A Minimal Periods Algorithm with Applications

Kosaraju in ``Computation of squares in a string'' briefly described a linear-time algorithm for computing the minimal squares starting at each position in a word. Using the same construction of suffix trees, we generalize his result and describe in detail how to compute in O(k|w|)-time the minimal k-th power, with period of length larger than s, starting at each position in a word w for arbitrary exponent $k\geq2$ and integer $s\geq0$. We provide the complete proof of correctness of the algorithm, which is somehow not completely clear in Kosaraju's original paper. The algorithm can be used as a sub-routine to detect certain types of pseudo-patterns in words, which is our original intention to study the generalization.Comment: 14 page

Enjoyment, Interest, and Achievement Levels of Third Grade Students in Separate Subject and Interrelated Subject Units in Science and Social Studies

The purpose of this study was to investigate the difference in the enjoyment, interest, perceived learning, and achievement levels of third grade students when social studies and science units were presented as interrelated subject units versus separate subject units. Eight units in social studies and science were chosen. Four of these units were selected at random to be presented as interrelated subject units and four to be presented as separate subject units. Interrelated units used the social studies or science topic as a core, and lessons in other subjects such as language arts, math, music, and art were related to this basic topic. Separate subject units focused on the particular topic of the unit and were not intentionally related to other subjects in curriculum. An attitude questionnaire and achievement test were administered as posttests after each unit. The results of the tests for matched pairs indicated a significant difference in the levels of enjoyment, interest, perceived learning, and achievement for the two types of units. It was concluded that the 28 third grade students taught using interrelated subject units showed a significantly higher level of enjoyment, interest, perceived learning, and achievement than the same group when taught using separate subject units

Analytical Techniques and the Air Force Logistics Readiness Officer

As the Air Force begins to implement the Expeditionary Combat Support System (ECSS), it is imperative that Air Force logisticians competently analyze logistics data. This exploratory study sought to determine which analytical skills are useful for Logistics Readiness Officers (LROs), as reported by active-duty LROs in grades O1-O5 and their supervisors. The research question was answered through a comprehensive literature review and the use of survey methodology. Over five hundred LROs and supervisors provided inputs. Analysis of survey responses found that Forecasting, Graphical Statistics and Descriptive Statistics are the analytical techniques valued most by both LROs and their supervisors. LROs and their supervisors valued the same techniques, though supervisors considered them to be more important. Company grade officers reported a higher degree of usefulness for each technique than field grade officers did. Responses were compared across groups of LROs and found to be consistently similar. This research noted the reported importance of Forecasting techniques among LROs and identified a potential gap between perceived usefulness and competence levels

Sound propagation over uneven ground and irregular topography

Theoretical, computational, and experimental techniques for predicting the effects of irregular topography on long range sound propagation in the atmosphere was developed. Irregular topography here is understood to imply a ground surface that is not idealized as being perfectly flat or that is not idealized as having a constant specific acoustic impedance. The interest focuses on circumstances where the propagation is similar to what might be expected for noise from low altitude air vehicles flying over suburban or rural terrain, such that rays from the source arrive at angles close to grazing incidence

Emotional and Adrenocortical Responses of Infants to the Strange Situation: The Differential Function of Emotional Expression

The aim of the study was to investigate biobehavioural organisation in infants with different qualities of attachment. Quality of attachment (security and disorganisation), emotional expression, and adrenocortical stress reactivity were investigated in a sample of 106 infants observed during Ainsworth’s Strange Situation at the age of 12 months. In addition, behavioural inhibition was assessed from maternal reports. As expected, securely attached infants did not show an adrenocortical response. Regarding the traditionally defined insecurely attached groups, adrenocortical activation during the strange situation was found for the ambivalent group, but not for the avoidant one. Previous ndings of increased adrenocortical activity in disorganised infants could not be replicated. In line with previous ndings, adrenocortical activation was most prominent in insecure infants with high behavioural inhibition indicating the function of a secure attachment relationship as a social buffer against less adaptive temperamental dispositions. Additional analyses indicated that adrenocortical reactivity and behavioural distress were not based on common activation processes. Biobehavioural associations within the different attachment groups suggest that biobehavioural processes in securely attached infants may be different from those in insecurely attached and disorganised groups. Whereas a coping model may be applied to describe the biobehavioural organisation of secure infants, an arousal model explanation may be more appropriate for the other groups

Photoabsorption spectra of the diamagnetic hydrogen atom in the transition regime to chaos: Closed orbit theory with bifurcating orbits

With increasing energy the diamagnetic hydrogen atom undergoes a transition from regular to chaotic classical dynamics, and the closed orbits pass through various cascades of bifurcations. Closed orbit theory allows for the semiclassical calculation of photoabsorption spectra of the diamagnetic hydrogen atom. However, at the bifurcations the closed orbit contributions diverge. The singularities can be removed with the help of uniform semiclassical approximations which are constructed over a wide energy range for different types of codimension one and two catastrophes. Using the uniform approximations and applying the high-resolution harmonic inversion method we calculate fully resolved semiclassical photoabsorption spectra, i.e., individual eigenenergies and transition matrix elements at laboratory magnetic field strengths, and compare them with the results of exact quantum calculations.Comment: 26 pages, 9 figures, submitted to J. Phys.