Supersonic axial-force characteristics of a rectangular-box cavity with various length-to-depth ratios in a flat plate

A wind-tunnel investigation has been conducted at Mach numbers of 1.50, 2.16, and 2.86 to obtain axial-force data on a metric rectangular-box cavity with various length-to-depth ratios. The model was tested at angles of attack from -4 deg to -2 deg. The results are summarized to show variations in cavity axial-force coefficient for deep- and shallow-cavity configurations with detached and attached cavity flow fields, respectively. The results of the investigation indicate that for a wide range of cavity lengths and depths, good correlations of the cavity axial-force coefficients (based on cavity rear-face area) are obtained when these coefficients are plotted as a function of cavity length-to-depth ratio. Abrupt increases in the cavity axial-force coefficients at an angle of attack of 0 deg. reflect the transition from an open (detached) cavity flow field to a closed (attached) cavity flow field. Cavity length-to-depth ratio is the dominant factor affecting the switching of the cavity flow field from one type to the other. The type of cavity flow field (open or closed) is not dependent on the test angles of attack except near the critical value of length-to-depth ratio

Primitive Words, Free Factors and Measure Preservation

Let F_k be the free group on k generators. A word w \in F_k is called primitive if it belongs to some basis of F_k. We investigate two criteria for primitivity, and consider more generally, subgroups of F_k which are free factors. The first criterion is graph-theoretic and uses Stallings core graphs: given subgroups of finite rank H \le J \le F_k we present a simple procedure to determine whether H is a free factor of J. This yields, in particular, a procedure to determine whether a given element in F_k is primitive. Again let w \in F_k and consider the word map w:G x G x ... x G \to G (from the direct product of k copies of G to G), where G is an arbitrary finite group. We call w measure preserving if given uniform measure on G x G x ... x G, w induces uniform measure on G (for every finite G). This is the second criterion we investigate: it is not hard to see that primitivity implies measure preservation and it was conjectured that the two properties are equivalent. Our combinatorial approach to primitivity allows us to make progress on this problem and in particular prove the conjecture for k=2. It was asked whether the primitive elements of F_k form a closed set in the profinite topology of free groups. Our results provide a positive answer for F_2.Comment: This is a unified version of two manuscripts: "On Primitive words I: A New Algorithm", and "On Primitive Words II: Measure Preservation". 42 pages, 14 figures. Some parts of the paper reorganized towards publication in the Israel J. of Mat

Delayed commutation in quantum computer networks

In the same way that classical computer networks connect and enhance the capabilities of classical computers, quantum networks can combine the advantages of quantum information and communications. We propose a non-classical network element, a delayed commutation switch, that can solve the problem of switching time in packet switching networks. With the help of some local ancillary qubits and superdense codes we can route the information after part of it has left the network node.Comment: 4 pages. 4 figures. Preliminar versio

Post- and peritraumatic stress in disaster survivors: An explorative study about the influence of individual and event characteristics across different types of disasters

Background: Examination of existing research on posttraumatic adjustment after disasters suggests that survivors’ posttraumatic stress levels might be better understood by investigating the influence of the characteristics of the event experienced on how people thought and felt, during the event as well as afterwards. Objective: To compare survivors’ perceived post- and peritraumatic emotional and cognitive reactions across different types of disasters. Additionally, to investigate individual and event characteristics. Design: In a European multi-centre study, 102 survivors of different disasters terror attack, flood, fire and collapse of a building were interviewed about their responses during the event. Survivors’ perceived posttraumatic stress levels were assessed with the Impact of Event Scale-Revised (IES-R). Peritraumatic emotional stress and risk perception were rated retrospectively. Influences of individual characteristics, such as socio-demographic data, and event characteristics, such as time and exposure factors, on post- and peritraumatic outcomes were analyzed. Results: Levels of reported post- and peritraumatic outcomes differed significantly between types of disasters. Type of disaster was a significant predictor of all three outcome variables but the factors gender, education, time since event, injuries and fatalities were only significant for certain outcomes. Conclusion: Results support the hypothesis that there are differences in perceived post- and peritraumatic emotional and cognitive reactions after experiencing different types of disasters. However, it should be noted that these findings were not only explained by the type of disaster itself but also by individual and event characteristics. As the study followed an explorative approach, further research paths are discussed to better understand the relationships between variables

Shadows and traces in bicategories

Traces in symmetric monoidal categories are well-known and have many applications; for instance, their functoriality directly implies the Lefschetz fixed point theorem. However, for some applications, such as generalizations of the Lefschetz theorem, one needs "noncommutative" traces, such as the Hattori-Stallings trace for modules over noncommutative rings. In this paper we study a generalization of the symmetric monoidal trace which applies to noncommutative situations; its context is a bicategory equipped with an extra structure called a "shadow." In particular, we prove its functoriality and 2-functoriality, which are essential to its applications in fixed-point theory. Throughout we make use of an appropriate "cylindrical" type of string diagram, which we justify formally in an appendix.Comment: 46 pages; v2: reorganized and shortened, added proof for cylindrical string diagrams; v3: final version, to appear in JHR

Cosmic censorship of smooth structures

It is observed that on many 4-manifolds there is a unique smooth structure underlying a globally hyperbolic Lorentz metric. For instance, every contractible smooth 4-manifold admitting a globally hyperbolic Lorentz metric is diffeomorphic to the standard $\R^4$. Similarly, a smooth 4-manifold homeomorphic to the product of a closed oriented 3-manifold $N$ and $\R$ and admitting a globally hyperbolic Lorentz metric is in fact diffeomorphic to $N\times \R$. Thus one may speak of a censorship imposed by the global hyperbolicty assumption on the possible smooth structures on $(3+1)$-dimensional spacetimes.Comment: 5 pages; V.2 - title changed, minor edits, references adde

Free subgroups of one-relator relative presentations

Suppose that G is a nontrivial torsion-free group and w is a word over the alphabet G\cup\{x_1^{\pm1},...,x_n^{\pm1}\}. It is proved that for n\ge2 the group \~G= always contains a nonabelian free subgroup. For n=1 the question about the existence of nonabelian free subgroups in \~G is answered completely in the unimodular case (i.e., when the exponent sum of x_1 in w is one). Some generalisations of these results are discussed.Comment: V3: A small correction in the last phrase of the proof of Theorem 1. 4 page

Growth Mindset: Associations with Apprehension, Self-Perceived Competence, and Beliefs about Public Speaking

The relationships among growth mindset for public speaking (i.e., the implicit theory that public speaking abilities can be developed and improved) and beliefs about the nature of public speaking, public speaking apprehension (PSA), and self-perceived public speaking competence (SPPSC) were investigated in intensive and traditional formats of a general education public speaking course. In general, growth mindset was associated with lower PSA, higher SPPSC, and more sophisticated beliefs about public speaking. Mindset remained somewhat stable, PSA significantly decreased, and SPPSC significantly increased from the beginning to the end of the course. More sophisticated beliefs about public speaking as an expressive, transformational, and audience-centric endeavor also tended to increase. However, there were several important differences between intensive and traditional formats. In particular, changes in the intensive format were more consistent across variables and had larger effect sizes