Extremal primes for elliptic curves without complex multiplication

Fix an elliptic curve E over Q. An extremal prime for E is a prime p of good reduction such that the number of rational points on E modulo p is maximal or minimal in relation to the Hasse bound. Assuming that all the symmetric power L-functions associated to E are automorphic and satisfy the Generalized Riemann Hypothesis, we give the first non-trivial upper bounds for the number of such primes when E is a curve without complex multiplication. In order to obtain this bound, we use explicit equidistribution for the Sato-Tate measure as in the work of Rouse and Thorner (arXiv:1305.5283) and refine certain intermediate estimates taking advantage of the fact that extremal primes have a very small Sato-Tate measure

The international growth of emerging market firms : evidence from a natural experiment

The recent international growth of some firms from emerging markets has attracted the attention of academics and managers alike. How do such emerging market firms achieve growth in international markets despite lacking foreign market knowledge and international competitiveness, and despite facing weak institutions in their home countries? The authors address this question by proposing a new concept—global market capital, the set of assets that prepare emerging market firms to compete globally. Global market capital consists of three elements: leadership capital (at the individual level), foreign marketing and financial capital (at the firm level), and network capital (at the inter-firm level). The authors argue that, taken together, these elements enable emerging market firms to overcome their weaknesses in foreign market knowledge, international competitiveness and home institutions. In particular, the authors highlight the prominent role that leadership capital, specifically CEOs’ foreign market experience, plays in helping emerging market firms grow internationally. The authors test their thesis using uniquely compiled data on Indian firms from the Bombay Stock Exchange 500 index. The Indian context helps to set up a natural experiment in which the independent variables of interest are measured prior to a major sudden and unanticipated regulatory shift in India’s outward investment policy and the dependent variable (international growth) is measured after this policy shift. Results from the paper highlight the crucial role of leadership capital in driving international growth both directly and through its synergistic interaction with the other elements of global market capital

Brownian cluster dynamics with short range patchy interactions. Its application to polymers and step-growth polymerization

We present a novel simulation technique derived from Brownian cluster dynamics used so far to study the isotropic colloidal aggregation. It now implements the classical Kern-Frenkel potential to describe patchy interactions between particles. This technique gives access to static properties, dynamics and kinetics of the system, even far from the equilibrium. Particle thermal motions are modeled using billions of independent small random translations and rotations, constrained by the excluded volume and the connectivity. This algorithm, applied to a single polymer chain leads to correct static and dynamic properties, in the framework where hydrodynamic interactions are ignored. By varying patch angles, various chain flexibilities can be obtained. We have used this new algorithm to model step-growth polymerization under various solvent qualities. The polymerization reaction is modeled by an irreversible aggregation between patches while an isotropic finite square-well potential is superimposed to mimic the solvent quality. In bad solvent conditions, a competition between a phase separation (due to the isotropic interaction) and polymerization (due to patches) occurs. Surprisingly, an arrested network with a very peculiar structure appears. It is made of strands and nodes. Strands gather few stretched chains that dip into entangled globular nodes. These nodes act as reticulation points between the strands. The system is kinetically driven and we observe a trapped arrested structure. That demonstrates one of the strengths of this new simulation technique. It can give valuable insights about mechanisms that could be involved in the formation of stranded gels.Comment: 55 pages, 32 figure

Assessment of Use and Utilisation of Library Resources, Services and Facilities by Law Students at Kristu Jayanti College of Law, Bangalore

The main aim of this study is to investigate the use of library resources, services and facilities by law students; it is mainly focused on use, purpose and satisfaction level with the library collection, services and facilities. This study used survey method to collect data. A well-structured questionnaire was distributed. Out of 110, only 91(83%) questionnaires were collected and select for analysis. Result revelled that library services and collection were satisfied further findings show users are not aware about Journals and E-Resources. So, study recommends that should conduct information literacy programme to promote awareness use of library services and use of resource

Harmonic Estimation Of Distorted Power Signals Using PSO – Adaline

In recent times, power system harmonics has got a great deal of interest by many Power system Engineers. It is primarily due to the fact that non-linear loads comprise an increasing portion of the total load for a typical industrial plant. This increase in proportion of non-linear load and due to increased use of semi-conductor based power processors by utility companies has detoriated the Power Quality. Harmonics are a mathematical way of describing distortion in voltage or current waveform. The term harmonic refers to a component of a waveform occurs at an integer multiple of the fundamental frequency. Several methods had been proposed, such as discrete Fourier transforms, least square error technique, Kalman filtering, adaptive notch filters etc; Unlike above techniques, which treat harmonic estimation as completely non-linear problem there are some other hybrid techniques like Genetic Algorithm (GA), LS-Adaline, LS-PSOPC which decompose the problem of harmonic estimation into linear and non-linear problem. The results of LS-PSOPC and LS-Adaline has most attractive features of compactness and fastness. . Our new proposed technique tries to reduce the pitfalls in the LS-PSOPC, LS-Adaline techniques. With new technique we tried to estimate the Amplitudes by Least square estimator, frequency of the signal by PSOPC and phases of the harmonics by Adaline technique using MATLAB program. Harmonic signals were estimated by using LS-PSOPC, PSOPC-Adaline. Errors in estimating the signal by both the techniques are calculated and compared with each other

Black hole scalar charge from a topological horizon integral in Einstein-dilaton-Gauss-Bonnet gravity

In theories of gravity that include a scalar field, a compact object's scalar charge is a crucial quantity since it controls dipole radiation, which can be strongly constrained by pulsar timing and gravitational wave observations. However in most such theories, computing the scalar charge requires simultaneously solving the coupled, nonlinear metric and scalar field equations of motion. In this article we prove that in linearly-coupled Einstein-dilaton-Gauss-Bonnet gravity, a black hole's scalar charge is completely determined by the horizon surface gravity times the Euler characteristic of the bifurcation surface, without solving any equations of motion. Within this theory, black holes announce their horizon topology and surface gravity to the rest of the universe through the dilaton field. In our proof, a 4-dimensional topological density descends to a 2-dimensional topological density on the bifurcation surface of a Killing horizon. We also comment on how our proof can be generalized to other topological densities on general G-bundles, and to theories where the dilaton is non-linearly coupled to the Euler density.Comment: v3: minor updates to references, published in PRD Rapid Comms. v2: more direct proof of Thm. 1, added comments on non-linear coupling in Sec.3, deleted Appendix B, updated references, version accepted in PRD Rapid Comms. v1: 5 pages + 2 pages appendices, 1 figur