Topology and Factorization of Polynomials

For any polynomial $P \in \mathbb{C}[X_1,X_2,...,X_n]$, we describe a $\mathbb{C}$-vector space $F(P)$ of solutions of a linear system of equations coming from some algebraic partial differential equations such that the dimension of $F(P)$ is the number of irreducible factors of $P$. Moreover, the knowledge of $F(P)$ gives a complete factorization of the polynomial $P$ by taking gcd's. This generalizes previous results by Ruppert and Gao in the case $n=2$.Comment: Accepted in Mathematica Scandinavica. 8 page

The hybrid and dualistic identity of full-time non-tenure-track faculty

Colleges and universities rely on full-time non-tenure-track (FTNT) faculty to achieve their teaching, research, and service missions. These faculty are deemed both symptomatic of and partly responsible for academe's shortcomings. The ascriptions, however, are made with little attention to the faculty themselves or to their consequences for FTNT faculty. Through analysis of interview data of university faculty, the authors present and explain FTNT faculty self-representations of professional and occupational identity. Assumptions drawn from institutional and professional theory contextualize the research, and narrative analysis infuses the application of the framework of cultural identity theory. These FTNT faculty are found to possess hybrid and dualistic identities. Their work and roles are a hybrid and contain some elements of a profession and some of a "job." Their identity is dualistic because as teachers, they express satisfaction, whereas as members of the professoriate, they articulate restricted self-determination and self-esteem. This troubled and indistinct view of self-as-professional is problematic both for FTNT faculty as they go about their daily work and for their institutions, which are in no small part responsible for the uncertain conditions and identities of FTNT faculty. © 2011 SAGE Publications

Active sensor fault tolerant output feedback tracking control for wind turbine systems via T-S model

This paper presents a new approach to active sensor fault tolerant tracking control (FTTC) for offshore wind turbine (OWT) described via Takagi–Sugeno (T–S) multiple models. The FTTC strategy is designed in such way that aims to maintain nominal wind turbine controller without any change in both fault and fault-free cases. This is achieved by inserting T–S proportional state estimators augmented with proportional and integral feedback (PPI) fault estimators to be capable to estimate different generators and rotor speed sensors fault for compensation purposes. Due to the dependency of the FTTC strategy on the fault estimation the designed observer has the capability to estimate a wide range of time varying fault signals. Moreover, the robustness of the observer against the difference between the anemometer wind speed measurement and the immeasurable effective wind speed signal has been taken into account. The corrected measurements fed to a T–S fuzzy dynamic output feedback controller (TSDOFC) designed to track the desired trajectory. The stability proof with H∞ performance and D-stability constraints is formulated as a Linear Matrix Inequality (LMI) problem. The strategy is illustrated using a non-linear benchmark system model of a wind turbine offered within a competition led by the companies Mathworks and KK-Electronic

A vision-guided parallel parking system for a mobile robot using approximate policy iteration

Reinforcement Learning (RL) methods enable autonomous robots to learn skills from scratch by interacting with the environment. However, reinforcement learning can be very time consuming. This paper focuses on accelerating the reinforcement learning process on a mobile robot in an unknown environment. The presented algorithm is based on approximate policy iteration with a continuous state space and a fixed number of actions. The action-value function is represented by a weighted combination of basis functions. Furthermore, a complexity analysis is provided to show that the implemented approach is guaranteed to converge on an optimal policy with less computational time. A parallel parking task is selected for testing purposes. In the experiments, the efficiency of the proposed approach is demonstrated and analyzed through a set of simulated and real robot experiments, with comparison drawn from two well known algorithms (Dyna-Q and Q-learning)

55-year-old Woman with Headache, Vomiting, and Visual Disturbance

Case Presentation: A 55-year-old woman with a past medical history of hypertension, hyperlipidemia, and iron deficiency anemia presented to the emergency department with three days of headache, nausea, vomiting, and visual changes. Her vital signs were within normal limits. She was noted to have a left cranial nerve six palsy on exam.Results: Her laboratory testing revealed leukocytosis, hyponatremia, and hypokalemia. A non-contrast computed tomography scan of the head revealed an enlarged sella turcica and pituitary gland with hemorrhage and deviation of the optic chiasm.Conclusion: Her symptoms improved and she was discharged from the hospital in stable condition