Taut contact hyperbolas on three-manifolds

In this paper, we introduce the notion of taut contact hyperbola on three-manifolds. It is the hyperbolic analogue of the taut contact circle notion introduced by Geiges and Gonzalo (Invent. Math., 121: 147–209, 1995), (J. Differ. Geom., 46: 236–286, 1997). Then, we characterize and study this notion, exhibiting several examples, and emphasizing differences and analogies between taut contact hyperbolas and taut contact circles. Moreover, we show that taut contact hyperbolas are related to some classic notions existing in the literature. In particular, it is related to the notion of conformally Anosov flow, to the critical point condition for the Chern–Hamilton energy functional and to the generalized Finsler structures introduced by R. Bryant. Moreover, taut contact hyperbolas are related to the bi-contact metric structures introduced in D. Perrone (Ann. Global Anal. Geom., 52: 213–235, 2017).

How Many Total Points Should Your Course Have?

Background Instructors often use a point-based system for grading students (e.g., 100 or 1000 total points). This system can impact student outcomes. Objective The purpose of this research was to examine the implications of different point value courses for student emotions, perceptions of courses, and classroom performance. Method The lab-based study used an experimental design to gather student responses to a hypothetical course with one of three potential total point values (100, 1,000, or 100,000 points). The classroom-based study examined student responses to different point values in 12 actual courses in which students were enrolled (with either 100 or 1000 total points). Results In the lab-based study, courses with greater total point values (i.e., 1000 and 100,000) had greater emotional impact than a course with 100 total points. Participants in these conditions also preferred a course that featured a pass/fail scheme. In the classroom-based study, students in the 100-point condition (vs. 1000-point condition) missed more assignments, and as a consequence, performed more poorly in their course. Conclusion Higher total point values in courses may have a more significant impact on students’ emotions, and as a consequence, they may miss less work, and perform better in the course overall.

Fractional linear maps in general relativity and quantum mechanics

This paper studies the nature of fractional linear transformations in a general relativity context as well as in a quantum theoretical framework. Two features are found to deserve special attention: the first is the possibility of separating the limit-point condition at infinity into loxodromic, hyperbolic, parabolic and elliptic cases. This is useful in a context in which one wants to look for a correspondence between essentially self-adjoint spherically symmetric Hamiltonians of quantum physics and the theory of Bondi–Metzner–Sachs transformations in general relativity. The analogy therefore arising suggests that further investigations might be performed for a theory in which the role of fractional linear maps is viewed as a bridge between the quantum theory and general relativity. The second aspect to point out is the possibility of interpreting the limit-point condition at both ends of the positive real line, for a second-order singular differential operator, which occurs frequently in applied quantum mechanics, as the limiting procedure arising from a very particular Kleinian group which is the hyperbolic cyclic group. In this framework, this work finds that a consistent system of equations can be derived and studied. Hence, one is led to consider the entire transcendental functions, from which it is possible to construct a fundamental system of solutions of a second-order differential equation with singular behavior at both ends of the positive real line, which in turn satisfy the limit-point conditions. Further developments in this direction might also be obtained by constructing a fundamental system of solutions and then deriving the differential equation whose solutions are the independent system first obtained. This guarantees two important properties at the same time: the essential self-adjointness of a second-order differential operator and the existence of a conserved quantity which is an automorphic function for the cyclic group chosen.

CLICKBAIT HEADLINES THROUGH THE PRISM OF SPEECH ACTS THEORY

Statement of the problem. The article discusses the peculiarities of YouTube video clickbait headlines. Some video makers are profit-conscious and deliberately headline their videos using eye-catching words that often have nothing to do with the real content in order to maximize the number of clicking the links. Such headlines aim at deceiving the recipients as for the content of the text or video, affecting their perception, attracting their attention and making them watch the video after all. Such headlines are known as clickbait, for they trap the reader or viewer with deliberately sensational or incomplete information. In this case promotional impact purposefully overrides the nominative function resulting in the peculiarity of the clickbait. The form of speech acts, including stylistic, lexical, syntactical, spelling and punctuation features, makes them stand out of other texts corpus. Particular attention is paid to discerning them as directive illocutionary acts and to proving that they meet all Searle’s requirements for such phenomena including illocutionary point, condition of sincerity, direction of fit. The purpose of the article is to analyze YouTube video clickbait headlines as directive illocutionary acts. Research methodology. The main method of research is qualitative content-analysis that involves revealing a specific meaning expressed with a clickbait headline as a significant element of a media text, as well as a communicative-pragmatic analysis aimed at identifying directive illocutionary force. Research results. Communicative success of clickbait headlines correlates with the “curiosity gap” manifesting itself in recipient’s information lacuna. The recipient should be able to bridge the former to avoid excessive cognitive attempts, clickbait headlines being a tool for that. Conclusions. Clickbait headlines analysis results in identifying them as directive illocutionary acts, for they foreground the perlocutionary function deliberately neglecting nominative one, thus manipulating an information recipient.

Changes in Spinal-Reflex Excitability during Static Stretch and/or Explosive Contraction

To examine individual or combined effects of static stretch and explosive contraction on quadriceps spinal-reflex excitability (the peak Hoffmann’s reflex normalized by the peak motor-response) and the latency times of the Hoffmann’s reflex and motor-response. Fourteen healthy young males randomly experienced four conditions (stretch, contraction, stretch + contraction, and control—no intervention). For the stretch condition, three sets of a 30 s hold using the modified Thomas test on each leg were performed. For the contraction condition, three trials of maximal countermovement vertical jump were performed. Quadriceps spinal-reflex excitability and the latent period of each value on the right leg were compared at pre- and post-condition. All measurement values across conditions were not changed at any time point (condition × time) in spinal-reflex excitability (F6,143 = 1.10, p = 0.36), Hoffmann’s reflex latency (F6,143 = 0.45, p = 0.84), motor-response latency (F6,143 = 0.37, p = 0.90), and vertical jump heights (F2,65 = 1.82, p = 0.17). A statistical trend was observed in the contraction condition that spinal-reflex excitability was increased by 42% (effect size: 0.63). Neither static stretch nor explosive contraction changed the quadriceps spinal-reflex excitability, latency of Hoffmann’s reflex, and motor-response. Since our stretch protocol did not affect jumping performance and our contraction protocol induced the post-activation potentiation effect, either protocol could be used as pre-exercise activity.

Investigation of Flow Separation Characteristics in a Pump as Turbines Impeller Under the Best Efficiency Point Condition

The impeller, which is the main energy conversion component of a pump as turbine (PAT), is designed for pumping mode, and its internal flow characteristics are quite complicated even at the best efficiency point (BEP) of the turbine mode. This study aims to investigate the flow separation characteristics in a PAT impeller under the BEP condition by numerical method. The hydraulic performance and transient pressure characteristics of PAT predicted numerically were verified through experimentation. The surface friction lines and flow topological structure were applied to diagnose the flow separation at the surface of the blade. The relationship between flow topological structure and vortex in the impeller and static pressure at the blade were analyzed. Analysis results show that the backflow and open flow separation are observed significantly in the leading region and near the shroud of the trailing region of suction side. The passage vortex always appears near the spiral node. The saddle point and spiral node correspond to the peak position of adverse pressure and the lowest position between two peak values of the static pressure of the blade, respectively. The inflow conditions of blade and shape of the trailing edge significantly influence the flow separations in the impeller.

Numerical implementation of solving a control problem for loaded differential equations with multi-point condition

A linear boundary value problem with a parameter for loaded differential equations with multi-point condition is considered. The method of parameterization is used for solving the considered problem. We offer an algorithm for solving a control problem for the system of loaded differential equations with multi-point condition. The linear boundary value problem with a parameter for loaded differential equations with multi-point condition by introducing additional parameters at the partition points is reduced to equivalent boundary value problem with parameters. The equivalent boundary value problem with parameters consists of the Cauchy problem for the system of ordinary differential equations with parameters, multi-point condition, and continuity conditions. The solution of the Cauchy problem for the system of ordinary differential equations with parameters is constructed using the fundamental matrix of differential equation. The system of linear algebraic equations concerning the parameters is composed by substituting the values of the corresponding points in the built solutions to the multi-point condition and continuity conditions. The numerical method for finding the solution of the problem is suggested, which based on the solving the constructed system and solving Cauchy problem on the subintervals by Adams method and Bulirsch-Stoer method. The proposed numerical implementation is illustrated by example.

Halpern–Ishikawa type iterative schemes for approximating fixed points of multi-valued non-self mappings

Let C be a nonempty closed convex subset of a real Hilbert space H and $$T: C\rightarrow CB(H)$$ T : C → C B ( H ) be a multi-valued Lipschitz pseudocontractive nonself mapping. A Halpern–Ishikawa type iterative scheme is constructed and a strong convergence result of this scheme to a fixed point of T is proved under appropriate conditions. Moreover, an iterative method for approximating a fixed point of a k-strictly pseudocontractive mapping $$T: C\rightarrow Prox(H)$$ T : C → P r o x ( H ) is constructed and a strong convergence of the method is obtained without end point condition. The results obtained in this paper improve and extend known results in the literature.