Solutions of differential equations in a Bernstein polynomial basis

AbstractAn algorithm for approximating solutions to differential equations in a modified new Bernstein polynomial basis is introduced. The algorithm expands the desired solution in terms of a set of continuous polynomials over a closed interval and then makes use of the Galerkin method to determine the expansion coefficients to construct a solution. Matrix formulation is used throughout the entire procedure. However, accuracy and efficiency are dependent on the size of the set of Bernstein polynomials and the procedure is much simpler compared to the piecewise B spline method for solving differential equations. A recursive definition of the Bernstein polynomials and their derivatives are also presented. The current procedure is implemented to solve three linear equations and one nonlinear equation, and excellent agreement is found between the exact and approximate solutions. In addition, the algorithm improves the accuracy and efficiency of the traditional methods for solving differential equations that rely on much more complicated numerical techniques. This procedure has great potential to be implemented in more complex systems where there are no exact solutions available except approximations

Traditional Conservation of Buffalo Breed by Pastoralists through Maintaining of Grassland Ecosystem, Banni-Kachchh, Gujarat-India

Banni region, situated at 23019’N to 23052’N to 68056’E to70032’E, comprises around 25,00 sq.km area under Bhuj taluka of Kutch district of Gujarat state, is home of Muslim nomadic pastoralists and Meghwal Hindus. Banni is situated in Arid climate, with high temperature in most of time which reached maximum up to 480C -500C during May June. Pastoral community, call themselves Maldhari, in Banni region depends on Banni Grassland for the raring of their livestock mainly Banni Buffalo which registered as 11th buffalo breed of India in 2011. Maldharis even rearing unique Kankarej Cattle for Milk Production and selling bullocks in Saurashtra region of Gujarat. Pastoral life style in Banni, promote pluralistic culture to stay united by respecting traditions of each community. Strong association with animals and nature, made them sensitive to grassland ecosystem therefore, they have been able to developed livestock rearing practices which are more ecologically sustainable. This paper attempts to understand the pastoral life of Maldharis as essential for breeding, marketing and sustainable use of resources particularly commons

Probabilistic Particle Flow Algorithm for High Occupancy Environment

Algorithms based on the particle flow approach are becoming increasingly utilized in collider experiments due to their superior jet energy and missing energy resolution compared to the traditional calorimeter-based measurements. Such methods have been shown to work well in environments with low occupancy of particles per unit of calorimeter granularity. However, at higher instantaneous luminosity or in detectors with coarse calorimeter segmentation, the overlaps of calorimeter energy deposits from charged and neutral particles significantly complicate particle energy reconstruction, reducing the overall energy resolution of the method. We present a technique designed to resolve overlapping energy depositions of spatially close particles using a statistically consistent probabilistic procedure. The technique is nearly free of ad-hoc corrections, improves energy resolution, and provides new important handles that can improve the sensitivity of physics analyses: the uncertainty of the jet energy on an event-by-event basis and the estimate of the probability of a given particle hypothesis for a given detector response. When applied to the reconstruction of hadronic jets produced in the decays of tau leptons using the CDF-II detector at Fermilab, the method has demonstrated reliable and robust performance.Comment: Accepted by Nuclear Instruments and Methods

Adaptive significance of within-site variation in morphological and reproductive traits of naturalized wild radish (Raphanus raphanistrum) populations in South-Western Australia

Genotypic variation between and within populations of the outbreeding wild radish (Raphanus raphanistrum L.), was studied using seeds collected from 55 sites across the West Australian wheat belt along 2 transects in December 1999 and February 2000. The seeds were grown at the University of Western Australia field station at Shenton Park, Perth, WA over the 2000 growing season, and 14 morphological and phenological characters were scored. A high degree of variation was present in all traits, and within site variation was greater than between sites. The greatest variation was recorded in the reproductive traits such as time to flowering, seed weight, and pod weight. Variation between sites was associated with geo-clusters based primarily on rainfall and temperature. Populations from sites with a high annual rainfall and low average temperature had longer and wider pods, larger seeds and pods with more segments, compared to populations from sites with a low annual rainfall and a high average temperature. These plants also tended to flower later than those from hotter, drier sites. The results show that wild radish in the wheat-belt of Western Australia has formed genotypically distinct populations in the 150 years since it was introduced, that are adapted to the climate at the site of collection

Ogbu and the debate on educational achievement: an exploration of the links between education, migration, identity and belonging

This paper looks at some of the issues raised by Ogbu’s work in relation to the education of different minority ethnic groups. Ogbu poses questions such as the value attached to education, its links to the future and its measurable outcomes in terms of ‘success’ as experienced by black participants. The desire for better life chances leads families to consider migration to a new country or resettlement within the same country, thus making migration both a local and a global phenomenon. As an example, attention is drawn to the situation facing South Asian children and their families in the UK. In terms of ethnicity and belonging, the wider question that is significant for many countries in the West after ‘Nine-Eleven’ is the education of Muslim children. A consideration of this current situation throws Ogbu’s identification of ‘autonomous minority’ into question. It is argued that a greater understanding of diverse needs has to be accompanied by a concerted effort to confront racism and intolerance in schools and in society, thus enabling all communities to make a useful contribution and to avoid the ‘risk’ of failure and disenchantment

Role of Activity in Human Dynamics

The human society is a very complex system; still, there are several non-trivial, general features. One type of them is the presence of power-law distributed quantities in temporal statistics. In this Letter, we focus on the origin of power-laws in rating of movies. We present a systematic empirical exploration of the time between two consecutive ratings of movies (the interevent time). At an aggregate level, we find a monotonous relation between the activity of individuals and the power-law exponent of the interevent-time distribution. At an individual level, we observe a heavy-tailed distribution for each user, as well as a negative correlation between the activity and the width of the distribution. We support these findings by a similar data set from mobile phone text-message communication. Our results demonstrate a significant role of the activity of individuals on the society-level patterns of human behavior. We believe this is a common character in the interest-driven human dynamics, corresponding to (but different from) the universality classes of task-driven dynamics.Comment: 5 pages, 6 figures. Accepted by EP

Calculation of the two-photon decay rates of hydrogen-like ions by using B-polynomials

A new approach is laid out to investigate the two photon atomic transitions. It is based on application of the finite basis solutions constructed from the Bernstein Polynomial (B-Polynomial) sets. We show that such an approach provides a very promising route for the relativistic second- (and even higher-order) calculations since it allows for analytical evaluation of the involved matrices elements. In order to illustrate possible applications of the method and to verify its accuracy, detailed calculations are performed for the 2s_{1/2}-1s_{1/2} transition in neutral hydrogen and hydrogen-like ions, and are compared with the theoretical predictions based on the well-established B-spline-basis-set approach

Branch facial nerve trauma after superficial temporal artery biopsy: a case report

<p>Abstract</p> <p>Introduction</p> <p>Giant cell arteritis is an emergency requiring prompt diagnosis and treatment. Superficial temporal artery biopsy is the gold diagnostic standard. Complications are few and infrequent; however, facial nerve injury has been reported, leaving an untoward cosmetic outcome. This case report is to the best of our knowledge only the fourth one presented in the available literature so far regarding facial nerve injury from superficial temporal artery biopsy.</p> <p>Case presentation</p> <p>A 73-year-old Caucasian woman presented for neurological evaluation regarding eyebrow and facial asymmetry after a superficial temporal artery biopsy for presumptive giant cell arteritis-induced cephalalgia.</p> <p>Conclusion</p> <p>Damage to branches of the facial nerve may occur after superficial temporal artery biopsy, resulting in eyebrow droop. Although an uncommon and sparsely reported complication, all clinicians of various specialties involved in the care of these patients should be aware of this given the gravity of giant cell arteritis and the widespread use of temporal artery biopsy.</p

The exact evaluation of the corner-to-corner resistance of an M x N resistor network: Asymptotic expansion

We study the corner-to-corner resistance of an M x N resistor network with resistors r and s in the two spatial directions, and obtain an asymptotic expansion of its exact expression for large M and N. For M = N, r = s =1, our result is R_{NxN} = (4/pi) log N + 0.077318 + 0.266070/N^2 - 0.534779/N^4 + O(1/N^6).Comment: 12 pages, re-arranged section