Mixed Modulation Spaces and Their Application to Pseudodifferential Operators

This paper uses frame techniques to characterize the Schatten class properties of integral operators. The main result shows that if the coefficients of certain frame expansions of the kernel of an integral operator are in (\ell^{2,p}), then the operator is Schatten p-class. As a corollary, we conclude that if the kernel or Kohn-Nirenberg symbol of a pseudodifferential operator lies in a particular mixed modulation space, then the operator is Schatten p-class. Our corollary improves existing Schatten class results for pseudodifferential operators and the corollary is sharp in the sense that larger mixed modulation spaces yield operators that are not Schatten class.Comment: To be published in Journal of Mathematical Analysis and Application

Schatten class Fourier integral operators

AbstractFourier integral operators with sufficiently smooth phase act on the time-frequency content of functions. However time-frequency analysis has only recently been used to analyze these operators. In this paper, we show that if a Fourier integral operator has a smooth phase function and its symbol is well localized in time and frequency, then the operator is Schatten p-class for p∈[1,2], with inclusion of the symbol in mixed modulation spaces serving as the appropriate measure of time-frequency localization. Our main results are sharp in the sense that larger mixed modulation spaces necessarily contain symbols of Fourier integral operators that are not Schatten p-class

The impact of positive reinforcement and self-recording on the on-task behavior of third grade students

The purpose of this study was to evaluate the impact of positive reinforcement and self-recording on the on-task behavior of third grade students. It was hypothesized that third grade students, within a learning community, who employ self-recording strategies and experience positive reinforcement rewards will be on-task a significantly longer length of time than third grade students who do not utilize those strategies. The study consisted of an experimental and a control group. Both groups were observed to determine baseline data. The experimental group was then asked to record their own on-task behavior and received rewards for being on-task a high percentage of the time. Both groups were then observed to determine if there were any improvements made. When the data was analyzed it was determined that the experimental group was on-task a longer length of time. It was also determined that there was a significant difference between the pre-test score and post-test score of the experimental group, therefore supporting the hypothesis

Supporting Parents as Teachers: Foundations of Family Education at the Children’s Museum of Houston

This article presents an overview of family learning at the Children’s Museum of Houston. Based on educational theory, and designed to support learning literacy and success in school, Museum programs provide parents with tools to help them nurture children’s intellectual development. The goal of this work is for parents to become better prepared to confidently engage their children in fun and meaningful learning experiences. The long-term benefits include strengthening family relationships and preparing children for success in secondary school and in the workplace

Gabor and wavelet analysis with applications to Schatten class integral operators

This thesis addresses four topics in the area of applied harmonic analysis. First, we show that the affine densities of separable wavelet frames affect the frame properties. In particular, we describe a new relationship between the affine densities, frame bounds and weighted admissibility constants of the mother wavelets of pairs of separable wavelet frames. This result is also extended to wavelet frame sequences. Second, we consider affine pseudodifferential operators, generalizations of pseudodifferential operators that model wideband wireless communication channels. We find two classes of Banach spaces, characterized by wavelet and ridgelet transforms, so that inclusion of the kernel and symbol in appropriate spaces ensures the operator is Schatten p-class. Third, we examine the Schatten class properties of pseudodifferential operators. Using Gabor frame techniques, we show that if the kernel of a pseudodifferential operator lies in a particular mixed modulation space, then the operator is Schatten p-class. This result improves existing theorems and is sharp in the sense that larger mixed modulation spaces yield operators that are not Schatten class. The implications of this result for the Kohn-Nirenberg symbol of a pseudodifferential operator are also described. Lastly, Fourier integral operators are analyzed with Gabor frame techniques. We show that, given a certain smoothness in the phase function of a Fourier integral operator, the inclusion of the symbol in appropriate mixed modulation spaces is sufficient to guarantee that the operator is Schatten p-class.Ph.D.Committee Chair: Heil, Christopher; Committee Member: Green, William; Committee Member: Lacey, Michael; Committee Member: Lubinsky, Doron; Committee Member: Moore, Ellio

Invariances of Frame Sequences under Perturbations

This paper determines the exact relationships that hold among the major Paley–Wiener perturbation theorems for frame sequences. It is shown that major properties of a frame sequence such as excess, deficit, and rank remain invariant under Paley–Wiener perturbations, but need not be preserved by compact perturbations. For localized frames, which are frames with additional structure, it is shown that the frame measure function is also preserved by Paley–Wiener perturbations

Examining clinical indications for cesarean section in a university hospital in Karachi, Pakistan

Background and objectives: Current research reports that Pakistan exceeds the recommended percent of deliveries via cesarean sections, including both emergent and non-emergent. In order to better understand the high rate of cesarean sections in Pakistan we examined the medical and non-medical indications of these surgeries at a private university hospital in Karachi. Methods: A retrospective analysis of patient medical record data was conducted from January 1st, 2018 to March 31st, 2018. The data collected was analyzed using SPSS 25. Results: The total number of deliveries during the period was n= 1,211, out of which n=602 (49.70%) were CS. The top five indications for CS were: repeat CS n=199 (44.20%), failure to progress n=58 (12.90%), abnormal lie n=42 (9.30%), fetal distress n=37 (8.20%), and fetal growth restriction n= 21 (4.70%). Conclusion: This study contributes to a broader understanding of the indications of cesarean section rates in the developing world. This information can be used to improve infant and maternal health by reducing the complications associated with operative deliveries

Successional change in phosphorus stoichiometry explains the inverse relationship between herbivory and lupin density on Mount St. Helens

Background: The average nitrogen-to-phosphorus ratio (N:P) of insect herbivores is less than that of leaves, suggesting that P may mediate plant-insect interactions more often than appreciated. We investigated whether succession-related heterogeneity in N and P stoichiometry influences herbivore performance on N-fixing lupin (Lupinus lepidus) colonizing primary successional volcanic surfaces, where the abundances of several specialist lepidopteran herbivores are inversely related to lupin density and are known to alter lupin colonization dynamics. We examined larval performance in response to leaf nutritional characteristics using gelechiid and pyralid leaf-tiers, and a noctuid leaf-cutter. Methodology/Principal Findings: We conducted four studies. First, growth of larvae raised on wild-collected leaves responded positively to leaf %P and negatively to leaf carbon (%C), but there was no effect of %N or quinolizidine alkaloids (QAs). Noctuid survival was also positively related to %P. Second, we raised gelechiid larvae on greenhouse-grown lupins with factorial manipulation of competitors and soil N and P. In the presence of competition, larval mass was highest at intermediate leaf N:P and high %P. Third, survival of gelechiid larvae placed on lupins in high-density patches was greater when plant competitors were removed than on controls. Fourth, surveys of field-collected leaves in 2000, 2002, and 2003 indicated that both %P and %N were generally greater in plants from low-density areas. QAs in plants from low-density areas were equal to or higher than QAs in high-density areas. Conclusions/Significance: Our results demonstrate that declines in lupin P content under competitive conditions are associated with decreased larval growth and survival sufficient to cause the observed negative relationship between herbivore abundance and host density. The results support the theoretical finding that declines in stoichiometric resource quality (caused here by succession) have the potential to cause a decrease in consumer abundance despite very dense quantities of the resource. © 2009 Apple et al