Search results for "Formula"
showing 10 items of 755 documents
Algebraic Curves and Riemann Surfaces in Matlab
2010
In the previous chapter, a detailed description of the algorithms for the ‘algcurves’ package in Maple was presented. As discussed there, the package is able to handle general algebraic curves with coefficients given as exact arithmetic expressions, a restriction due to the use of exact integer arithmetic. Coefficients in terms of floating point numbers, i.e., the representation of decimal numbers of finite length on a computer, can in principle be handled, but the floating point numbers have to be converted to rational numbers. This can lead to technical difficulties in practice. One also faces limitations if one wants to study families of Riemann surfaces, where the coefficients in the al…
On global solutions of the Maxwell-Dirac equations
1987
We prove, for the Maxwell-Dirac equations in 1+3 dimensions, that modified wave operators exist on a domain of small entire test functions of exponential type and that the Cauchy problem, inR+×R3, has a unique solution for each initial condition (att=0) which is in the image of the wave operator. The modification of the wave operator, which eliminates infrared divergences, is given by approximate solutions of the Hamilton-Jacobi equation, for a relativistic electron in an electromagnetic potential. The modified wave operator linearizes the Maxwell-Dirac equations to their linear part.
Ideal and physical barrier problems for non-linear systems driven by normal and Poissonian white noise via path integral method
2016
Abstract In this paper, the probability density evolution of Markov processes is analyzed for a class of barrier problems specified in terms of certain boundary conditions. The standard case of computing the probability density of the response is associated with natural boundary conditions, and the first passage problem is associated with absorbing boundaries. In contrast, herein we consider the more general case of partially reflecting boundaries and the effect of these boundaries on the probability density of the response. In fact, both standard cases can be considered special cases of the general problem. We provide solutions by means of the path integral method for half- and single-degr…
La Méthode como hermenéutica musical Homenaje a Edgar Morin por su 100º cumpleaños
2021
The present work addresses the principles and properties of the complex thought formulated by the French thinker Edgar Morin and the way in which he was able me to articulate his conception of organizational complexity with one of the most important theories of musical analysis, which emerged at the beginning of the 20th century: the schenkerian analysis. It is a review and extension of a few pages of my doctoral thesis, which are intended to pay tribute to who has been, in addition to my teacher, Honorary President of Itamar since its first issue. His teachings and support has always been the engine for my quest for musical organization. On July 21, 2021, Morin celebrated his 100th birthda…
L'échange dans la documentation diplomatique bourguignonne : autour du vocabulaire des transferts
2013
Cette étude propose une approche du vocabulaire des transferts à partir d'une masse importante de documents diplomatiques médiévaux (VIIIe-XIIIe siècle), réunis principalement au sein de la base des données des CBMA (Chartae Burgundiae Medii Aevi - http://www.artehis-cbma.eu/) soumise au traitement du logiciel Philologic, et mise en regard par rapport aux différentes catégories de sources publiées dans la Patrologie latine. L'analyse de la fréquence et des cooccurrences des formes et dérivés de commutatio, cambio, permutatio a permis de dégager les tendances générales qui concernent et articulent entre eux, le champ sémantique des transferts (la proximité des mots désignant différents types…
Synthesis and detection of a seaborgium carbonyl complex
2014
A carbonyl compound that tips the scales Life is short for the heaviest elements. They emerge from high-energy nuclear collisions with scant time for detection before they break up into lighter atoms. Even et al. report that even a few seconds is long enough for carbon to bond to the 106th element, seaborgium (see the Perspective by Loveland). The authors used a custom apparatus to direct the freshly made atoms out of the hot collision environment and through a stream of carbon monoxide and helium. They compared the detected products with theoretical modeling results and conclude that hexacarbonyl Sg(CO) 6 was the most likely structural formula. Science , this issue p. 1491 ; see also p. 14…
Euler characteristic formulas for simplicial maps
2001
In this paper, various Euler characteristic formulas for simplicial maps are obtained, which generalize the Izumiya–Marar formula [ 14 ], the Banchoff triple point formula [ 3 ] and the formula due to Szucs for maps of surfaces into 3-space [ 27 ]. Moreover, we obtain new results about the Euler characteristics of the multiple point sets and the images of generic smooth maps and the numbers of their singularities.
Stability limits of elemental 2D metals in graphene pores
2019
Two-dimensional (2D) materials can be used as stabilizing templates for exotic nanostructures, including pore-stabilized, free-standing patches of elemental metal monolayers. Although these patches represent metal clusters under extreme conditions and are thus bound for investigations, they are poorly understood as their energetic stability trends and the most promising elements remain unknown. Here, using density-functional theory simulations and liquid drop model to explore the properties of 45 elemental metal candidates, we identify metals that enable the largest and most stable patches. Simulations show that pores can stabilize patches up to $\sim 8$ nm$^2$ areas and that the most promi…
A Wavelet-Galerkin Method for a 1D Elastic Continuum with Long- Range Interactions
2009
An elastic continuum model with long-range forces is addressed in this study. The model stems from a physically-based approach to non-local mechanics where non-adjacent volume elements exchange mutual central forces that depend on the relative displacement and on the product between the interacting volume elements; further, they are taken as proportional to a material dependent and distance-decaying function. Smooth-decay functions lead to integrodifferential equations while hypersingular, fractional-decay functions lead to a fractional differential equation of Marchaud type. In both cases the governing equations are solved by the Galerkin method with different sets of basis functions, amon…
Path Integral Methods for the Probabilistic Analysis of Nonlinear Systems Under a White-Noise Process
2020
Abstract In this paper, the widely known path integral method, derived from the application of the Chapman–Kolmogorov equation, is described in details and discussed with reference to the main results available in literature in several decades of contributions. The most simple application of the method is related to the solution of Fokker–Planck type equations. In this paper, the solution in the presence of normal, α-stable, and Poissonian white noises is first discussed. Then, application to barrier problems, such as first passage problems and vibroimpact problems is described. Further, the extension of the path integral method to problems involving multi-degrees-of-freedom systems is anal…