Theta Graph Designs

We solve the design spectrum problem for all theta graphs with 10, 11, 12, 13, 14 and 15 edges

The Southern Vilnius Photometric System. IV. The E Regions Standard Stars

This paper is the fourth in a series on the extension of the Vilnius photometric system to the southern hemisphere. Observations were made of 60 stars in the Harvard Standard E regions to increase a set of standard stars.Comment: 6 pages, TeX, requires 2 macros (baltic2.tex, baltic4.tex) included no figures, to be published in Baltic Astronomy, Vol 6, pp1-6 (1997

Strategy and tactics in mediaeval Scotland

Offensive operations by the Scots in the Middle Ages were confined to the single sphere of the north of England and can be divided into two chronological periods. In the twelfth century the object of the invasions was the conquest and retentio7 of the northern counties; in the thirteenth, fourteenth, fifteenth and sixteenth, the aim was simply to cause diversions of the strength of England from more vital points at home or abroad.Permanent conquest necessitated the existence of elaborate siege equipment and a disciplined army of occupation at a time when Scotland possessed neither the one nor the other. In occupying a district which is meant to be held indefinitely, care must be taken to secure possession of the fortresses, the fetters of the country, and to conciliate the inhabitants by respecting their lives and property. The armies of David I and of William the Lion could not do these things. Their attempts at sieges were gene rally unsuccessful, and the composition of their bands rendered sporadic plundering inevitable. The leaders were not responsible for this state of affairs; the state of civilisation in Scotland e was not yet far enough advanced to allow of the formation of a wei disciplined host,or, which was more important, of a properly organised system of supply which would have rendered wasteful foraging unnecessary. It may be, however, that the attacks, failures as they were, served the purpose of a true defensive at a time when the lack of unification in Scotland would have made the country a prey to an organised English conquest.The mistaken nature of the policy of running risks on behalf of France has already been commented on. The true military sphere of raids of diversion in the north of England was to draw away the southern forces from an attack on a northern fortress or district or to bring pressure to bear on the southern government and thus secure a favourable peace. Thus the attacks made by Bruce and his lieutenants were truly defined in their scope and resulted in the saving of Berwick and in the extraction of the peace of Northampton from an exhausted enemy. The successful handling of these raids required a high degree of perseverance at a time when things might be going badly elsewhere. When thef qualm ty was lacking disaster followed, as in the battles of Dunbar and Ialidon Hill. On the other hand, even when Walter was hard pressed in Berwick, Bruce steadfastly refused to risk a battle for the town. Pitched battles, as distinct from combats, had to be avoided in these expeditions. Neville's Cross and Flodden were avoidable disasters brought about by violation of this rule. Otterburn was a successful battle, but it brought to the Scots only a gain in prestige. The most disastrous campaign which the English fought in their own country, that of Weardale, did not contain a single open action.In this work, where detailed attention can only be directed to the more outstanding actions, the cumulative effect of raids has not been stressed. No account can be taken of the scores of minor parties which crossed the English border at various periods, but the mass result cf these operations was very great. This system of warfare gradually created a line of defence which was difficult to pass, but it also brought about in a later stage of the country's development as state of anarchy which was with difficulty corrected by the later rulers.In the Middle Ages military power was mostly in the hands of the barons who constituted, as it were, the military aristocracy. This was an inevitable sequel to the feudal system of landholding, which made the tenants-in-chief the king's lieutenants in the national levy. While all men of rank were soldiers, there were practically no professional leaders of armies. From his very nature the soldier of fortune was an adventurer or mandless man. As an adviser or as the leader of a contingent of mercenaries he was welcome, but it was very rarely that he rose to the command of an army. In most cases the barons would not have tolerated such promotion over their heads, though there. is little doubt that such men as Walter Manny had as much military intelligence as most of the barons put together. Occasionally a country, especially England, produced a king who could bring to his natural position of leadership great military intelligence. Generally, however, the multiplicity of the king's duties prevented his becoming proficient as a general and he was dependent upon the advice of a council of barons with no more ability in the matter than himself; this was almost constantly true in the case of France.As a general rule the barons made good fighters, but most indifferent leaders. When the list of English successes gained at the expense of the Scots is examined, it is found that at Dunbar, Falkirk, and Halidon Hill the king led the army and that in the latter two cases he directed its movements in person. At the Standard and at Neville's Cross the northern barons of England did not show any outstanding skill; rather it was the Scottish leaders who showed ineptitude. At Flodden Surrey did not show himself in any way a distinguished master of war. Edward II was the only English king defeated in plain battle by the Scots, and it is out the question to say that he controlled the English army at Bannockburn. In brief the tide of English success rose highest during the reigns of her two general- kings, Edward I and Edward III, and that of Scottish victory during the period of Bruce. The Scottish barons had the melancholy privilege of possessing a long list of such incompetent generals as Archibald Douglas and Donald, Earl of March cannot be plausibly alleged that the failure of the baronial leaders was due to the fact that the successful principles of Scottish war had not been adequately demonstrated. They appeared clearly under Wallace in a defensive sense and developed under Bruce in an offensive direction. Yet after the peace of Northampton there appeared a most unfortunate neglect of the lessons learned at so great a cost, and repeatedly the most elementary rules of Scottish warfare were violated in glaring fashion. It is not easy to find an explanation of this negligent behaviour. English leaders did apply the teaching of Dupplin Moor to some practical purpose, and even the French tried to avoid in later actions the primary error of the Crecy catastrophe. But the Scottish barons, in a fashion almost systematic, forgot the old tricks and failed to produce any new ones. Even in an inbred aristocracy depending on brawn rather than on brains, something better than this was to be expected. Perhaps it was due to the fact that most of the barons were absent from Scotland at the period of the war of Independence. The more probable explanation is, however, that no pains were taken to pass on the fruits of acquired experience from one generation to another. Scotland in the Middle Ages could not foster a Staff College, but it might have possessed a few elementary rules and regulations in written form. Yet the fact remains that, apart from Bruce's testament, there exists nothing approaching a text book on the principles of Scottish warfare.The redeeming feature is the prolific crop of partisan leaders which Scotland invariably produced from the ranks of the knights and of the common people in times of danger. This is a tribute to the undoubted military ability of the commons, which has appeared even more markedly in modern times. It was also the primary explanation of% the fact that Scotland was able to maintain her independence, a performance which, despite the defeats suffered in the process will remain on record as a wonderful effort in the face of natural disadvantages, misdirected leadership, and an exceptionally formidable enemy. Our summing up must be in favour of the people and adverse to their leaders as a whole

The optical and near-infrared properties of nearby groups of galaxies

We present a study of the optical (BRI) and near-infrared (JHK) luminosity fuctions (LFs) of the GEMS sample of 60 nearby groups of galaxies between 0<z<0.04, with our optical CCD photometry and near-IR photometry from the 2MASS survey. The LFs in all filters show a depletion of galaxies of intermediate luminosity, two magnitudes fainter than L*, within 0.3 R{500} from the centres of X-ray faint groups. This feature is not as pronounced in X-ray bright gropus, and vanishes when LFs are found out to R{500}, even in the X-ray dim groups. We argue that this feature arises due to the enhanced merging of intermediate-mass galaxies in the dynamically sluggish environment of low velocity-dispersion groups, indicating that merging is important in galaxy evolution even at z~0.Comment: to appear in the proceedings of the ESO workshop "Groups of Galaxies in the Nearby Universe", Santiago, Dec 5-9, 2005. Eds. I. Saviane, V. Ivanov, & J. Borissova (Springer Verlag); 5 page

Characterization of high-dimensional entangled systems via mutually unbiased measurements

Mutually unbiased bases (MUBs) play a key role in many protocols in quantum science, such as quantum key distribution. However, defining MUBs for arbitrary high-dimensional systems is theoretically difficult, and measurements in such bases can be hard to implement. We show experimentally that efficient quantum state reconstruction of a high-dimensional multi-partite quantum system can be performed by considering only the MUBs of the individual parts. The state spaces of the individual subsystems are always smaller than the state space of the composite system. Thus, the benefit of this method is that MUBs need to be defined for the small Hilbert spaces of the subsystems rather than for the large space of the overall system. This becomes especially relevant where the definition or measurement of MUBs for the overall system is challenging. We illustrate this approach by implementing measurements for a high-dimensional system consisting of two photons entangled in the orbital angular momentum (OAM) degree of freedom, and we reconstruct the state of this system for dimensions of the individual photons from d=2 to 5.Comment: 8 page

Diamonds on the Hat: Globular Clusters in The Sombrero Galaxy (M104)

Images from the HST ACS are used to carry out a new photometric study of the globular clusters (GCs) in M104, the Sombrero galaxy. The primary focus of our study is the characteristic distribution function of linear sizes (SDF) of the GCs. We measure the effective radii for 652 clusters with PSF-convolved King and Wilson dynamical model fits. The SDF is remarkably similar to those measured for other large galaxies of all types, adding strong support to the view that it is a "universal" feature of globular cluster systems. We develop a more general interpretation of the size distribution function for globular clusters, proposing that the shape of the SDF that we see today for GCs is strongly influenced by the early rapid mass loss during their star forming stage, coupled with stochastic differences from cluster to cluster in the star formation efficiency (SFE) and their initial sizes. We find that the observed SDF shape can be accurately predicted by a simple model in which the protocluster clouds had characteristic sizes of $0.9 \pm 0.1$ pc and SFEs of $0.3 \pm 0.07$. The colors and luminosities of the M104 clusters show the clearly defined classic bimodal form. The blue sequence exhibits a mass/metallicity relation (MMR), following a scaling of heavy-element abundance with luminosity of $Z \sim L^{0.3}$ very similar to what has been found in most giant elliptical galaxies. A quantitative self-enrichment model provides a good first-order match to the data for the same initial SFE and protocluster size that were required to explain the SDF. We also discuss various forms of the globular cluster Fundamental Plane (FP) of structural parameters, and show that useful tests of it can be extended to galaxies beyond the Local Group.Comment: In press for MNRA

XLVI. Account of a remarkable meteor, seen December 19, 1849

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USING CROWDFUNDING AS PART OF THE PRODUCT DEVELOPMENT PROCESS

AbstractCrowdfunding is the process of taking a project in need of investment and asking a large group of people to supply the investment. It allows organisations to sell their product before production, reducing the risk of new product development. Organisations such as Tesla and General Electric have used crowdfunding successfully but crowdfunding is yet to be explored as part of a formalised product development framework. This paper includes the business case for commercialising new products with crowdfunding and presents crowdfunding as part of a product development and commercialisation framework.</jats:p