The “Q-curves” Q1(c) = c,Q2(c) = c + c, . . . , Qn(c) = (Qn−1(c)) + c = f c (0) have long been observed and studied as the shadowy curves which appear illusively — not explicitly drawn — in the familiar orbit diagram of Myrberg’s map fc(x) = x + c. We illustrate that Q-curves also appear implicitly, for a different reason, in a computer-drawn bifurcation diagram of x + c as well — by “bifurcati...

In this paper we look at polynomials arising from statistics on the classes of involutions, In, and involutions with no fixed points, Jn, in the symmetric group. Our results are motivated by F. Brenti’s conjecture [3] which states that the Eulerian distribution of In is logconcave. Symmetry of the generating functions is shown for the statistics d, maj and the joint distribution (d, maj). We sh...

A new distance-based estimator for forest regeneration assessment, the mean distance method, was developed by combining ideas and techniques from the wandering quarter method, T-square sampling and the random pairs method. The performance of the mean distance method was compared to conventional 4.05 square meter plot sampling through simulation analysis on 405 square meter blocks of a field sur...

Statisticians routinely plot ordered observations against expected values to validate a model using a random sample. In fact, it is possible to construct a probability plot for a random sample from any continuous distribution function, and this is accommodated by the probability integral transform which facilitates a uniform probability plot of the ordered transformed observations against their...

The Amazon is a center of diversity for Capsicum chinense Jacq., with wide genetic and morphological variability, but little exploration has been performed there to facilitate their improvement. This study aimed characterize evaluate C. genotypes the development cultivars by determining optimal size experimental plot minimum sample ensure precise estimation yield. A total 23 were evaluated, in ...

OBJECTIVE The present study aims to evaluate the relation between PON1 L55M polymorphism and ischemic stroke by a meta-analysis method. METHODS English and Chinese databases were retrieved to find qualified studies; a random or fixed effects model was used to merge the odds ratio (OR); Q test was used to assess the heterogeneity among studies, and Egger's test and funnel plot were used for th...

Analysis of variance (ANOVA) is an extremely important method in exploratory and confirmatory data analysis. Unfortunately, in complex problems (e.g., split-plot designs), it is not always easy to set up an appropriate ANOVA. We propose a hierarchical analysis that automatically gives the correct ANOVA comparisons even in complex scenarios. The inferences for all means and variances are perform...

In this paper, we study the optimal fixed-time, two-impulse rendezvous between two spacecraft orbiting along two coplanar circular orbits in the same direction. The fixed-time two-impulse transfer problem between two fixed points on two circular orbits, called a fixed-time fixed-endpoint transfer problem, is solved first. Our solution scheme involves first the solution to the related multiple-r...