On the zeros of a minimal realization

AbstractIn an earlier work, the authors have introduced a coordinate-free, module-theoretic definition of zeros for the transfer function G(s) of a linear multivariable system (A,B,C). The first contribution of this paper is the construction of an explicit k[z]-module isomorphism from that zero module, Z(G), to V∗/R∗, where V∗ is the supremal (A,B)-invariant subspace contained in kerC and R∗ is the supremal (A,B)-controllable subspace contained in kerC, and where (A,B,C) constitutes a minimal realization of G(s). The isomorphism is developed from an exact commutative diagram of k-vector spaces. The second contribution is the introduction of a zero-signal generator and the establishment of a relation between this generator and the classic notion of blocked signal transmissions

Faculty Recital: Timothy Bostwick, Baritone; Elizabeth Thompson, Voice; Michael McAndrew, Pianist; March 21, 2023

Center for the Performing ArtsMarch 21, 2023Tuesday Evening7:00 p.m

On the zeros and poles of a transfer function

AbstractThe poles and zeros of a linear transfer function can be studied by means of the pole module and the transmission zero module. These algebraic constructions yield finite dimensional vector spaces whose dimensions are the number of poles and the number of multivariable zeros of the transfer function. In addition, these spaces carry the structure of a module over a ring of polynomials, which gives them a dynamical or state space structure. The analogous theory at infinity gives finite dimensional spaces which are modules over the valuation ring of proper rational functions. Following ideas of Wedderburn and Forney, we introduce new finite dimensional vector spaces which measure generic zeros which arise when a transfer function fails to be injective or surjective. A new exact sequence relates the global spaces of zeros, the global spaces of poles, and the new generic zero spaces. This sequence gives a structural result which can be summarized as follows: “The number of zeros of any transfer function is equal to the number of poles (when everything is counted appropriately).” The same result unifies and extends a number of results of geometric control theory by relating global poles and zeros of general (possibly improper) transfer functions to controlled invariant and controllability subspaces (including such spaces at infinity)

Long-Term Outcomes for Patients with Prostate Cancer Having Intermediate and High-Risk Disease, Treated with Combination External Beam Irradiation and Brachytherapy

Background. Perception remains that brachytherapy-based regimens are inappropriate for patients having increased risk of extracapsular extension (ECE). Methods. 321 consecutive intermediate and high-risk disease patients were treated between 1/92 and 2/97 by one author (M. Dattoli) and stratified by NCCN guidelines. 157 had intermediate-risk; 164 had high-risk disease. All were treated using the combination EBRT/brachytherapy ± hormones. Biochemical failure was defined using PSA >0.2 and nadir +2 at last followup. Nonfailing patients followup was median 10.5 years. Both biochemical data and original biopsy slides were independently rereviewed at an outside institution. Results. Overall actuarial freedom from biochemical progression at 16 years was 82% (89% intermediate, 74% high-risk) with failure predictors: Gleason score (P = .01) and PSA (P = .03). Hormonal therapy did not affect failure rates (P = .14). Conclusion. This study helps to strengthen the rationale for brachytherapy-based regimens as being both durable and desirable treatment options for such patients. Prospective studies are justified to confirm these positive results

Mechanical Impact Performance of Additively Manufactured Negative Stiffness Honeycombs

Negative stiffness honeycombs materials are comprised of negative stiffness beams arranged in ordered arrays. They are capable of providing isolation from impacts and returning to their initial shape. Previous research by the authors focused on the behavior of negative stiffness honeycombs to quasi-static loading conditions. This paper investigates the behavior of similar negative stiffness honeycombs under impact. The construction of an impact testing rig for the experimental evaluation of negative stiffness honeycombs is discussed. Experimental results from impact tests performed on honeycomb prototypes manufactured using selective laser sintering (SLS) in nylon 11 material are presented and compared with analytical and finite element predictions as well as quasi-static test results.Mechanical Engineerin

Implementation of a Novel Social-Emotional Learning Program to Advance Integration of Wellness in Education Practice

Social-emotional learning (SEL) programs aim to enhance emotional intelligence by teaching problem solving, self-awareness, self-management, social awareness, and relationship building skills. SEL interventions have been shown to improve quality of life and wellbeing, increasingly important outcomes in the wake of the staggering effects of the COVID-19 crisis on mental health. HappiGenius is a novel SEL program with the addition of mindful attention and self-compassion. We hypothesized HappiGenius would improve positive emotions, self-compassion, attention, mindful self-awareness, and social skills in a group of students. This observational cohort study took place at a diverse elementary school in a midsize midwestern city and included 48 students across four 3rd grade classrooms. HappiGenius included 12 lessons, approximately 45 minutes each, delivered twice a week for 6 weeks. The results demonstrated increased frequency of positive emotions (Positive Affect Scale for Children, median increase from 3.57 to 4.04, p=0.04) and improved self-compassion (Self-Compassion Scale for Children, 3.04 to 3.25, p=0.0094). Changes in student reported mindful self-awareness (Mindful Attentive Awareness Scale for Children, 3.27 to 3.47, p=0.56) and teacher ratings of hyperactivity/ inattention (Strengths and Difficulties Questionnaire, 3.0 to 2.5, p=0.26) were not statistically significant. Strong positive changes were observed in other teacher-reported behavioral outcomes on the Strengths and Difficulties Questionnaire, including total difficulties (6.0 to 3.5, p=0.0004) and prosocial skills (9.0 to 10.0,

Keepers\u27 from Remote/Hybrid Teaching: What I\u27ve Learned that I will Incorporate into F2F Classes

Faculty presenters share tools and techniques used during remote/hybrid teaching they plan to incorporate into face-to-face courses post-pandemic

Pnictogens Allotropy and Phase Transformation during van der Waals Growth

Pnictogens have multiple allotropic forms resulting from their ns2 np3 valence electronic configuration, making them the only elemental materials to crystallize in layered van der Waals (vdW) and quasi-vdW structures throughout the group. Light group VA elements are found in the layered orthorhombic A17 phase such as black phosphorus, and can transition to the layered rhombohedral A7 phase at high pressure. On the other hand, bulk heavier elements are only stable in the A7 phase. Herein, we demonstrate that these two phases not only co-exist during the vdW growth of antimony on weakly interacting surfaces, but also undertake a spontaneous transformation from the A17 phase to the thermodynamically stable A7 phase. This metastability of the A17 phase is revealed by real-time studies unraveling its thickness-driven transition to the A7 phase and the concomitant evolution of its electronic properties. At a critical thickness of ~4 nm, A17 antimony undergoes a diffusionless shuffle transition from AB to AA stacked alpha-antimonene followed by a gradual relaxation to the A7 bulk-like phase. Furthermore, the electronic structure of this intermediate phase is found to be determined by surface self-passivation and the associated competition between A7- and A17-like bonding in the bulk. These results highlight the critical role of the atomic structure and interfacial interactions in shaping the stability and electronic characteristics of vdW layered materials, thus enabling a new degree of freedom to engineer their properties using scalable processes