Pulmonary sarcoidosis was studied with respect to lung mechanical properties and to the influence of these on lung volumes. Sixty-six patients, with histological support for the diagnosis of sarcoidosis, and radiological signs of pulmonary involvement, i.e., stage II or III, were studied. The static pressure/volume (P/V) curves showed that the static elastic recoil pressure (PelL) tended to be ...

In this paper, we introduce a tiling approach to (p,q)-Fibonacci and (p,q)-Lucas numbers that generalize of the well-known Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal ve Jacobsthal-Lucas numbers. We show nth number is interpreted as ways tile 1×n board with cells labeled 1,2,...,n using colored 1×1 squares 1×2 dominoes, where there are p kind colors for q dominoes. Then circular also present...

The role of the topological index, ZG, proposed by the present author in 1971, in various problems and topics in elementary mathematics is introduced, namely, (i) Pascal’s and asymmetrical Pascal’s triangle, (ii) Fibonacci, Lucas, and Pell numbers, (iii) Pell equation, (iv) Pythagorean, Heronian, and Eisenstein triangles. It is shown that all the algebras in these problems can be easily obtaine...

and Applied Analysis 3 If p, 1/q ∈ Z, then solutions f : N0 → Z of the difference equation 1.7 are called the Lucas sequences see, e.g., 24 ; in some special cases they are given specific names; that is, the Fibonacci numbers p −1, q −1, f 0 0, and f 1 1 , the Lucas numbers p −1, q −1, f 0 2, and f 1 1 , the Pell numbers p −2, q −1, f 0 0, and f 1 1 , the Pell-Lucas or companion Lucas numbers p...

It was already observed by Euler [Eul1773] that the method of continued fractions occasionally requires a lot of tedious calculations, and even Fermat knew – as can be seen from the examples he chose to challenge the English mathematicians – a few examples with large solutions. To save work, Euler suggested a completely different method, which allows to compute even very large solutions of cert...

In this paper we study the Diophantine equations ck(f +42fg+49g) + 28dk(f g + 7fg) = m, where (ck, dk) are solutions of the Pell equation c 2−7d2= 1.

OBJECTIVES This study recorded and evaluated the intra- and inter-group agreement degree by different examiners for the classification of lower third molars according to both the Winter's and Pell & Gregory's systems. STUDY DESIGN An observational and cross-sectional study was realized with forty lower third molars analyzed from twenty digital panoramic radiographs. Four examiner groups (unde...

Several types of infinite series are considered, which are defined by a fixed real number α and the denominators and numerators of the convergents of α. In this paper we restrict α to the irrational square roots of positive integers. We express the corresponding error sums in terms of a finite number of convergents. It is shown that an error sum formed by convergents with even indices takes onl...

We review selected known results on partially ordered patterns (POPs) that include co-unimodal, multiand shuffle patterns, peaks and valleys ((modified) maxima and minima) in permutations, the Horse permutations and others. We provide several (new) results on a class of POPs built on an arbitrary flat poset, obtaining, as corollaries, the bivariate generating function for the distribution of pe...