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Thermal Soliton Correlation Functions in Theories with a Z(N) Symmetry  [PDF]
Leonardo Mondaini
Journal of Modern Physics (JMP) , 2012, DOI: 10.4236/jmp.2012.311221
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.
The Rise of Solitons in Sine-Gordon Field Theory: From Jacobi Amplitude to Gudermannian Function  [PDF]
Leonardo Mondaini
Journal of Applied Mathematics and Physics (JAMP) , 2014, DOI: 10.4236/jamp.2014.213141
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.
Obtaining a New Representation for the Golden Ratio by Solving a Biquadratic Equation  [PDF]
Leonardo Mondaini
Journal of Applied Mathematics and Physics (JAMP) , 2014, DOI: 10.4236/jamp.2014.213134
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.
Geometric Analogy and Products of Vectors in n Dimensions  [PDF]
Leonardo Simal Moreira
Advances in Linear Algebra & Matrix Theory (ALAMT) , 2013, DOI: 10.4236/alamt.2013.31001
Abstract:

The cross product in Euclidean space IR3 is an operation in which two vectors are associated to generate a third vector, also in space IR3. 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.

On the Rotation of a Vector Field in a Four-Dimensional Space  [PDF]
Leonardo Simal Moreira
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.51015
Abstract:

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 IR4. 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.

Experimental Assessment of the Battery Lifetime in WSN Based on the Duty-Cycle Current Average Method  [PDF]
Leonardo Barboni, Maurizio Valle
Wireless Sensor Network (WSN) , 2014, DOI: 10.4236/wsn.2014.610021
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.
Entanglement in the Quantum Phase Transition of the Half-Integer Spin One-Dimensional Heisenberg Model  [PDF]
Leonardo S. Lima
Journal of Modern Physics (JMP) , 2015, DOI: 10.4236/jmp.2015.615228
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 \"\".
Comment to : Uncertainty in the Multielemental Quantification by Total-Reflection X-ray Fluorescence: Theoretical and Empirical Approximation
Leonardo Aguero,Leonardo Bennun
Statistics , 2013,
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.
Towards a Mathematical Model for Elastic Wave Propagation in Granular Materials  [PDF]
Leonardo Trujillo, Vanessa Torres, Franklin Peniche, Leonardo Di G. Sigalotti
Engineering (ENG) , 2012, DOI: 10.4236/eng.2012.412A123
Abstract:

A theoretical model for the propagation of acoustic waves in dry granular media is presented within the framework of the nonlinear granular elasticity. An essential ingredient is the dependence of the elastic moduli on compression. For the purpose of illustration, we analyze the case of a time-harmonic plane wave propagation under isotropic compression. We derive explicit relations for the wave speed dependence with the confining pressure. The present approach provides an accurate description of acoustic wave propagation in granular packings and represents a powerful tool to interpret the results of current experiments.

The Role of Heat Shock Proteins in Mammary Neoplasms: A Brief Review  [PDF]
Leonardo Della Salda, Mariarita Romanucci
Journal of Cancer Therapy (JCT) , 2012, DOI: 10.4236/jct.2012.325095
Abstract: Research into heat shock proteins (HSPs) for the clinical management of tumours has intensified as new evidence shows they can be used as biomarkers in carcinogenesis and are related to poor prognosis in some cancer types. Members of small HSP, HSP70 and HSP90 families have been studied extensively in breast cancer. This article reviews current understanding of the role of HSP and HSF-1 (Heat shock factor 1) expression in human breast cancer and looks at its potential diagnostic, prognostic and therapeutic value. The exciting progress that has been made using HSP 90 inhibitors in breast cancer treatment is examined and the results of preliminary studies on the expression of stress proteins in the animal model canine mammary tumours are also presented.
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