Fractional derivatives of the H-function of several variables

AbstractIn the present paper we derive a number of key formulas involving fractional derivatives for the H-function of several variables, which was introduced and studied in a series of papers by H. M. Srivastava and R. Panda [cf., e.g., J. Reine Angew. Math. 283/284 (1976), 265–274; J. Reine Angew. Math. 288 (1976), 129–145; Comment. Math. Univ. St. Paul. 24 (1975), fasc. 2, 119–137; ibid. 25 (1976), fasc. 2, 167–197; Nederl. Akad. Wetensch. Proc. Ser. A 81 = Indag. Math. 40 (1978), 118–131 and 132–144; Nederl. Akad. Wetensch. Proc. Ser. A 82 = Indag. Math. 41 (1979), 353–362; see also Bull. Inst. Math. Acad. Sinica 9 (1981), 261–277].We make use of the generalized Leibniz rule for fractional derivatives in order to obtain one of the aforementioned results, which involves a product of two multivariable H-functions. Each of these results is shown to apply to yield interesting new results for certain multivariable hypergeometric functions and, in addition, several known results due, for example, to J. L. Lavoie, T. J. Osler and R. Tremblay [SIAM Rev. 18 (1976), 240–268], H. L. Manocha and B. L. Sharma [J. Austral. Math. Soc. 6 (1966), 470–476; J. Indian Math. Soc. (N.S.) 38 (1974), 371–382] and R. K. Raina and C. L. Koul [Jñānābha 7 (1977), 97–105]

Seismic stratigraphy and history of deep circulation and sediment drift development in Baffin Bay and the Labrador Sea

Drilling results and seismic-reflection records at and across Ocean Drilling Program (ODP) Sites 645 (western Baffin Bay), 646, and 647 (Labrador Sea) provide important constraints on the history of deep-water circulation and sedimentation in response to Cenozoic climatic change, as well as the tectonic evolution of the region. Sites 646 and 647 were drilled on the flanks of two sediment drift deposits—the Eirik Ridge and Gloria Drift, respectively. Age control at Site 645 was poor because of the restricted biotas there, but the drill site provides a continuous sequence from the lower Miocene to the present. Sediment at Site 646 was deposited at high rates, providing a high resolution record of the last 8.5 Ma. At Site 647 sedimentation was variable and discontinuous, but a complete upper-lower Eocene through lower Oligocene sequence was recovered, whereas the upper Oligocene to Holocene sequence was interrupted by several hiatuses. The drift sequence at Site 646 was constructed after the middle to early Pliocene (ca. 4.5 Ma). Before that time, evidence exists for variable bottom-current activity, with events at about 7.5 Ma (a change in water-mass characteristics and decreasing velocities) and 5.6 Ma (an increase in current velocity preceding the major 4.5-Ma event; R2 regional reflector). The 7.5-Ma event produced a major regional reflector (R3/R4), which was originally thought to be Eocene/ Oligocene in age. A major water-mass change also occurred at the onset of ice-rafting at about 2.5 Ma in the late Pliocene. In seismic records no evidence exists of drift building before the early Pliocene, but a probable late-middle Miocene erosional event occurred on the south flank of Eirik Ridge and along the West Greenland margin. Sediment supply from the Imarssuak mid-ocean canyon (IMOC) increased concurrently with the advent of drift construction. Gloria Drift also was built largely after the late Miocene. A major increase in sediment supply occurred in the early Pliocene, following a major hiatus (5.6 to 2.5 Ma; equivalent to the youngest possible age for the R2 reflector underlying Gloria Drift), and most seismic records exhibit sediment waves above this horizon. This increased sediment supply is the result of hemipelagic deposition from encroaching deposits of the North Atlantic mid-ocean canyon, as well as to supply of ice-rafted detritus in the late Pliocene. A hiatus encompasses the interval from approximately 17.5 to 8,2 Ma, and the interval between the two major hiatuses is extremely condensed. A deeper reflector (R3) corresponds to a change from calcareous (below) to opal-rich hemipelagic strata in the lower Oligocene, not to a regional unconformity reflecting increased bottom-water activity, as previously thought. However, some evidence exists to support a latest Eocene-earliest Oligocene increase in bottom-current activity on Gloria Drift. In Baffin Bay, there is evidence for bottom-water activity from textural studies of cores and from apparent drift features exhibited in multichannel lines along the western margin. Probable contour-currents have been active since at least the late middle Miocene, with episodes of decreasing intensity that apparently occurred in the late Miocene and Quaternary. The record from Site 645 and in seismic lines may indicate that formation of bottom water occurred in the late Neogene in Baffin Bay in conjunction with climatic deterioration, but Baffin Bay was not an important source of deep-water masses to the Labrador Sea after the late Pliocene. Not surprisingly, many of the Labrador Sea deep-circulation events correspond closely to major North Atlantic events and to important global climatic and paleoceanographic events, but a major drift-building episode may have occurred later in the Labrador Sea than it did in either the eastern North Atlantic or the western North Atlantic

A theorem relating a certain generalized Weyl fractional integral with the Laplace transform and a class of Whittaker transforms

AbstractIn the present paper the authors prove a theorem which asserts an interesting relationship between the classical Laplace transform, a certain class of Whittaker transforms, and a Weyl fractional integral involving a general class of polynomials with essentially arbitrary coefficients. By specializing the various parameters involved, this general theorem would readily yield several (known or new) results involving simpler integral operators. It is also shown how the relationship asserted by the theorem can be applied to evaluate the generalized Weyl fractional integrals of various special functions

Fuzzy Intelligent Controller for the Maximum Power Point Tracking of a Photovoltaic Module at Varying Atmospheric Conditions

This paper presents the modeling of a photovoltaic (PV) module at varying atmospheric conditions such as irradiation and temperature. It also includes the maximum power point tracking (MPPT) of the PV module using conventional perturb and observe (P&O) method and fuzzy logic controller. For the performance analysis, the simulation of the PV module along with MPPT controller is done by using MATLAB/Simulink software. The voltage, current and power transitions at varying irradiation and temperature conditions is observed using conventional P&O and fuzzy logic based MPPT controllers. Finally the percentage improvement in power tracking time by fuzzy logic controller against the P&O controller has been evaluated Keywords: Photovoltaic Module, MPPT, P&O method, Fuzzy logic Controller, Irradiatio

Psychiatric comorbidity in multiple sclerosis

Aim: To study the prevalence of psychiatric comorbidities in patients of multiple sclerosisand their association to the degree of disability. Method: Psychiatric symptoms were assessed in 90 patients of multiple sclerosis using GHQ-12, MMSE, HADS, Beck Depression Inventory and AUDIT. Neurological disability wasassessed using Expanded Disability Status Scale. Correlations were determined between EDSS scores and psychiatric scale scores. Result: 61% of patients had significant psychological distress. Depression was most common (38.8%) which was followed by anxiety symptoms (27.8%). Cognitive functioning was relatively intact in patients with mild to moderate neurological disability. Alcohol abusewas mostly restricted to male gender. Conclusion: Psychiatric illness is highly prevalent in patients of multiple sclerosis leading to poor quality of life and significant distress. Psychiatric disability was higher in patients who had greater deterioration in neurological function. All cases of MS should be assessed for psychiatric morbidities as can be alleviated by appropriate intervention

Multiscale modeling and simulation of nanotube-based torsional oscillators

In this paper, we propose the first numerical study of nanotube-based torsional oscillators via developing a new multiscale model. The edge-to-edge technique was employed in this multiscale method to couple the molecular model, i.e., nanotubes, and the continuum model, i.e., the metal paddle. Without losing accuracy, the metal paddle was treated as the rigid body in the continuum model. Torsional oscillators containing (10,0) nanotubes were mainly studied. We considered various initial angles of twist to depict linear/nonlinear characteristics of torsional oscillators. Furthermore, effects of vacancy defects and temperature on mechanisms of nanotube-based torsional oscillators were discussed

Neutrino oscillations in a model with a source and detector

We study the oscillations of neutrinos in a model in which the neutrino is coupled to a localized, idealized source and detector. By varying the spatial and temporal resolution of the source and detector we are able to model the full range of source and detector types ranging from coherent to incoherent. We find that this approach is useful in understanding the interface between the Quantum Mechanical nature of neutrino oscillations on the one hand and the production and detection systems on the other hand. This method can easily be extended to study the oscillations of other particles such as the neutral K and B mesons. We find that this approach gives a reliable way to treat the various ambiguities which arise when one examines the oscillations from a wave packet point of view. We demonstrate that the conventional oscillation formula is correct in the relativistic limit and that several recent claims of an extra factor of 2 in the oscillation length are incorrect. We also demonstrate explicitly that the oscillations of neutrinos which have separated spatially may be "revived" by a long coherent measurement.Comment: 30 pages, 6 figures, Late

Prediction Space Weather Using an Asymmetric Cone Model for Halo CMEs

Halo coronal mass ejections (HCMEs) are responsible of the most severe geomagnetic storms. A prediction of their geoeffectiveness and travel time to Earth's vicinity is crucial to forecast space weather. Unfortunately coronagraphic observations are subjected to projection effects and do not provide true characteristics of CMEs. Recently, Michalek (2006, {\it Solar Phys.}, {\bf237}, 101) developed an asymmetric cone model to obtain the space speed, width and source location of HCMEs. We applied this technique to obtain the parameters of all front-sided HCMEs observed by the SOHO/LASCO experiment during a period from the beginning of 2001 until the end of 2002 (solar cycle 23). These parameters were applied for the space weather forecast. Our study determined that the space speeds are strongly correlated with the travel times of HCMEs within Earth's vicinity and with the magnitudes related to geomagnetic disturbances

Birthing practices of traditional birth attendants in South Asia in the context of training programmes

Traditional Birth Attendants (TBA) training has been an important component of public health policy interventions to improve maternal and child health in developing countries since the 1970s. More recently, since the 1990s, the TBA training strategy has been increasingly seen as irrelevant, ineffective or, on the whole, a failure due to evidence that the maternal mortality rate (MMR) in developing countries had not reduced. Although, worldwide data show that, by choice or out of necessity, 47 percent of births in the developing world are assisted by TBAs and/or family members, funding for TBA training has been reduced and moved to providing skilled birth attendants for all births. Any shift in policy needs to be supported by appropriate evidence on TBA roles in providing maternal and infant health care service and effectiveness of the training programmes. This article reviews literature on the characteristics and role of TBAs in South Asia with an emphasis on India. The aim was to assess the contribution of TBAs in providing maternal and infant health care service at different stages of pregnancy and after-delivery and birthing practices adopted in home births. The review of role revealed that apart from TBAs, there are various other people in the community also involved in making decisions about the welfare and health of the birthing mother and new born baby. However, TBAs have changing, localised but nonetheless significant roles in delivery, postnatal and infant care in India. Certain traditional birthing practices such as bathing babies immediately after birth, not weighing babies after birth and not feeding with colostrum are adopted in home births as well as health institutions in India. There is therefore a thin precarious balance between the application of biomedical and traditional knowledge. Customary rituals and perceptions essentially affect practices in home and institutional births and hence training of TBAs need to be implemented in conjunction with community awareness programmes

Endothelial cell-glucocorticoid receptor interactions and regulation of Wnt signaling

Vascular inflammation is present in many cardiovascular diseases, and exogenous glucocorticoids have traditionally been used as a therapy to suppress inflammation. However, recent data have shown that endogenous glucocorticoids, acting through the endothelial glucocorticoid receptor, act as negative regulators of inflammation. Here, we performed ChIP for the glucocorticoid receptor, followed by next-generation sequencing in mouse endothelial cells to investigate how the endothelial glucocorticoid receptor regulates vascular inflammation. We identified a role of the Wnt signaling pathway in this setting and show that loss of the endothelial glucocorticoid receptor results in upregulation of Wnt signaling both in vitro and in vivo using our validated mouse model. Furthermore, we demonstrate glucocorticoid receptor regulation of a key gene in the Wnt pathway, Frzb, via a glucocorticoid response element gleaned from our genomic data. These results suggest a role for endothelial Wnt signaling modulation in states of vascular inflammation.</p