arXiv subjects

Raoelina Andriambololona

Publications and source records attributed to Raoelina Andriambololona.

33 records · Page 2Linked to original sources

arXiv2016

Dispersion Operators Algebra and Linear Canonical Transformations

This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given

quant-ph↗

arXiv2016

Study on a Phase Space Representation of Quantum Theory

A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current formulation of quantum mechanics which is based on the use of Hilbert space and linear operators theory. Phase space representation of quantum states and wave functions in phase space are introduced using properties of a set of functions called harmonic Gaussian functions. Then, new operators called dispersion operators are defined and identified as the operators which admit as eigenstates the basis states of the phase space representation. Generalization of the approach for multidimensional cases is shown. Examples of applications are given.

quant-ph↗

arXiv2015

Study on linear canonical transformation in a framework of a phase space representation of quantum mechanics

We present a study on linear canonical transformation in the framework of a phase space representation of quantum mechanics that we have introduced in our previous work [1]. We begin with a brief recall about the so called phase space representation. We give the definition of linear canonical transformation with the transformation law of coordinate and momentum operators. We establish successively the transformation laws of mean values, dispersions, basis state and wave functions.Then we introduce the concept of isodispersion linear canonical transformation.

quant-ph↗

arXiv2015

Multi-Input Multi-Channel Analyzer (MIMCA) using universal FPGA board

Instrumentation for nuclear applications is developing very fast, due to fast changing of technology in electronics in connection to Moore's Prediction ("doubling of transistor density integration on an IC for every two years"). The maintenance concept has changed accordingly and moved from repairing at electronic component level to software solving approach, which leads to customize application to fit the local needs. Therefore, Madagascar-INSTN has developed some R&D projects in instrumentation to support and fit to the local needs: one example is the FPGA-based Multi-Input Multi-Channel Analyzer using the UNIO52 standard board from Jülich, which could be used to strengthen the capability and speed-up the routine for radionuclide measurement and analysis of samples. The test results of the MIMCA performance (Linearity, Count-rate accuracy tests) show that the configurable digital system can be used as an alternative issue compared to branded acquisition equipments, which are very expensive and limited technical support from supplier.

physics.ins-det↗

arXiv2014

A new operator giving integrals and derivatives operators for any order at the same time

Let E be the set of integrable and derivable causal functions of x defined on the real interval I from a to infinity, a being real, such f(a) is equal to zero for x lower than or equal to a. We give the expression of one operator that yields the integral operator and derivative operators of the function f at any s-order. For s positive integer real number, we obtain the ordinary s-iterated integral of f. For s negative integer real number we obtain the |s|-order ordinary derivatives of f. Any s positive real or positive real part of s complex number corresponds to s-integral operator of f. Any s negative real number or negative real part of s complex number corresponds to |s|-order derivative operator of f. The results are applied for f being a monom. And remarkable relations concerning the e and π order integrals and e and π order derivatives are given, for e and π transcendental numbers. Similar results may also be obtained for anticausal functions. For particular values of a and s, the operator gives exactly Liouville fractional integral, Riemann fractional integral, Caputo fractional derivative, Liouville-Caputo fractional derivative. Finally, the new operator is neither integral nor derivative operator. It is integral and derivative operators at the same time. It deserves of being named:raoelinian operator is proposed.

math.GM↗

arXiv2014

Derivation of equations for scalar and fermion fields using properties of dispersion-codispersion operators

We establish equations for scalar and fermion fields using results obtained from a study on a phase space representation of quantum theory that we have performed in a previous work. Our approaches are similar to the historical ones to obtain Klein-Gordon and Dirac equations but the main difference is that ours are based on the use of properties of operators called dispersion-codispersion operators. We begin with a brief recall about the dispersion-codispersion operators. Then, introducing a mass operator with its canonical conjugate coordinate and applying rules of quantization, based on the use of dispersion - codispersion operators, we deduce a second order differential operator relation from the relativistic expression relying energy, momentum and mass. Using Dirac matrices, we derive from this second order differential operator relation a first order one. The application of the second order differential operator relation on a scalar function gives the equation for the scalar field and the use of the first order differential operator relation leads to the equation for fermion field.

quant-ph↗

arXiv2013

Time-frequency analysis and Harmonic Gaussian Functions

A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called harmonic Gaussian functions. Then these functions are used to define a set of transformations,noted T_n, which associate to a function ψ,of the time variable t, a set of functions Ψ_n which depend on time, frequency and frequency (or time) standard deviation. Some properties of the transformations T_n and the functions Ψ_n are given. It is proved in particular that the square of the modulus of each function Ψ_n can be interpreted as a representation of the energy distribution of the signal, represented by the function ψ, in the time-frequency plane for a given value of the frequency (or time) standard deviation. It is also shown that the function ψ, can be recovered from the functionsΨ_n.

math.GM↗

arXiv2013

Two definitions of fractional derivatives of power functions

We consider the set of power functions defined on the set of positive real number, and their linear combinations. After recalling some properties of the gamma function, we give two general definitions of derivatives of positive and negative integers, positive and negative fractional orders.Properties of linearity and commutativity are studied and the notions of semi-equality,semi-linearity and semi-commutativity are introduced. Our approach gives a unified definition of the common derivatives and integrals and their generalization.

math.GM↗

arXiv2013

Definitions of complex order integrals and derivatives using operator approach

For a complex number s, the s-order integral of function f fulfilling some conditions is defined as action of an operator, noted J^s, on f. The definition of the operator J^s is given firstly for the case of complex number s with positive real part. Then, using the fact that the operator of one order derivative, noted D^1, is the left- hand side inverse of the operator J^1, an s-order derivative operator, noted D^s, is also defined for all complex number s with positive real part. Finally, considering the relation J^s=D^(-s), the definition of the s-order integral and s-order derivative is extended for all complex number s.An extension of the definition domain of the operators is given too.

math.CV↗

arXiv2013

Definitions of real order integrals and derivatives using operator approach

The set E of functions f fulfilling some conditions is taken to be the definition domain of s-order integral operator J^s (iterative integral), first for any positive integer s and after for any positive s (fractional, transcendental π and e). The definition of k-order derivative operator D^k for any positive k (fractional, transcendental π and e) is derived from the definition of J^s. Some properties of J^s and D^k are given and demonstrated. The method is based on the properties of Euler's gamma and beta functions.

math.GM↗

arXiv2013

Real and complex order integrals and derivatives operators over the set of causal functions

The fractional integrals and fractional derivatives problem is tackled by using the operator approach. The definition domain E of operators is causal functions.Many properties of fractional integrals are given. Fractional derivatives definition is derived from fractional integrals one. Then an unified definition of fractional integrals and derivatives operator is obtained according to the sign of the real part of the order s. The study utilizes many properties of the Euler's gamma and beta functions and their extensions in R and C. Comparison with the definitions given by other authors (Liouville, Riemann,Liouville-Caputo)is done too.

math.GM↗

arXiv2012

Air pollution studies in terms of PM2.5, PM2.5-10, PM10, lead and black carbon in urban areas of Antananarivo - Madagascar

Atmospheric aerosols or particulate matters are chemically complex and dynamic mixtures of solid and liquid particles. Sources of particulate matters include both natural and anthropogenic processes. The present work consists in determining the concentrations of existing elements in the aerosols collected in Andravoahangy and in Ambodin'Isotry in Antananarivo city (Madagascar). The size distribution of these elements and their main sources are also studied. The Total Reflection X-Ray Fluorescence spectrometer is used for the qualitative and quantitative analyses. The results show that the concentrations of the airborne particulate matters PM2.5-10 are higher than those of PM2.5. The identified elements in the aerosol samples are Ti, Cr, Mn, Fe, Ni, Cu, Zn, Br, Sr and Pb. The average concentrations of these elements are also higher in the coarse particles than in the fine particles. The calculation of the enrichment factors by Mason's model shows that Cr, Ni, Cu, Zn, Br and Pb are of anthropogenic origins. The average concentrations of lead (2.8 ng.m-3, 31.3 ng.m-3 and 19.6 ng.m-3 respectively in aerosols collected in Andravoahangy in 2007 and in 2008 and in Ambodin'Isotry in 2008) are largely lower than the average concentration of 1.8 μg.m-3 obtained in 2000 in the Antananarivo urban areas. The concentration of black carbon is higher in the fine particles. The Air Quality Index category is variable in the two sites.

physics.ao-ph↗

arXiv2012

Crystallographic Study of U-Th bearing minerals in Tranomaro, Anosy Region- Madagascar

As an alternative to conventional fossil fuel, there is a renewed interest in the nuclear fuel to support increasing energy demand. New studies are then undertaken to characterize Madagascar U-Th bearing minerals. This is the case for the urano-thorianite bearing pyroxenites in the south East of Madagascar. In this region, several quarries were abandoned, after being mined by the French Atomic Energy Commission (C.E.A) in the fifties and sixties and are now explored by new mining companies. For this purpose, seven U-Th bearing mineral samples from old abandoned uranium quarries in Tranomaro, Amboasary Sud, Madagascar (46° 28' 0"E, 24° 36' 0"S), have been collected. To determine the mineral microstructure, they were investigated for qualitative and quantitative identification of crystalline compounds using X-ray powder diffraction analytical method (XRD). Results showed that the U and Th compounds, as minor elements, are present in various crystalline structures. This is important to understand their environmental behaviours, in terms of crystallographic dispersion of U-Th minerals and their impacts on human health.

physics.geo-ph↗

arXiv2012

Isotope characterization of shallow aquifers in the Horombe region, South of Madagascar

The present study deals with the problem of evaluation of the recharge mechanism and the characterization of the groundwater flow system in the basement shallow aquifer, which is one of the groundwater resource in the semi-arid South region of Madagascar. Stable isotopes (deuterium and oxygen-18) and tritium are used to achieve with accuracy the hydrogeological and geochemical dynamics study. Chemical analysis is used to provide complementary information to the investigation. A space distribution of tritium concentration and isotopic composition in groundwater shows evidence of two opposite categories of aquifers, which is confirmed by the chemical analysis results and by the geological features of the study site. Some groundwater flow path directions have been identified in the study area thanks to the tritium concentration space distribution and the geological formation. Besides, the groundwater recharge of the shallow aquifers in the South of Madagascar has been characterized by the exponential mixing model.

physics.geo-ph↗

arXiv2009

A Study of the Dirac-Sidharth Equation

The Dirac-Siddharth Equation has been constructed from the Siddharth hamiltonian by quantization of the energy and momentum in Pauli algebra. We have solved this equation by using tensor product of matrices.

math-ph↗