Let f be a piecewise analytic function on the unit interval (respectively, the unit circle of the complex plane). Starting from the Chebyshev (respectively, Fourier) coefficients of f , we construct a sequence of fast decreasing polynomials (respectively, trigonometric polynomials) which “detect” the points where f fails to be analytic, provided f is not infinitely differentiable at these points.

We define Poincaré series associated to a toric or analytically irreducible quasi-ordinary hypersurface singularity, (S, 0), by a finite sequence of monomial valuations, such that at least one of them is centered at the origin 0. This involves the definition of a multi-graded ring associated to the analytic algebra of the singularity by the sequence of valuations. We prove that the Poincaré ser...

We define Poincaré series associated to a toric or analytically irreducible quasiordinary hypersurface singularity, (S, 0), by a finite sequence of monomial valuations, such that at least one of them is centered at the origin 0. This involves the definition of a multigraded ring associated to the analytic algebra of the singularity by the sequence of valuations. We prove that the Poincaré serie...

A recurrent sequence of polynomials is a sequence of polynomials that satisfies a linear recursion with fixed polynomial coefficients. Our paper proves that the sequence of Newton polytopes of a recurrent sequence of polynomials is quasi-linear. Our proof uses the Lech-Mahler-Skolem theorem of p-adic analytic number theory with recent results in tropical geometry. A subsequent paper lists some ...

1.2. Dirichlet. A sequence of numbers a1, a2, . . . gives rise to a Dirichlet series f(s) = ∑ n≥1 ann −s. This is but a method of encoding the infinitely many numbers (an) into a single mathematical object f . If the numbers an grow at most polynomially, then f will actually be an analytic function on a half-plane { (s) > λ}; and the abscissa of convergence λ is related to the growth of the seq...

A new technique is presented that can perfectly &&rat& two cochannel FM signals in a noiseless environment. The method involves the analytic solution of the phases to within one of two possibilities, and a two-state trellis algorithm to trace the correct sequence of phase solutions. This method represents an improvement over other cochanne! interference separatio2 methods (e.g., joint Viterbi a...

We look at a problem with motivation from computational biology: Given the number of breakpoints in a permutation (representing a gene sequence), compute the expected number of inversions that have occured. For this problem, we obtain an analytic approximation that is correct within a percent or two. For the inverse problem, computing the expected number of breakpoints after any number of inver...

Repeating an arbitrary sequence of RF pulses and magnetic field gradients will eventually lead to a steady-state condition in any magnetic resonance system. While numerical methods can quantify this trajectory, analytic analysis provides significantly more insight and a means for faster calculation. Recently, an analytic analysis using homogeneous coordinates was published. The current work fur...