Summation of some infinite series by the methods of Hypergeometric functions and partial fractions

In this article we obtain the summations of some infinite series by partial fraction method and by using certain hypergeometric summation theorems of positive and negative unit arguments, Riemann Zeta functions, polygamma functions, lower case beta functions of one-variable and other associated functions. We also obtain some hypergeometric summation theorems for: 8F7[9/2, 3/2, 3/2, 3/2, 3/2, 3, 3, 1; 7/2, 7/2, 7/2, 7/2, 1/2, 2, 2; 1], 5F4[5/3, 4/3, 4/3, 1/3, 1/3; 2/3, 1, 2, 2; 1], 5F4[9/4, 5/2, 3/2, 1/2, 1/2; 5/4, 2, 3, 3; 1], 5F4[13/8, 5/4, 5/4, 1/4, 1/4; 5/8, 2, 2, 1; 1], 5F4[1/2, 1/2, 5/2, 5/2, 1; 3/2, 3/2, 7/2, 7/2; -1], 4F3[3/2, 3/2, 1, 1; 5/2, 5/2, 2; 1], 4F3[2/3, 1/3, 1, 1; 7/3, 5/3, 2; 1], 4F3[7/6, 5/6, 1, 1; 13/6, 11/6, 2; 1] and 4F3[1, 1, 1, 1; 3, 3, 3; -1]

Summation of some infinite series by the methods of Hypergeometric functions and partial fractions

In this article we obtain the summations of some infinite series by partial fraction method and by using certain hypergeometric summation theorems of positive and negative unit arguments, Riemann Zeta functions, polygamma functions, lower case beta functions of one-variable and other associated functions. We also obtain some hypergeometric summation theorems for: 8F7[9/2, 3/2, 3/2, 3/2, 3/2, 3, 3, 1; 7/2, 7/2, 7/2, 7/2, 1/2, 2, 2; 1], 5F4[5/3, 4/3, 4/3, 1/3, 1/3; 2/3, 1, 2, 2; 1], 5F4[9/4, 5/2, 3/2, 1/2, 1/2; 5/4, 2, 3, 3; 1], 5F4[13/8, 5/4, 5/4, 1/4, 1/4; 5/8, 2, 2, 1; 1], 5F4[1/2, 1/2, 5/2, 5/2, 1; 3/2, 3/2, 7/2, 7/2; −1], 4F3[3/2, 3/2, 1, 1; 5/2, 5/2, 2; 1], 4F3[2/3, 1/3, 1, 1; 7/3, 5/3, 2; 1], 4F3[7/6, 5/6, 1, 1; 13/6, 11/6, 2; 1] and 4F3[1, 1, 1, 1; 3, 3, 3; −1]

Direction-Dependent CMB Power Spectrum and Statistical Anisotropy from Noncommutative Geometry

Modern cosmology has now emerged as a testing ground for theories beyond the standard model of particle physics. In this paper, we consider quantum fluctuations of the inflaton scalar field on certain noncommutative spacetimes and look for noncommutative corrections in the cosmic microwave background (CMB) radiation. Inhomogeneities in the distribution of large scale structure and anisotropies in the CMB radiation can carry traces of noncommutativity of the early universe. We show that its power spectrum becomes direction-dependent when spacetime is noncommutative. (The effects due to noncommutativity can be observed experimentally in the distribution of large scale structure of matter as well.) Furthermore, we have shown that the probability distribution determining the temperature fluctuations is not Gaussian for our noncommutative spacetimes.Comment: 26 pages. v3: Minor correction

MEDICAL STUDENTS' PERCEPTIONS OF COMPLEMENTARY AND ALTERNATIVE MEDICINE THERAPIES: A PRE- AND POST-EXPOSURE SURVEY IN MAJMAAH UNIVERSITY, SAUDI ARABIA

Background: Evidently, Complementary and Alternative Medicine (CAM) is increasingly a recognized medical practice that efficiently uses multiple treatment therapies and techniques in promoting the health and wellbeing of people as well as preventing and managing a variety of human disorders. Research in CAM, which courses exposure to diverse healthcare professionals, is important from many perspectives including improvement in teaching skills of faculty, enhancing capacity building, and innovative curriculum development. This pre- and post-design crosssectional study aimed to assess perceptions, training needs, personal usage, use in office practice, and knowledge of two batches of medical students toward CAM therapies in Majmaah University, Saudi Arabia. Materials and Methods: The second year medical students of the first (year 2012-13) and second (year 2013-2014) batch [n=26 & 39, respectively] were selected for this study. A reliable 16-item self-administered questionnaire was distributed among all students for answering before and after the 48-hour specific 19 CAM therapies course, in terms of CAM therapies are clearly conventional or alternative, training needs, effectiveness, personal use, use in practice, management of two clinical cases by CAM or conventional therapies, and views about which evidence based approach strongly support individual CAM modalities. Results: Medical students' knowledge and perceptions of CAM therapies significantly improved across some sub-items of CAM questionnaire with a positive trend in the rest of its items including their views about CAM therapies, need for further training, personal use of therapies and advising patients regarding CAM practices strongly supported by randomized clinical controlled trials and published case studies. Conclusion: CAM course tends to have positive impact on the knowledge and perceptions of medical students, in addition to need for further training, and personal use and use of CAM therapies in practice in line with strong evidence-based data regarding therapeutic efficacy. The preliminary results of this study call for further research in specific CAM modalities with a larger sample in academic settings across the nation

Reply to commentary on "History of spinal neurosurgery and spine societies"

Scientific Assessment and Innovation in Neurosurgical Treatment Strategie

The international legal theory of IMF conditionality An alternative approach

SIGLEAvailable from British Library Document Supply Centre-DSC:DX201788 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

An analysis of beef and bovine marketing systems in Pothwar Plateau of Punjab, Pakistan

SIGLEAvailable from British Library Document Supply Centre-DSC:DXN030898 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Carotid intervention following transient ischaemic attack: What are we waiting for?

Transient ischaemic attack secondary to carotid stenosis has the highest risk of stroke recurrence compared with other aetiological subtypes. International guidelines advocate carotid intervention within one to two weeks of the index neurological event. Traditionally, delayed carotid intervention was perceived to be a safer management strategy, yet classic trials of endarterectomy and recent meta-analysis of carotid intervention demonstrate the safety of hyperacute carotid intervention. Data from international studies suggest that targets are not being met, the reasons for which are multifactorial, but patients suffering transient or ocular symptoms are particularly delayed. Efforts should be made to conduct regional studies investigating the root causes of delayed intervention, with subsequent policy adjustment to expedite intervention, and interim optimisation of medical management to reduce the incidence of recurrent stroke. </jats:p