para o valor esperado de uma dada observável fı́sica A = A(p, q, t) representada pelo operador Â. As equações (1) e (2) são válidas desde que o potencial externo V varie vagarosamente dentro de um pacote de onda bem localizadoψPE (Pacote de Ehrenfest). Assim, de acordo com os livros-texto [1], as equações de Newton são obtidas como limite clássico da equação de Schrödinger. No entanto, Ballentin...

We present a new approach to cyclic homology that does not involve Connes’ differential and is based on (Ω q A)[u], d + u · ı∆, a noncommutative equivariant de Rham complex of an associative algebra A. Here d is the Karoubi-de Rham differential, which replaces the Connes differential, and ı∆ is an operation analogous to contraction with a vector field. As a byproduct, we give a simple explicit ...

We give a new construction of cyclic homology of an associative algebra A that does not involve Connes’ differential. Our approach is based on an extended version of the complex Ω q A, of noncommutative differential forms on A, and is similar in spirit to the de Rham approach to equivariant cohomology. Indeed, our extended complex maps naturally to the equivariant de Rham complex of any represe...

The self-similar representation for the Schrödinger equation is derived. The general form Schrödinger equation ı¯ h ∂ψ ∂t = ˆ Hψ, (1) which is the generalization of the free particle wave equation ı¯ h ∂ψ ∂t = − ¯ h 2 2m ∂ 2 ψ ∂x 2 , describes the evolution of the wave function ψ(x, t) for the quantum system with a general form of HamiltonianˆH. The solution of the Schrödinger equation (1), if ...

In this work, we study the asymptotic geometry of the mapping class group and Teichmuller space. We introduce tools for analyzing the geometry of “projection” maps from these spaces to curve complexes of subsurfaces; from this we obtain information concerning the topology of their asymptotic cones. We deduce several applications of this analysis. One of which is that the asymptotic cone of the ...

In this paper, we propose a generic automatic approach for the par-cellation of the cortical surface into labelled gyri. These gyri are defined from a set of pairs of sulci selected by the user. The selected sulci are first automatically identified in the data, then projected onto the cortical surface. The parcellation stems from two nested Vorono¨ı diagrams computed geodesically to the cortica...

İslam dini’nin beş temel şartından olan hac, fıkhî çalışmaların konusu olduğu gibi, edebî mahsullerin de farklı vesilelerle edilmiştir. Hacnâme veya menazilnâme tarzında yazılan eserlerin yanı sıra hac esnasında uyulması gereken kuralları ele alan “menâsik-i hac”lar da yazılmıştır. Bu ürünlerin yazılma amacı, vazifesi için kutsal topraklara giden hacı adayını, uyması kurallar, emir ve yasaklar ...

In this work we solve the problem of the minimization of the spectral norm of the SOR operator associated with a block two-cyclic consistently ordered matrix A ∈ C, assuming that the corresponding Jacobi matrix has eigenvalues μ ∈ [−β, β] ∪ [−ıα, ıα], with β ∈ [0, 1), α ∈ [0,+∞) and ı = √ −1. Previous results obtained by other researchers are extended.

In this chapter we review the development of astronomy between two specific dates, roughly from 1300 BC to AD 500. Although this development is best understood by an examination of the Vedic and post-Vedic texts 1 , note that not all scientific knowledge of those early times can be assumed to have been committed to writing or, if written down, has survived. There are gaps in the sequence of ide...