On the Three-Cusped Hypocycloid

1945 ◽  
Vol 29 (284) ◽  
pp. 66-67
Author(s):  
J. Hadamard

I have had a recent opportunity to recall an early article (1884) which I wrote on the three-cusped hypocycloid. My starting point was the property that the asymptotes of any pencil of equilateral hyperbolas envelop such a hypocycloid. I proved this analytically in the aforesaid article ; perhaps there is some interest in finding geometrical reasons for it. Principles on pencils of conies are well known. According to these principles : (1) The polars of any point a with respect to the various conies of the pencil are concurrent at one and the same point a, which we shall call the corresponding point of a. (2) If a describes a straight line D, then a. describes a certain conic C. (3) This conic C is also the locus of the poles of D with respect to the conies of the pencil, a consequence being: (4) If m, a point of C, is the pole of D with respect to one of the conies H of the pencil and a a point of D with the corresponding point α, then the polar line of a with respect to H is mα.

2014 ◽  
Vol 4 (1) ◽  
pp. 1-8
Author(s):  
Tanvi Gautam

Subject area Leadership, human resource management, crisis management, change management and communication. Study level/applicability Executive education; postgraduate; undergraduate. Case overview This case study describes the collapse of Satyam, a leading IT industry service provider from India. Satyam went into a crisis mode after revelation of financial fraud by its Chairman. This resulted in a crisis not just for the company, its clients and employees – but it also had the potential to shake up the entire Indian IT industry the world over, by shattering investor and client confidence in the Indian IT sector. The case provides the students with an inside view of the unfolding of events at Satyam and the people challenges that emerge in a crisis scenario. The case outlines reactions from the industry, government, clients and employees as they tried to make sense of a very chaotic situation, and its multi-level ramifications both within India and outside. The case ends with Thallapalli Hari, the Global Head of Marketing and Communication and ex-head of HR, trying to visualise and prioritise a course of action to propose to other members of the leadership team. Expected learning outcomes The key aim of this case is to provide a backdrop to the crisis, and also help students put themselves in the role of an HR crisis manager as well as portray the decision making and communication challenges that emerge in chaotic situations. The importance of an immediate and yet strategic response is emphasised and the case is a great starting point to have a discussion on the competencies and skills required in HR to lead under unusual circumstances. This case allows participants to get an in-depth understanding of the collapse of Satyam. The case also illustrates principles of leadership, change management and communication, in particular: Leadership: The Satyam story is an HR and leadership crisis nightmare come true. What should an HR leader do when you wake up to find your company with a ruined reputation, minimal financial capital, 53,000 employees on the payroll and more than 500 clients with pending deliverables worldwide. Where do you begin? The case illustrates a situation where immediate action is required to stop the tailspin into which the company was heading. Change management: The situation demanded that change be managed from a chaotic system to a stable system. The big issue though remains as to how one can get a system into a state of stability when everything is changing at the same time. Most change management plans have some stable variables, however in the case of Satyam there were multiple changes taking place simultaneously. A combination of change in leadership, client relationships, employee trust and confidence, market reactions together make for a perfect storm. Dealing with even one of these changes is a challenge for a company. In the case of Satyam, its entire existence was at stake. Communication: The demands for communicating effectively in a crisis situation are different than communicating under stable systems. The choice of medium, the speed of response, the content all need careful monitoring. Whereas most companies have teams that separately deal with internal and external communication, Satyam provides a unique situation where managing both effectively at the same time was critical to the future of the firm. The stakes for effective communication are much higher under the circumstances. This case can be used in organizational behaviour, human resources and corporate communications modules being taught to under-graduates, post-graduates and for executive education. Supplementary materials Teaching notes are available for educators only. Please contact your library to gain login details or email [email protected] to request teaching notes.


2017 ◽  
Vol 27 (01n02) ◽  
pp. 121-158 ◽  
Author(s):  
Martin Nöllenburg ◽  
Roman Prutkin ◽  
Ignaz Rutter

A greedily routable region (GRR) is a closed subset of [Formula: see text], in which any destination point can be reached from any starting point by always moving in the direction with maximum reduction of the distance to the destination in each point of the path. Recently, Tan and Kermarrec proposed a geographic routing protocol for dense wireless sensor networks based on decomposing the network area into a small number of interior-disjoint GRRs. They showed that minimum decomposition is NP-hard for polygonal regions with holes. We consider minimum GRR decomposition for plane straight-line drawings of graphs. Here, GRRs coincide with self-approaching drawings of trees, a drawing style which has become a popular research topic in graph drawing. We show that minimum decomposition is still NP-hard for graphs with cycles and even for trees, but can be solved optimally for trees in polynomial time, if we allow only certain types of GRR contacts. Additionally, we give a 2-approximation for simple polygons, if a given triangulation has to be respected.


1976 ◽  
Vol 20 (01) ◽  
pp. 1-6
Author(s):  
Joseph B. Keller ◽  
Daljit S. Ahluwalia

The wave resistance R and wave height h(x, z) are evaluated asymptotically for small Froude number F = U(gL)−½ for a slender hull of any shape. Michell's theory for a thin ship of length L moving with constant speed U along a straight line is the starting point. It is found that asymptotically R and h depend only upon four properties of the ship—the slope of the hull and the slope of the profile curve of the hull at the waterline at bow and stern. Simple formulas are obtained for R and h in terms of these slopes. The wave pattern consists of four waves—a longitudinal and a transverse wave from the bow and a similar pair from the stern. Their phases are the same as those of Kelvin waves due to pressure points at the bow and stern, and they also decay with distance like cylindrical waves. However, their amplitudes have different angular variations from those of Kelvin waves.


2019 ◽  
Author(s):  
Tania Fort ◽  
Charlie Pauvert ◽  
Amy E. Zanne ◽  
Otso Ovaskainen ◽  
Thomas Caignard ◽  
...  

SummaryTrees, as foundation species, play a pivotal role in the species interaction networks that constitute forest ecosystems. From the seed stage, they interact with microbial communities that affect their growth, health and fitness. Despite their eco-evolutionary importance, the processes shaping seed microbial communities in natural forests have received little attention.To unravel these processes, we analyzed the microbial communities of seeds collected in populations of sessile oak (Quercus petraea) growing along elevation gradients. We focused on the fungal communities as this group includes seed pathogens. Ecological processes shaping the communities were quantified using joint species distribution models.Fungi were present in all seed tissues, including the embryo. Fungal communities differed significantly among oak populations along the elevation gradients, and among mother trees within the same population. These maternal effects remained significant after seed fall, despite colonization by fungal species on the ground. Associations between tree pathogens and their antagonists were detected in the seeds.Our results demonstrate that both maternal effects and environmental filtering shape seed microbial communities of sessile oak. They provide a starting point for future research aimed at identifying the seed extended phenotypic traits that influence seed dispersal and germination, and seedling survival and growth across environments.


2019 ◽  
Vol 10 (1) ◽  
pp. 141-172
Author(s):  
Ďurčo Peter ◽  
Hornáček Banášová Monika ◽  
Fraštíková Simona ◽  
Tabačeková Jana

Abstract The paper focuses on the problems of the lexicon-grammar continuum using the example of the lexical-syntagmatic combinatorics of minimal phrases. The focus is on binary preposition + noun phrases with their recurrent collocation partners and syntagmatic context patterns. Together with other (con)textual elements, they form conventionalized and lexically stabilized patterns that have flowed together through recurrent use and repeated occurrence of related linguistic structures in various contexts. The phenomenon requires an inductive bottom-up analysis process. Statistically calculated syntagmatic profiles of selected German prepositions based on linguistic corpora serve as our analytic starting point. The German preposition–noun constructions are then subjected to a corpus-based examination in the contrast language Slovak with respect to their equivalence from the following aspects: –individual language specifics and cross-language regularities of the lexical stabilization of individual phrases –nature of lexical fillers in comparable patterns –equivalence of meanings and/or functions by different contextual factors.


2018 ◽  
Vol 15 (5) ◽  
pp. 172988141880385
Author(s):  
Yuanzhen Li ◽  
Yue Zhao

Two linear calibration methods based on space-line projection properties for a paracatadioptric camera are presented. Considering the central catadioptric system, a straight line is projected into a circle on the viewing spherical surface for the first projection. The tangent lines in a group at antipode point pairs with respect to the circle are parallel, with the infinity point being the intersection point; therefore, the infinity line can be obtained from two groups of antipode point pairs. Further, the direction of the polar line of an infinity point with respect to the circle is orthogonal to the direction of its infinity point. Hence, on the imaging plane, images of the circular points or orthogonal vanishing points are used to determine the intrinsic parameters. On the basis of the properties of the antipodal point pairs and a least-squares fitting, a corresponding optimization algorithm for line image fitting is proposed. Experimental results demonstrate the robustness of the two calibration methods, that is, for images of the circular points and orthogonal vanishing points.


2011 ◽  
Vol 12 (1) ◽  
pp. 34-57 ◽  
Author(s):  
Regina Ogorek

Historical evaluations are expected to mark a starting point and, at the end, produce a result, which then shows a “development” from the starting point. This development need not be in a straight line. It may have made detours and suffered set-backs. Altogether, however, it connects beginning and end like a red thread; it is possible to see from this the task of the historian, picking up this thread like a careful housewife, undoing knots and loops, winding up assiduously and finally presenting a tidy ball of work.


2018 ◽  
Vol 24 (6) ◽  
pp. 412-421 ◽  
Author(s):  
Rowena Jacobs ◽  
Martin Chalkley ◽  
María José Aragón ◽  
Jan R. Böhnke ◽  
Michael Clark ◽  
...  

SUMMARYFunding for mental health services in England faces many challenges, including operating under financial constraints where it is not easy to demonstrate the link between activity and funding. Mental health services need to operate alongside and collaborate with acute physical hospital services, where there is a well-established system for paying for activity. The funding landscape is shifting at a rapid pace and we outline the distinctions between the three main options – block contracts, episodic payment and capitation. Classification of treatment episodes via clustering presents an opportunity to demonstrate activity and reward it within these payment approaches. We discuss the results of our research into how well the clustering system is performing against a number of fundamental criteria. We find that, according to these criteria, clusters are falling short of providing a sound basis for measuring and financing services. Nevertheless, we argue that clustering is the best available option and is essential for a more transparent funding approach for mental healthcare to demonstrate its claim on resources, and that clusters should therefore be a starting point for evolving a better funding system.LEARNING OBJECTIVES•Understand the different payment models currently being used and proposed in mental health services in England•Understand the role of clustering in measuring mental health activity and providing a basis for funding•Understand how a robust model of clustering can benefit the provision of mental health servicesDECLARATION OF INTERESTNone.


Philosophy ◽  
1929 ◽  
Vol 4 (15) ◽  
pp. 346-355
Author(s):  
Herbert Wildon Carr

Nothing is more surprising to the ordinary reflective man than the concept of a finite universe, yet it is to such a concept that the latest development of mathematical science, so admirably expounded in Jeans's Astronomy and Cosmogony, requires us to adapt ourselves. A finite universe is one in which anything moving outwards in a straight line, and maintaining its direction, must after an interval return to its starting-point. This seems a self-contradiction. A straight line, we think, must go on for ever.


1951 ◽  
Vol 4 (02) ◽  
pp. 117-125 ◽  
Author(s):  
William S. von Arx

Recently an electromagnetic method for measuring the velocities of ocean currents for oceanographic purposes has been shown to be reliable enough for the observed velocity of the surface current to be taken into account in dead reckoning navigation in the open ocean. A preliminary test of the electromagnetic method as a navigational aid was made in 1949 on one cruise covering a distance of 1000 miles across the Gulf Stream and back. A total of 52 miles of lateral drift was corrected to produce a straight line of travel through the observed currents, and this correction enabled the ship to return to within 2 miles of the starting point. Seven less formal experiments performed in 1950 indicate that ordinarily, on straight-away courses, the lateral drift component caused by currents can be measured and corrected with the expectation that the undetected drift will be less than 1 percent of the distance travelled.


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