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The Chabauty–Kim method allows one to find rational points on curves under certain technical conditions, generalising Chabauty’s proof of the Mordell conjecture for curves with Mordell–Weil rank less than their genus. We show how the Chabauty–Kim method, when these technical conditions are satisfied in depth 2, may be applied to bound the number of rational points on a curve of higher rank. This provides a non-abelian generalisation of Coleman’s effective Chabauty theorem.
To compare nasal mucociliary clearance in adult non-smokers, cigarette smokers and bidi smokers using the methylene blue dye test.
The study sample consisted of 20 non-smokers, 20 cigarette smokers and 20 bidi smokers (age range, 20–40 years). A single drop of the methylene blue dye was placed at the anterior end of the inferior turbinate of the participants’ nasal cavity. The distance travelled by the methylene blue in 15 minutes inside the nasal cavity was measured. Nasal mucociliary clearance of the three groups was compared using the Kruskal Wallis test.
Nasal mucociliary clearance was significantly decreased in bidi smokers as compared to cigarette smokers and non-smokers (p < 0.05). Multivariate analysis revealed a significant association between nasal mucociliary clearance and bidi smoking, number of cigarettes or bidis smoked per day, and pack-years (all p < 0.05).
Nasal mucociliary clearance measurement is a simple and useful index for assessing the effect of smoking on the mucociliary activity of nasal mucosa.
Sequential order statistics can be used to describe the ordered lifetimes of components of a system when the failure of a component may affect the reliability of the remaining components. After a reliability system consisting of n components fails, some of its components may still be alive. In this paper we first establish some univariate stochastic orderings and ageing properties of the residual lifetimes of the live components in a sequential (n-r+1)-out-of-n system. We also obtain a characterizing result for the exponential distribution based on uncorrelated residual lifetimes of live components. Finally, we provide some sufficient conditions for comparing vectors of residual lifetimes of the live components from two sequential (n-r+1)-out-of-n systems. The results established here extend some well-known results in the literature.
Seedling vigour is an important indicator of crop establishment, subsequent crop growth and yield. Initial seedling vigour is most vital in case of water-limited conditions and in environments where the crop is exposed to different stresses at the early growth stage. Wild and weedy species are well known for their vigour and survival in adverse environmental conditions. Seedling vigour traits of backcross introgression lines (BILs) derived from Swarna × Oryza nivara IRGC81848(S) (accession from Uttar Pradesh, India) and IRGC81832 (K) (accession from Bihar, India) were studied in wet (Kharif) and dry (Rabi) seasons. Seedling vigour was estimated in terms of plant height and tiller number at 30 and 60 d after transplanting under field conditions. In both the seasons, 148S showed highest seedling vigour for plant height. The highest number of tillers were produced by 7K in Kharif and 248S in Rabi season. 75S showed the highest percentage increase in tiller number consistently. High yielding BILs 166S, 14S and 148S showed higher seedling vigour indices compared with checks Tulasi and Sahbhagidhan. Seedling vigour was also evaluated using paper roll method and shoot length, root length and dry weight were used to estimate vigour index. Season-wise association studies were conducted to determine the relative contribution of seedling vigour to yield traits. Seedling vigour was significantly correlated with yield traits. Markers RM217 and RM253 on chromosome 6 differentiated lines with high seedling vigour from those with low seedling vigour and have the potential for use in marker-assisted breeding.
For many practical situations in reliability engineering, components in the system are usually dependent since they generally work in a collaborative environment. In this paper we build sufficient conditions for comparing two coherent systems under different random environments in the sense of the usual stochastic, hazard rate, reversed hazard rate, and likelihood ratio orders. Applications and numerical examples are provided to illustrate all the theoretical results established here.
In this paper we prove that a parallel system consisting of Weibull components with different scale parameters ages faster than a parallel system comprising Weibull components with equal scale parameters in the convex transform order when the lifetimes of components of both systems have different shape parameters satisfying some restriction. Moreover, while comparing these two systems, we show that the dispersive and the usual stochastic orders, and the right-spread order and the increasing convex order are equivalent. Further, some of the known results in the literature concerning comparisons of k-out-of-n systems in the exponential model are extended to the Weibull model. We also provide solutions to two open problems mentioned by Balakrishnan and Zhao (2013) and Zhao et al. (2016).
Interest in active metamaterial (MM) devices has recently increased due to their potential for tunable, switchable, and scalable optical responses. More specifically, a dynamic, on-chip MM polarizer has applications ranging from material characterization to sensing without the need for cumbersome external filters. This work demonstrates efforts to optimize MM devices for dynamic polarization filtering by combining elements from split-ring resonators, wire-pairs, and fishnet patterns. The polarization grid has been designed to operate under an applied voltage with simulated on/off ratios of 75% and dynamic polarization selectivity of 70%. Samples have been fabricated using epitaxial GaAs on sapphire with various n-type doping concentrations to approximate electrical tuning.
In this paper, we discuss the ordering properties of sample ranges arising from multiple-outlier exponential and proportional hazard rate (PHR) models. The purpose of this paper is twofold. First, sufficient conditions on the parameter vectors are provided for the reversed hazard rate order and the usual stochastic order between the sample ranges arising from multiple-outlier exponential models with common sample size. Next, stochastic comparisons are separately carried out for sample ranges arising from multiple-outlier exponential and PHR models with different sample sizes as well as different hazard rates. Some numerical examples are also presented to illustrate the results established here.
Dysphagia is a relatively common symptom following laryngectomy. An anterior pharyngeal diverticulum is a rare cause of post-laryngectomy dysphagia. However, it is often an incidental finding on rigid telescopic examination.
Methods and results:
This article describes two patients with a symptomatic anterior pharyngeal diverticulum. They were treated by transoral micro-endoscopic potassium titanyl phosphate 532 nm laser assisted resection. Both patients could take feeds orally after the procedure without any difficulty. One patient died one and a half years after the procedure because of secondary lung cancer. The other patient died after three years as a result of regional recurrence. The patients were able to swallow during their survival period post treatment.
Laser-assisted micro-endoscopic resection is a relatively safe, quick and effective procedure for the management of anterior pharyngeal diverticulum.
The present experimental work highlights the acoustic far field and flow field characteristics of confined co-axial swirling pipe jets. Co-axial confinements with six vanes at angles of 0°, 20° and 40° are considered here. Two pipe lengths of L/D=0.5 and 2 are studied. The Mach numbers studied range from 0.85 to 1.83. An increase in the pipe length causes suppression of the transonic tones in non-swirl pipe jets. Swirl reduces the low frequency noise components and increases the high-frequency components compared to non-swirl jet. The broadband shock associated noise is mitigated by the swirl pipe jets. However, the screech tone is completely eliminated by the swirl pipe jets. Further, swirl pipe jets radiate low levels of noise at all the emission angles compared to non-swirl pipe jets, for both the pipe length cases at supersonic Mach numbers. Increase in the pipe length enhances the shock associated noise and OASPL for the non-swirl pipe jet. Centreline pitot survey and schlieren visualisation show a reduction in core length, reduction in the number of shock cells, weakening/destruction of the shock cells by the swirl pipe jets compared to the non-swirl pipe jets.
The past ten years has been a decade of land wars in India. Some of the most violent and contentious land conflicts were over the use of land-based financing: the state acquired surplus land, more than was needed for the actual infrastructural project, with the justification that property development on the surplus land can generate revenues and cross-subsidize the building of the new infrastructure. The conflicts over the building of new infrastructural projects, including tolled highways such as the Bangalore-Mysore Infrastructure Corridor and the Yamuna Expressway and new greenfield airports such as the Bangalore International Airport, are clear examples of this new type of land conflict.
Proponents of land-based financing see the mode of financing infrastructure as heralding a new paradigm of infrastructure provision: that of public-private partnerships (PPPs). The frenetic pace of 21st century urbanization in India generates new infrastructural demands that the fiscally strapped Indian state cannot meet by itself. $1.2 trillion dollars in capital investment for urban infrastructure, 2.5 billion square meters of roads to be paved (which is twenty times the road capacity added in the past decade), commercial and residential space equivalent to the built-up area of Chicago has to be added every year: these are some of the statistics that convey the giddying pace at which infrastructure has to be developed in India (Dobbs, Gulati, Mohan, Sankhe and Vittal, 2010). Advocates of PPPs argue that the public sector lack, by itself, lacks the capacity to mobilize such large-scale financial resources and it has to combine in new ways with private sector financing to meet these infrastructural demands. But infrastructure projects, as long gestation projects, hold little attraction for the private sector. The state, then, has to experiment with new incentives to rope the private sector into the infrastructural sector, and one such incentive is surplus land: the lure of high returns from property development on the surplus land can bring a reluctant private sector into the infrastructural sector. Surplus land, then, is the bait for the private sector to enter infrastructure, in the absence of which India cannot build the new types of infrastructure needed to propel a country with what Raj Krishna disparagingly called the ‘Hindu rate of growth’ into double-digit growth figures.
Given a sextic CM field
, we give an explicit method for finding all genus-
hyperelliptic curves defined over
whose Jacobians are simple and have complex multiplication by the maximal order of this field, via an approximation of their Rosenhain invariants. Building on the work of Weng [J. Ramanujan Math. Soc. 16 (2001) no. 4, 339–372], we give an algorithm which works in complete generality, for any CM sextic field
, and computes minimal polynomials of the Rosenhain invariants for any period matrix of the Jacobian. This algorithm can be used to generate genus-3 hyperelliptic curves over a finite field
with a given zeta function by finding roots of the Rosenhain minimal polynomials modulo
Most systematic tables of data associated to ranks of elliptic curves order the curves by conductor. Recent developments, led by work of Bhargava and Shankar studying the average sizes of
-Selmer groups, have given new upper bounds on the average algebraic rank in families of elliptic curves over
, ordered by height. We describe databases of elliptic curves over
, ordered by height, in which we compute ranks and
-Selmer group sizes, the distributions of which may also be compared to these theoretical results. A striking new phenomenon that we observe in our database is that the average rank eventually decreases as height increases.
Lactate levels are increasingly used to guide resuscitation efforts. Some surgical literature suggests that tourniquet use during phlebotomy falsely elevates results, although studies in healthy volunteers have not demonstrated this. The purpose of this study was to determine in clinical practice whether tourniquet use during the drawing of a lactate results in significantly altered levels compared to the result of a level drawn without a tourniquet.
A prospective cohort study was carried out on emergency department patients whose clinical presentation led a physician to order a lactate level. Written informed consent was obtained from patients or their proxies. Study lactates were obtained using a tourniquet during the draw sequence of other laboratory studies. Lactate levels for clinical use were drawn per hospital protocol with no tourniquet. The time of lactate measurements and patient demographic information were recorded. Lactate levels for each patient were compared with the Wilcoxon Rank-Sum Test.
40 patients were consented and enrolled. The median clinical lactate level was 1.9 (interquartile range 1.5-2.6), and the median study lactate level was 1.9 (interquartile range 1.4-2.7). There was no difference between paired lactate values (p=0.95).
Tourniquet use appears to have no impact on measured lactate levels. Our findings suggest that current practices at many institutions regarding lactate collection are likely too stringent and should be changed.
We are reporting on stress engineering utilizing AlN/GaN superlattices (SLs) for epitaxy of GaN layers on 200 mm silicon substrates carried out in Veeco's Propel™ rotating disk, single wafer metal organic chemical vapor deposition (MOCVD) reactor. The Turbodisc® reactor is designed to have homogeneous alkyl/hydride flow distribution and uniform temperature profile, which translate into excellent uniformity and concentric symmetry in epilayer thickness and alloy composition. This feature results in uniform and controllable stress in epilayers across large-size substrates. Crack-free 2 μm GaN layers were grown on 200 mm Si using uniformly strained AlN/GaN SLs with periods of 3–5 and 10–30 nm, respectively. Compressive and tensile stress can be precisely adjusted by changing the thickness of the AlN and GaN layers in the SLs, resulting in controllable wafer curvature/bow after cool down. For a fixed period thickness structure, the effects of growth conditions, such as growth rate of GaN, AlN V/III ratio, and growth temperature, on wafer stress were investigated.
Starfish are echinoderms that live among corals and occur from the supra-littoral to the hadal zone. Deviation from pentamerism is a rare phenomenon in starfish and was observed in the red-knobbed starfish (Protoreaster linckii) collected from the Tuticorin coast, India. Eighty-five specimens were collected and, among these, one was found to be abnormal and had only four arms. The reasons for this abnormality may be due to the changes that occur during larval metamorphosis or caused by an abnormal regeneration of the arm.