Abstract:
We show that the quantum solitons occurring in theories describing a complex scalar field in (1 + 1)-dimensions with a Z(N) symmetry may be identified with sine-Gordon quantum solitons in the phase of this field. Then using both the Euclidean thermal Green function of the two-dimensional free massless scalar field in coordinate space and its dual, we obtain an explicit series expression for the corresponding solitonic correlation function at finite temperature.

Abstract:
We show how the famous soliton solution of the classical sine-Gordon
field theory in (1 + 1)-dimensions may be obtained as a particular case of a
solution expressed in terms of the Jacobi amplitude, which is the inverse
function of the incomplete elliptic integral of the first kind.

Abstract:
In the present work we show how different ways to solve biquadratic
equations can lead us to different representations of its solutions. A
particular equation which has the golden ratio and its reciprocal as solutions
is shown as an example.

Abstract:
We develop a field theory-inspired stochastic model for description of tumour growth based on an analogy with an SI epidemic model, where the susceptible individuals (S) would represent the healthy cells and the infected ones (I), the cancer cells. From this model, we obtain a curve describing the tumour volume as a function of time, which can be compared to available experimental data.

The cross product in Euclidean space IR^{3} is an operation in which two vectors are associated to generate a third vector, also in space IR^{3}. This product can be studied rewriting its basic equations in a matrix structure, more specifically in terms of determinants. Such a structure allows extending, for analogy, the ideas of the cross product for a type of the product of vectors in higher dimensions, through the systematic increase of the number of rows and columns in determinants that constitute the equations. So, in a n-dimensional space with Euclidean norm, we can associate n – 1 vectors and to obtain an n-th vector, with the same geometric characteristics of the product in three dimensions. This kind of operation is also a geometric interpretation of the product defined by Eckman [1]. The same analogies are also useful in the verification of algebraic properties of such products, based on known properties of determinants.

Recently I published a
paper in the journal ALAMT (Advances in
Linear Algebra & Matrix Theory) and explored the possibility of
obtaining products of vectors in dimensions higher than three [1]. In
continuation to this work, it is proposed to develop, through dimensional
analogy, a vector field with notation and properties analogous to the curl, in
this case applied to the space IR^{4}.
One can see how the similarities are obvious in relation to the algebraic properties and the geometric structures,
if the rotations are compared in spaces of three and four dimensions.

Abstract:
A great amount of work addressed methods for predicting the battery lifetime in wireless sensor systems. In spite of these efforts, the reported experimental results demonstrate that the duty-cycle current average method, which is widely used to this aim, fails in accurately estimating the battery life time of most of the presented wireless sensor system applications. The aim of this paper is to experimentally assess the duty-cycle current average method in order to give more effective insight on the effectiveness of the method. An electronic metering system, based on a dedicated PCB, has been designed and developed to experimentally measure node current consumption profiles and charge extracted from the battery in two selected case studies. A battery lifetime measurement (during 30 days) has been carried out. Experimental results have been assessed and compared with estimations given by using the duty-cycle current average method. Based on the measurement results, we show that the assumptions on which the method is based do not hold in real operating cases. The rationality of the duty-cycle current average method needs reconsidering.

Abstract:
We use the Bethe’s ansatz method to study the entanglement of spinons in the quantum phase transition of half integer spin one-dimensional magnetic chains known as quantum wires. We calculate the entanglement in the limit of the number of particles . We obtain an abrupt change in the entanglement next the quantum phase transition point of the anisotropy parameter ？from the gapped phase ？to gapless phase .

Abstract:
The interaction between an electron with a three-dimensional domain wall was investigated using the Born’s expansion of the S scattering matrix. We obtain an influence of the scattering of the electron with the ferromagnetic domain wall in the spin wave function of the electron with the aim to generate the knowledge about the state of the electron spin after the scattering. It relates to the recent problem of generation of the spin polarized electric current. We also obtain the contribution of the electron-wall domain interaction on the electric conductivity , through the wall domain, where we have obtained a peak of resonance in the conductivity for one value of .

Abstract:
In this work, basic statistical concepts referred to both precision and accuracy of measurements are described. These concepts are later related to the characterization of the Total Reflection X-Ray Fluorescence Technique (TXRF). In the assessment of uncertainties of the TXRF technique, in the case of a confusion between both concepts, errors would be produced in such process, resulting in incomplete mathematical expressions.