A new method to obtain trigonometry for the real spaces of constant curvature and metric of any (even degenerate) signature is presented. The method could be described as ‘curvature/signature (in)dependent trigonometry’ and encapsulates trigonometry for all these spaces into a single basic trigonometric group equation. This brings to its logical end the idea of an ‘absolute trigonometry’, and p...

The intermediate polar HT Cam is unusual in that it shows no evidence for dense absorption in its spectrum. We analyse an XMM-Newton observation of this star, which confirms the absence of absorption and shows that the X-ray spin-pulse is energy independent. The modulation arises solely from occultation effects and can be reproduced by a simple geometrical model in which the lower accretion foo...

Two related methods exist for sampling from posterior distributions of the MLE with a known prior Newton & Raftery (1994) [8], Efron (2011) [4]. We compare them by examining asymptotic Edgeworth expansions of their pivotal distributions. The result is that Newton & Raftery (1994) is 2nd order consistent to the posterior distribution with prior proportional to the Fisher Information, under some ...

We consider the fast solution of large, piecewise smooth minimization problems as typically arising from the nite element discretization of porous media ow. For lack of smoothness, usual Newton multigrid methods cannot be applied. We propose a new approach based on a combination of convex minization with constrained Newton linearization. No regularization is involved. We show global convergence...

Australotarsius Solodovnikov & Newton, gen. nov., a new genus of rove beetles of the tribe Staphylinini, endemic to Australia, is described and compared to other Staphylinini. It includes two new species, A. grandis Solodovnikov & Newton, sp. n. from Queensland and New South Wales, and A. tasmanicus Solodovnikov & Newton, sp. n. from Tasmania. The systematic position of Australotarsius within S...

In this article, the numerical solution of mixed Volterra–Fredholm integro-differential equations multi-fractional order less than or equal to one in Caputo sense (V-FIFDEs) under initial conditions is presented with powerful algorithms. The method based upon quadrature rule aid finite difference approximation derivative usage collocation points. For treatments, our technique converts V-FIFDEs ...

We derive an indefinite quadrature formula, based on a theorem of Ganelius, for Hp functions, for p > 1, over the interval (−1, 1). The main factor in the error of our indefinite quadrature formula is O(e−π √ ), with 2N nodes and 1 p + 1 q = 1. The convergence rate of our formula is better than that of the Stenger-type formulas by a factor of √ 2 in the constant of the exponential. We conjectur...

We consider a positive measure on [0,∞) and a sequence of nested spaces L0 ⊂ L1 ⊂ L2 · · · of rational functions with prescribed poles in [−∞, 0]. Let {φk}k=0, with φ0 ∈ L0 and φk ∈ Lk \ Lk−1, k = 1, 2, . . . be the associated sequence of orthogonal rational functions. The zeros of φn can be used as the nodes of a rational Gauss quadrature formula that is exact for all functions in Ln · Ln−1, a...

Let {Q„)denote a sequenceof quadrature formulas, Q„(j) m Yfj-iW^fix^), such that ß„(/) -> P0 j(x) dx for all / G CTO, 1], Let 0 < e < \ and a sequence (aX_j.be given, where a, ä si ^ a, 5 • • • , and where a„ —> 0 as n —* c°. Then there exists a function / G CTO, l]and a sequence |nt-)"=i suchthat |/(x)| g 2(7,71(1 4e)|, and such that n,Kx)dx Q„k(1) = ak,k = 1,2, 3, ••• .

In this paper a new method for inverting the Laplace transform from the real axis is formulated. This method is based on a quadrature formula. We assume that the unknown function f(t) is continuous with (known) compact support. An adaptive iterative method and an adaptive stopping rule, which yield the convergence of the approximate solution to f(t), are proposed in this paper. MSC: 15A12; 47A5...