Continuous lower bounds for moments of zeta and L-functions

We obtain lower bounds of the correct order of magnitude for the 2k-th moment of the Riemann zeta function for all k > 1. Previously such lower bounds were known only for rational values of k, with the bounds depending on the height of the rational number k. Our new bounds are continuous in k, and thus extend also to the case when k is irrational. The method is a refinement of an approach of Rudnick and Soundararajan, and applies also to moments of L-functions in families.Comment: 9 page

Why Gandhi matters

This essay is a lightly revised version of the 2011 address to the General Assembly of the United Nations, to mark the International Day of Non-Violence, observed every year on Mahatma Gandhi’s birthday, 2nd October

Incompressible lifting-surface aerodynamics for a rotor-stator combination

Current literature on the three dimensional flow through compressor cascades deals with a row of rotor blades in isolation. Since the distance between the rotor and stator is usually 10 to 20 percent of the blade chord, the aerodynamic interference between them has to be considered for a proper evaluation of the aerothermodynamic performance of the stage. A unified approach to the aerodynamics of the incompressible flow through a stage is presented that uses the lifting surface theory for a compressor cascade of arbitrary camber and thickness distribution. The effects of rotor stator interference are represented as a linear function of the rotor and stator flows separately. The loading distribution on the rotor and stator flows separately. The loading distribution on the rotor and stator blades and the interference factor are determined concurrently through a matrix iteration process

Acoustic pressures emanating from a turbomachine stage

A knowledge of the acoustic energy emission of each blade row of a turbomachine is useful for estimating the overall noise level of the machine and for determining its discrete frequency noise content. Because of the close spacing between the rotor and stator of a compressor stage, the strong aerodynamic interactions between them have to be included in obtaining the resultant flow field. A three dimensional theory for determining the discrete frequency noise content of an axial compressor consisting of a rotor and a stator each with a finite number of blades are outlined. The lifting surface theory and the linearized equation of an ideal, nonsteady compressible fluid motion are used for thin blades of arbitrary cross section. The combined pressure field at a point of the fluid is constructed by linear addition of the rotor and stator solutions together with an interference factor obtained by matching them for net zero vorticity behind the stage

India: the next superpower?: will India become a superpower?

More than sixty years ago, in the summer of 1948, the Indian nation, then newly-born, was struggling for its very survival. It was pierced from the left by the Communists, and pinched from the right by Hindu extremists. And there were other problems aplenty. Eight million refugees had to be resettled; provided with land, homes, employment and a sense of citizenship. Five hundred princely states had to be integrated, one by one, a process that involved much massaging of egos (for the Maharajas tended to think very highly of themselves), and just a little coercion

Predicting the Construction of New Highway Links

This paper examines new highway construction based on the status of the network, traffic demand, project costs, and budget constraints. The data span two decades and consist of descriptions of physical attributes of the network, the construction and expansion history, and average annual daily traffic values on each of the links. An algorithm is developed to designate adjacent and parallel links in a large network. A nonlinear cost model for new construction and highway expansion is developed for the Minneapolis-St. Paul metropolitan area. Results show that new links providing greater potential access are more likely to be constructed and that more links will be constructed when the budget is larger, which supports the underlying economic theory. The models developed here have important implications for planning and forecasting, allowing us to predict how networks might be altered in the future in response to changing conditions. .

An analysis for the sound field produced by rigid wide cord dual rotation propellers of high solidarity in compressible flow

An unsteady lifting service theory for the counter-rotating propeller is presented using the linearized governing equations for the acceleration potential and representing the blades by a surface distribution of pulsating acoustic dipoles distributed according to a modified Birnbaum series. The Birnbaum series coefficients are determined by satisfying the surface tangency boundary conditions on the front and rear propeller blades. Expressions for the combined acoustic resonance modes of the front prop, the rear prop and the combination are also given