Properly stratified algebras and tilting

We study the properties of tilting modules in the context of properly stratified algebras. In particular, we answer the question when the Ringel dual of a properly stratified algebra is properly stratified itself, and show that the class of properly stratified algebras for which the characteristic tilting and cotilting modules coincide is closed under taking the Ringel dual. Studying stratified algebras, whose Ringel dual is properly stratified, we discover a new Ringel-type duality for such algebras, which we call the two-step duality. This duality arises from the existence of a new (generalized) tilting module for stratified algebras with properly stratified Ringel dual. We show that this new tilting module has a lot of interesting properties, for instance, its projective dimension equals the projectively defined finitistic dimension of the original algebra, it guarantees that the category of modules of finite projective dimension is contravariantly finite, and, finally, it allows one to compute the finitistic dimension of the original algebra in terms of the projective dimension of the characteristic tilting module.Comment: A revised version of the preprint 2003:31, Department of Mathematics, Uppsala Universit

Autocrat of the Armchair

Structural analysis is a standard tool to identify submodels that can be used to design model based diagnostic tests. Structural approaches typically operate on models described by a set of equations. This work extends such methods to be able to handle models with constraints, e.g. inequality constraints on state variables. The objective is to improve isolability properties of a diagnosis system by extending the class of redundancy relations. An algorithm is developed that identifies which are the constraints and equations that can be used together to derive a new test that can not be found using previous approachesCADIC

Assessing Conceptual Knowledge of Differential Equations

The differential equations and linear algebra math classes at Valparaiso University participate in an online tutoring survey consisting of conceptual questions from the field. The test was originally constructed by a team of math professors from San Diego State University. The questions are available in an online format and most questions provide scaffolding, or a tutoring set of questions when a primary question is answered incorrectly. This project analyzes the effectiveness of the scaffolding on a subset of questions with specific focus on areas of separable variables and Euler’s method. Special attention has been given to questions with multiple knowledge components, which may complicate the effectiveness of the scaffolding. In several questions, we have found that the scaffolding is not impacting student understanding of the subject area. We are also discovering surprising anomalies in students’ conceptions that the test creators did not predict. Thus, in some cases, it may be necessary to adapt the scaffolding or question wording to maximize test efficiency and overall student comprehension

Simple preparation of Bell and GHZ states using ultrastrong-coupling circuit QED

The ability to entangle quantum systems is crucial for many applications in quantum technology, including quantum communication and quantum computing. Here, we propose a new, simple, and versatile setup for deterministically creating Bell and Greenberger-Horne-Zeilinger (GHZ) states between photons of different frequencies in a two-step protocol. The setup consists of a quantum bit (qubit) coupled ultrastrongly to three photonic resonator modes. The only operations needed in our protocol are to put the qubit in a superposition state, and then tune its frequency in and out of resonance with sums of the resonator-mode frequencies. By choosing which frequency we tune the qubit to, we select which entangled state we create. We show that our protocol can be implemented with high fidelity using feasible experimental parameters in state-of-the-art circuit quantum electrodynamics. One possible application of our setup is as a node distributing entanglement in a quantum network.Comment: 15 pages, 7 figure

Undoing measurement-induced dephasing in circuit QED

We analyze the backaction of homodyne detection and photodetection on superconducting qubits in circuit quantum electrodynamics. Although both measurement schemes give rise to backaction in the form of stochastic phase rotations, which leads to dephasing, we show that this can be perfectly undone provided that the measurement signal is fully accounted for. This result improves upon that of Phys. Rev. A, 82, 012329 (2010), showing that the method suggested can be made to realize a perfect two-qubit parity measurement. We propose a benchmarking experiment on a single qubit to demonstrate the method using homodyne detection. By analyzing the limited measurement efficiency of the detector and bandwidth of the amplifier, we show that the parameter values necessary to see the effect are within the limits of existing technology

Gym Dance

In lieu of an abstract, below is the essay\u27s first paragraph. Two . Three . Four

A Week In The Life Of An Old Man

In lieu of an abstract, below is the essay\u27s first paragraph. June 23, 2031 Art came by with the kids today. They\u27ll be here for a week or so. It\u27s nice to have family that cares enough to spend their vacation with an old guy like me. Now I know how my grandmother must have felt when my parents brought Paul, Annette and myself to visit, except we saw her every day

Att existera i ögonblicket -Töj, en textil sittmöbel

This project started with an exploration of geometric shapes and textile materials. It resulted in a chair made out of textile bands with different elasticity. The surface for sitting is flat when the chair is not used, and changes in the moment you sit down and gets a new shape. A piece of furniture that adapts to each individual. The chair emphasizes the important relationship between human and product as the person using it becomes a part of the chair for a moment