We present and analyze novel hierarchical a posteriori error estimates for self-adjoint elliptic obstacle problems. Our approach differs from straightforward, but nonreliable estimators by an additional extra term accounting for the deviation of the discrete free boundary in the localization step. We prove efficiency and reliability on a saturation assumption and a regularity condition on the u...

Aims. Power-law cosmologies, in which the cosmological scale factor evolves as a power law in the age, a ∝ t with α >∼ 1, regardless of the matter content or cosmological epoch, is comfortably concordant with a host of cosmological observations. Methods. In this article, we use recent measurements of the X-ray gas mass fractions in clusters of galaxies to constrain the α parameter with curvatur...

Among various approximation formulas for the gamma function, Smith showed that [Formula: see text] which is a little-known but accurate and simple one. In this note, we prove that the function [Formula: see text] is strictly increasing and concave on [Formula: see text], which shows that Smith's approximation is just an upper one.

The high prevalence of eating disorders in Arab countries indicates a need for an Arabic language screening tool. This study aimed to validate an Arabic version (A-SCOFF) of the British SCOFF questionnaire, a brief tool for the screening of eating disorders in primary health care. After translation and back-translation the A-SCOFF was given to 123 female patients [mean age 32 (SD 8.8) years] vi...

This is largely a survey paper in which we discuss new and old problems about the reductions Ep modulo primes p of a fixed elliptic curve E defined over the field of rational numbers. We investigate, in particular, how the “noncyclic” part of the group of points of Ep is distributed, thus making progress toward a conjecture of R. Takeuchi. The new result is Theorem 2 of Section 3. Many interest...

In this note we study the effect of adding fixed points to justification logics. We introduce two extensions of justification logics: extensions by fixed point (or diagonal) operators, and extensions by least fixed points. The former is a justification version of Smoryǹski’s Diagonalization Operator Logic, and the latter is a justification version of Kozen’s modal μcalculus. We also introduce f...

Peak-to-Average Power Ratio (PAPR) is an important parameter for the analysis of Orthogonal frequency division multiplexing (OFDM) signals. CCDF curves are known to have great importance in the study of signal performance on the basis of power level. This paper presents the CCDF performance of the OFDM signal with different number of carriers. Simulation is used to implement the CDF equation an...

The standard references for this section are [Gro91], [Kol90] and [McC91]. Let E be an elliptic curve over Q of conductor N . Let K = Q( √ −D), where −D is a fundamental discriminant, D #= 3, 4, and all prime factors of N are split in K, i.e. (N) = NN̄ for an ideal N of the ring of integers OK of K with OK/N $ Z/NZ. We call such a discriminant a Heegner discriminant for E/Q. By the modularity th...

Background: External beam radiotherapy and brachytherapy plays a vital role in the management of cancer cervix.  High dose rate brachytherapy is being presently used worldwide for the brachytherapy applications. At present, 2-Dimensional linear array detectors   are the most common QA tool used for pretreatment patient specific quality assurance in external beam radiotherapy alon...

Background: Tramadol is one of the most commonly used analgesics, thanks to its efficacy and safety. It is widely used in Myanmar for postoperative and cancer pain control. The use of generic drugs has been steadily increasing worldwide, mostly in developing countries. Generic drugs should have efficacy and safety comparable to their innovators or other approved generic products.  Objectives: ...