Adjacent Squares Research Articles

Three Annihilation Games

A new class of superficially simple games in which tokens move to adjacent squares and are removed when two tokens cohabit.

The distribution of the distance between random points

This paper considers the distribution of distance between random points and shows how the distribution can be found when the points are chosen uniformly and independently in a hypersphere or in two adjacent unit squares. The value of a powerful extension of the classical Crofton technique is illustrated here for solving such geometric probability problems. This method is quite different from those employed by Hammersley and Oser.

The distribution of the distance between random points

This paper considers the distribution of distance between random points and shows how the distribution can be found when the points are chosen uniformly and independently in a hypersphere or in two adjacent unit squares. The value of a powerful extension of the classical Crofton technique is illustrated here for solving such geometric probability problems. This method is quite different from those employed by Hammersley and Oser.

Use of an Energy Dispersive X-ray Spectrometer on a Transmission Electron Microscope

An Ortec Si(Li) energy dispersive X-ray detector designed for use on a Cambridge scanning electron microscope has been coupled to a Siemens transmission electron microscope by replacing the side tilt control on the Siemens by a brass tube as shown in figure 1. The Siemens specimen holder was modified to tilt the specimen approximately 20° from a horizontal position and to elevate it such that it is just visible to the detector through the side port. This increased specimen height requires an objective focal length of greater than 8 mm and consequently effects a lower resolution of the image, especially at low accelerating voltages. The peak/background in the X-ray spectra is best at 40kV, however, and deteriorates progressively with increasing accelerating voltage.Experiments similar to those of Fuchs, who employed a wavelength dispersive system on a Siemens TEM to measure film thickness, were repeated with the present energy dispersive system by analysing spectra from vacuum deposited gold films of various thicknesses. A linear relation between peak height and thickness was confirmed for several films up to 2000Å thick by comparing spectra from two adjacent grid squares, one covered by a single thickness of gold, the other covered by a double thickness, and noting that the peak heights were in the ratio of 1:2 to within a few percent.

Transportation System In The Central Parts Of Urban Areas

The central parts of urban areas (the city cores) are susceptible to intensive traffic flows, public transportation vehicles and private cars. The traffic flows are intensive due to the attractive contents in the cores and historical monuments. The current use of certain areas and their uneven distribution result from the great number of trips in the city core and on the adjacent streets and squares. The city of Split boasts many attractive historical monuments as well as Diocletian's Palace, recognized by the united Nations as a part of the World's cultural heritage. This city center is also the destination of a great number of trips from other parts of the town and suburbs. The total number of trips to the city core was determined by applying a traditional model: trip generation analysis, trip distribution analysis, modal split analysis and traffic assignment analysis; the interaction between the number of trips and types of land use as obtained by applying multiple regression analysis. The optimal land use in all parts of the city core will ensure comfortable pedestrian flows in the area under consideration and on the adjacent streets and squares within walking distances and to the planned parking places for private vehicles and public transportation means. The investigations and the obtained results will be used for the development of the urban planning and physicalplanning documentation.

Quantitative Erfassung benthischer Organismen mit Hilfe der Tauchtechnik an der schwedischen Westküste

1. In the Gullmar Fjord (west coast of Sweden) bottom test squares had been sampled 40 years ago byGislen (1929–30). Studying the same squares in 1966, using skin diving equipment, has led to different results in regard to the fauna and flora found. 2. If the old records are compared with a number of new ones, obtained from the same place and depth, the degree of variation encountered in the new samples may serve as indicator for assessing true differences between biocoenoses in 1926 and 1966. 3. Differences between adjacent test squares depend mainly on the slope of the rock. Other factors which may affect the community structure over short distances are direction and light. 4. Certain organisms settle on bottom areas where calm waters allow sedimentation. 5. Increasing pollution demands sufficient and extensive registration of the actual situation in order to allow for comparisons. For this purpose even a lot of scattered observations can never be equal to numerous data from each of a few chosen places, which are representing the main trends in the sea bottom mosaic.

Pantactic Squares

Consider a square array of 25 grid squares, the grid squares being of two types distinguished by the colours black and white. A basic square of four adjacent grid squares can be selected from such a square array in 16 possible ways. If these 16 basic squares are all distinguishably coloured, then the 5x5 square array is said to be pantactic.

On the precision of the gravimetric determination of the geoid

On the basis of the gravity material available, the author studies two statistical functions: G2 = the rms (root mean square) anomaly in a square with side s, and E2 = the rms deviation of one actual point anomaly from the actual mean anomaly in a square with side s.The function E2, is called the error of representation, for if inside a square there is only one observed anomaly and this anomaly is accepted to represent the mean anomaly of the entire square, a standard mean error E can be used for the estimation of accuracy. On the other hand, if there are no observations inside the square and the mean anomaly of the square is assumed to be zero, G can be used as the standard mean error.For points or for very small squares, E is zero and G has a maximum value G0. For a hemisphere, G is zero and E has a maximum value G0. There is a critical size at about s = 3°, where E = G. When s is greater, it is not advisable to use the observed anomaly at a single station, as the representative of the mean anomaly of the square, because for zero the error to be expected is smaller. The weighted mean of zero and the observed anomaly is recommended.Because the regions without any observations are still large, it is necessary to estimate the size of the smallest squares, where the mean anomaly can be assumed to be independent of the mean anomalies of the adjacent squares. On the basis of the present gravity data, an estimated value of s = 30° seems to be acceptable.Using the functions E and G and the accepted values s = 3° and s = 30°, the precision obtainable for the gravimetric determination of the elevations N of the geoid (Stokes' formula) and of the deflections δ of the vertical (Vening Meinesz' formula) has been estimated. In the most favorable cases (Central Europe and the central parts of the United States) the standard mean error of N is ±10 meters and that of δ ± 0.″85. The former figure is almost entirely due to the great unexplored areas of the Earth'; the latter depends half on these unexplored areas and half on the small gaps within a distance of 50° from the point where δ is computed.