We establish the following new Stirling-type approximation formulas for the factorial function n! ≈ √ 2πnne−n √ n+ 1 6 + 1 72n − 31 6480n2 − 139 155520n3 + 9871 6531840n4 and n! ≈ √ 2πnne−n 4 √ n2 + n 3 + 1 18 − 2 405n − 31 9720n2 . Our estimations give much more accurate values for the factorial function than some previously published strong formulas. We also derive new sequences converging to...

that by enlarging the memory and processing more data as they come in, an acceleration of the rate of convergence can be obtaine~. The probabilistic search procedure presented here does not have these disadvantages. After proving the optimality of our procedure, both the convergence as it is defined for other random search procedures [14]-[16] and the convergences of state functions of interest...

Increasing atmospheres of absolute pressure (ATA) on the cardiopulmonary system results in a marked diuresis. The present investigation was designed to determine if the diuresis observed with increasing ATA is associated with increased release of the N-terminus of the atrial natriuretic factor (ANF) prohormone that contains two potent diuresis-producing hormones consisting of amino acids (aa) 1...

Among 4,780 consecutive adult acute lymphoblastic/myeloblastic leukemia patients, we identified 117 (2.4%) patients with mixed-phenotype acute leukemia fulfilling WHO 2008 criteria; these were classified as: Blymphoid+ myeloid (n=64), T-lymphoid+myeloid (n=38), B+T-lymphoid (n=14) and trilineage (n=1). Of 92 patients karyotyped, 59 were abnormal and were classified as: complex (22 of 92), t(9;2...

background: seborrheic keratoses (sk) are common, benign and often multiple skin tumors with disputed etiology. a follicular origin, late onset nevoid disturbance or local arrest in maturation of keratinocytes have been proposed. human papilloma virus (hpv) has been detected in a small number of cases, particularly those from the genital region. objectives: the aim of our study was to evaluate ...