A new species of Craugastoridae frog encountered from 1000-1700 m in elevation in the premontane forests of the Peruvian central Andes is described. The new species is similar in appearance to many other species of Pristimantis, but is easily distinguishable from these species by having bright red coloration on the groin, posterior surface of thighs, and shanks. The new species is only known fo...

We show how to adapt Terr’s variant of the babystep giant-step algorithm of Shanks to the computation of the regulator and of generators of principal ideals in real-quadratic number fields. The worst case complexity of the resulting algorithm depends only on the square root of the regulator, and is smaller than that of all other previously specified unconditional deterministic algorithm for thi...

Situations that present individuals with a conflict between local and global gains often result in a behavioral pattern known as melioration — a preference for immediate rewards over higher long-term gains. Using a variant of a paradigm by Tunney & Shanks (2002), we explored the potential role of feedback as a means to reduce this bias. We hypothesized that frequent and informative feedback abo...

Slowly convergent series that have special sign patterns have been used in testing the efficiency of convergence acceleration methods. In this paper, we study the series Sm,n = P∞ k=0 (−1) k/m (k+1)2n+1 when m ≥ 1, n ≥ 0, which has m positive terms followed by m negative terms periodically. Using special functions, we first derive its sum in simple terms involving only the Riemann Zeta function...

Given a Tonelli Hamiltonian H : T ∗M → R of class C, with k ≥ 2, we prove the following results: (1) Assume there exist a recurrent point of the projected Aubry set x̄, and a critical viscosity subsolution u, such that u is a C critical solution in an open neighborhood of the positive orbit of x̄. Suppose further that u is “C at x̄”. Then there exists a C potential V : M → R, small in C topology, ...

The molecule solution of an extended discrete Lotka-Volterra equation is constructed, from which a new sequence transformation is proposed. A convergence acceleration algorithm for implementing this sequence transformation is found. It is proved that our new sequence transformation accelerates some kinds of linear sequences and factorial sequences with good numerical stability. Some numerical e...

A square root (SQRT) algorithm inGF (p) (m=r0r1 · · · rn−12, ri: odd prime, d>0: integer) is proposed in this paper. First, the TonelliShanks algorithm is modified to compute the inverse SQRT in GF (p d ), where most of the computations are performed in the corresponding subfields GF (p i ) for 0 i d − 1. Then the Frobenius mappings with an addition chain are adopted for the proposed SQRT algor...

This means that every F ∈ Fd satisfies: (i) (non-negativity). For finite intervals I = (a1, b1] × · · · × (ad, bd] ≡ (a, b], with a, b ∈ Rd, F (I) = ∆dF (a, b] ≥ 0 where ∆d denotes the d−dimensional difference operator. (ii) (continuity from above). If y ↓ x, then F (y) ↓ F (x). (iii) (normalization). If x1∧. . .∧xd → −∞, then F (x) → 0; if x1∧. . .∧xd → +∞, then F (x) → 1. (See Billingsley [4]...

We study, in a unified way, the following questions related to the properties of Pontryagin extremals for optimal control problems with unrestricted controls: i) How the transformations, which define the equivalence of two problems, transform the extremals? ii) How to obtain quantities which are conserved along any extremal? iii) How to assure that the set of extremals include the minimizers pr...

This is an expository paper devoted to the Morse index of Chaperon’s generating families of Hamiltonian diffeomorphisms. After reviewing the construction of such generating families, we present Bott’s iteration theory in this setting: we study how the Morse index of a critical point corresponding to an iterated periodic orbit depends on the order of iteration of the orbit. We also investigate t...