Twist of fractional oscillations

Using the method of the Laplace transform, we consider fractional oscillations. They are obtained by the time-clock randomization of ordinary harmonic vibrations. In contrast to sine and cosine, the functions describing the fractional oscillations exhibit a finite number of damped oscillations with an algebraic decay. Their fractional differential equation is derived.Comment: 12 pages, 2 figure

Demography of fan-throated lizard, Sitana ponticeriana (Cuvier) in a cotton field in Dharwad district of Karnataka state, India

The demographic studies on Sitana ponticeriana show that the species is abundant in Gabbur village. The lizards exhibited a diurnal variation in their activity pattern (basking, foraging, seeking refuge, etc.). They were active in the morning hours when air temperature was ≤ 33° C and census yielded maximum numbers (45 ± 2.19 in 18,748 sq m or ~ 1.9 ha area). The study provides a pilot index as well as a reliable and accurate methodology for population survey of the lizard. The pilot index is essential for any large scale monitoring project and population trend analysis in future

Preferred reporting items for studies mapping onto preference-based outcome measures: The MAPS statement

'Mapping' onto generic preference-based outcome measures is increasingly being used as a means of generating health utilities for use within health economic evaluations. Despite publication of technical guides for the conduct of mapping research, guidance for the reporting of mapping studies is currently lacking. The MAPS (MApping onto Preference-based measures reporting Standards) statement is a new checklist, which aims to promote complete and transparent reporting of mapping studies. The primary audiences for the MAPS statement are researchers reporting mapping studies, the funders of the research, and peer reviewers and editors involved in assessing mapping studies for publication. A de novo list of 29 candidate reporting items and accompanying explanations was created by a working group comprised of six health economists and one Delphi methodologist. Following a two-round, modified Delphi survey with representatives from academia, consultancy, health technology assessment agencies and the biomedical journal editorial community, a final set of 23 items deemed essential for transparent reporting, and accompanying explanations, was developed. The items are contained in a user friendly 23 item checklist. They are presented numerically and categorised within six sections, namely: (i) title and abstract; (ii) introduction; (iii) methods; (iv) results; (v) discussion; and (vi) other. The MAPS statement is best applied in conjunction with the accompanying MAPS explanation and elaboration document. It is anticipated that the MAPS statement will improve the clarity, transparency and completeness of reporting of mapping studies. To facilitate dissemination and uptake, the MAPS statement is being co-published by eight health economics and quality of life journals, and broader endorsement is encouraged. The MAPS working group plans to assess the need for an update of the reporting checklist in five years' time. This statement was published jointly in Applied Health Economics and Health Policy, Health and Quality of Life Outcomes, International Journal of Technology Assessment in Health Care, Journal of Medical Economics, Medical Decision Making, PharmacoEconomics, and Quality of Life Research

Simulation of natural convective boundary layer flow of a nanofluid past a convectively heated inclined plate in the presence of magnetic field

AbstractThis paper deals with the numerical simulation of transient magnetohydrodynamics natural convective boundary layer flow of a nanofluid over an inclined plate. In the modeling of nanofluids, dynamic effects including the Brownian motion and thermophoresis are taken into account. Numerical solutions have been computed via the Galerkin-finite element method. The effects of angle of inclination, buoyancy-ratio parameter, Brownian motion, thermophoresis and magnetic field are taken into account and controlled by non-dimensional parameters. To compute the rate of convergence and error of the computed numerical solution, the double mesh principle is used. Similarity solutions are calculated and presented graphically for non-dimensional velocity, temperature, local rate of heat and mass transfer with pertinent parameters. The modified Nusselt number decreases with increasing inclination angle, buoyancy-ratio parameter, Brownian motion and thermophoresis parameter, whereas it increases with increasing Prandtl number. Validation of the results is achieved with earlier results for forced convective flow and non-magnetic studies. Such problems have several applications in engineering and petroleum industries such as electroplating, chemical processing of heavy metals and solar water heaters. External magnetic fields play an important role in electrical power generation, inclination/acceleration sensors, fine-tuning of the final materials to industrial specification because of their controlling behaviour on the flow characteristics of nanofluids

Average flow constraints and stabilizability in uncertain production-distribution systems

We consider a multi-inventory system with controlled flows and uncertain demands (disturbances) bounded within assigned compact sets. The system is modelled as a first-order one integrating the discrepancy between controlled flows and demands at different sites/nodes. Thus, the buffer levels at the nodes represent the system state. Given a long-term average demand, we are interested in a control strategy that satisfies just one of two requirements: (i) meeting any possible demand at each time (worst case stability) or (ii) achieving a predefined flow in the average (average flow constraints). Necessary and sufficient conditions for the achievement of both goals have been proposed by the authors. In this paper, we face the case in which these conditions are not satisfied. We show that, if we ignore the requirement on worst case stability, we can find a control strategy driving the expected value of the state to zero. On the contrary, if we ignore the average flow constraints, we can find a control strategy that satisfies worst case stability while optimizing any linear cost on the average control. In the latter case, we provide a tight bound for the cost

Approximate Solutions to Fractional Subdiffusion Equations: The heat-balance integral method

The work presents integral solutions of the fractional subdiffusion equation by an integral method, as an alternative approach to the solutions employing hypergeometric functions. The integral solution suggests a preliminary defined profile with unknown coefficients and the concept of penetration (boundary layer). The prescribed profile satisfies the boundary conditions imposed by the boundary layer that allows its coefficients to be expressed through its depth as unique parameter. The integral approach to the fractional subdiffusion equation suggests a replacement of the real distribution function by the approximate profile. The solution was performed with Riemann -Liouville time-fractional derivative since the integral approach avoids the definition of the initial value of the time-derivative required by the Laplace transformed equations and leading to a transition to Caputo derivatives. The method is demonstrated by solutions to two simple fractional subdiffusion equations (Dirichlet problems): 1) Time-Fractional Diffusion Equation, and 2) Time-Fractional Drift Equation, both of them having fundamental solutions expressed through the M-Write function. The solutions demonstrate some basic issues of the suggested integral approach, among them: a) Choice of the profile, b) Integration problem emerging when the distribution (profile) is replaced by a prescribed one with unknown coefficients; c) Optimization of the profile in view to minimize the average error of approximations; d) Numerical results allowing comparisons to the known solutions expressed to the M-Write function and error estimations.Comment: 15 pages, 7 figures, 3 table

"The fruits of independence": Satyajit Ray, Indian nationhood and the spectre of empire

Challenging the longstanding consensus that Satyajit Ray's work is largely free of ideological concerns and notable only for its humanistic richness, this article shows with reference to representations of British colonialism and Indian nationhood that Ray's films and stories are marked deeply and consistently by a distinctively Bengali variety of liberalism. Drawn from an ongoing biographical project, it commences with an overview of the nationalist milieu in which Ray grew up and emphasizes the preoccupation with colonialism and nationalism that marked his earliest unfilmed scripts. It then shows with case studies of Kanchanjangha (1962), Charulata (1964), First Class Kamra (First-Class Compartment, 1981), Pratidwandi (The Adversary, 1970), Shatranj ke Khilari (The Chess Players, 1977), Agantuk (The Stranger, 1991) and Robertsoner Ruby (Robertson's Ruby, 1992) how Ray's mature work continued to combine a strongly anti-colonial viewpoint with a shifting perspective on Indian nationhood and an unequivocal commitment to cultural cosmopolitanism. Analysing how Ray articulated his ideological positions through the quintessentially liberal device of complexly staged debates that were apparently free, but in fact closed by the scenarist/director on ideologically specific notes, this article concludes that Ray's reputation as an all-forgiving, ‘everybody-has-his-reasons’ humanist is based on simplistic or even tendentious readings of his work

Thromboxane biosynthesis in cancer patients and its inhibition by aspirin: a sub-study of the Add-Aspirin trial

BACKGROUND: Pre-clinical models demonstrate that platelet activation is involved in the spread of malignancy. Ongoing clinical trials are assessing whether aspirin, which inhibits platelet activation, can prevent or delay metastases. METHODS: Urinary 11-dehydro-thromboxane B2 (U-TXM), a biomarker of in vivo platelet activation, was measured after radical cancer therapy and correlated with patient demographics, tumour type, recent treatment, and aspirin use (100 mg, 300 mg or placebo daily) using multivariable linear regression models with log-transformed values. RESULTS: In total, 716 patients (breast 260, colorectal 192, gastro-oesophageal 53, prostate 211) median age 61 years, 50% male were studied. Baseline median U-TXM were breast 782; colorectal 1060; gastro-oesophageal 1675 and prostate 826 pg/mg creatinine; higher than healthy individuals (~500 pg/mg creatinine). Higher levels were associated with raised body mass index, inflammatory markers, and in the colorectal and gastro-oesophageal participants compared to breast participants (P < 0.001) independent of other baseline characteristics. Aspirin 100 mg daily decreased U-TXM similarly across all tumour types (median reductions: 77-82%). Aspirin 300 mg daily provided no additional suppression of U-TXM compared with 100 mg. CONCLUSIONS: Persistently increased thromboxane biosynthesis was detected after radical cancer therapy, particularly in colorectal and gastro-oesophageal patients. Thromboxane biosynthesis should be explored further as a biomarker of active malignancy and may identify patients likely to benefit from aspirin