On a two variable class of Bernstein-Szego measures

The one variable Bernstein-Szego theory for orthogonal polynomials on the real line is extended to a class of two variable measures. The polynomials orthonormal in the total degree ordering and the lexicographical ordering are constructed and their recurrence coefficients discussed.Comment: minor change

Asymptotics for Sobolev orthogonal polynomials for exponential weights

38 pages, no figures.-- MSC2000 codes: 42C05, 33C25.MR#: MR2164139 (2006c:41040)Zbl#: Zbl 1105.42016^aLet $\lambda >0,\alpha >1$, and let $W( x) =\exp ( -\vert x\vert ^{\alpha })$, x\in \mbox{\smallbf R}. Let \psi \in L_{\infty }(\mbox{\smallbf R}) be positive on a set of positive measure. For $n\geq 1$, one may form Sobolev orthonormal polynomials $( q_{n})$, associated with the Sobolev inner product ( f,g) =\int_{\mbox{\scriptsize\bf R}}fg( \psi W) ^{2}+\lambda \int_{\mbox{\scriptsize\bf R}}f^{\prime }g^{\prime }W^{2}. We establish strong asymptotics for the $( q_{n})$ in terms of the ordinary orthonormal polynomials $( p_{n})$ for the weight $W^{2}$, on and off the real line. More generally, we establish a close asymptotic relationship between $( p_{n})$ and $( q_{n})$ for exponential weights $W=\exp ( -Q)$ on a real interval $I$, under mild conditions on $Q$. The method is new and will apply to many situations beyond that treated in this paper.The work by F. Marcellan has been supported by Dirección General de Investigación (Ministerio de Ciencia y Technología) of Spain under grant BFM 2003-06335-C03-07, as well as NATO Collaborative grant PST.CLG 979738. J. Geronimo and D. Lubinsky, respectively, acknowledge support by NSF grants DMS-0200219 and DMS-0400446.Publicad

Localization for Random Unitary Operators

We consider unitary analogs of $1-$dimensional Anderson models on $l^2(\Z)$ defined by the product $U_\omega=D_\omega S$ where $S$ is a deterministic unitary and $D_\omega$ is a diagonal matrix of i.i.d. random phases. The operator $S$ is an absolutely continuous band matrix which depends on a parameter controlling the size of its off-diagonal elements. We prove that the spectrum of $U_\omega$ is pure point almost surely for all values of the parameter of $S$. We provide similar results for unitary operators defined on $l^2(\N)$ together with an application to orthogonal polynomials on the unit circle. We get almost sure localization for polynomials characterized by Verblunski coefficients of constant modulus and correlated random phases

The Regge Limit for Green Functions in Conformal Field Theory

We define a Regge limit for off-shell Green functions in quantum field theory, and study it in the particular case of conformal field theories (CFT). Our limit differs from that defined in arXiv:0801.3002, the latter being only a particular corner of the Regge regime. By studying the limit for free CFTs, we are able to reproduce the Low-Nussinov, BFKL approach to the pomeron at weak coupling. The dominance of Feynman graphs where only two high momentum lines are exchanged in the t-channel, follows simply from the free field analysis. We can then define the BFKL kernel in terms of the two point function of a simple light-like bilocal operator. We also include a brief discussion of the gravity dual predictions for the Regge limit at strong coupling.Comment: 23 pages 2 figures, v2: Clarification of relation of the Regge limit defined here and previous work in CFT. Clarification of causal orderings in the limit. References adde

TEACHING CRAFT AS AN ART: TEACHER’S REPERTOIRE OF SKILLS AND STRATEGIES VIA PROFESSIONAL ENHANCEMENT

This research discloses one of the dimensions of the teachers’ quality of work life among secondary teachers. It was found out that professional growth and development through continuing education had a significant correlation with the amount of trainings that the teachers had. The more training the teachers had engaged with, the better they become as a professional teacher. It equipped them to be more productive and skillful. They felt the great importance of this dimension in their teaching career. Teachers became aware of the current trends and innovations through career progression. It also showed the greatest impact on the teachers quality of work life. Teachers positively embraced the significant contributions it could bring to the teaching profession and that secondary teachers could possess varied repertoire of skills and strategies in the teaching and learning process through professional growth and continuing education

Gender-based analysis on self-efficacy beliefs of pre-service teachers and their readiness in taking licensure examination

The study aimed to determine whether preservice teachers’ self-efficacy belief differs according to gender and whether this belief relates to their readiness in taking the licensure examination for teachers (LET). Participants of the study were 545 preservice teachers who were undergoing in-service training both from the secondary and elementary programs that came from four campuses of the university. The researcher utilized a descriptive quantitative approach with weighted mean, t-test for the independent sample, and Pearson R correlation statistical treatments for the data. Results revealed that females are statistically higher in self-efficacy beliefs than their male counterparts. Further, the study disclosed that female preservice teachers are significantly more ready to take the examination than their male peers. In addition, the male students’ self-efficacy beliefs statistically have a positive significant relationship to their readiness to take examination. Meanwhile, a positive significant relationship exists also between self-efficacy beliefs and readiness in taking the test with their female counterparts

TEACHING CRAFT AS AN ART: TEACHER’S REPERTOIRE OF SKILLS AND STRATEGIES VIA PROFESSIONAL ENHANCEMENT

This research discloses one of the dimensions of the teachers’ quality of work life among secondary teachers. It was found out that professional growth and development through continuing education had a significant correlation with the amount of trainings that the teachers had. The more training the teachers had engaged with, the better they become as a professional teacher. It equipped them to be more productive and skillful. They felt the great importance of this dimension in their teaching career. Teachers became aware of the current trends and innovations through career progression. It also showed the greatest impact on the teachers quality of work life. Teachers positively embraced the significant contributions it could bring to the teaching profession and that secondary teachers could possess varied repertoire of skills and strategies in the teaching and learning process through professional growth and continuing education

Noise Characterization and Filtering in the MicroBooNE Liquid Argon TPC

The low-noise operation of readout electronics in a liquid argon time projection chamber (LArTPC) is critical to properly extract the distribution of ionization charge deposited on the wire planes of the TPC, especially for the induction planes. This paper describes the characteristics and mitigation of the observed noise in the MicroBooNE detector. The MicroBooNE's single-phase LArTPC comprises two induction planes and one collection sense wire plane with a total of 8256 wires. Current induced on each TPC wire is amplified and shaped by custom low-power, low-noise ASICs immersed in the liquid argon. The digitization of the signal waveform occurs outside the cryostat. Using data from the first year of MicroBooNE operations, several excess noise sources in the TPC were identified and mitigated. The residual equivalent noise charge (ENC) after noise filtering varies with wire length and is found to be below 400 electrons for the longest wires (4.7 m). The response is consistent with the cold electronics design expectations and is found to be stable with time and uniform over the functioning channels. This noise level is significantly lower than previous experiments utilizing warm front-end electronics.Comment: 36 pages, 20 figure