X iv :1 00 8. 50 35 v1 [ m at h. N T ] 3 0 A ug 2 01 0 RECOVERING FOURIER COEFFICIENTS OF MODULAR FORMS AND FACTORING OF INTEGERS Sergei N. Preobrazhenskĭi It is shown that if a function defined on the segment [−1, 1] has sufficiently good approximation by partial sums of the Legendre polynomial expansion, then, given the function’s Fourier coefficients cn for some subset of n ∈ [n1, n2], one c...

Introduction T HE propulsion system of a short takeoff and vertical landing aircraft, such as the F-35 Joint Strike Fighter, must operate over a wide range of conditions, provide good fuel efficiency at cruise, and deliver high thrust in augmented mode for transonic acceleration and supersonic operation. The propulsion system must be efficient for both high-speed flight and during hover, while ...

We investigate the kinetics of diffusion-controlled heterogeneous single-species annihilation, where the diffusivity of each particle may be different. The concentration of the species with the smallest diffusion coefficient has the same time dependence as in homogeneous single-species annihilation, A+A → 0. However, the concentrations of more mobile species decay as power laws in time, but wit...

Triangular discrimination, Jensen-Shannon divergence, and the square of the Hellinger distance, are popular distance functions for mixture models, and are known to be similar. Here we expound upon their equivalence in terms of their functional forms after transformations, factorizations, and series expansions, and in terms of the geometry of their contours. The ratio between these distances is ...

In this paper, to generate slow light with large group index, wideband, and low dispersion in suggested line defect photonic crystal waveguide, a systematic optimization procedure is performed. Two structural parameters in the adjacent rows of the waveguide are carefully adjusted. Dispersion engineering in the proposed structure is done by using plane wave expansion method. By tuning the struct...

We define a class of “algebraic” random matrix channels for which one can generically compute the limiting Shannon transform using numerical techniques and often enumerate the low SNR series expansion coefficients in closed form. We describe this class, the coefficient enumeration techniques and compare theory with simulations.

In this work we present a targeted gene expression strategy employing trinucleotide threading (TnT) amplification and massive parallel sequencing. We have previously shown that TnT combined with array readout accurately monitors expression levels. However, with this detection strategy spurious products go undetected. Accordingly, we adapted the TnT protocol to massive parallel sequencing to acq...

CLUSTER EXPANSION WITH APPLICATIONS 3 Assumption 2. There exists a nonnegative function a on X such that for almost all x ∈ X, ∫ d|μ|(y) |ζ(x, y)| e 6 a(x). In order to guess the correct form of a, one should consider the left side of the equation above with a(y) ≡ 0. The integral may depend on x; a typical situation is that x is characterized by a length l(x), which is a positive number, so th...

Convergence analysis of iterative detectors for narrowband multiple access is performed by using extrinsic information transfer charts. The system has no bandwidth expansion, so K users are using the same bandwidth as one single user. The load (the number of bits per channel use) of the system is therefore higher than the load in, for example, conventional CDMA systems. The analysis provide use...

We define a class of “algebraic” random matrix channels for which one can generically compute the limiting Shannon transform using numerical techniques and often enumerate the low SNR series expansion coefficients in closed form. We describe this class, the coefficient enumeration techniques and compare theory with simulations.