Fractional Bessel integrals and derivatives on semi-axes

In this paper we study fractional powers of the Bessel differential operator. The fractional powers are defined explicitly in the integral form without use of integral transforms in its definitions. Some general properties of the fractional powers of the Bessel differential operator are proved and some are listed. Among them are different variations of definitions, relations with the Mellin and Hankel transforms, group property, evaluation of resolvent integral operator in terms of the Wright or generalized Mittag-Leffler function

On some generalizations of the properties of the multidimensional generalized Erdélyi-Kober operators and their applications

In this paper we investigate the composition of a multidimensional generalized Erdélyi-Kober operator with differential operators of high order. In particular, with powers of the differential Bessel operator. Applications of proved properties to solving the Cauchy problem for a multidimensional polycaloric equation with a Bessel operator are show

Single\u2010sided NMR to estimate morphological parameters of the trabecular bone structure

Purpose Single\u2010sided 1H\u2010NMR is proposed for the estimation of morphological parameters of trabecular bone, and potentially the detection of pathophysiological alterations of bone structure. In this study, a new methodology was used to estimate such parameters without using an external reference signal, and to study intratrabecular and intertrabecular porosities, with a view to eventually scanning patients. Methods Animal trabecular bone samples were analyzed by a single\u2010sided device. The Carr\u2010Purcell\u2010Meiboom\u2010Gill sequence of 1H nuclei of fluids, including marrow, confined inside the bone, was analyzed by quasi\u2010continuous T2 distributions and separated into two 1H pools: short and long T2 components. The NMR parameters were estimated using models of trabecular bone structure, and compared with the corresponding micro\u2010CT. Results Without any further assumptions, the internal reference parameter (short T2 signal intensity fraction) enabled prediction of the micro\u2010CT parameters BV/TV (volume of the trabeculae/total sample volume) and BS/TV (external surface of the trabeculae/total sample volume) with linear correlation coefficient >0.80. The assignment of the two pools to intratrabecular and intertrabecular components yielded an estimate of average intratrabecular porosity (33 \ub1 5)%. Using the proposed models, the NMR\u2010estimated BV/TV and BS/TV were found to be linearly related to the corresponding micro\u2010CT values with high correlation (>0.90 for BV/TV; >0.80 for BS/TV) and agreement coefficients. Conclusion Low\u2010field, low\u2010cost portable devices that rely on intrinsic magnetic field gradients and do not use ionizing radiation are viable tools for in vitro preclinical studies of pathophysiological structural alterations of trabecular bone

International Standard Set of Patient-Centered Outcome Measures After Stroke

BACKGROUND AND PURPOSE: Value-based health care aims to bring together patients and health systems to maximize the ratio of quality over cost. To enable assessment of healthcare value in stroke management, an international standard set of patient-centered stroke outcome measures was defined for use in a variety of healthcare settings. METHODS: A modified Delphi process was implemented with an international expert panel representing patients, advocates, and clinical specialists in stroke outcomes, stroke registers, global health, epidemiology, and rehabilitation to reach consensus on the preferred outcome measures, included populations, and baseline risk adjustment variables. RESULTS: Patients presenting to a hospital with ischemic stroke or intracerebral hemorrhage were selected as the target population for these recommendations, with the inclusion of transient ischemic attacks optional. Outcome categories recommended for assessment were survival and disease control, acute complications, and patient-reported outcomes. Patient-reported outcomes proposed for assessment at 90 days were pain, mood, feeding, selfcare, mobility, communication, cognitive functioning, social participation, ability to return to usual activities, and health-related quality of life, with mobility, feeding, selfcare, and communication also collected at discharge. One instrument was able to collect most patient-reported subdomains (9/16, 56%). Minimum data collection for risk adjustment included patient demographics, premorbid functioning, stroke type and severity, vascular and systemic risk factors, and specific treatment/care-related factors. CONCLUSIONS: A consensus stroke measure Standard Set was developed as a simple, pragmatic method to increase the value of stroke care. The set should be validated in practice when used for monitoring and comparisons across different care settings