Riccati equations and normalized coprime factorizations for strongly stabilizable infinite-dimensional systems

The first part of the paper concerns the existence of strongly stabilizing solutions to the standard algebraic Riccati equation for a class of infinite-dimensional systems of the form Σ(A,B,S−1/2B*,D), where A is dissipative and all the other operators are bounded. These systems are not exponentially stabilizable and so the standard theory is not applicable. The second part uses the Riccati equation results to give formulas for normalized coprime factorizations over H∞ for positive real transfer functions of the form D+S−1/2B*(author−A)−1,B

Mathematics as a Language

During my student teaching process, I observed a separation between my students’ procedural knowledge of mathematics, and their mathematical reasoning. I attempted to bridge this gap by conducting research on the role of academic language in the classroom. Academic language is a way to communicate ideas, concepts, and higher thinking processes, but it is used so that students may acquire a greater insight into the material (Gottlieb & Ernst-Slavit, 2013). I specifically discuss how the incorporation of academic language affects student learning as well as possible implementations of academic language in the classroom. I constructed a series of lesson plans that focused on students engaging in mathematics through language and I constructed quizzes that focused on mathematical reasoning and justifying results. I content analyzed the quizzes, department tests, and review assignments using both qualitative and quantitative approaches. The results of my analysis demonstrate that the incorporation of academic language into the classroom is beneficial for the students because it forces the students to delve deeply into the mathematics and to find meaning in their work. My results also support that incorporating academic language is beneficial for student learning because it lends more opportunity for teachers to understand student thinking and a result, easily spot misconceptions about topics

Eigenvalues and Stability Properties of Multiplication Operators and Multiplication Semigroups

We investigate uniform, strong, weak and almost weak stability of multiplication semigroups on Banach space valued $L^p$-spaces. We show that, under certain conditions, these properties can be characterized by analogous ones of the pointwise semigroups. Using techniques from selector theory, we prove a spectral mapping theorem for the point spectra of the pointwise and global semigroups and apply this as a major tool for determining almost weak stability

Symmetries shape the current in ratchets induced by a bi-harmonic force

Equations describing the evolution of particles, solitons, or localized structures, driven by a zero-average, periodic, external force, and invariant under time reversal and a half-period time shift, exhibit a ratchet current when the driving force breaks these symmetries. The bi-harmonic force $f(t)=\epsilon_1\cos(q \omega t+\phi_1)+\epsilon_2\cos(p\omega t+\phi_2)$ does it for almost any choice of $\phi_{1}$ and $\phi_{2}$, provided $p$ and $q$ are two co-prime integers such that $p+q$ is odd. It has been widely observed, in experiments in Josephson-junctions, photonic crystals, etc., as well as in simulations, that the ratchet current induced by this force has the shape $v\propto\epsilon_1^p\epsilon_2^q\cos(p \phi_{1} - q \phi_{2} + \theta_0)$ for small amplitudes, where $\theta_0$ depends on the damping ($\theta_0=\pi/2$ if there is no damping, and $\theta_0=0$ for overdamped systems). We rigorously prove that this precise shape can be obtained solely from the broken symmetries of the system and is independent of the details of the equation describing the system.Comment: 4 page

Comparative assessment of young learners' foreign language competence in three Eastern European countries

This paper concerns teacher practices in, and beliefs about, the assessment of young learners' progress in English in three Eastern European countries (Slovenia, Croatia, and the Czech Republic). The central part of the paper focuses on an international project involving empirical research into assessment of young learners' foreign language competence in Slovenia, Croatia and the Czech Republic. With the help of an adapted questionnaire, we collected data from a non-random sample of primary and foreign language teachers who teach foreign languages at the primary level in these countries. The research shows that English as a foreign language is taught mostly by young teachers either primary specialists or foreign language teachers. These teachers most frequently use oral assessment/interviews or self-developed tests. Other more authentic types of assessment, such as language portfolios, are rarely used. The teachers most frequently assess speaking and listening skills, and they use assessment involving vocabulary the most frequently of all. However, there are significant differences in practice among the three countries

Ratchet effect on a relativistic particle driven by external forces

We study the ratchet effect of a damped relativistic particle driven by both asymmetric temporal bi-harmonic and time-periodic piecewise constant forces. This system can be formally solved for any external force, providing the ratchet velocity as a non-linear functional of the driving force. This allows us to explicitly illustrate the functional Taylor expansion formalism recently proposed for this kind of systems. The Taylor expansion reveals particularly useful to obtain the shape of the current when the force is periodic, piecewise constant. We also illustrate the somewhat counterintuitive effect that introducing damping may induce a ratchet effect. When the force is symmetric under time-reversal and the system is undamped, under symmetry principles no ratchet effect is possible. In this situation increasing damping generates a ratchet current which, upon increasing the damping coefficient eventually reaches a maximum and decreases toward zero. We argue that this effect is not specific of this example and should appear in any ratchet system with tunable damping driven by a time-reversible external force.Comment: 1 figur

Berberine and Coptidis Rhizoma as novel antineoplastic agents: A review of traditional use and biomedical investigations

Ethnopharmacological relevance: Coptidis Rhizoma (Huanglian) and its major component, berberine, have drawn extensive attention toward their antineoplastic effects in the recent years. The antineoplastic effects are related to the Chinese Medicine (CM) properties of Huangliang in treating diseases by removing damp-heat and purging fire and counteracting toxicity. Aim of the review: To trace the long history of the traditional use of Huanglian from folk medicines, especially from Chinese medicine, to recent pharmacological studies of Huanglian and berberine, with an emphasis on their antineoplastic effects and the promise as novel antineoplastic agents. Methods: A total of seven databases were extensively searched for literature research. The terms and keywords for searching included Huanglian, berberine, Coptis, Coptidis Rhizoma, anticancer, anti-invasion, antimatastasis and mechanism. The papers including ours with studies on anticancer and mechanism, pharmacology and toxicology of Huanglian and/or berberine were focused. Results: In view of traditional use, the anticancer effects of Huanglian can be ascribed to its CM trait by removing damp-heat, fire and toxicity. From modern biomedical studies, anticancer effects have been demonstrated in both Huanglian and berberine. The underlying molecular mechanisms involve cell-cycle arrest, apoptosis induction and anti-inflammation. Berberine is an essential anticancer compound in Huanglian. In some studies, the use of Huanglian was shown to be more effective and beneficial than the use of berberine alone. The presence of other protoberberine-type alkaloids in Huanglian might give synergistic effects for the anticancer effects. Berberine also demonstrates effects of antiangiogenesis, anti-invasion and anti-metastasis in some cancer cell lines, however, more investigations are required to unravel the underlying mechanisms involved. Conclusions: The modern evidences of treating cancer with Huanglian and berberine have a strong linkage with traditional concept and rules of using Huanglian in CM practice. As anticancer candidates with low toxicity, berberine and its altered structure, as well as Huanglian and its formulae, will attract scientists to pursue the potential anticancer effects and the mechanisms by using technologies of genomics, proteomics and other advanced approaches. On the other hand, relatively few in vivo studies have been conducted on anticancer effects of Huanglian and berberine. The clinical application of berberine or Huanglian as novel cancer therapeutic agents requires in vivo validations and further investigations of their anticancer mechanisms. © 2009 Elsevier Ireland Ltd. All rights reserved.published_or_final_versio

The usefulness of confusion, urea, respiratory rate, and shock index or adjusted shock index criteria in predicting combined mortality and/or ICU admission compared to CURB-65 in community-acquired pneumonia

Peer reviewedPublisher PD