Purpose. This article reports on our experience treating vertebral fractures with percutaneous vertebroplasty. A clinical and imaging follow-up designed to identify the early (especially pulmonary embolism of bone cement) and late complications of the technique is proposed. Material and methods. On the basis of the current guidelines, 101 patients were selected: 64 osteoporotic and 37 neoplastic. A total of 173 vertebrae were treated. Procedures were performed with both computed tomography and fluoroscopic guidance. Residual pain was evaluated with a visual analogue scale score immediately after vertebroplasty and 1, 15, 30, 90, 180 and 270 days later. Spine and chest radiographs were obtained 24 h after vertebroplasty; spine radiography was repeated 30 days later. Results. Therapeutic success was obtained in 88% of osteoporotic patients and in 84% of neoplastic patients. Pulmonary cement emboli were identified in four patients, all of whom were asymptomatic.
Conclusions. Percutaneous vertebroplasty is a safe and
This paper shows how the study of colored compositions of integers reveals some unexpected and original connection with the Invert operator. The Invert operator becomes an important tool to solve the problem of directly counting the number of colored compositions for any coloration. The interesting consequences arising from this relationship also give an immediate and simple criterion to determine whether a sequence of integers counts the number of some colored compositions. Applications to Catalan and Fibonacci numbers naturally emerge, allowing to clearly answer to some open questions. Moreover, the definition of colored compositions with the "black tie" provides straightforward combinatorial proofs to a new identity involving multinomial coefficients and to a new closed formula for the Invert operator. Finally, colored compositions with the "black tie" give rise to a new combinatorial interpretation for the convolution operator, and to a new and easy method to count the number of parts of colored compositions.
In this paper the properties of Rédei rational functions are used to derive rational approximations for square roots and both Newton and Padé approximations are given as particular cases. Moreover, Rédei rational functions are introduced as convergents of particular periodic continued fractions and are applied for approximating square roots in the field of p-adic numbers and to study periodic representations. Using the results over the real numbers, we show how to construct periodic continued fractions and approximations of square roots which are simultaneously valid in the real and in the p-adic field.
We study linear divisibility sequences of order 4, providing a characterization by means of their characteristic polynomials and finding their factorization as a product of linear divisibility sequences of order 2. Moreover, we show a new interesting connection between linear divisibility sequences and Salem numbers. Specifically, we generate linear divisibility sequences of order 4 by means of Salem numbers modulo 1.
We present a different proof of the characterization of non-degenerate recurrence sequences, which are also divisibility sequences, given by Van der Poorten, Bezevin, and Pethö in their paper [1]. Our proof is based on an interesting determinant identity related to impulse sequences, arising from the evaluation of a generalized Vandermonde determinant. As a consequence of this new proof we can find a more precise form for the resultant sequence presented in [1], in the general case of non-degenerate divisibility sequences having minimal polynomial with multiple roots.
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