to complete the study we investigate its kinematics aspects, such as the effective equation of state parameter, acceleration parameter and transition redshift. Particularizing those parameters for the best fit one appreciates that an effective phantom is preferred.     

Kinetic determination of atrazine in foods based on stopped-flow fluorescence polarization immunoassay

A very simple and fast method for the direct determination of atrazine in food samples based on the use of stopped-flow fluorescence polarization immunoassay is described. Unlike other immunoassay methods where the analytical signal is obtained when the immunochemical reaction has reached or is close to the equilibrium, this method uses the initial rate of this reaction as the analytical parameter, which is measured in only 4-5 s. This approach minimizes the static signal from the sample matrix, allows the direct analysis of the samples and can be easily adapted to the routine automatic determination of atrazine. The dynamic range of the calibration graph was 0.7-100 ng ml(-1) and the detection limit was 0.2 ng ml(-1). The precision and selectivity of the method were also studied. The analytical recoveries obtained by applying the method to white and red wine, orange juice and tea samples ranged from 80 to 104%.     

Decrease of free amino acids in high-pressure treated cheese

Abstract

High-pressure treatment of cheese has been studied with a view to preserving fresh cheese [1], and also of developing a method of accelerating its ripening [2-7]. While these objectives can be reached, other changes also occur in cheese when high pressure is applied. One of those changes is the decrease of free amino acids (FAA) in cheese treated in pressures over 200-300MPa. In this paper we will try to summarize the results obtained by different research groups, as well as our own. These results have been published separately, but not previously tied together and explained.     

Behavior of the Fiber and the Base Points of Parametrizations Under Projections

Given a rational parametrization ${{\mathcal{P}(\overline {t}), {\overline {t}}=(t_1, \ldots, t_r)}}$ , of an r-dimensional unirational variety, we analyze the behavior of the variety of the base points of ${\mathcal{P}(\overline {t})}$ in connection to its generic fibre, when successively eliminating the parameters t _i . For this purpose. we introduce a sequence of generalized resultants whose primitive and content parts contain the different components of the projected variety of the base points and the fibre. In addition, when the dimension of the base points is strictly smaller than 1 (as in the well known cases of curves and surfaces), we show that the last element in the sequence of resultants is the univariate polynomial in the corresponding Gröbner basis of the ideal associated to the fibre; assuming that the ideal is in t ₁-general position and radical.     

Chemical cleavage reactions of DNA on solid support: application in mutation detection

Background  

The conventional solution-phase Chemical Cleavage of Mismatch (CCM) method is time-consuming, as the protocol requires purification of DNA after each reaction step. This paper describes a new version of CCM to overcome this problem by immobilizing DNA on silica solid supports.     

The effect of nonlinearity on unstable zones of Mathieu equation

Mathieu equation is a well-known ordinary differential equation in which the excitation term appears as the non-constant coefficient. The mathematical modelling of many dynamic systems leads to Mathieu equation. The determination of the locus of unstable zone is important for the control of dynamic systems. In this paper, the stable and unstable regions of Mathieu equation are determined for three cases of linear and nonlinear equations using the homotopy perturbation method. The effect of nonlinearity is examined in the unstable zone. The results show that the transition curves of linear Mathieu equation depend on the frequency of the excitation term. However, for nonlinear equations, the curves depend also on initial conditions. In addition, increasing the amplitude of response leads to an increase in the unstable zone.