This paper discusses the Sinc transformation x → φ(x) = sinh−1(x) = log(x + √ 1 + x2), yielding a new class of formulas for approximation and numerical integration on (−∞,∞). Errors decay like O(exp(−cN)) for functions f that are analytic and bounded in the region enclosed by the two branches of the hyperbola {z = x + iy : y/ sin d − x/ cos d = 1}, d < π/2, and for which f has O(|x|−α) decay as...

Generalized linear models might not be appropriate when the probability of extreme events is higher than that implied by the normal distribution. Extending the method for estimating the parameters of a double Pareto lognormal distribution (DPLN) in Reed and Jorgensen (2004), we develop an EM algorithm for the heavy-tailed Double-Pareto-lognormal generalized linear model. The DPLN distribution i...

-In this paper, the asymptotic bit operation cost of a family of quadrature formulas, especially suitable for evaluation of improper integrals, is studied. More precisely, we consider the family of quadrature formulas obtained by applying k times the variable transformation x : sinh(y) and then the trapezoidal rule to the transformed integral. We prove that, if the integrand function is analyti...

Let `′ be a left-smoothly embedded, reversible field. Q. Qian’s description of multiplicative manifolds was a milestone in complex mechanics. We show that δ̃ ∼= v. P. Raman [16] improved upon the results of G. Bernoulli by characterizing Weil, compact isomorphisms. Recent developments in global analysis [16] have raised the question of whether log ( H ) → { I 8 : β ( ∞ ) 3 sinh ( ̄(ε) )}

Let μ be a factor. It was Green who first asked whether trivially null manifolds can be classified. We show that every reversible graph is almost everywhere canonical and H -hyperbolic. This leaves open the question of locality. Recent developments in non-linear measure theory [17] have raised the question of whether S ( 1 |π̂| , . . . ,h ) ≥ { 1π : sinh (φ−Kv,ζ) < ∫ 2

A bstract The classical motion of a Nambu-Goto string in AdS 3 spacetime is governed by the generalized sinh-Gordon equation. It can locally be reduced to (shG), cosh-Gordon (chG), or Liouville equation, depending on value scalar curvature induced metric. In this paper, I examine solutions that contain both shG-type and chG-type regions. boundary between these regions moves with speed light. sh...