Heisenberg modules as function spaces

Let $\Delta$ be a closed, cocompact subgroup of $G \times \widehat{G}$, where $G$ is a second countable, locally compact abelian group. Using localization of Hilbert $C^*$-modules, we show that the Heisenberg module $\mathcal{E}_{\Delta}(G)$ over the twisted group $C^*$-algebra $C^*(\Delta,c)$ due to Rieffel can be continuously and densely embedded into the Hilbert space $L^2(G)$. This allows us to characterize a finite set of generators for $\mathcal{E}_{\Delta}(G)$ as exactly the generators of multi-window (continuous) Gabor frames over $\Delta$, a result which was previously known only for a dense subspace of $\mathcal{E}_{\Delta}(G)$. We show that $\mathcal{E}_{\Delta}(G)$ as a function space satisfies two properties that make it eligible for time-frequency analysis: Its elements satisfy the fundamental identity of Gabor analysis if $\Delta$ is a lattice, and their associated frame operators corresponding to $\Delta$ are bounded.Comment: 24 pages; several changes have been made to the presentation, while the content remains essentially unchanged; to appear in Journal of Fourier Analysis and Application

Gabor Duality Theory for Morita Equivalent C∗C^*-algebras

The duality principle for Gabor frames is one of the pillars of Gabor analysis. We establish a far-reaching generalization to Morita equivalent $C^*$-algebras where the equivalence bimodule is a finitely generated projective Hilbert $C^*$-module. These Hilbert $C^*$-modules are equipped with some extra structure and are called Gabor bimodules. We formulate a duality principle for standard module frames for Gabor bimodules which reduces to the well-known Gabor duality principle for twisted group $C^*$-algebras of a lattice in phase space. We lift all these results to the matrix algebra level and in the description of the module frames associated to a matrix Gabor bimodule we introduce $(n,d)$-matrix frames, which generalize superframes and multi-window frames. Density theorems for $(n,d)$-matrix frames are established, which extend the ones for multi-window and super Gabor frames. Our approach is based on the localization of a Hilbert $C^*$-module with respect to a trace.Comment: 36 page

Differences in macrofauna communities among three north Norwegian fjords

Masteroppgave i marin økologi - Nord universitet, 201

A Profile of Women in Broadcasting in South Dakota

The purpose of this study is to develop a profile of South Dakota\u27s typical women broadcasters. The profile will report how long they have worked in broadcasting, what their age was when they started in the industry, how many stations they have worked for, if their previous job was in broadcasting, if they were living in the present town before they took their current job, how they first heard about the opening for their position, and why they entered the broadcasting profession. The study is also an attempt to find out the attitudes of women in broadcasting toward job performance, sex discrimination, job satisfaction, and eventual job objectives. In addition, the profile includes basic demographic data such as age, marital status, number of children, educational status, major fields of study, salary, working hours, specific job duties and time spent in each duty. The profile is based on a questionnaire sent to the 154 women currently working in nonclerical jobs in broadcasting in South Dakota. The results of this research are compared with other studies of women in broadcasting, particularly a national study conducted by Abigail Jones Nash in 1974 of women working in broadcast journalism. The Nash study assessed newswomen\u27s job satisfaction. Nash found that two-thirds of the newswomen’s aid they had been discriminated against on the job because of their sex. Are as of pay, promotion, and story assignments were frequently mentioned examples. But despite perceived discrimination, more than eight out of ten newswomen responding to the survey expressed overall satisfaction with their jobs. The data on salaries indicated that newswomen were being paid less than the average news staffer. And from one - third to three-fourths of the respondents felt their opportunities in various areas of employment were not as good as those of men

Effects of peer mentoring on the achievement and persistence of academically underprepared college freshmen

PURPOSE: The purpose of this study was to determine whether a peer mentoring program incorporating learning styles impacts upon the achievement and persistence of entry-level academically underprepared college students. PROCEDURE: Subjects were freshmen at Bemidji State University during the fall terms of 1985 and 1986 who were assigned to remedial/developmental English because of low placement test scores. An experimental group of 31 English 100 students participated in Connections: The Student-to-Student Mentoring Network, a pilot program designed to help underprepared students make a successful transition into college. The experimental group was compared to a control group of 40 students who were not mentored but who took the course the previous year from the same instructors. Analysis of covariance procedures and chi-square statistics were used to assess the effects of peer mentoring on grades and reenrollment status. Effects of mentors and students matching and mismatching in learning style, age-level, and gender were analyzed by comparing grades and reenrollment status of matched and nonmatched pairs. The Meyers-Briggs Type Indicator was used to assess level of learning style match. FINDINGS: 1. Students in remedial/developmental English who received peer mentoring achieved a more favorable reenrollment status than comparable students who took the course without mentoring. 2. Mentored students attained more satisfactory grades than nonmentored students. 3. Matching students and mentors by learning style was not found to be a factor in improving students\u27 grades or reenrollment status. 4. Matching students and mentors by gender was not found to be a factor in improving students\u27 grades or reenrollment status. 5. Matching students and mentors by age-level was not found to be a factor in improving students\u27 grades or reenrollment status. Contrary to the research hypothesis, the findings suggested that students who had mentors of a higher age-level attained a more favorable reenrollment status. 6. Mentored students were more knowledgeable about campus resources and used them more frequently

Real-Time Performance of Industrial IoT Communication Technologies: A Review

With the growing need for automation and the ongoing merge of OT and IT, industrial networks have to transport a high amount of heterogeneous data with mixed criticality such as control traffic, sensor data, and configuration messages. Current advances in IT technologies furthermore enable a new set of automation scenarios under the roof of Industry 4.0 and IIoT where industrial networks now have to meet new requirements in flexibility and reliability. The necessary real-time guarantees will place significant demands on the networks. In this paper, we identify IIoT use cases and infer real-time requirements along several axes before bridging the gap between real-time network technologies and the identified scenarios. We review real-time networking technologies and present peer-reviewed works from the past 5 years for industrial environments. We investigate how these can be applied to controllers, systems, and embedded devices. Finally, we discuss open challenges for real-time communication technologies to enable the identified scenarios. The review shows academic interest in the field of real-time communication technologies but also highlights a lack of a fixed set of standards important for trust in safety and reliability, especially where wireless technologies are concerned.Comment: IEEE Internet of Things Journal 2023 | Journal article DOI: 10.1109/JIOT.2023.333250

Bounding the End-to-End Execution Time in Distributed Real-Time Systems: Arguing the case for Deterministic Networks in Lingua Franca

Designing and implementing distributed systems with real-time requirements quickly reveal the complexity of handling time and logic across multiple systems. As data traverse a network, it is subjected to variable delay due to interfering traffic and variable load on network components. This introduces an element of non-determinism in execution time for distributed algorithms, which translates into increased error logic and pessimistic worst-case estimates. Over the next few years, it is expected that Cyber-Physical Systems will see many new use cases, and the network connecting these will play an ever more important role. Combined with the onset of the fourth industrial revolution, IEEEs Time Sensitive Networking, IETFs Deterministic Networking, and 3GPPs Ultra Reliable Low Latency profile will play a vital role in realizing these systems. Coordination languages such as Lingua Franca can offer a substantial contribution to the design process and implementation of distributed systems such as Cyber-Phyiscal Systems, both through its model of computation which elevates time to a first-class citizen and with its support for distributed models. In this paper, we show that by introducing deterministic network channels with a fixed delay, the worst-case execution time is not increased whereas the variance in total execution time from start to finish is greatly reduced. For a coordination language such as LF, this means that we can analyze a system using much tighter delay bounds for network traffic, which in turn can yield better resource utilization.publishedVersio