Attraction Points Research Articles

A ‘realistic’ computing exercise in complex variables

A mathematical model of spatial interaction in geography is translated into complex variables so that a map of a small region is represented by part of the complex plane, with a function of a complex variable used to represent vectorially the net interactive ‘force’ at any point due to the presence of a finite set of points of attraction. The zeros of this function represent equilibrium points of the force field in the region and can be obtained by writing a computer program in complex variables.

A Home Range Model Incorporating Biological Attraction Points

SUMMARY (1) A distinction is made between the domain and utilization distribution of an animal's space-use pattern, and the need for a reappraisal of model-based approaches to the description of utilization distributions is indicated. In particular, the symmetry of the widely used bivariate normal model is considered to provide an inadequate characterization of individual space-use intensity in many ecological situations. (2) A field worker is often aware of the position of biological attraction points, termed nuclei, of which there may be several for a particular home range. There is evidence that such nuclei have important influences over the space utilization intensity of a given individual. The home range model proposed here assumes a circular normal distribution of activity about each nucleus. The strength and range of the attractive fields about each nucleus are parameters which may be estimated. (3) Independent fixes of an individual's locations are used to obtain model parameter estimates using the Maximum Likelihood method, enabling a description of the utilization distribution, and calculation of probability domains. (4) The model is applied to field data collected from the grey squirrel (Sciurus carolinensis, Gmelin) and a hypothetical data set. The resulting domain and utilization distribution properties are discussed in relation to the bivariate normal model, and various advantages of the present model are demonstrated.

On minimal centers of attraction and generic points.

On minimal centers of attraction and generic points.

長崎県におけるブリ飼付漁業の漁獲量と漁獲諸要因との関係

1. Fishing ground of domesticated yellowtail distribute in sea areas where the Tsushima Current directly flows. The best fishing season is the period from Septembe to October. Body size of the yellowtail caught is smaller in Tsushima fishing grounds than in Goto Islands, and larger in the deeper fishing grounds. 2. There are rocks 20-40 m in height on the sea floor 50-75 m deep in the fishing grounds. Sea deposits around the rocks are white sands and the sea conditions of almost all fishing grounds are satisfactory. Considering sea depth of the fishing grounds, height of the attraction points, sea deposits and other factors in relation to the catch, any especially good condition for catch can not be recognized. 3. It is likely that there are relationships between quantity of ground-bait and catch, because the ground-bait might be controlled in accordance with the amount of the yellowtail catch. There are two groups of the yellowtail, one which shows small catch in spite of high efficienoy of the ground-bait, and the other shows large catch in spite of low efficiency of the ground-bait. The reason why these two groups are seen is an economical problem that there is a difference between a boss who wants to ger more catch by using less quantity of the gron-bait and a boss who wants to ger more catch by using much ground-bait.

The molecular structure of some insect virus inclusion bodies

Electron microscopic investigation have revealed very regular dot and line patterns in different crystalline insect virus inclusion bodies, the so-called polyhedra and capsules. The crystalline lattice has a very high degree of regularity without dislocations. Contrary to previous results, it was found that the inclusion body protein molecules are not ellipsoids arranged in a pseudohexagonal system, but spheres arranged in a face-centered cubic system. Between the molecule rows, angles of 90 and 125 degrees could readily be observed. The diameters of the molecules vary from about 65 to 90 A, depending on the insect specied from which the inclusion bodies were obtained. All observed dot and line patterns could be explained with the aid of light and X-ray micrographs of molecule models arranged in a cubic system, but cut at different angles. X-ray photographs of the molecule models suggest that sections were in the neighborhood of about 100 A thick since only sections of such a thickness reveal electron-density differences great enough to resolve dot patterns of more than 90 degree angles between the rows. The arrangement of inclusion body protein molecules in a face-centered cubic system indicated that there are six relative points of special attraction on the surface of each molecule, which leads to the cubic system. Without these selective points of attraction, one would expect a close-packed hexagonal arrangement which never could be found in any of the inclusion bodies. Virus particles, irregularly distributed and in random position within the inclusion bodies, do not disturb the crystalline lattice, or act as crystallization centers. No other components were ever found within the crystalline lattice of the inclusion bodies.

An Introduction to the Theory of Newtonian Attraction

THE preface states that this book was written at the suggestion of some students who were unable to find a book on the subject suitable for their requirements. The seven chapters deal with preliminary mathematics ; gravitational attraction and potential, simple applications ; attraction and potential internal points, spheres ; theorems of Laplace, Poisson and Gauss, general theory ; Green's theorem; harmonic functions ; attraction of ellipsoids.

Regions of attraction, limits and end points of an exterior discrete semi-flow

An exterior space is a topological space equipped with a distinguished quasi-filter of open subsets (closed by finite intersections) that we call externology. For an exterior space one can consider limits, bar-limits and different sets of end points (Steenrod, Cech, Brown-Grossman). In this work we analyze relations between exterior spaces and discrete semiflows. In order to do this we introduce the notion of exterior discrete semi-flow, which is a mixture of exterior space and discrete semi-flow. We see that any classical discrete semi-flow can be provided with the structure of an exterior discrete semi-flow by taking the quasi-filter of right-absorbing open subsets. Such a family of open subsets is used to study the relations between limits and periodic points and connections between bar-limits and omega-limits. The different notions of end points are used to decompose the region of attraction of an exterior discrete semi-flow as a disjoint union of basins of end points. We also analyze the exterior discrete semiow structure induced by the family of open neighborhoods of a given sub-semi-flow.

XVI. —On the elasticity of threads of glass, with some of the most useful applications of this property to torsion balances

1. From facts connected with crystallization and elasticity, it seems extremely probable, that the atoms of matter do not attract each other indifferently on all sides. There appears to be peculiar points on their surfaces which have a more powerful attraction for each other, than for other points on the same molecule. This property is not peculiar to the atoms of ponderable matter, but seems also to belong to those of light and heat. It is as impossible to prove directly the existence of this property, as it is to prove the existence of atoms themselves; but on account of the satisfactory manner in which it enables us to explain the phsenomena of crystallization and elasticity, it is now generally adopted. 2. If the atoms of solid bodies be slightly displaced by any mechanical means, they will endeavour to return to their former state of aggregation when the disturbing cause is removed. This property belongs in very different degrees to different substances. In lead it scarcely exists, and but slightly so in soft copper. In brass, iron and silver, especially when drawn into wires, it exists in a considerable degree. But all these substances have limits beyond which the property does not hold. If for example an iron wire be twisted several times, it will not return exactly to its former state, but remain partially twisted. In threads of glass, on the contrary, there seems to be no limit to this property, whilst the thread remains entire. Let a fine glass thread be suspended from a moveable index, and let a light horizontal needle of wood or straw be fixed to its lower extremity as in the annexed figure. If the thread be now twisted by means of the handle H, whilst the needle N is prevented turning round, and then allowed to untwist itself, the needle will return exactly to its former position after it has ceased to oscillate. If the vitreous molecules be held together by the attraction of their poles or points of greatest affinity, it is obvious that these points will be displaced by torsion along the whole line of communication. The points of greatest attraction thus displaced, will therefore endeavour to regain their former state of stable equilibrium, and the thread will of course untwist itself till the needle returns to its former position. It would be curious to ascertain if a thread of glass, twisted as much as it can safely bear, and kept in that position for several months or years, would return exactly to its former position, or whether the atoms might not in course of time take up a new state of stable equilibrium.

III. On the Granite Tors of Cornwall.

I have the honor of presenting to the Society three drawings which I have selected from my portfolio, for the purpose of illustrating the changes which the influence of time and weather produces on certain varieties of granite. The subjects are all chosen among the granites of the west of England; and that I might at the same time preserve memorials of circumstances which are remarkable independently of their geological interest, I have taken two of my examples from places which have called forth more admiration from the common spectator than even from the philosopher, and which form two points of attraction for the curious or idle who annually visit Cornwall. Not only indeed have idle curiosity and ignorant speculation busied themselves in accounting for phenomena which many of the vulgar have deemed little less than miraculous, but learned antiquaries have tortured their inventions and have constructed religious systems for the purpose of explaining these very simple and intelligible natural appearances, by the rites of a mysterious and Druidical worship. I trust I shall be pardoned, if while I deduce from these facts the geological consequences which depend on them, I likewise give a more particular detail of the appearances themselves which have excited so much of the attention of all visitors. The Logging rock (Pl. III.) is situated on a peninsula of granite, in the parish of St. Levin, which stretches out about 200 yards into the sea, its isthmus still exhibiting remains of the ancient fortification of Castle

An account of the cause of the change of the variation of the magnetical needle. with an hypothesis of the structure of the internal parts of the earth: as it was proposed to the Royal Society in one of their late meetings

Some years since I published in these Transactions, (Numb. 148.) a Theory of the Variation of the Magnetical Compass, wherein having collected as many Observations as at that time I could procure, and having carefully compared them together, I came at length to this general conclusion, That the Globe of the Earth might be supposed to be on great Magnet, having four Magnetical Poles or Points of Attraction, near each Pole of the Equator two :