Suppose we have a function s(t) that measures the sound level at time t of an analog audio signal. We assume that s(t) is piecewise-continuous and of finite duration: s(t) = 0 when t is outside some interval a ≤ t ≤ b. Make a change of variable x = (t− a)/(b− a) and set f(x) = s(t). Then 0 ≤ x ≤ 1 when a ≤ t ≤ b, and f(x) is a piecewise continuous function of x. We convert f(x) into a digital s...

We investigate qualitative properties of local solutions u(t, x) ≥ 0 to the fast diffusion equation, ∂tu = ∆(u )/m with m < 1, corresponding to general nonnegative initial data. Our main results are quantitative positivity and boundedness estimates for locally defined solutions. They combine into forms of new Harnack inequalities that are typical of fast diffusion equations. Such results are ne...

A method is described to generate collisions for the hash function FFT-Hash that was presented by Claus Schnorr at Crypto '91. A set of colliding messages is given that was obtained by this method.

This paper is concerned with an inverse random source problem for the one-dimensional stochastic Helmholtz equation, which is to reconstruct the statistical properties of the random source function from boundary measurements of the radiating random electric field. Although the emphasis of the paper is on the inverse problem, we adapt a computationally more efficient approach to study the soluti...

We consider the first-order Cauchy problem ∂zu + a(z, x,Dx)u = 0, 0 < z ≤ Z, u |z=0 = u0, with Z > 0 and a(z, x,Dx) a k×k matrix of pseudodifferential operators of order one, whose principal part a1 is assumed symmetrizable: there exists L(z, x, ξ) of order 0, invertible, such that a1(z, x, ξ) = L(z, x, ξ) (−iβ1(z, x, ξ) + γ1(z, x, ξ)) (L(z, x, ξ))−1, where β1 and γ1 are hermitian symmetric and...

We calculate the local Fourier transformations for a class of Q l -sheaves. In particular, we verify a conjecture of Laumon and Malgrange ([L] 2.6.3).

K e y W o r d s a n d P h r a s e s : V L S I , s w i t c h i n g n e t w o r k s , d e l t a n e t w o r k s , omega n e t w o r k s , m u l t i p r o c e s s i n g . CR C a t e g o r i e s : 6 . 1 , 4 . 3 2 , 3 . 8 1 , 3 . 8 3 .

The type of signal studied in this paper is a periodic pulse, with the pulse length short compared to the period, and the signal is buried in noise. If standard techniques such as the fast Fourier transform are used to study the signal, the data record needs to be very long. Additionally, there would be a very large number of calculations. The rapid binary gage function was developed to quickly...

s of IWANASP, October 22 – 24, 2015, Lagos, Portugal A FAST FOURIER–GALERKIN METHOD SOLVING A BOUNDARY INTEGRAL EQUATION FOR THE BIHARMONIC EQUATION

When an extreme earthquake occurs, it is essential to detect the severe structural damage that affect the structural safety immediately. This paper proposes a method for quick earthquake damage detection/evaluation of reinforced concrete bridge columns. An intelligent sensor unit is developed that captures changes in the natural period of a bridge column by FFT of response acceleration recorded...