Exactness of the Original Grover Search Algorithm

It is well-known that when searching one out of four, the original Grover's search algorithm is exact; that is, it succeeds with certainty. It is natural to ask the inverse question: If we are not searching one out of four, is Grover's algorithm definitely not exact? In this article we give a complete answer to this question through some rationality results of trigonometric functions.Comment: 8 pages, 2 figure

Shape invariance approach to exact solutions of the Klein-Gordon equation

Using the shape invariance property we obtain exact solutions of the (1+1)dimensional Klein-Gordon equation for certain types of scalar and vector potentials. We also discuss the possibility of obtaining real energy spectrum with non-Hermitian interaction within this framework

Web line resonant frequencies

The goal of this paper is to investigate the resonant frequencies of a system of idle rollers and web spans. Of particular interest is the determination of the minimum resonant frequency as a function of the number of idle rollers, web span lengths between idle rollers, web properties such as the modulus of elasticity and area of cross-section, and inertia and radius of the idle rollers. Any conclusions from the analysis that can provide insights into maximizing the minimum resonant frequency by choosing particular web paths or span lengths are of benefit to the web machine designer as well as the control system engineer. Knowledge of the minimum resonant frequency and the factors that influence it can assist the machine designer in reconfiguring web paths and/or number of idle rollers between two driven rollers such that the machine induced vibrations do not excite resonances. Further, the knowledge of the minimum resonant frequency will assist the control engineer to better select the bandwidth of the closed-loop system as well as the crossover frequency of the controller.A simple linear model that describes the dynamics of tension in a web span is considered. It is shown with experimentation on a web platform that the simple model is able to predict resonant frequencies in an idler roller system. Therefore, the simple model is used to investigate the behavior of the minimum resonant frequency as a function of the number of idle rollers and span lengths. Analytical solutions for computing the minimum resonant frequency for one idler (one idle roller and two spans) and two idler (two idle rollers and three spans) systems are given. Numerical analysis and discussions on how to maximize the minimum resonant frequency for two, three, and four idler systems are also given. An analytical approximation of the minimum resonant frequency for equal span lengths and any number of idle rollers is derived. This approximation tends to converge to the actual minimum resonant frequency with increase in the number of idle rollers. This is useful in getting a quick and reliable estimate of the minimum resonant frequency in festoons/accumulators that contain many idle rollers and equal span lengths.Mechanical and Aerospace Engineerin

Archiving scientific data

We present an archiving technique for hierarchical data with key structure. Our approach is based on the notion of timestamps whereby an element appearing in multiple versions of the database is stored only once along with a compact description of versions in which it appears. The basic idea of timestamping was discovered by Driscoll et. al. in the context of persistent data structures where one wishes to track the sequences of changes made to a data structure. We extend this idea to develop an archiving tool for XML data that is capable of providing meaningful change descriptions and can also efficiently support a variety of basic functions concerning the evolution of data such as retrieval of any specific version from the archive and querying the temporal history of any element. This is in contrast to diff-based approaches where such operations may require undoing a large number of changes or significant reasoning with the deltas. Surprisingly, our archiving technique does not incur any significant space overhead when contrasted with other approaches. Our experimental results support this and also show that the compacted archive file interacts well with other compression techniques. Finally, another useful property of our approach is that the resulting archive is also in XML and hence can directly leverage existing XML tools

The genetics of mate preferences in hybrids between two young and sympatric Lake Victoria cichlid species

The genetic architecture of mate preferences is likely to affect significant evolutionary processes, including speciation and hybridization. Here, we investigate laboratory hybrids between a pair of sympatric Lake Victoria cichlid fish species that appear to have recently evolved from a hybrid population between similar predecessor species. The species demonstrate strong assortative mating in the laboratory, associated with divergent male breeding coloration (red dorsum versus blue). We show in a common garden experiment, using DNA-based paternity testing, that the strong female mate preferences among males of the two species are fully recovered in a large fraction of their F2 hybrid generation. Individual hybrid females often demonstrated consistent preferences in multiple mate choice trials (more than or equal to five) across a year or more. This result suggests that female mate preference is influenced by relatively few major genes or genomic regions. These preferences were not changed by experience of a successful spawning event with a male of the non-preferred species in a no-choice single-male trial. We found no evidence for imprinting in the F2 hybrids, although the F1 hybrid females may have been imprinted on their mothers. We discuss this nearly Mendelian inheritance of consistent innate mate preferences in the context of speciation theory