By Aurelio Baldor
Álgebra es un libro del matemático cubano Aurelio Baldor. los angeles primera edición se produjo el 19 de junio de 1941. El libro contiene unos Preliminares, 39 capítulos más un apéndice. Los capítulos, en orden, son: Suma, Resta, Signos de Agrupación, Multiplicación, División, Productos y Cocientes Notables, Teorema del Residuo, Ecuaciones enteras de primer grado con una incógnita, Descomposición factorial, Máximo común divisor, Mínimo común múltiplo, Fracciones Algebraicas-Reducción de Fracciones, Operaciones con Fracciones Algebraicas, Ecuaciones Numéricas fraccionarias de primer grado con una incógnita, Ecuaciones literales de primer grado con una incógnita, Problemas sobre Ecuaciones Fraccionarias de Primer Grado_Problemas de los Móviles, Fórmulas, Desigualdades-Inecuaciones, Funciones, Representación gráfica de funciones, Gráficas-Aplicaciones Prácticas, Ecuaciones Indeterminadas, Ecuaciones Simultáneas de Primer Grado con dos incógnitas, Ecuaciones Simultáneas de primer grado con tres o más incógnitas, Problemas que se resuelven por ecuaciones simultáneas, Estudio elemental de l. a. Teoría coordinatoria, Potenciación, Teoría de los exponentes, Radicales, Cantidades imaginarias, Ecuaciones de segundo grado con una incógnita, Problemas que se resuelven por ecuaciones de segundo grado-Problema de las luces, Teoría de las Ecuaciones de segundo y también grados-Estudio del trinomio de segundo grado, Ecuaciones binomias y trinomias, Progresiones, Logaritmos, Interés compuesto-Amortizaciones-Imposiciones.
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45) also for Pf(B) > 0. The fact that the BPS condition ends up being the same (even though the unbroken supersymmetry is completely different) for Pf(B) > 0 or Pf(B) < 0 looks rather miraculous from the point of view of the supersymmetric DBI theory. 12), is manifestly independent of the sign of the Pfaffian. 67). 47) 2πα B which is finite in the limit. Given any antisymmetric tensor Λ, such as B or F , denote E=− its selfdual projection relative to the open string metric G = (EE t )−1 by Λ+ G (as before, we write simply Λ+ and B + for the selfdual projections of Λ in the closed string metric g).
5) is possible because these two Lagrangians are derived in string theory in the approximation of neglecting derivatives of F , and therefore they can differ by such terms. 5). 5) it is enough to prove its derivative with respect to θ holding fixed the closed string parameters g, B, gs and the commutative gauge field A. 5) vanishes. In order to keep the equations simple we will set 2πα = 1; the α dependence can be easily restored on dimensional grounds. 6) where δG and δΦ are symmetric and antisymmetric respectively.
2) Even if we are on Rn , there can be at most one value of B for which the noncommutative curvature vanishes at infinity. Thus, if we are going to investigate background independence in the form proposed above, we have to be willing to consider noncommutative gauge fields whose curvature measured at infinity is constant. (3) This has a further consequence. 24) to be background independent. Even the condition that this action converges will not be background independent. 25) which will be background independent.