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[en] Given the many conflicting experimental results, examination is made of the neutrino mass matrix in order to determine possible masses and mixings. It is assumed that the Dirac mass matrix for the electron, muon, and tau neutrinos is similar in form to those of the quarks and charged leptons, and that the smallness of the observed neutrino masses results from the Gell-Mann-Ramond-Slansky mechanism. Analysis of masses and mixings for the neutrinos is performed using general structures for the Majorana mass matrix. It is shown that if certain tentative experimental results concerning the neutrino masses and mixing angles are confirmed, significant limitations may be placed on the Majorana mass matrix. The most satisfactory simple assumption concerning the Majorana mass matrix is that it is approximately proportional to the Dirac mass matrix. A very recent experimental neutrino mass result and its implications are discussed. Some general properties of matrices with structure similar to the Dirac mass matrices are discussed
[en] An exact method for treating multiple collisions is developed. The formalism is valid at all energies and all densities. The multiple scattering formalism is based on the amplitude density function method, which was originally derived for solving single collision problems numerically. The formalism yields a relationship between the total transition matrix due to multiple collisions and the transition matrices due to single collisions. Relations are given for multiple scattering to all orders of a molecule from nonoverlapping fixed scattering centers. The application of the formalism to scattering from a rotor and the necessary approximations which lead to the complete decoupling of the scattering equations are discussed
[en] There are illogical and irrational rules in numbers writing and pronunciation in almost of languages. A part of the aim is to show the electronic applications possibility of logical and systematic rules which are proposed by Raoelina Andriambololona to write and pronounce numbers; we had studied and created the arithmetic operations representation corresponding in binary basis and in hexadecimal basis. The brand new found concept corresponds as well as the method which uses the matrix product calculation, in according with the writing and the pronunciation of numbers. It was shown how to concept the arithmetic operators in digital electronics; and we proposed and assumed to make headway and to do amelioration for technical conception of calculator and arithmetic unite those are at the basic function of all computers and almost domestic sophisticated machine. The left hand side- right hand side and increasing order writing of number is exploited to build a new computer programming for a scientific calculator.
[fr]Il y a des regles illogiques et non rationnelles pour l'ecriture et la prononciation des nombres dans presque toutes les langues. Pour plus de precision, Raoelina Andriambololona a propose de nouvelles regles qui peuvent etre appliquees dans toutes les langues. L'utilisation du calcul matriciel en arithmetique est parfaitement en accord avec ces regles. Ce travail consiste a etudier un nouveau concept plus logique puis a trouver toutes les consequences et les possibilites de ses applications. En electronique, on a etudie la representation, dans la base binaire et dans la base hexadecimale, des operations arithmetiques. De nouvelles techniques pour la conception electronique des operateurs arithmetiques sont inventees ; et nous avons propose d'ameliorer, en utilisant la numeration Malagasy, les techniques de conception des calculateurs et de l'Unite Arithmetique qui demeurent desormais dans tous les micro-ordinateurs et dans les appareils modernes ou sophistiquees de nos jours. On a aussi trouve des algorithmes correspondants en informatique ; et on a programme une machine calculatrice scientifique.
[en] One of the biggest challenges of modern cosmology is to gain a more precise knowledge of the dark energy and the dark matter nature. Fortunately, the dark matter can be traced directly through its gravitational effect on galaxies shapes. The European Spatial Agency Euclid mission will precisely provide data for such a purpose. A critical step is analyzing these data will be to accurately model the instrument Point Spread Function (PSF), which the focus of this thesis.We developed non parametric methods to reliably estimate the PSFs across an instrument field-of-view, based on unresolved stars images and accounting for noise, under sampling and PSFs spatial variability. At the core of these contributions, modern mathematical tools and concepts such as sparsity. An important extension of this work will be to account for the PSFs wavelength dependency. (author)
[fr]L'un des challenges majeurs de la cosmologie moderne reside en la nature meme de la matiere et de l'energie noire. La matiere noire peut etre directement tracee a travers son effet gravitationnel sur les formes des galaxies. La mission Euclid de l'Agence Spatiale Europeenne fournira precisement des donnees a cette fin. L'exploitation de telles donnees requiert une modelisation precise de la Fonction d'etalement du Point (FEP) de l'instrument d'observation, ce qui constitue l'objectif de cette these. Nous avons developpe des methodes non-parametriques permettant d'estimer de maniere fiable la FEP sur l'ensemble du champ de vue d'un instrument, a partir d'images non resolues d'etoiles, ceci en tenant compte du bruit, d'un possible sous-echantillonnage des observations et de la variabilite spatiale de la FEP. Ce travail tire avantage d'outils et concepts mathematiques modernes parmi lesquelles la parcimonie. Une extension importante de ce travail serait de prendre en compte la dependance en longueur d'onde de la FEP
[en] In the cascade theory of isotope separation, a set of comparisons rises with n unknowns (Gsup(i)sub(s), i=1, 2...n), which is written in matrix notation as MGsub(s) = K, where M is a n x n matrix and K is a n x 1 matrix. Usually the value of n is very big, so that numerical methods must be use to determine the unknowns Gsup(i)sub(s) (i=1,n). The rounding errors which occur in the computer calculations, cause that the numerical solutions of the equations are sensitive to the numerical method which is used for the calculations. The stability or unstability of numerical methods is often describe in terms of the eigenvalue of the involved matrix. This thesis deals with techniques that are used in the analysis of eigenvalues of a matrix with parameters and this techniques are implemented in the cascade theory
[en] An experimental program to perform a proof of principle of transverse to longitudinal emittance exchange (εx#sub in# (Leftrightarrow) εz#sub out# and εz#sub in# (Leftrightarrow) εx#sub out#) has been developed at the Fermilab A0 Photoinjector. A new beamline, including two magnetic dogleg channels and a TM110 deflecting mode radio frequency cavity, were constructed for the emittance exchange experiment. The first priority was a measurement of the Emittance Exchange beamline transport matrix. The method of difference orbits was used to measure the transport matrix. Through varying individual beam input vector elements, such as xin, x'in, yin, y'in, zin, or (delta)in, and measuring the changes in all of the beam output vector's elements, xout, x'out, yout, y'out, zout, (delta)out, the full 6 x 6 transport matrix was measured. The measured emittance exchange transport matrix was in overall good agreement with our calculated transport matrix. A direct observation of an emittance exchange was performed by measuring the electron beam's characteristics before and after the emittance exchange beamline. Operating with a 14.3 MeV, 250pC electron bunch, εz#sub in# of 21.1 ± 1.5 mm·mrad was observed to be exchanged with εx#sub out# of 20.8 ± 2.00 mm·mrad. Diagnostic limitations in the εz#sub out# measurement did not account for an energy-time correlation, thus potentially returning values larger than the actual longitudinal emittance. The εx#sub in# of 4.67 ± 0.22 mm·mrad was observed to be exchanged with εz#sub out# of 7.06 ± 0.43 mm·mrad. The apparent εz#sub out# growth is consistent with calculated values in which the correlation term is neglected.
[en] In this work the particle reinforced Al-alloys 359 T6 + 20 % SiC and 2124 + 17 % SiC which differ significantly in their production and microstructure are investigated. Standard and in-situ tensile tests show, that in the powder metallurgically produced alloy 2124 reinforcement leads to a higher Young's modulus, yield and ultimate tensile stress where the cast alloy 359 + 20 % SiC exhibit increased stiffness, but low ductility due to cast porosity of some 100 μm. The failure mechanism governed by microstructural parameters is found to play an important role for ductility. The fatigue properties are investigated with specific regard to the influence of the in-service condition (load ratio, temperature, variable amplitude loading) in the foreseen applications in the automobile- and aerospace industry. Standard fatigue tests point out that the endurance limit is improved by reinforcement, but is strongly dependent on the size of given initial defects. The fatigue crack properties are characterised by standard crack growth curves and r(esistance)-curves for the threshold of stress intensity factor range. Both composites exhibit a higher effective threshold than their unreinforced alloys. Furthermore the fatigue resistance described by the R-curve as well as the long crack threshold are improved in the alloy 2124 + 17 % SiC. While in crack growth tests under constant amplitude loading the alloy 2124 + 17 % SiC shows lower crack growth rates than its unreinforced alloy, the opposite case is in the alloy 359 + 20 % SiC at high DK. Periodic overloads lead in the 359 + 20 % SiC to particle fracture at the crack tip and to a steeper increase in the crack growth rate. In the 2124 + 17% SiC the fatigue crack grows predominately in the matrix and a retardation effect due to overloads is observed. In order to describe the fatigue limit of components as a function of initial defect size an analytical concept is developed assuming that the fatigue limit is controlled by the condition of propagation/non-propagation of given small defects. The dependence of the threshold on the crack length is taken into account by the experimentally determined R-curves. The R-curve concept is applied on both composites to describe the influence of microstructure and load ratio on the fatigue limit. The model is assessed and successfully validated by fatigue tests on standard specimens and component testing. (author)
[en] In this dissertation a subclass of the general q4-vertex model is defined whose configurations correspond to closed colored strings on the bonds of the lattice. Derivations are presented of solutions of the star-triangle equations for three cases within this class