Tethering in pastures new

2018 ◽  
Vol 102 (554) ◽  
pp. 233-245
Author(s):  
John D. Mahony

In a recent and illuminating article that provided much food for thought [1], the problem of tethering a goat at the edge of a circular pasture so as to restrict its attentions to only one half of the grazing supply was elegantly addressed and developed further to embrace the corresponding three-dimensional scenario involving a bird. The exercises resulted in mathematical formulations that required the use of numerical methods to extract practical results. Following the article, various questions and different scenarios sprang to my mind. The following poser perhaps best illustrates one of these, and it is the purpose of this Article to address this particular conundrum:A grazier has three troublesome beasts that are water averse, eat grass and who will, given half a chance, eat one another also in some fashion. The first will eat the other two and the second will eat only the third, which eats just grass. Having stabled and fed them in separate stalls during the winter months he plans to release them in the spring to an arbitrarily elliptic shaped pasture up to the water's edge in the middle of a lake. He has at his disposal: (1)A drum of tethering rope from which he can cut just once any required length, TBD (To Be Determined).(2)Slip rings and two tethering pegs that can be positioned only on the pasture boundary (i.e. at the water's edge).

2011 ◽  
Vol 21 (6) ◽  
pp. 1253-1299 ◽  
Author(s):  
ISABELLA MASTROENI ◽  
ANINDYA BANERJEE

This paper explores a three dimensional characterisation of a declassification-based non-interference policy and its consequences. Two of the dimensions consist of specifying:(a)the power of the attacker, that is, what public information a program has that an attacker can observe; and(b)what secret information a program has that needs to be protected.Both these dimensions are regulated by the third dimension:(c)the choice of program semantics, for example, trace semantics or denotational semantics, or any semantics in Cousot's semantics hierarchy.To check whether a program satisfies a non-interference policy, one can compute an abstract domain that over-approximates the information released by the policy and then check whether program execution can release more information than permitted by the policy. Counterexamples to a policy can be generated by using a variant of the Paige–Tarjan algorithm for partition refinement. Given the counterexamples, the policy can be refined so that the least amount of confidential information required for making the program secure is declassified.


1976 ◽  
Vol 72 ◽  
pp. 129-133
Author(s):  
W. C. Seitter

Work on the third part of the Bonner Spectral Atlas: Peculiar Stars has well progressed during the past year. Observations of the more than 200 stars – photographed with a dispersion of 240 Å mm−1 at Hγ on I-N plates – is nearing completion.The arrangement of the spectra will be as follows: 1.WR-stars2.O-stars Of sequence3.Peculiar B-type stars emission-line objects4.Ap-stars with various sequences: Cr-Mn-Hg-rare earths5.Asi-stars6.Am-stars7.Late-type peculiar stars Ba II, CH8.C-stars9.Late M-type stars10.S-stars11.Composite spectra12.Spectra with large rotational broadeningThe 12 groups are displayed on 40 plates, each with 6–8 objects. Stars of groups 8 to 10 will be presented with different exposures in order to facilitate the discovery of faint objects.Sample plates will be shown and discussed.


1969 ◽  
Vol 73 (700) ◽  
pp. 255-270
Author(s):  
H. Caplan

The purpose of this prologue is to outline how I have approached the arrogant and impossible task of surveying an unborn century of law. I may also be able to illustrate that the nature and quality of the task is completely different from that attempted in the preceding papers. In the whole paper I have done little more than infer repeatedly, in different ways (a) that the shape of the future so far as law is concerned will be determined by the methods of communication adopted between sectors of the aerospace community and between the aerospace community and society at large, and (b) that the search for effective methods of communication is urgent. But my target is not the lawyers of our community—who I am not qualified to advise. I write for the other members of the Royal Aeronautical Society and I return to the task of persuading them that they have a role to play in evolving future laws for aerospace activities.


2012 ◽  
Vol 68 (9) ◽  
pp. m265-m268 ◽  
Author(s):  
Kai-Long Zhong ◽  
Ming-Yi Qian

The title compound, {[Co(H2O)6][Co(SO4)(C10H8N2)(H2O)3][Co(SO4)2(C10H8N2)(H2O)2]}n, contains three crystallographically unique CoIIcentres, all of which are in six-coordinated environments. One CoIIcentre is coordinated by two bridging 4,4′-bipyridine (4,4′-bipy) ligands, one sulfate ion and three aqua ligands. The second CoIIcentre is surrounded by two N atoms of two 4,4′-bipy ligands and four O atoms,i.e.two O atoms from two monodentate sulfate ions and two from water molecules. The third CoIIcentre forms part of a hexaaquacobalt(II) ion. In the crystal structure, there are two different one-dimensional chains, one being anionic and the other neutral, and adjacent chains are arranged in a cross-like fashion around the mid-point of the 4,4′-bipy ligands. The structure features O—H...O hydrogen-bonding interactions between sulfate anions and water molecules, resulting in a three-dimensional supramolecular network.


1968 ◽  
Vol 5 (02) ◽  
pp. 314-333
Author(s):  
Edward Pollak

Summary Generations are assumed to be non-overlapping. We consider a haploid population divided into K parts, each of which contain N adults in any generation. These are obtained by a random sampling of the offspring of the previous generation. We assume that the probability of an adult offspring of an individual in one subpopulation being in some other subpopulation is the same small positive number, no matter what two subpopulations are considered. If the population initially has individuals of two types, A and a, it is of interest to study approximations, if n is large, to (1) the rate at which A or a is lost between generations n-1 and n, (2) the probability that A and a are still present in generation n, (3) the joint distribution of frequencies of A in the subpopulations. A solution is given for the first problem. It is found that if the mean number of migrants per generation from one subpopulation to another is at least as large as 1, the population behaves almost as if it were not subdivided. But if this number is considerably less that 1, then the rate at which one or the other gene is lost is slower than in an undivided population. The other two problems are discussed for K = 2.


Radiocarbon ◽  
2003 ◽  
Vol 45 (2) ◽  
pp. 293-328 ◽  

TIRI was officially launched at the 14th International Radiocarbon Conference in Arizona in 1991. Prior to the conference, 150 laboratories received a letter describing the general intention to organize an intercomparison and over 90 laboratories from around the world responded positively to the invitation to participate. Simply stated, the aims of this intercomparison were: 1.To function as the third arm of the quality assurance (QA) procedure.2.To provide an objective measure of the maintenance and improvement in analytical quality.3.To assist in the development of a “self-help” scheme for participating laboratories.


1968 ◽  
Vol 5 (2) ◽  
pp. 314-333 ◽  
Author(s):  
Edward Pollak

SummaryGenerations are assumed to be non-overlapping. We consider a haploid population divided into K parts, each of which contain N adults in any generation. These are obtained by a random sampling of the offspring of the previous generation. We assume that the probability of an adult offspring of an individual in one subpopulation being in some other subpopulation is the same small positive number, no matter what two subpopulations are considered.If the population initially has individuals of two types, A and a, it is of interest to study approximations, if n is large, to (1)the rate at which A or a is lost between generations n-1 and n,(2)the probability that A and a are still present in generation n,(3)the joint distribution of frequencies of A in the subpopulations.A solution is given for the first problem. It is found that if the mean number of migrants per generation from one subpopulation to another is at least as large as 1, the population behaves almost as if it were not subdivided. But if this number is considerably less that 1, then the rate at which one or the other gene is lost is slower than in an undivided population. The other two problems are discussed for K = 2.


2015 ◽  
Vol 47 ◽  
pp. 485-491

Brief in which King Henry III recalls that as there are people who might perhaps convey to the lord pope and cardinals certain business which has recently been transacted by him as a result of the advice of his magnates and vassals, who may put a malicious interpretation on it, and as the affair might be a potential hindrance to him, he (so the recipients are better prepared to argue against the cunning deceits of such men) is minded to explain here the whole sequence of certain of his affairs, so that they may not be uninformed about what has passed, on which it may happen that they or others might otherwise be deceived. [2] So they are to be aware that whereas, at the time when the bishop of Norwich was legate (1218–1221), the earl Marshal still occupied the castles of Marlborough and Ludgershall, and was proposing to marry the sister of Count Robert of Dreux, and there were also other magnates in England who were endeavouring to distance him from the king by injurious alliances, the idea of betrothing the earl to one of the king's sisters was discussed between the legate, his justiciar and certain other magnates, partly because the political alliance with foreigners was thought alarming should the earl marry the sister of the count of Dreux – so as not to render England more accessible to foreigners, especially since Richard Marshal, the brother of the earl, might obtain all the Marshal lands in Normandy – and partly because of fear of the malice of those people who endeavoured to seduce the earl's allegiance from the king; and indeed because the castles of Marlborough and Ludgershall ought to be returned to him (which many times the earl promised) so that the other magnates might the more readily be persuaded likewise to return to the king his castles which they also held. [3] Because of his tender years and the fragile state of his kingdom, one of the king's sisters was destined for the said Marshal, by the authority of the legate and the counsel of certain magnates. The said Marshal swore to marry her, if it pleased the king and the magnates of the realm. The justiciar swore to hand her over to the Marshal, if the magnates of the kingdom agreed. The legate, the justiciar and others who were present faithfully promised that they would approach this matter conscientiously. The said castles were handed back to the legate, so that if the contract were not fulfilled within a space of time long now expired, they should be given back promptly to the Marshal. [4] Further to this, when these matters were communicated to other magnates, notably to the earl of Chester who at that point returned from the Holy Land (July 1220) – the earl strongly approved the match and many others agreed, with no dissenters. But afterwards, when certain dissensions had emerged, some people demurred, claiming – just as indeed was said on their behalf in the papal curia – that the king should have no greater an aid for his own marriage as for his sisters, as a result of which his sisters’ marriage arrangements would be impeded, about which he was negotiating a considerable treaty in foreign parts, and so at that time the Marshal arrangement remained unfulfilled. [5] But when recently (June 1222) the same Marshal obtained a papal mandate addressed to the archbishop of Canterbury and bishop of Salisbury, that either they should cause him to be entirely absolved from the conditions of the oath, or the marriage contract be confirmed, the Marshal insisted vociferously that one of those options should be followed, since he cared for nothing other than that he be married. So now as before it is a worry that Marshal – a man of great power in England as much as Ireland – might marry the sister of the said count of Dreux or a daughter of the duke of Brabant, who was likewise offered to him – which on account of the matters already alluded to would assist the king in no way – or even the sister of the king of Scots, where similarly no small danger might arise, for by how much nearer Scotland is to Ireland and the Marshal lands, so much the more dangerous would the marriage be to the king. [6] So having considered the energy and power of the said Marshal, as well as the faithful service he has openly and strenuously performed for the king especially in the region of Wales – his castles which Llywelyn prince of Gwynedd held which Marshal vigorously reclaimed (in April 1223) would scarcely have been taken without his capacity and hard work – and also bearing in mind the example of Philip, the late king of France (died 14 July 1223) – who for a long time freely married off his daughters, sisters, and nieces to the likes of the counts of Namur and Ponthieu and others of his men rather than to foreigners, just as the current king of France recently married off his niece, the daughter of Guichard de Beaujeu to the count of Champagne (after August 1223); because of all these precedents and the great things which are hoped for from the Marshal, it should not be objectionable to the king and his council – all things considered – that he may at some time permit him to marry his sister to his advantage and honour. The king, on the advice of such and such men, having discussed this business extensively, conceded the Marshal his younger sister, without lessening of his lands, castles or money. [September 1223 × January 1224]A= Kew, National Archives (PRO), SC1/2/109.Printed, Royal Letters, 1: 244–246; Diplomatic Documents, 95–97.


1988 ◽  
Vol 20 (1) ◽  
pp. 677-681
Author(s):  
S. Grzedzielski ◽  
L.F. Burlaga

The area of interest to the Commission includes: 1.Solar wind composition and dynamics;2.Solar Interaction of solar wind with extended interplanetary sources of plasma and gases of non-solar origin;3.SolarStructure and dynamics of the three-dimensional heliosphere;4.SolarInteraction of heliosphere with the local interstellar medium.The following reports summarize recent developments in the aforementioned fields.


Author(s):  
Peter W. R. Corfield ◽  
Emma Cleary ◽  
Joseph F. Michalski

In the title compound, {(C6H16NO)[Cu2(CN)3]}n, the cyanide groups link the CuIatoms into an open three-dimensional anionic network, with the molecular formula Cu2(CN)3−. One CuIatom is tetrahedrally bound to four CN groups, and the other CuIatom is bonded to three CN groups in an approximate trigonal-planar coordination. The tetrahedrally coordinated CuIatoms are linked into centrosymmetric dimers by the C atoms of two end-on bridging CN groups which bring the CuIatoms into close contact at 2.5171 (7) Å. Two of the cyanide groups bonded to the CuIatoms with trigonal-planar surrounding link the dimeric units into columns along theaaxis, and the third links the columns together to form the network. TheN,N-diethylethanolamine molecules used in the synthesis have become protonated at the N atoms and are situated in cavities in the network, providing charge neutrality, with no covalent interactions between the cations and the anionic network.


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