The group of invariants of an inner function with finite spectrum

This paper determines the group of continuous invariants corresponding to an inner function circle dot with finitely many singularities on the unit circle T; that is, the continuous mappings g : T -> T such that circle dot o g = circle dot on T. These mappings form a group under composition.

Hearing Delzant Polytopes From the Equivariant Spectrum

Let M^{2n} be a symplectic toric manifold with a fixed T^n-action and with a toric K\"ahler metric g. Abreu asked whether the spectrum of the Laplace operator $\Delta_g$ on $\mathcal{C}^\infty(M)$ determines the moment polytope of M, and hence by Delzant's theorem determines M up to symplectomorphism. We report on some progress made on an equivariant version of this conjecture. If the moment polygon of M^4 is generic and does not have too many pairs of parallel sides, the so-called equivariant spectrum of M and the spectrum of its associated real manifold M_R determine its polygon, up to translation and a small number of choices. For M of arbitrary even dimension and with integer cohomology class, the equivariant spectrum of the Laplacian acting on sections of a naturally associated line bundle determines the moment polytope of M.

INCREASING PARTICIPATION IN THE CLASSROOM FOR CHILDREN WITH AUTISM SPECTRUM DISORDERS

Active participation is as essential a skill to children with autism as it is for children without autism, as children are expected to engage in these skills both in and outside the classroom. Without participation skills, children are at a disadvantage when it comes to school and other settings, such as extracurricular activities and the workforce. Recent research has shown that there are interventions available that aim to improve the social skills of children in the home and in the school. These interventions can be delivered in varying forms with the primary caregiver as the interventionist, the specialist as the interventionist, and naturalistic interventions. The purpose of this study was to investigate one of the naturalistic interventions, the Competent Learner Model, and determine its effects on the participation and social skills of students with autism. Three middle school male students diagnosed with autism from a rural northeast middle school participated in the study. They were assessed using the Competent Learner Repertoire Assessments of the Competent Learner Model and the adaptive measures of the Vineland-II and ABAS-II. The results showed improvement for one of the three students and little to no improvement for the other two students.

Vibrational Relaxation of N2O (v2) by Atomic Oxygen Measured by Tunable Diode Laser Absorption Spectroscopy

Through the use of Transient Diode Laser Absorption Spectroscopy (TDLAS), the rate coefficient for the vibrational relaxation of N2O (ν2) by O(3P) at room temperature (32 ºC)) was determined to be (1.51 ± 0.11)x10-12 cm3molecule-1sec-1. A Q-switched, frequency quadrupled (266 nm) Nd:YAG laser pulse was used as the pump for this experiment. This pulse caused the photodissociation of O3 into O2 and O atoms.Excited oxygen (O(1D)) was collisionally quenched to ground state (O(3P)) by Ar and/or Xe. Photodissociation also caused a temperature jump within the system, exciting the ν2 state of N2O molecules. Population in the ν2 state was monitored through a TDLASobservation of a ν3 transition. Data were fit using a Visual Fortran 6.0 Global Fitting program. Analysis of room temperature data taken using only Ar to quench O atoms to the ground state gave the same rate coefficient as analysis of data taken using an Ar/Xe mixture, suggesting Ar alone is a sufficient bath gas. Experimentation was alsoperformed at -27 ºC and -82 ºC for a temperature dependence analysis. A linear regression analysis gave a rate coefficient dependence on temperature of ... for the rate coefficient of the vibrational relaxation of N2O (ν2) by atomic oxygen.

Vibrational Relaxation of 13CO2(v2) by Atomic Oxygen

Carbon dioxide (CO2) has been of recent interest due to the issue of greenhouse cooling in the upper atmosphere by species such as CO2 and NO. In the Earth’s upper atmosphere, between altitudes of 75 and 110 km, a collisional energy exchange occurs between CO2 and atomic oxygen, which promotes a population of ground state CO2 to the bend excited state. The relaxation of CO2 following this excitation is characterized by spontaneous emission of 15-μm. Most of this energy is emitted away from Earth. Due to the low density in the upper atmosphere, most of this energy is not reabsorbed and thus escapes into space, leading to a local cooling effect in the upper atmosphere. To determine the efficiency of the CO2- O atom collisional energy exchange, transient diode laser absorption spectroscopy was used to monitor the population of the first vibrationally excited state, 13CO2(0110) or ν2, as a function of time. The rate coefficient, kO(ν2), for the vibrational relaxation 13CO2 (ν2)-O was determined by fitting laboratory measurements using a home-written linear least squares algorithm. The rate coefficient, kO(ν2), of the vibrational relaxation of 13CO2(ν2), by atomic oxygen at room temperature was determined to be (1.6 ± 0.3 x 10-12 cm3 s-1), which is within the uncertainty of the rate coefficient previously found in this group for 12CO2(ν2) relaxation. The cold temperature kO(ν2) values were determined to be: (2.1 ± 0.8) x 10-12 cm3 s-1 at Tfinal = 274 K, (1.8 ± 0.3) x 10-12 cm3 s-1 at Tfinal = 239 K, (2 ± 1) x 10-12 cm3 s-1 at Tfinal = 208 K, and (1.7 ± 0.3) x 10-12 cm3 s-1 at Tfinal = 186 K. These data did not show a definitive negative temperature dependence comparable to that found for 12CO2 previously.

Examining The Genetic, Social-Cognitive, And Neural Correlates Of Autism Spectrum Disorder Behaviors In Typically Developing Chi

Autism spectrum disorders (ASD) are pervasive developmental disorders that affect approximately 1 in 50 children (Blumberg et al., 2013). Due to the social nature of the deficits that characterize the disorders, many have classified them as disorders of social cognition, which is the process that individuals use in order to successfully interact with members of their own species (Frith & Frith, 2007). Previous research has typically neglected the spectrum nature of ASD in favor of a more categorical approach of ¿autistic¿ versus ¿non-autistic,¿ but the spectrum requires a more continuous approach. Thus, the present study sought to examine the genetic, social-cognitive, and neural correlates of ASD-like traits as well as the relationship between these dimensions in typically developing children. Parents and children completed several quantitative measures examining several areas of social-cognitive functioning, including theory of mind and social functioning, restricted/repetitive behaviors and interests, and adaptive/maladaptive functioning. Children were also asked to undergo an EEG and both parents and children contributed a saliva sample that was used to sequence four single nucleotide polymorphisms (SNPs) of the OXTR gene, rs1042778, rs53576, rs2254298, and rs237897. We successfully demonstrated a significant relationship between behavioral measures of social-cognition and differences in face perception via the N170. However, the directionality of these relationships varied based on the behavioral measure and particular N170 difference scores. We also found support for the associations between the G_G allelic combination of rs1042778 and the A_A and A_G allelic combinations of rs2254298 and increased ASD-like behavior with decreased social-cognitive functioning. In contrast, our results contradict previous findings with rs237897 and imply that individuals with the A_A and A_G genotypes are less similar to those with ASD and have higher social cognitive functioning than those with the G_G genotype. In conclusion, we have demonstrated the existence of ASD-like traits in typically developing children and have shown a link between behavioral, genetic, and neural correlates of social-cognition. These findings demonstrate the importance of considering autism as a spectrum disorder and provide support for the move to a more continuous approach to neurodevelopmental disorders.

Vibrational Relaxation of O3(nu2) by O((3)P)

Laboratory measurements of the rate coefficient for quenching of O3(nu2) by ground-state atomic oxygen, kO(nu2), at room temperature are presented. kO(nu2) is currently not well known and is necessary for appropriate nonlocal thermodynamic equilibrium modeling of the upper mesosphere and lower thermosphere. In this work, a 266 nm laser pulse photolyzes a small amount of O3 in a slow-flowing gas mixture of O3, Xe, and Ar. This process simultaneously produces atomic oxygen and increases the temperature of the gas mixture slightly, thereby increasing the population in the O3(nu2) state. Transient diode laser absorption spectroscopy is used to monitor the populations of the O3(nu2) and ground vibrational states as the system re-equilibrates. Relaxation rates are measured over a range of quencher concentrations to extract the rate coefficient of interest. The value of kO(nu2) was determined to be (2.2 0.5) * 10(-12) cm(3) s(-1).