1,407 research outputs found
Corrigendum to “Transcendence of the log gamma function and some discrete periods” [J. Number Theory 129 (9) (2009) 2154–2165]
No full textRefers to
Sanoli Gun, M. Ram Murty, Purusottam Rath
Transcendence of the log gamma function and some discrete periods
Journal of Number Theory, Volume 129, Issue 9, September 2009, Pages 2154-216
Plasma propellant interactions in an electrothermal-chemical gun
No full textThis Thesis covers work conducted to understand the mechanisms
underpinning the operation of the electrothermal-chemical gun. The
initial formation of plasma from electrically exploding wires, through to
the development of plasma venting from the capillary and interacting
with a densely packed energetic propellant bed is included. The prime
purpose of the work has been the development and validation of
computer codes designed for the predictive modelling of the
elect rothe rmal-ch em ical (ETC) gun.
Two main discussions in this Thesis are:
a proposed electrically insulating vapour barrier located around
condensed exploding conductors and
the deposition of metallic vapour resulting in a high energy flux to
the surface of propellant, leading to propellant ignition.
The vapour barrier hypothesis is important in a number of fields where
the passage of current through condensed material or through plasma
is significant. The importance may arise from the need to disrupt the
fragments by applying strong magnetic fields (as in the disruption of
metallic shaped charge jets); in the requirement to generate a metallic
vapour efficiently from electrically exploding wires (as per ETC ignition systems); or in the necessity to re-use the condensed material after a
discharge (as with lightning divertor strips).
The ignition by metallic vapour deposition hypothesis relies on the
transfer of latent heat during condensation. It is important for the
efficient transfer of energy from an exploded wire (or other such
metallic vapour generating device) to the surface of energetic material.
This flux is obtained far more efficiently through condensation than
from radiative energy transfer, because the energy required to
evaporate copper is far less than that required to heat it to
temperatures at which significant radiative flux would be emitte
Eisenstein Series of Weight One, q-Averages of the 0-Logarithm and Periods of Elliptic Curves
No full textFor any elliptic curve E over k ⊂ R with E(C) = C^×/q^Z, q = e^(2πiz),Im(z) >, we study the q-average D_(0,q), defined on E(C), of the function D_0(z) = Im(z/(1−z)). Let Ω+(E) denote the real period of E. We show that there is a rational function R ∈ Q(X_1(N)) such that for any non-cuspidal real point s ∈ X_1(N) (which defines an elliptic curve E(s) over R together with a point P(s) of order N), πD_(0,q)(P(s)) equals Ω+(E(s))R(s). In particular, if s is Q-rational point of X_1(N), a rare occurrence according to Mazur, R(s) is a rational number
A gasdynamic gun driven by gaseous detonation
No full textA gasdynamic gun driven by gaseous detonation was developed to address the disadvantages of the insufficient driving capability of high-pressure gas and the constraints of gunpowder. The performance of this gasdynamic gun was investigated through experiments and numerical simulations. Much more powerful launching capability was achieved by this gun relative to a conventional high-pressure gas gun, owing to the use of the chemical energy of the driver gas. To achieve the same launching condition, the initial pressure required for this gun was an order of magnitude lower than that for a gun driven by high-pressure H-2. Because of the presence of the detonation, however, a more complex internal ballistic process of this gun was observed. Acceleration of projectiles for this gun was accompanied by a series of impulse loads, in contrast with the smooth acceleration for a conventional one, which indicates that this gun should be used conditionally. The practical feasibility of this gun was verified by experiments. The experiments demonstrated the convenience of taking advantage of the techniques developed for detonation-driven shock tubes and tunnels. (C) 2016 AIP Publishing LLC
Transcendental Zeros Of Certain Modular Forms
No full textKohnen showed that the zeros of the Eisenstein series Ek in the standard fundamental domain other than i and ρ are transcendental. In this paper, we obtain similar results for a more general class of modular forms, using the earlier works of Kanou, Kohnen and the recent work of Getz
ON LARGE PRIME FACTORS OF FOURIER COEFFICIENTS OF NEWFORMS (Zeta functions and their representations)
No full textThis is an expository article showcasing some existing results about large Fourier coefficients of normalized Hecke eigenforms which are non CM forms. We also allude to some very recent works in this direction
ON LARGE PRIME FACTORS OF FOURIER COEFFICIENTS OF NEWFORMS (Zeta functions and their representations)
No full textThis is an expository article showcasing some existing results about large Fourier coefficients of normalized Hecke eigenforms which are non CM forms. We also allude to some very recent works in this direction
On the Zeros of Certain Cusp Forms
No full textF. K. C. Rankin and H. P. F. Swinnerton–Dyer proved that all the zeros of the Eisenstein Series Ek contained in the standard fundamental domain F lie on the arc A ={eiθ π/3 ≤ θ ≤ π/2}. Recently, J. Getz has generalized the method of Rankin and Swinnerton–Dyer to show that modular forms under certain conditions have similar properties. In this paper we prove similar results for certain types of cusp forms, motivated by the work of R. A. Rankin. Further, we give a closed formula for the zeros of a class of cusp forms in terms of the Fourier coefficients following the method of Kohnen
Limited Government and Gun Control
No full textIn the following, the author presents a case for federally mandated gun control regulations. Specifically, the author argues—with reference to The Declaration of Independence, the Constitution, and the Bill of Rights—that the principle of limited government often used against federal gun control laws actually provides legitimate justification for them. The aim is to persuade gun advocates to accept such regulations from their own point of view
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