Directional variation of geomagnetic cut-off rigidity around Hyderabad,India

The geomagnetic cut-off rigidities for cosmic ray particles arriving at the top of the atmosphere over Hyderabad, India (geographic latitude 17.6°N. and longitude 78.5° E.), as a function of zenith and azimuthal angles and the vertical cut-off rigidities for a few neighbouring locations, have been made using the sixth degree simulation of the geomagnetic field by the C.D.C. 3600 Computer.     

Atmospheric gamma-rays of 1–200 GeV over Hyderabad

Using a stack of hypersensitized nuclear emulsions, exposed under 10.2 g.cm^?2 of residual atmosphere over Hyderabad, India, gamma-rays of energy > 1 GeV have been studied. It is found that the observed differential energy spectrum can be best represented by two power law spectra, one for energies less than 30 GeV and the other for higher energies but with the same spectral index of 2.6; however the intensities at energies greater than 30 GeV are about three times higher than what would be expected from the extrapolation of the spectrum at lower enerjies. The implication of this observation has been examined. The neutral pion production spectrum over Hyderabad has been derived from the gamma-ray spectrum. Using this information the energy spectrum of atmospheric electrons has been deduced and a comparison made with the observed spectrum below the geomagnetic threshold energy over Hyderabad; therefrom an upper limit of 0.5 particles/(m².sr.sec.) has been deduced for the flux of re-entrant albedo electrons above 2 GeV.     

The low energy gamma-ray spectrum in space

Balloon, satellite and other deep space probe observations on the intensity of low energy (0·1–10 MeV) gamma-rays are carefully examined with a view to understand the existing anomalies in their intensities and energy spectra. The observed spectral data is “unfolded” to deduce the true gamma-ray energy spectrum. The recently observed flattening in the spectral shape at about 1 MeV is shown to be likely to arise as a result of the gamma-ray detector response to a simple power law input spectrum.     

Low rank matrix recovery from rank one measurements

We study the recovery of Hermitian low rank matrices $X\in {\mathbb{C}}^{n\times n}$ from undersampled measurements via nuclear norm minimization. We consider the particular scenario where the measurements are Frobenius inner products with random rank-one matrices of the form $a_j{a}_j^{?}$ for some measurement vectors $a_1,\dots ,a_m$, i.e., the measurements are given by $b_j=\mathrm{tr}(X{a}_j{a}_j^{?})$. The case where the matrix $X=x{x}^{?}$ to be recovered is of rank one reduces to the problem of phaseless estimation (from measurements $b_j=|〈x,a_j〉{|}^2$) via the PhaseLift approach, which has been introduced recently. We derive bounds for the number m of measurements that guarantee successful uniform recovery of Hermitian rank r matrices, either for the vectors $a_j$, $j=1,\dots ,m$, being chosen independently at random according to a standard Gaussian distribution, or $a_j$ being sampled independently from an (approximate) complex projective t-design with $t=4$. In the Gaussian case, we require $m\ge Crn$ measurements, while in the case of 4-designs we need $m\ge \mathit{Cr}n\log ?(n)$. Our results are uniform in the sense that one random choice of the measurement vectors $a_j$ guarantees recovery of all rank r-matrices simultaneously with high probability. Moreover, we prove robustness of recovery under perturbation of the measurements by noise. The result for approximate 4-designs generalizes and improves a recent bound on phase retrieval due to Gross, Krahmer and Kueng. In addition, it has applications in quantum state tomography. Our proofs employ the so-called bowling scheme which is based on recent ideas by Mendelson and Koltchinskii.     

Periodicities in the series of cyclonic disturbances over India

The time series of yearly occurrence frequency of cyclonic disturbances over the Indian region for 1891–1970 is subjected to power spectrum analysis by the maximum entropy method (MEM) of Burg. Earlier analyses by the conventional Blackman-Tukey method had indicated periodicities atT= 2·3-2·5, 5 and 30–45 years at about 90–95% significance level. The present analysis shows peaks atT = 1·2, 2·4, 2·9, 3·7, 4·7, 6·4, 7·4, 9·2, 10·5, 20 and 40–60 years but the significance level may not be better than the earlier method. When data are analysed separately for first half and latter half, periodicities observed are quite different, the earlier half revealingT= 1· 2, 2·3, 2·9, 4·7, 9·0 and 23 years and the latter half revealingT= 1·2, 2·1, 2·4, 3·8, 6·7 and 21 years. Thus, a change of pattern before and after about 1920 is indicated. However, the power in the various peaks is small and a random origin cannot be ruled out. An analysis of several artificially produced samples of pseudo-Gaussian random white noise of the same mean, standard deviation and length (80 values) as the above physical samples indicated that similar peaks could occur by pure chance also. Physically, T=l·2 years corresponds to the Chandler’s wobble and other peaks could be harmonics of the sunspot cycleT= 11 years or double sunspot cycleT = 22 years. However, no peak is noticed at or nearT= 11 years whereasT near 22 years is noticed.     

Simulated annealing with noisy or imprecise energy measurements

The annealing algorithm (Ref. 1) is modified to allow for noisy or imprecise measurements of the energy cost function. This is important when the energy cannot be measured exactly or when it is computationally expensive to do so. Under suitable conditions on the noise/imprecision, it is shown that the modified algorithm exhibits the same convergence in probability to the globally minimum energy states as the annealing algorithm (Ref. 2). Since the annealing algorithm will typically enter and exit the minimum energy states infinitely often with probability one, the minimum energy state visited by the annealing algorithm is usually tracked. The effect of using noisy or imprecise energy measurements on tracking the minimum energy state visited by the modified algorithms is examined.The research reported here has been supported under Contracts AFOSR-85-0227, DAAG-29-84-K-0005, and DAAL-03-86-K-0171 and a Purdue Research Initiation Grant.     

Impedance eduction from energy dissipation measurements with flow

An optimization method for the calculation of the wall impedance of a perforate from measurements under grazing flow conditions is presented. It is in particular characterized by the simultaneous eduction of the parameter set defining the impedance as function of frequency, which allows interpolation and extrapolation. The Extended Helmholtz Resonator is applied as impedance model and the simultaneous eduction is performed using a time–domain CAA method. Furthermore, the method uses processed energy data from experiments to define the objective function. The results give an insight in the effect of bias flow on the wall impedance under grazing flow conditions. It proves to be an important acoustic design parameter. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Low energy scattering for nonlinear Klein-Gordon equations

The scattering operator which belongs to a pair of PDEs consisting of the Klein-Gordon equation and a perturbation of it by a power-like nonlinearity z.hfl;(u) is studied. It is shown that this operator can be defined on a whole neighbourhood of the origin in energy space if $\text{z.hfl;(u) = ±¦u¦}{}^{\mathrm{p\; ?\; 1}}\text{u}\text{or}\text{±¦u¦}{}^{\mathrm{p}}$, where $\text{1+4}\text{(n ? 1)}\text{<p <}\text{1 + 4}\text{(n ? 2)}$ and the space dimension n ? 2 is arbitrary.     

Low energy π-nucleus elastic scattering analysis

Résumé Un modèle, construit à l'aide de l'équation deKisslinger pour un noyau sphérique de densité nucléaire homogène, est ajusté aux mesures de diffusion élastique ^––C à trois énergies différentes. Les valeurs des potentiels ajustant ces mesures sont indiquées.     

Atmospheric electricity measurements in the upper air over Poona

Atmospheric electricity measurements made during the last decade at Poona using balloon-borne sondes are briefly reviewed. The vertical distribution of potential gradient in the free atmosphere follows theoretical values only during the monsoon months, when the air is comparatively free from dust. During the summer months, the potential gradient is constant above the exchange layer and this is associated with the presence of the deep, dense dust layer that lies over the region and extends to over 10 km. into the atmosphere. The increase with height of the potential gradient above the 10 km. level during winter is shown to be closely related to the presence of the subtropical jet stream, which presumably transports electric charges to the upper levels over Poona.     

Low energy properties of the random displacement model

We study low-energy properties of the random displacement model, a random Schrödinger operator describing an electron in a randomly deformed lattice. All periodic displacement configurations which minimize the bottom of the spectrum are characterized. While this configuration is essentially unique for dimension greater than one, there are infinitely many different minimizing configurations in the one-dimensional case. The latter leads to unusual low energy asymptotics for the integrated density of states of the one-dimensional random displacement model. For symmetric Bernoulli-distributed displacements it has a 1/log²-singularity at the bottom of the spectrum. In particular, it is not Hölder-continuous.     

Finite Group Schemes over Bases with Low Ramification

Let A be a complete characteristic (0,p) discrete valuation ring with absolute ramification degree e and a perfect residue field. We are interested in studying the category FF _A' of finite flat commutative group schemes over A withp-power order. When e= 1, Fontaine formulated the purely linear algebra notion of a finite Honda system over A and constructed an anti-equivalence of categories betweenineFF _A'> and the category of finite Honda systems over A when p> 2. We generalize this theory to the case e – 1.     

Generalised twists,stationary loops,and the Dirichlet energy over a space of measure preserving maps

Let be a bounded Lipschitz domain and consider the Dirichlet energy functional

Estimating energy consumption of transport modes in India using DEA and application to energy and environmental policy

Energy is consumed both by passenger and freight traffic, and it is generally not possible to apportion energy consumption exclusively to either of the traffic without making restrictive assumptions on the energy consumption norms of vehicles. The use of data envelopment analysis (DEA) has been suggested earlier in the literature for comparing energy efficiencies without requiring any such restrictive assumptions. In this paper, the applicability of DEA is further extended to estimate energy consumption of rail and/or road transport that would result in a pre-specified DEA efficiency. Using this new approach, effects of capturing some modal split in favour of rail transport on future energy consumption and emissions of carbon dioxide are presented in the paper via a scenario analysis. It is shown that if rail could capture 50% modal share in the years 2005–2006 and 2020–2021, it would save nearly 35% energy consumption and emissions compared to the situation when existing patterns of modal split are allowed to continue without policy intervention.     

Multiple scattering measurements on high energy protons with long cell lengths

Scattering measurements on individual tracks and relative scattering measurements on pairs of tracks have been made in two stacks exposed to 6·2 and 5·7 BeV protons respectively from the Berkeley Bevatron. Spurious scattering was determined in these two stacks for cell lengths ranging from 1 mm. to 8 mm. In one stack the magnitude of spurious scattering was very low while in the other it was fairly high. Our results indicate that:

1. (a)
   Spurious scattering varies with cell lengtht, as t^x, wherex is about 0·8 fort = 1 mm. to 3 mm. and about 0·5 fort = 3 mm. to 8 mm.     
   
   

Low dimensional modules over quantum complete intersections in two variables

We classify all the indecomposable modules of dimension ≤ 5 over the quantum exterior algebra k(x, y)/(x^2, y^2, xy + qyx) in two variables, and all the indecomposable modules of dimension ≤3 over the quantum complete intersection k(x,y)/(x^m,y^n,xy + qyx) in two variables, where m or n ≥3, by giving explicitly their diagram presentations.     

Defining synergy thermodynamically using quantitative measurements of entropy and free energy

Synergy is often defined as the creation of a whole that is greater than the sum of its parts. It is found at all levels of organization in physics, chemistry, biology, social sciences, and the arts. Synergy occurs in open irreversible thermodynamic systems making it difficult to quantify. Negative entropy or negentropy ( ) has been related to order and complexity, and so has work efficiency, information content, Gibbs Free Energy in equilibrium thermodynamics, and useful work efficiency in general ( ). To define synergy in thermodynamic terms, we use the quantitative estimates of changes in and in seven different systems that suffer process described as synergistic. The results show that synergistic processes are characterized by an increase in coupled to an increase in . Processes not associated to synergy show a different pattern. The opposite of synergy are dissipative processes such as combustion where both and decrease. The synergistic processes studied showed a relatively greater increase in compared to opening ways to quantify energy—or information—dissipation due to the second law of thermodynamics in open irreversible systems. As a result, we propose a precise thermodynamic definition of synergy and show the potential of thermodynamic measurements in identifying, classifying and analysing in detail synergistic processes. © 2016 Wiley Periodicals, Inc. Complexity 21: 235–242, 2016     

Low temperature measurements of electrical activity and Hall mobility of boron implanted silicon

This work investigates the electrical behaviour of boron implanted silicon at temperatures from 300k to 4.2k by means of Hall effect and sheet resistivity measurements. The ion energy is 100 Kev and the doses are 1×10¹², 2×10¹², 5×10¹², 1×10¹³, 2×10¹³, 5×10¹³, 1×10¹⁴, 2.5×10¹⁴, 5×10¹⁴, and 1×10¹⁵ ions/cm².The most accurate information about the electrical activity can be only found from measurements at low temperatures. Furthermore, a reverse annealing takes place in the annealing temperature range from 500 to 600 °C, and this range is found to be independent of the ion dose. It is also clear that the electrical activity depends strongly on the annealing temperatures, especially for annealing temperatures greater than 600 °C. For ion dose 1×10¹⁵ ions/cm² complete activity can be obtained by annealing up to 900 °C.

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Zusammenfassung Die vorliegende Arbeit beschreibt Untersuchungen über das elektrische Verhalten des Borimplantierten Siliziums mittels Hall Effekt- und Schicht-Widerstand-Messungen im Temperaturbereich von 300k bis 4.2k. Die Ionenenergie betrug dabei 100 Kev, und die Ionendosen waren 1×10¹², 2×10¹², 5×10¹², 1×10¹³, 2×10¹³, 5×10¹³, 1×10¹⁴, 2.5×10¹⁴, 5×10¹⁴, und 1×10¹⁵ Ionen/cm².Es wurde festgestellt, daß genauere Informationen über die Aktivierung der implantierten Dopanden nur aus Tieftemperatur-Messungen erhalten werden können. Weiterhin findet man ein negatives Ausheilen im Bereich von 500 bis 600 °C. Die Grenzen dieses negativen Ausheilbereiches sind von den Ionendosen unabhängig. Es ist eindeutig, daß die Aktivierung der Dopanden sehr stark von der Ausheiltemperatur abhängig ist, insbesondere für Ausheiltemperaturen größer als 600 °C. Für die Ionendosis 1×10¹⁵ Ionen/cm² kann bei einer Ausheiltemperatur von 900 °C eine vollständige Aktivierung erreicht werden.

     

Alteration of tremolite to talc in the dolomite marbles of Yellandu Warangal District (Hyderabad,DN.)

Proceedings - Mathematical Sciences -