Range inclusion and the UUP-property

AbstractLet A and B be positive operators on a complex Hilbert space H. The parallel sum A: B of A and B is the strong operator limit (as ε ↓ 0) of the net (A + ε)(A + B + 2ε)−1 (B + ε). If this net converges in norm, then (following Green and Morley), we say that the pair (A, B) is of class UUP. It is known that if Range A ⊆ Range(A + B), then (A, B) is a UUP-pair. In this work we establish that Range(A) ⊆ Range(A + B) if and only Range(B) ⊆ Range(A + B). We also show that if AB + BA + B2 ⩾ 0, then Range A ⊆ Range(A + αB) for all real α with α ⩾ 1 and that if AB + BA ⩾ 0, then Range (A) ⊆ Range(A + αB) for all α ⩾ 0. This implies several previously known results, e.g., that if AB = BA, then (A, B) is a UUP-pair. Finally we establish a number of other results which relate the class UUP to range inclusion

We Need New Myths: Art-making in the Pandemic and What Follows

Writer and professor Laleh Khadivi in We Need New Myths juxtaposes the stillness born from shelter-in-place orders with the constant motion of migrants around the world—seeking asylum, a new life, and survival

Range Inclusion and Operator Equations

AbstractLetAandDbe positive operators on a complex Hilbert spaceH. In this work we show that the operator equationlDX+X*A=A(l>0) has a unique solutionClsatisfying certain conditions, if there exists a positive operatorBsuch thatAB+(D−B)A≥0. This implies several previously known results in special cases on this class of operator equations. Also, along with some definitions, a counterexample to a previous conjecture will be given

Experimental and Numerical Study of Flow Structures Associated with Low Aspect Ratio Elliptical Cavities

The flow regimes associated with a 2:1 aspect ratio, elliptical planform cavity in a turbulent flat plate boundary layer have been systematically examined for various depth/width ratios (0.1 to 1.0) and yaw angles (0° to 90°), using a combination of wind tunnel experiments (involving Particle Image Velocimetry and helium bubble visualization) and Computational Fluid Dynamics (CFD) simulations (employing three- dimensional steady calculations with the Reynolds Stress model turbulence closure). Satisfactory agreement has been found between the results using the two methods, indicating that the steady numerical simulations can be a cost-effective tool to predict the mean flow features. The flow has been found to be highly dependent on yaw angle and cavity depth. For each of the three broad flow categories specified according to yaw angle, which include the symmetric flow regime (yaw angle = 0°), the straight vortex regime (yaw angle = 90°) and the asymmetric flow regime (15° ≤ yaw angle ≤ 60°) different regimes are found to exist, depending on cavity depth. For each combination of yaw angle and depth, the flow has been analyzed through investigation of shear layer parameters, the three-dimensional vortex structure, pressure distribution and drag, wake flow, and vortex oscillations. While the elliptical cavity flows have been found to have some similarities with those of nominally two-dimensional and rectangular cavities, the three-dimensional effects due to the low aspect ratio and curvature of the walls give rise to features exclusive to low aspect ratio elliptical cavities, including formation of cellular structures at intermediate depths and unique vortex structures within and downstream of the cavity. The three-dimensional flow structure of the flow is most pronounced in the asymmetric regimes with large yaw angles (45° and 60°). The dominant feature in this regime is the formation of a trailing vortex that is associated with high drag and flow oscillations within the cavity

The viewpoints of interns and clerkship students about community medicine course

Introduction. Community-Oriented Medical Education (COME), compared to traditional education in hospitals is considered a new educational approach in the school of medicine. This study was designed to determine the quality of education during the Clerkship and internship in community medicine course in Shahrekord Medical University. Methods. In a descriptive cross-sectional study, 41 clerckship students and 14 interns selected by convenience sampling method were studied. The data was collected by a valid and reliable questionnaire and analyzed by descriptive statistics using SPSS software. Results. Eighty percent of Clerkship students and less than 50% of interns were satisfied with the course plan, the content of the workshop, the presence of faculty members and answering Students’ questions. In addition, more than 80% of Clerkship students and less than 42% of interns revealed their satisfaction from teaching health management such as collecting data, data analysis, prioritizing the problems, and planning and evaluation. Teaching specific programs such as vaccination, family planning and so on was supported by more than 85% of clerkship students, and almost 97.5% of them were satisfied with teaching situational analysis of health care system. Conclusion. Considering community oriented education approach in medical schools of the world and spending one month community medicine as an obligatory course in all medical schools of Iran, the revision of community medicine course seems necessary