The solution of transcendental equations

Some of the existing methods to globally approximate the roots of transcendental equations namely, Graeffe's method, are studied. Summation of the reciprocated roots, Whittaker-Bernoulli method, and the extension of Bernoulli's method via Koenig's theorem are presented. The Aitken's delta squared process is used to accelerate the convergence. Finally, the suitability of these methods is discussed in various cases

Verifying proofs in constant depth

In this paper we initiate the study of proof systems where verification of proofs proceeds by NC circuits. We investigate the question which languages admit proof systems in this very restricted model. Formulated alternatively, we ask which languages can be enumerated by NC functions. Our results show that the answer to this problem is not determined by the complexity of the language. On the one hand, we construct NC proof systems for a variety of languages ranging from regular to NP-complete. On the other hand, we show by combinatorial methods that even easy regular languages such as Exact-OR do not admit NC proof systems. We also present a general construction of proof systems for regular languages with strongly connected NFA's

Management and Performance of APPLE Battery in High Temperature Environment

India's first experimental communication satellite, APPLE, carried a 12 AH Ni-Cd battery for supplying power during eclipse. Failure to deploy one of the two solar panels resulted in the battery operating in a high temperature environment, around 40 C. This also resulted in the battery being used in diurnal cycles rather than just half yearly eclipse seasons. The management and performance of the battery during its life of two years are described. An attempt to identify the probable degradation mechanisms is also made

Semi-Contained Neutrino Events in MACRO

Updated results are presented of low-energy ($\bar{E_\nu} \sim 5 GeV$) neutrino interactions observed by the MACRO detector. Two analyses (of different topologies) are presented; individually, and especially in their ratio, they are inconsistent with no oscillations and consistent with maximal mixing at $\Delta m^2$ of a few times $10^{-3}$.Comment: Paper presented at DPF2000, the American Physical Society's Division of Particles and Fields conferenc

Stacking the Equiangular Spiral

We present an algorithm that adapts the mature Stack and Draw (SaD) methodology for fabricating the exotic Equiangular Spiral Photonic Crystal Fiber. (ES-PCF) The principle of Steiner chains and circle packing is exploited to obtain a non-hexagonal design using a stacking procedure based on Hexagonal Close Packing. The optical properties of the proposed structure are promising for SuperContinuum Generation. This approach could make accessible not only the equiangular spiral but also other quasi-crystal PCF through SaD

How and Where Should I Ride This Thing? “Rules Of The Road” for Personal Transportation Devices

In recent years, “Personal Transportation Devices” (PTDs) have exploded onto streets and sidewalks. These small devices transport individual persons at slow speeds and are either human-powered or motorized. Examples include electric (kick) scooters, skateboards, e-skateboards, roller blades, and Segways. One key to successfully integrating PTDs into community streets will be the implementation of consistent and suitable regulations over user behavior: “rules of the road” for PTD riders. To help local officials identify appropriate rules for rider behavior, this report documents and analyzes existing PTD regulations across 176 jurisdictions and then presents recommendations for a set of state-level “rules of the road” designed to balance safety and freedom of movement for all road users, including PTD riders.To identify the current state of PTD rules of the road, we documented and analyzed the existing regulations at three levels of government: all 50 states and 5 U.S. territories, 101 cities, and 20 college campuses. This review found that PTD users operate in a murky regulatory environment, with rules often poorly defined, contradictory, or altogether absent.Results of this analysis, a literature review, and interviews with 21 stakeholders, were used to craft a model state-level regulatory code that aims to introduce consistent and well-grounded regulation of PTDs. The general philosophy underpinning the model legislation is that PTD rules should protect public safety, permit PTD use as a convenient travel option, be easy to understand and remember, allow for new devices without new regulations, and be based on facts about PTD use and users. Working from these principles, core recommended elements of the recommended PTD regulations are as follows: states should set comprehensive regulations for PTD riders (with local gov-ernments given flexibility to limit certain uses when necessitated by local conditions); PTDs should be regulated as a class, not device-by-device; and PTD users should be permitted to ride on both streets and sidewalks, subject to rules that protect safety and free movement for all travelers

GIS based modeling of socio-environmental impacts due to a highway development project- A case study

Infrastructure development is the basic need for economic development of a country. Highway is an important infrastructure for movement of goods and passenger traffic. In the recent years, the need for developing adequate road transportation infrastructure has been realized by Government of India and various state Governments.  Major road development projects have been formulated at national level in India. Analysis of socio-environmental impact is an essential component of environmental impact assessment (EIA) that is required for the planning of all major road projects. Most of the socio-environmental attributes are spatial in nature and for a rational assessment of these impacts it is necessary to quantify the impacts considering their spatial variations.In this paper a methodology is demonstrated with reference to a case study of highway development project in India, for the quantification of impact on individual socio-environmental attributes based on the perception of public in the influence area of the project, and the spatial variation of impacts is modeled using Geographic Information System (GIS). &nbsp

GRBs from unstable Poynting dominated outflows

Poynting flux driven outflows from magnetized rotators are a plausible explanation for gamma-ray burst engines. We suggest a new possibility for how such outflows might transfer energy into radiating particles. We argue that the Poynting flux drives non-linearly unstable large amplitude electromagnetic waves (LAEMW) which ``break'' at radii $r_t \sim 10^{14}$ cm where the MHD approximation becomes inapplicable. In the ``foaming'' (relativisticly reconnecting) regions formed during the wave breaks the random electric fields stochastically accelerate particles to ultrarelativistic energies which then radiate in turbulent electromagnetic fields. The typical energy of the emitted photons is a fraction of the fundamental Compton energy $\epsilon \sim f \hbar c/r_e$ with $f \sim 10^{-3}$ plus additional boosting due to the bulk motion of the medium. The emission properties are similar to synchrotron radiation, with a typical cooling time $\sim 10^{-4}$ sec. During the wave break, the plasma is also bulk accelerated in the outward radial direction and at larger radii can produce afterglows due to the interactions with external medium. The near equipartition fields required by afterglow models maybe due to magnetic field regeneration in the outflowing plasma (similarly to the field generation by LAEMW of laser-plasma interactions) and mixing with the upstream plasma.Comment: 15 pages, 1 figur

Atmospheric Neutrino Physics with the MACRO detector

We present the measurement of the the flux and angular distribution of atmospheric muon neutrinos using the MACRO detector. Three different event topologies are detected in two different energy ranges. High energy neutrinos (E~80 GeV) via the identification of upward throughgoing muons. Lower energy neutrinos (E~ 4 GeV) via the upgoing stopping and partially contained downgoing muons (ID+UGS), or via the partially contained upgoing muons (IU). The measured flux is reduced with respect to the predictions. For the high energy sample, globally the flux reduction is $0.74\pm 0.054_{stat+sys} \pm 0.12_{th}$ and varies with the zenith angle. The ratio of measured to expected events is almost constant with the zenith angle for the low energy events, and is $0.57 \pm 0.08_{stat+sys} \pm 0.14_{theor}$ for the IU sample, and $0.71 \pm 0.09_{stat+sys} \pm 0.17_{theor}$ for the (ID+UGS). All the data sets are consistent within a scenario of neutrino oscillations, with maximum mixing and $\Delta m^2 \sim 10^{-3}\div 10^{-2} eV^2$.Comment: 7 pages, 7 figures. Invited talk at 6th Topical Seminar on Neutrino and AstroParticle Physics, San Miniato, Italy, 17-21 May 199