Commutation Relations for Unitary Operators

Let $U$ be a unitary operator defined on some infinite-dimensional complex Hilbert space ${\cal H}$. Under some suitable regularity assumptions, it is known that a local positive commutation relation between $U$ and an auxiliary self-adjoint operator $A$ defined on ${\cal H}$ allows to prove that the spectrum of $U$ has no singular continuous spectrum and a finite point spectrum, at least locally. We show that these conclusions still hold under weak regularity hypotheses and without any gap condition. As an application, we study the spectral properties of the Floquet operator associated to some perturbations of the quantum harmonic oscillator under resonant AC-Stark potential

Commutation Relations for Unitary Operators III

Let $U$ be a unitary operator defined on some infinite-dimensional complex Hilbert space ${\cal H}$. Under some suitable regularity assumptions, it is known that a local positive commutation relation between $U$ and an auxiliary self-adjoint operator $A$ defined on ${\cal H}$ allows to prove that the spectrum of $U$ has no singular continuous spectrum and a finite point spectrum, at least locally. We prove that under stronger regularity hypotheses, the local regularity properties of the spectral measure of $U$ are improved, leading to a better control of the decay of the correlation functions. As shown in the applications, these results may be applied to the study of periodic time-dependent quantum systems, classical dynamical systems and spectral problems related to the theory of orthogonal polynomials on the unit circle

Alien Registration- Bourget, Agnes M. (Winslow, Kennebec County)

https://digitalmaine.com/alien_docs/16352/thumbnail.jp

On Hold: Relationships in the Age of Mobile Phone Distraction

Interpersonal communication has been transformed by the more than 70 percent of adults who own smartphones (Greenwood, Perrin & Duggan, 2016) and other forms of portable technology. It is now more convenient than ever to stay in touch, find lost friends, and access constantly updated information online, but research has linked mobile phone use to decreased relationship and interaction quality. For example, McDaniel and Coyne (2016) found that self-reported technology use among married couples predicted more partner conflict and less relationship satisfaction, particularly for women. Brown, Manago and Trimble (2016) found similar results in that the more friend dyads were observed using their mobile phones in each other’s presence, the lower they subsequently rated the quality of their interactions. Przybylski and Weinstein (2012) found that even the mere presence of a cell phone was linked to lower levels of trust, relationship quality, and perceived partner empathy among dyads instructed to talk about a meaningful topic. The current study addressed the call for more research on the links between computer mediated communication, relationships and well-being (Schiffrin, Edelman, Falkenstern & Stewart, 2010). Participants answered survey questions about five close relationships and completed standardized scales to measure cell phone use and other individual differences, including locus of control, subjective well-being and satisfaction with life. Results revealed a pattern across the five relationships; participants indicated that in-person communication was more common in family relationships than in romantic and friend relationships, in-person interactions were rated as more important than online interactions, and more in-person interactions predicted higher relationship quality scores. An external locus of control was significantly positively correlated with cell phone dependence and mobile phone usage, and predicted lower relationship quality, subjective well-being and satisfaction with life

Colmatage microbien des forages et circulation de l'eau - Résultats d'un « colmatomètre » expérimental

Un modèle physique est constitué de quatre éprouvettes de sable percolées à des vitesses de flux différentes par L'eau d'un forage colmaté.On a pu ainsi obtenir, en quelques semaines, un colmatage différentiel de deux éprouvettes percolées à des vitesses supérieures à 1 cm/s, et confirmer les hypothèses émises sur l'influence de La vitesse réelle des filets liquides dans L'apparition du colmatage, et sur ta nature bactérienne du processus colmatant.Ce modèle constitue un véritable "colmatomètre" qui a donné lieu au dépôt d'un brevet (BOURGUET et al., 1985). Avant La réalisation d'un champ captant nouveau, L'emploi d'un tel colmatomètre devrait permettre d'apprécier les risques de colmatage spécifiques au site, et de définir Les normes de crépinage et d'exploitation permettant de Les éviter, ou du moins de les minimiser.INTRODUCTIONA study on 300 wells drilled in the Ypresian aquifer, over 60 % of which were clogged, revealed that there were significant statistic relationships between the frequency of ctogging, the high velocities of the water close to the well screens and the presence of hydrogen sulfide in the water; the latter means the existence of sulfato-reducing bacterial activity.The experimental model described here was designed to check the effect of the velocity of the water in the aquifer on the creation of clogging, as well as its relationship with the development of the bacterial population induced by a sufficient nutrient flow rate.This model, comprising sterilized sand, through wich water from a clogged well percolated, was set up prior to a model which will soon be built, consisting of cores of Ypresian sand containing its own microorganisms.APPARATUS AND METHODSFour stainless-steel tubes (length 14 cm, inner diameter 26 mm) were filled with sterilized siliceous sand, the initial porosity of which was 35 %. The particle size distribution (40 to 140 µm) and the permeability were similar to those of the Ypresian sand. Tube seeding was carried out for a week by percolation with water from a clogged well; no clogging in the tubes was observed. This water was then percotated simultaneously through the tubes (figure 2) for 58 days at rates, maintained by weekly corrections, close to 1, 3, 12 and 30 mm/s respectively (figure 3).The microbiological analyses consisted in : direct numeration of bacterial bodies by epifluorescence microscopy, indirect numeration by counting revivifiable heterotrophic aerobic bacteria after 15 days incubation within a medium chosen to be the least selective possible and, lastly, the numeration of both permanent and casual anaerobia, as well as sulfatoreducing bacteria following Hungate's method.HYDRODYNAMIC RESULTS (figure 4)The reduction of permeability, which results from clogging, after 58 days of percolation was the following :- tube nb 1          0 % for an average percolation rate of 0.8 mm/s,- tube nb 2         2 % for an average percolation rate of 2.5 mm/s,- tube nb 3         29,5 % for an average percolation rate of 11.5 mm/s,- tube nb 4         59 % for an average percolation rate of 30.8 mm/s.Tubes nb 1, 2 and 4 were destroyed in order to carry out microbiological analyses. Tube nb 3, maintained in percolation, reached 99,4 % clogging after 142 days.MICROBIOLOGICAL RESULTS AND DISCUSSIONSampling procedures for analyses were set up by using tube nb 2. Three different samples of sand were used for analyses : from the inlet, from the middle and from the outlet of tubes nb 1 et 4. Moreover analyses were made on the percolation water upstream and downstream of tube nb 4.The revivifiable heterotrophic aerobic bacteria are more numerous in the water at the outlet of tube nb 4 than at the inlet, white direct counting shows a slight decrease.There are greater quantities of microorganisms in the sand than in the percolation water. The presence of sulfato-reducing bacteria can even be observed whereas they are too few to be counted in the percolation water. The filtering effect of the sand is not the only, element responsible for the increase amount of bacteria. Indeed the ratio between the number of revivifiable heterotrophic bacteria in the clogged tube and the non clogged tube was about 3 times greater than the ratio between their flow rates.The higher velocity in tube nb 4 induced favorable conditions for the development of certain species of bacteria, some of which generate hydrogen producing organic molecules, thus allowing the development of sulfato-reducing bacteria.Clogging itself should depend either on the increase of the biomass or on the development of microorganisms producing a significant quantity of organic molecules outside the cells. By taking into account the amount of bacteria and the volumes of percolated water, it can be seen that 2.01 x 1011 cells, i.e. 0.2 cm3 , were retained by filtration in tube nb 1, and 0.7 cm3 in tube nb 4. Basing the estimations on bacterial counts in the sand, biovolumes of 0.2 mm3 are obtained for tube nb 1 (non clogged), and 8 mm3 for tube nb 4 (clogged). Consequently the clogging substances consist mainly of products situated outside the cells.The tube is the center of chemolithotrophic organisms (made evident by C14 tracers), thus the aerobic heterotrophic microflora and the sulfato-reducing species are no doubt linked to the use of the metabolism products of these organisms.After 142 days percolation, the sand in tube nb 3 (clogged at 99,4 %) had a cell content of 1011 cells/cm3 of sand at the inlet (filamentous aggregates) and 107 cells/cm3 at the outlet (no aggregates). On an average, roughly a third of the pore volume is filled with cells, which is in agreement with a decrease in porosity from 35 to 27 % and therefore with the clogging in the tubes.CONCLUSIONTubes of sand could be clogged experimentalty and rapidly. The most significant clogging was obtained for the fastest percolation rate.It seems as though clogging is due to a proliferation of bacteria, essentially oligotrophic, and to the creation of a nutrient-chain rising to the sulfato-reducing bacteria (which are heterotrophic).The clogging process described in the case of the Ypresian sand aquifer is certainly similar to the processes occurring in other granular aquifers.The model " clog-meter" could be used by water supptiers exploiting aquifers fiable to clogging. Indeed it can determine the best flow rate, to avoid clogging in newly exploited pumping fields and decide on the most adequate well equipment, the number of wells needed in newly exploited areas and their exploitation yield in order to obtain the desired flow rates

Fractional Moment Estimates for Random Unitary Operators

We consider unitary analogs of $d-$dimensional Anderson models on $l^2(\Z^d)$ 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 parameters controlling the size of its off-diagonal elements. We adapt the method of Aizenman-Molchanov to get exponential estimates on fractional moments of the matrix elements of $U_\omega(U_\omega -z)^{-1}$, provided the distribution of phases is absolutely continuous and the parameters correspond to small off-diagonal elements of $S$. Such estimates imply almost sure localization for $U_\omega$

Localization Properties of the Chalker-Coddington Model

The Chalker Coddington quantum network percolation model is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We study the model restricted to a cylinder of perimeter 2M. We prove firstly that the Lyapunov exponents are simple and in particular that the localization length is finite; secondly that this implies spectral localization. Thirdly we prove a Thouless formula and compute the mean Lyapunov exponent which is independent of M.Comment: 29 pages, 1 figure. New section added in which simplicity of the Lyapunov spectrum and finiteness of the localization length are proven. To appear in Annales Henri Poincar

STEAM (SCIENCE, TECHNOLOGY, ENGINEERING, ART, AND MATHEMATICS) EDUCATION AND TEACHERS’ PEDAGOGICAL DISCONTENTMENT LEVELS

Literature focused on the emerging implementation of STEAM (Science, Technology, Engineering, Art, and Mathematics) education within K-12 education programs in the USA emphasizes the need for researchers to address the potential for disrupting the pedagogical contentment of teachers assigned to teach in STEAM disciplines who have no backgrounds in the fields represented by STEAM and/or who have no prior teaching experience in the areas of STEAM. Research objectives for the current study focused on examining the influence of intensive professional development on K-12 teachers’ pedagogical discontentment levels relative to the implementation of STEAM in all classrooms within a rural school district in the southeast region of the United States. Data sources included: (a) pre-post assessments of 93 teachers’ pedagogical discontentment levels; (b) classroom observation data collected by external observers; and (c) teachers’ perceptions of STEAM coaching.  Data retrieved were analyzed using quantitative analyses. Study findings indicated teachers’ pedagogical discontentment levels decreased over time. Future research must support teachers new to STEAM activities