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29.01.2016
Synagogue Visits In Istanbul.Jewish community have lived in the geographic area of Asia Minor for more than 2,400 years. A large body of experimental data now exists for (e,2e) differential cross section (DCS) ionisation studies in which the scattered and ejected electrons are detected with the same energy and at the 'same' asymptotic scattering angles with respect to the incident electron direction.
A detection plane spanned by the scattered and ejected electron momenta ka and kb is initially defined.
The energy region from around 3eV to 100eV excess energy is defined here as the 'intermediate energy' region. Studies at lower energies are considered to lie in the threshold region where correlation effects between outgoing electrons dominate the reaction.
Differential cross section studies at energies in excess of 100eV are predominantly governed by single binary collisions between the incident and ejected electrons, the core playing a decreasing role in the reaction as this energy increases. Common to all these models is the importance of correlations between the outgoing electrons brought about through electrostatic coupling as they emerge from the reaction zone (see figure 2). As the excess energy above ionisation decreases, the outgoing electrons have more time to mutually interact and so the probability that they will emerge asymptotically at a mutual angle of p radians increases, whereas their 'memory' of the incident electron direction correspondingly decreases.
In this page a model-independent parameterisation of the ionisation differential cross section is discussed.
The parameterisation is in terms of a complete orthogonal set of irreducible tensorial angular functions which define correlation between any three vectors in space. This parameterisation was first proposed for the (e,2e) process by Klar and Fehr (1992), and has a long and distinguished history in the field of nuclear particle interactions proceeding through sharply defined states, where the analysis gives information about the angular momenta carried into and out of the reaction. By contrast, in the (e,2e) reaction the intermediate state is not normally sharply defined, and so the parameters do not directly reveal the angular momenta associated with the reaction, but rather indicate the degree of correlation between ingoing and outgoing electrons. The (e,2e) differential cross section is parameterised as a coherent superposition of partial waves up to L = 2 defining scattering in the reaction zone which is modulated by a Gaussian function modelling correlations between the outgoing electrons. There is no evidence of the complex structure discussed above for the intermediate energy regime. Comprehensive experimental data exists for ionisation of helium in the intermediate energy region over a very wide range of scattering geometries.
In these results the DCS is assumed to be zero when x = 0 and x = p since the probability of detection of two electrons of equal energy emerging in the same direction is very small. At 1eV excess energy a single structure is observed due to strong outgoing electron correlation, as previously noted.
At 3eV and 5eV above ionisation both a forward and a backward structure start evolving from the central peak at low incident electron angles y, whereas at higher angles y the DCS is still approximately Gaussian. Backward scattering, probably dominated by elastic scattering of the incoming electron from the atom into the backward direction in the detection plane followed by a binary collision with a valence electron, is the dominant contribution to the overall DCS structure. At the higher excess energy (30 - 50eV) forward scattering starts to dominate, reflecting the importance of single binary collisions.
Only the central peak is attainable through a single collision process and there will additionally be significant contributions to this peak through outgoing electron correlations at the lower energies. Indistinguishability of the outgoing electrons requires the DCS at (y,x) to be equated to that at (y, 2mp-x) where m is an integer.
Reflection symmetry is necessary in the detection plane since no preferred direction is defined with respect to this plane, and hence s(y,x) = s(-y,x). When electron spin is not considered the (e,2e) differential cross section is a function only of the momenta of the ingoing and outgoing electrons. The choice of angular functions Ilalbl0 required to characterise the (e,2e) DCS is restricted by the symmetries inherent in the ionisation process. Here the set for which la = lb when l0 is even and (la,A l0)A < lb when l0 is odd is chosen. It is clear that plotting the absolute magnitude of the I110 function as a radial vector when scanning over all possible values of theta and phi produces a 3-D surface which represents the function. Since the magnitude can be positive as well as negative, it is important to represent this facet when describing the function in this way. It is necessary to consider the magnitude and sign of the functions as the (e,2e) Differential Cross Section is parameterised as a linear sum of the angular functions (see equation 6), and so for various values of theta and phi the functions can cancel each other to allow zeroes in the cross section. The complete set of 3-D images of the 44 Angular Functions Ila,lb,l0 required to parameterise the symmetric (e,2e) Differential Cross Section over the energy range from 1eV to 50eV above the Helium ionisation threshold have been generated. The summation is over the experimental data points i each with an associated weight wi evaluated from the uncertainty in the data.
This linear fitting was fast and reliable, yielding excellent starting parameters for the second non-linear fitting method. A Simplex method was used to minimise the c2 function by adjusting the Blalbl0 parameters (see figure 7). Any trial for which the fitting function did not obey the assumptions was rejected and the Simplex routine was reset to explore alternative regions of the c2 surface.
This method converges far more slowly than the linear fitting method but requires no inferred data. The maximum significant values of la, lb and l0 were established using a statistical F-test. At 1eV excess energy only l0 = 0 to 4 contribute, and the la and lb terms are all of the same sign, reinforcing each other in each l0 manifold. The relative magnitudes of the terms in each manifold combine to produce the lobe structure at the mutual angle of p radians. As the energy increases this regular pattern quickly disappears as the forward and backward lobes evolve from the central 'Gaussian' profile. Higher order l0 correlation terms become significant as the intermediate energy region is entered, indicating an increasing contribution of higher order partial waves to the DCS.
Additionally the la and lb terms start to compete in magnitude and sign to produce the more complex structures observed. At excess energies above about 30eV the parameters tend to stabilise in sign and vary smoothly with energy. The maximum significant number of la and lb terms in each l0 manifold also decreases as the energy increases, indicating that the number of partial waves required in the outgoing channel decreases with increasing energy. Figure 9 shows 3-D representations of the (e,2e) differential cross sections at each energy from 1eV to 50eV excess energy as obtained from fitting the data to the parameterisation. The 3-D surface is generated from a vector whose length is given by the magnitude of the differential cross section as the surface is generated throughout space for all angles (q,f). The backward scattering region is towards the viewer, whereas the forward scattering region is away from the viewer. The results shown in figure 9 show 3 dimensional representations of the (e,2e) differential cross sections derived from the parameterisation at the energies where experiments were conducted. It is useful to establish a technique which allows interpolation between these results at the eight discrete excess energies, to enable the differential cross section to be estimated as a function of the three angular and one energy variables over the complete range of energies from threshold to 50eV excess energy. The (e,2e) differential cross section s is then projected onto a four dimensional space, whose axes are defined by the independant variables (s, q,f & Eexc).
As this cannot be visualised as a single projection on these pages, it is instructive to map one of these variables onto the time co-ordinate. In this case, we choose the excess energy to be varied in time, whereas the other 3 variables are mapped onto conventional 3-dimensional co-ordinate space, as has been done in the previous figures.a€?Hence, once the DCS is parameterised as a function of energy as well as a function of the scattering angle, this parameterisation can be used to derive 3-D images at discrete energy intervals. These images can then be projected as a moving film, where the time from the start to the end of the film depicts the energy change from 1eV to 50eV excess energy.
A cubic spline is interpolated through the parameters as a function of the ratio of excess energy to the ionisation energy of 24.6eV.
These are fitted using a ninth order polynomial fit which closely emulates the cubic spline through the data.
Details of these cubic spline fits to the Blalbl0 parameters can be found by accessing the appropriate interlink page splinefit.htm. The b-parameters which define the normalised DCS as a function of energy and angle can be downloaded here as a text file.
Although the b-parameters do not have a direct physical meaning, they allow the normalised DCS surfaces to be generated at any energy from 1eV to 50eV as has been discussed. 100 of these images have been generated at 0.5eV intervals, and compressed into a Quicktime movie. Note that these files are around 3MB in size, so may take some time to download should internet access be busy. Additionally the evolution of the 44.6eV DCS as successive angular functions are added together can be seen!
Description: Gerardus Mercator (1512-94) is perhaps the only figure in the history of cartography whose name has become a household word, and his system of map projection, called the Mercator projection, is still widely used today, albeit usually in slightly modified forms. The first edition, first state Mercatora€™s map of the North Polar regions, represents the first separate map of the North Polar Regions.
Published one year after his death by his son Rumold, Gerard Mercatora€™s classic map of the arctic is in hemispherical form framed by four medallions and a handsome floral border.
In 1569 Gerard Mercator published an 18-sheet world map using the projection that, to this day, bears his name. In 1595 - never mind 1569 - no explorer had been anywhere near the North Pole, and today we view the ring of islands shown surrounding the North Pole on this map as pure fantasy. Among the ideas shown on this map - ideas which are curious to us today - are that the North Pole was encircled by four land masses, separated from each other by rivers or channels in which the water flowed northwards from the surrounding oceans and then flowed into the earth at the North Pole, flowing beneath a large and tall black rock, 33 leagues around, that is located there.
Another idea, expressed in one of the text annotations on the map, is that a€?pygmies,a€? at most four feet tall, live on one of these four arctic islands. The suggestion that there must be a large mountain of lodestone at the North Pole to account for the eartha€™s magnetism goes back to at least the 13th century, not long after the invention of the compass, but what was the source of the four islands and the inward-flowing rivers, of the mountains and the Pygmies? In the four corners of the map are the title and three insets showing islands of the North Atlantic: the Shetlands, the Faroes, and Frisland. More remarkable than this map itself is the fact that many other contemporary maps, maps by the most respected cartographers of the time, show a very similar configuration around the North Pole.
It should be noted that on world maps centered on the equator, rather than the Pole, the northern islands appear as elongated strips across the top of the map, due to the distortions involved in projecting the surface of a sphere onto a two-dimensional map.
Another surprising feature of the map is the place-name California, which appears on a very northerly part of the American landmass.
Not long after this atlas map was published, the Dutch discovered Spitsbergen, an island archipelago north of Norway.
Smaller sized editions of Mercatora€™s Atlas were produced by a number of Dutch publishers in the early 17th century, and these contained miniaturized versions of this map.
Duzer, Chet Van, a€?The Mythic Geography of the Northern Polar Regions: Inventio fortunata and Buddhist Cosmologya€?, Culturas Populares. Ginsberg, William B., Printed Maps of Scandinavia and the Arctic 1482-1601, New York, Septentrionalium Press, 2006, pp. Electron-electron angular correlation experiments, or so-called (e,2e) coincidence experiments, provide the most detailed test of theories which attempt to describe the ionisation of a target atom by an incoming electron. The parameters (Ea,qa,fa,Eb,qb,fb) are freely selectable experimentally within the constraints that energy and momentum must be conserved during the collision.
In the experiments described here the DCS has been measured in the perpendicular plane using a helium target with incident electron energies ranging from 10eV to 80eV above the ionisation threshold. The electron coincidence spectrometer was designed to measure angular and energy correlations between low energy electrons emerging from near-threshold electron impact ionisation of helium and is capable of accessing all geometries from the perpendicular plane to coplanar geometry.
A number of modifications to the original spectrometer as described in Hawley-Jones et al (1992) have been implemented and are detailed elsewhere. Unique to this (e,2e) electron spectrometer is the computer interface which controls and optimises the spectrometer during normal operation. Figure 2 is a block diagram of the hardware interface between the computer and the spectrometer. At the heart of the operation is an IBM 80286 PC which controls the spectrometer and receives information about the system status from monitors around the spectrometer. The electrostatic lens and deflector voltages in the system are supplied by separate optically isolated active supplies controlled by 12A bit digital to analogue converter (DAC) cards, while a digital monitor measures the voltages and currents on the various lens and deflector elements around the system. The analyser positions are measured by potentiometers located in the drive shafts external to the spectrometer, and are monitored by a datalogger located on the main PC bus, which also monitors the EHT supplies and the vacuum pressure in the system. Count rates from the channel electron multipliers and photomultiplier tube are monitored by a 32 bit counter board, and the TAC output is sent directly to an MCA card installed in the main PC. The software controlling the electron coincidence spectrometer is written to address specific tasks unique to the coincidence experiment. The main PC controls the spectrometer lens and deflector tuning during operation, optimising these voltages using a Simplex method.
Following input of relevant control information, the system is switched to computer control. The electron gun is then optimised to the counts detected by the photomultiplier tube, thus ensuring that the electron current is focussed to a beam of diameter approximately 1mm at the gas jet.
The analyser input lenses and deflectors are then adjusted by the computer to optimise the non-coincidence counting rate of each analyser.
A coincidence correlation spectrum is then acquired for a predetermined time, after which the analysers are moved to a new position and the optimisation procedure repeated in the inner loop. Once the analysers have moved around the detection plane, the whole system is reoptimised and the process of data collection repeated.
A correlation function between the scattered and ejected electrons is therefore accumulated over many sweeps of the detection plane until the results are statistically significant. During operation the running conditions are monitored every 50 seconds by the data logger, allowing any anomalies in the data to be accounted for when final results are considered.
Results from experiment for the symmetric case, where the outgoing electrons following the collision have equal energy, are shown in the figures 4a - 4h. In the perpendicular plane, the symmetry about the incident electron beam direction requires that the DCS must be symmetric about f = 180A° and this is evident in the data.
Inspection of the 94.6eV data (35eV scattered and ejected electron energies) indicates that this result does not follow the trends of the other data in the set. The resolution of the spectrometer (~ 1eV) does not allow these contributions to be excluded, and so the 94.6eV data set cannot strictly be considered as part of the overall set of data which is presented here.


The first result in this data set therefore is the same as the first result in the previous set, allowing a convenient point for common normalisation of the data sets.
Above 54.6eV incident energy the results differ markedly, the angular correlation evolving into a single broad peak instead of the three distinct peaks observed in the symmetric case.
This is most clearly evident at 74.6eV incident energy, where the symmetric case shows three distinct peaks of approximately equal intensity, whereas the non-symmetric case shows only a broad featureless structure centred about 180A°. The sets of data shown in figures 4 and 5 were each normalised relative to the result obtained at 34.6eV incident energy, where both the electrons emerge from the interaction region with an energy of 5eV.
The relative angular data presented at any particular energy is normalised by consideration of the electron singles counting rate, which depends on the Double Differential Cross Section at 90A° but is independent of the azimuthal angle f.
The procedure adopted here allows an upper and lower bound to be estimated, as no facility exists to allow these overlap volumes to be accurately determined experimentally as is implemented by other electron scattering groups.
The DDCS gives the probability of obtaining an electron from the scattering event at an angle q1 in a solid angle dW1 at an energy E1 A± dE1.
The solid angle of detection depends upon the geometry and operating potentials of the electrostatic lenses, and is therefore also a function of the detected electron energy. VA(E1) is given by the three way overlap of the gas beam, electron beam and volume as seen by the analyser. The DDCS varies only slowly over the energy range dE accepted by the analyser (Jones et al 1991) as does the efficiency and solid angle of detection of the analyser as determined from electrostatic lens studies. The energy resolution DEA is independent of E1 because the pass energy of the hemispherical deflector is kept constant. This expression can be rearranged to yield the ratios of analyser efficiency and solid angle in terms of the DDCS, singles count rates and overlap volumes at the two energies E1 and E2 for an incident energy Einc.. The ratios on the left-hand side of this equation were obtained from the DDCS data of MA?ller-Fiedler et al (1986) at an incident energy of 200eV for each analyser at the selected energies of interest.
The first three terms in this expression are evaluated directly from the experiment, while the fourth and fifth terms are taken from the data of MA?ller-Fiedler et al (1986).
As no experimental facilities existed to measure these parameters, a SIMION ray-tracing model was set-up to allow a computational determination of these volumetric terms.
The analyser input electrostatic lenses were also modelled to determine the volume viewed at the interaction point for the varying energies of electrons selected. Figure 6 indicates the experimental geometry as viewed by the analysers in the perpendicular plane, where the atomic beam direction is at 45A° to the incident electron beam trajectory.
Table 1 indicates the calculated relationship GV as determined from the SIMION ray tracing model, and these values have been used to calculate the normalisations as given in figure 4. The dominant error in the expression is given by the double differential cross sections as measured by MA?ller-Fiedler et al (1986), since these terms arise four times in the expression, and typically have measurement errors of A± 15%.
This is possible since the q = 90A° coplanar symmetric energy-sharing result is identical to the perpendicular plane f = 180A° energy-sharing result.
Since data was not obtained at an incident energy of 100eV in these experiments, an interpolation between the energy normalised symmetric results yields a relative value.
The uncertainty in the normalisations of the relative energy is approximately A±30%, as discussed in the previous section.
The absolute differential cross sections as presented in figures 4 and 5 therefore have uncertainties of approximately A±44%.
These latter calculations, normalised to one energy, produced results that were close to those of the experiment. A simple descriptive model for the symmetric case illuminates a possible scattering processes involved.
On the other hand the peak that is observed at 180A° can be explained in terms of either single or multiple scattering. In terms of single scattering it is due to the incident electron selecting a bound electron whose momentum is equal in magnitude but opposite in direction to its own momentum. In terms of multiple scattering, particularly at the lower incident energies, the peak at 180A° has additional contributions that may be described by outgoing electron correlations as in the Wannier model. The mass equivalence of the scattered and ejected electrons requires that a quasi-free collision results in electrons emerging at approximately 90A° to each other irrespective of their resulting energies, and so application of this model would once again yield three peaks, although the relative peak intensities might be expected to change. These results predict a single peak at 180A° due to a mechanism following elastic scattering of the incident electron from the nucleus that is more delicate and complex than the quasi-free collision, however the wings at the lower energies in the experiment are not predicted by this model. This may not be entirely unexpected as the DWBA model gives better results at higher energies. The central peak predicted by the theory also differs in width and height from the results presented here, when normalised to the 34.6eV data. DESCRIPTION: It should be emphasized that most of all of the previous maps discussed in these first three volumes have been one-of-a-kind, manuscript maps. The conservatism of the Higden maps (#232) can be explained by their 14th century model, but in the late 15th century a world map appeared in print which was extremely peculiar and whose antecedents we do not know. Among the numerous fine woodcut illustrations and genealogical tables are two double-page maps: one of Palestine and one of the world. The world map is oriented to the East with Asia on top and the other two continents below, T-O style, though the three water divisions (Don, Nile, Mediterranean) are not shown (Book II, #205). This description corresponds completely with the picture on the map and the olive branches also are now clear. Other pictures on the map include two dragons in Libya, crowned kings and a queen in various kingdoms, the Pope in Rome, a figure in the holy land which is perhaps Saint Jerome (a major source for the book), and a phoenix in flames in Africa. This world map is often described as a€?the first modern printed mapa€?, in that it bears no relation to Ptolemy and it is not of medieval schematic type.
Of more convincing pictorial quality is the map of Palestine, which, measuring 58 x 40 cm, presents a birda€™s eye view over the hills and seas of the Holy Land. Over 100 places-names and geographic features are identified, with towns and countries named. Arguably the greatest technical advance in human history was the invention of printing, and it is ironic that the first use of this invention in the service of cartography marked a€?the end of an era rather than the beginning of a new onea€? a€“ Tony Campbell.
Winter, H., a€?Notes on the World map in a€?Rudimentum Novitioruma€?, Imago Mundi, Volume 9, p. This map does not have Adam and Eve in the east (at the top), as others do, but shows, on a mountain from which four rivers rise, within a group of trees, two pulpits with a man in each holding a green leaf in a lifted hand. Of more convincing pictorial quality is the map of Palestine, which, measuring 58 x 40 cm, presents a birda€™s eye view over the hills and seas of the Holy Land.A A  This map is believed to be based upon an important lost delineation of Burchard of Mt. In the later Middle Ages, Ashkenazi Jews migrating to the Byzantine Empire and Ottoman Empire supplemented the original Jewish population of Asia Minor. These experiments have recently been carried out principally by two groups at Kaiserslautern group and at Manchester (see references for examples). This region is now successfully modelled to a large degree using the Born approximation and its associated derivatives. Although theoretical interest in this region is increasing, no theory adequately explains the experimental data accumulated so far.
The Paris coplanar and Manchester Perpendicular plane results at an excess energy of 1eV ionising Helium as the target.
In the experimentally inaccessible regions centred at x = 0A° and x = p the DCS is constrained to be positive and to have no points of inflection, and at the angles x = 0A° and p themselves the DCS is put equal to zero. The choice of la, lb and l0 used to define the subset is arbitrary within the constraint that the angular functions must be unrelated.
These images are established by plotting the magnitude of the angular function against the angles theta and phi that are defined in the function.
These artificially generated points were given low weighting to minimise the constraints placed upon the fit. Consideration of the data sets at all excess energies established that 44 angular functions up to la, lb = 7 and l0 = 6 gave the best overall fit to the data. The fitting parameters can be downloaded as a TAB deliminated text file by linking to the file Blalbl0.dat.
Further information can be obtained by linking from the figures to the appropriate WWW page. 3-D representations of the DCS calculated from the fitted parameters Blalbl0 for the 8 data sets from 1eV to 50eV.
The 3D Quicktime movie can be downloaded at the end of this page by linking to the appropriate file. Mercator was famous for his meticulous research and accuracy, and thus it is quite a surprise to see for the first time Mercatora€™s map of the northern polar regions, Septentrionalium terrarum descriptio (1595): the map shows a North Pole that is very unfamiliar to modern eyes. The Mercator Projection increasingly spreads out the vertical space required to portray each degree as the latitude increases towards each pole. Yet Mercator based his polar depiction on the most credible information available to him at the time. This latter, Frisland, is one of the a€?phantoma€? islands that have appeared over the centuries in maps of the Atlantic.
Martin Behaim (Book III, #258), who died before Mercator was born, made a famous globe in 1492 (this is in fact the oldest surviving terrestrial globe) that shows land surrounding the North Pole.
There are many, many other contemporary maps, literally scores, including examples from as late as the 1700s that show the same configuration of islands around the Pole. Mercatora€™s Septentrionalium terrarum descriptio was popular enough to inspire a number of blatant imitations, including maps by Matthis Quad (Cologne, 1600), Petrus Bertius and Jodocus Hondius Jr.
This is not the first time the name California appeared on a printed map (it first appeared in a map published in 1562), but the northern location of the place-name on Mercatora€™s map is very unusual. Jodocus Hondius, who acquired the plates to Mercatora€™s Atlas in 1604, made a change to this plate, erasing part of one of the four arctic landmasses and putting in a depiction of Spitsbergen. Two smaller versions of this map were also published by the Cologne mapmaker Matthias Quad, the first of these in 1600. These experiments measure the angular correlation between a projectile electron which is scattered from a target and a resulting electron which is ionised from the target. For an unpolarised target and unpolarised incident electron beam the only azimuthal angle of significance is given by f = fa - fb. When the electrons are detected in the perpendicular plane, the two angles qa and qb are both equal to 90A°. The perpendicular plane is accessed mainly through double collision processes (Hawley-Jones et al (1992), which represent only part of the full dynamical picture. The computer loads all the voltage supplies from either a manually selected set of voltages or from the results of a previous optimisation run. This decouples the tuning of the electron gun from any tuning requirements of the electron analysers. This should be compared with the data obtained near threshold by Hawley-Jones et al (1992), which also shows a single peak with an approximately Gaussian structure. This is considered to be due to the contribution to the cross section of a number of resonances in helium for scattered and ejected electron energies around 35eV. The model indicated that the electron gun operating at the voltages determined by the optimisation routines produced an electron beam of diameter approximately 1.0mm at the interaction region, consistent with the tuning of the electron beam onto counts from the photomultiplier which views a 1mm3 volume.
For the non-symmetric data no compensation is required for volume effects since GV = 1.0 at all values of Ei.
The electrons are then able to emerge at approximately 90A° with respect to each other in the perpendicular plane, as is observed. As the momentum distribution of the bound electron peaks at zero for helium, the peak at 180A° diminishes with increased incident electron energy as the probability of finding a bound electron with the required momentum decreases. Printed in LA?beck in 1475, the map was an illustration for a universal history in Latin entitled Rudimentum Novitiorum sive chronicarum historiarum epitome [A Handbook for Beginners].
The province of Palestine is more or less in the center, where Jerusalem, unnamed, is represented by a formidable castle. They are not, however Adam and Eve, but two men, each holding what may be an olive branch in his hand, apparently having a conversation. They undertook to unite themselves in the pleasures of (worldly) goods and the love of God in one law and in one road to wisdom.
This question is interesting also for the cartographer, considering that it is the first reliably dated printed map. A man-eating devil in northern Asia is already in the process of devouring a victima€™s severed arm. Each country is represented as a separate hill accompanied by either a figure of the sovereign or several small buildings representing towns. It contains the reproduction of a theological treatise a€?De Adventu Messiea€? taken from a MS. Beginning with the invention in Europe of the printing process and the publication of the first printed map in 1472, the traditional T-O map in the EtymologiA¦ of St. Sion, the 13th century Dominican from Magdeburg whose account and map of his pilgrimage (Prologus) were widely known throughout late medieval and early renaissance Europe.
The Wannier model parameterisation transformed to the (y,x) geometry is shown as a fit to the data. The function can either be positive or negative depending upon the value of theta and phi, and the sign is therefore represented by two colours, PURPLE indicating a positive magnitude and RED representing a negative magnitude. The example here shows the method for finding the minimum of a 3-D Gaussian function of the form z = - exp(-x^2 + y^2). Higher resolution images together with a downloadable EPS file for each of the data sets can be obtained by linking to either of the above low resolution images. At the center of the map, and right at the Pole, stands a huge black mountain; this mountain was made of lodestone, and was the source of the eartha€™s magnetic field. This map, the first separate map devoted to the Arctic regions, is drawn from an inset on Mercatora€™s world map of 1569 (#406). In fact, an infinite spread would be required to reach the actual North or South Pole in this projection. Ruysch (#313) cites the same sources, and Fridtjof Nansen (In Northern Mists: Arctic Exploration in Early Times) argues convincingly that Behaim (#258) was working from the Inventio fortunata also. There are two large islands right near the Pole in the western hemisphere, while extensions of Europe and Asia reach northwards so as to form, together with the two islands just mentioned, a broken circle of land around the Pole.


These maps are derived from the world maps of the Jesuit missionary Matteo Ricci (1552-1610), who established a mission at Zhaoquing Prefecture (in present-day Guangdong Province) in 1583. Mercatora€™s Atlas went through many editions, under the stewardship of Hondius and his brother-in-law Jan Jansson. But by the 1630a€™s cartographers had begun to doubt the island-encircled view of the North Pole, and began producing maps showing a blank polar area - more accurately reflecting the lack of knowledge that existed at the time.
Further it allows the electron gun to be aligned and focussed accurately onto the interaction region whose centre is located at the intersection of the axes of rotation of the analysers and the electron gun.
This type of double collision process must therefore be modelled using higher order scattering terms as is done using the DWBA. According to its publisher, Lucas Brandis, it was designed so that a€?poor men unable to afford a library can have a brief manual always on hand in place of many books.a€? The paupers of whom Brandis spoke may have meant poor preachers or friars minor but also may have referred to a growing number of book owners among the merchant class in a thriving commercial city such as LA?beck. In the west, three columns stand for the Pillars of Hercules at the entrance of the Mediterranean. Schwarz arrives only at the conclusion that the author had been a cleric, and infers from the word noster at a specific place that the author was of Lubeck or its vicinity. We do not know if there was a manuscript version that formed its base, as none has ever been found, but there are a great number of universal histories of this type, which were very popular in the late Middle Ages. Theodore Schwarz describes this image only very briefly, although it is natural to see in them two disputing men, two priests.
Shirley.A  The Rudimentum Novitiorum would go on to become more widely known through later French translations under the title Mer des Hystoires.
Despite emigration during the 20th century, modern day Turkey continues a Jewish population.The present size of the Jewish Community is estimated at around 26,000 according to the Jewish Virtual Library. This electron, and the incident electron that has lost almost all of its energy in the reaction have similar energies and therefore as they emerge from the reaction zone feel the Coulombic influence of each other and the ion core following ionisation. The scattering is more complex than in the threshold region, since the incident electron can penetrate deeper into the neutral target electron cloud, and therefore there is more complex interactions between the electrons and the core. The Simplex, in this case a 2-D triangle whose vertices are defined by points on the surface, proceeds by reflection, contraction, expansion or shrinking along the surface as shown.
The central mountain is surrounded by open water, and then further out by four large islands that form a ring around the Pole.
The map is extended to 60 degrees, to incorporate the recent explorations in search of the North West and North East Passages by Frobisher and Davis. No copy of this book is known to have survived, but Mercator quoted from this book in letters he wrote to the British polymath John Dee, in which he explained the source of his ideas regarding the geography of the far north. Mercator and his contemporaries believed the author of the Inventio fortunata, the English Minorite, to be Nicholas de Linna (Nicholas of Kinga€™s Lynn); others have argued against this identification. Mercator copied Frisland from an Italian map of the mid 16th century, but he was unknowingly perpetuating an earlier cartographera€™s error since no island actually exists in that location.
Mercator-influenced maps also appear in Japan: Abe Yasuyukia€™s Banukoku Chikyu Yochi Zenzu or Map of the World (1853), shows the four northern islands. Only the first two editions of the Atlas, published by Mercatora€™s son Rumold in 1595 and 1602, contain the pre-Spitsbergen version of this map. This is essential for experiments where all of these may be varied over 3-Dimensional space.
Like Higden, the anonymous author of Rudimentum included several lengthy geographical digressions, one on the world and one on the holy land.
The mapa€™s most striking feature is its conformation of the land as a succession of a€?hillocksa€?, each surmounted by a castle or tower and bearing the name of a province or territory.
The scholar Anna-Dorothee von den Brincken thinks they might be a Jew and a Christian having a harmonious discussion, thus symbolizing the unity of the Old and New Testaments.
If, however, the second is true, it would be interesting to know why the words of the Majorcan scholar (born 1235) found an echo precisely in LA?beck. We must however note that this would be true only for the version printed in Lubeck but not of possible of the earlier MSS. Von den Brincken notes that the twenty years before the booka€™s publication are barely covered in the history and opines that the printer updated an older work. The leaf, the well-known symbol of peace, might signify here that the disputing men are not enemies, but friends. The prologue of the treatise shows that the idea on which the drawing in Rudimentum Novitiorum is based is not original. If, however, the second is true, it would be interesting to know why the words of the Majorcan scholar (born 1235) found an echo precisely in Lubeck. The low relative velocity of the electrons allows them to mutually interact for sufficient time to tightly correlate their respective asymptotic directions. There is now a finite probability of exchange, capture, ingoing and outgoing correlations between all charged particles in the reaction.
The largest of these islands perhaps 700 by 1100 miles, and they all have high mountains along their southern rims.
California is identified as Spanish Territory and El Streto de Anian [Alaskaa€™s Bering Strait] is clearly shown. Mercator, however, wanted to depict the north polar regions on his map, so he came up with the idea of including a small inset map, on a polar projection, which he drew in the lower left-hand corner of his large wall map. He labels the waters within the four islands as the Mare Sugenum, and speaks of a violent whirlpool that sucks the incoming waters down into the earth; in addition, his map shows a ring of small, very mountainous islands around the four islands, which numerous islands Ruysch says are uninhabited. Basically though Mercatora€™s view of the northern regions lost favor after 1598, when the Dutchman Willem Barentsz made his famous chart of the northern polar regions showing open water there. The Rudimentum is a fascinating world history and encyclopedia structured on medieval Christian theology.
Another idea is that they represent Enoch and Elijah, Old Testament characters who went directly to heaven without suffering death. In this grove for a long time they disputed in friendly conversation the advent of the Messiasa€?. Burcharda€™s narrative account appears in its entirety in the same third section as the map of Palestine in Rudimentum Novitiorum. The book was, however, translated into French, maps and all, under the title Mer des Hystoires in 1488. The question is now: is this an original idea of the artist, or is it based on something which existed before? Rav Izak Haleva, is assisted by a religious Council made up of a Rosh Bet Din and three Hahamim. This leads to both forward and backward scattering possibilities, depending upon the complexity of these interactions.
In this map the pole itself is made up of four surrounding islands, which myth had it were separated by four strong flowing rivers. The map shown here, published in the first edition of Mercatora€™s famous Atlas, is basically a copy of the polar inset from his 1569 world map, but with some added features.
Paradise is not labeled, but near one of the streams is the word Evilath [Havilah], one of the regions watered by the four rivers mentioned in the book of Genesis.
Sinai are the burning bush and Moses receiving the Tablets of the Law, and, on Calvary, the Crucifixion.A  This map of Palestine is considered the earliest printed regional map. Mercatora€™s notes inform us that the waters of the oceans are carried northward to the Pole through these rivers with great force, such that no wind could make a ship sail against the current. These carried the oceans of the world towards a giant whirlpool at the pole where there stood a large rock. There is no encircling ocean, and the only labeled sea is a€?Mare Amasorieo,u,,,, in the north, possibly intended for the Caspian Sea. Or these may be the Master and his Novice, source of rivers and all knowledge; alternatively according to Winter they may represent a€?.
The French editor added material on French history and some new illustrations, including a woodcut of the baptism of Clovis.
The waters then disappear into an enormous whirlpool beneath the mountain at the Pole, and are absorbed into the bowels of the earth. On the re-cut map a few new images appear-ships, birds, and trees-but the basic format was unchanged.
Published in 1475, the illustrated world history, Rudimentum Novitiorum, included two remarkable maps - one of Palestine and this one of the world.
A bronze column found in Ankara confirms the rights the Emperor Augustos accorded the Jews of Asia Minor.Ottoman Period,1299 - 1492 As the Ottoman Empire expands more and more Jewish populations , mostly Romaniot ( Greek-speaking Jews who lived in the Roman Empire ) are incorporated into Ottoman lands.
Of many examples, Nicomedia (from Asia Minor) is shown next to the Pope near Rome and again in Africa, perhaps an error for Numidi, India is north of Persia, which is next to Taprobana. They are officially recognised as dhimmi,a protected non-Muslim community.1326 The Ottoman capture Bursa and make in their capital. The Septentrionalium terrarum descriptio was printed (posthumously) in 1595, and is very similar to an inset map of the northern polar region Mercator made on his world map of 1569, Nova et aucta orbis terrae descriptio ad usum navigantium emendate accommodata, commonly referred to as Ad usum navigantium.
Founded by Ashkenazim of Austrian origin in 1900, it is the last remaining synagogue among a total of three built by Ashkenazim. The question is now whether the same pictorial representation is not found in possible earlier MSS.
Visits con be made during weekday mornings and for Shabbat services on Saturday mornings.,The Neve Shalom Synagogue ,uilt and opened in 1951 and the scene of a tragic terrorist attack in 1986, it is the largest synagogue in Istanbul where most of the religiou,s ceremonies are held. The Neve Shalom is open to the public for morning visits during the weekdays and for Shabbat prayers every Saturday morning.,,The Ahrida Synagogue ,Located in Balat near the Golden Horn, built by Jews of Ohri (Macedonia) more than 550 years ago and recently renovated during the Quincentennial Celebrations in 1992, the Ahrida Synagogue is known foremost by its boat-shaped bimah.
The challenged typesetter, working backwards, probably had some problems with the difficult geographical names. 4914 of 1381, and 4915, of about the same time), but according to a kind communication from the Bibl.
It can only be visited during weekday mornings.,Etz Ahayim Synagogue ,Located in Ortakoy, near the European leg of the Bosphorus Bridge. When the previous synagogue burned down in 1941 with only the marble Aron-ha-Kodesh remaining, the new synagogue was rebuilt on the location of the then midrash. In an article by Carmelo Ottaviano there is a reproduction of a theological treatise a€?De Adventu Messiea€? taken from a MS. Indeed, Turkey could serve as a model to be emulated by any nation which finds refugees from any of the four corners of the world standing at its doors.In 1992, Turkish Jewry celebrated not only the anniversary of this gracious welcome, but also the remarkable spirit of tolerance and acceptance which has characterized the whole Jewish experience in Turkey. The events being planned - symposiums, conferences, concerts, exhibitions, films and books, restoration of ancient Synagogues etc - commemorated the longevity and prosperity of the Jewish community.
As a whole, the celebration aimed to demonstrate the richness and security of life Jews have found in the Ottoman Empire and the Turkish Republic over seven centuries, and showed that indeed it is not impossible for people of different creeds to live together peacefully under one flag.,A History Predating 1492 The history of the Jews in Anatolia started many centuries before the migration of Sephardic Jews.
A bronze column found in Ankara confirms the rights the Emperor Augustus accorded the Jews of Asia Minor.Jewish communities in Anatolia flourished and continued to prosper through the Turkish conquest. When the Ottomans captured Bursa in 1326 and made it their capital, they found a Jewish community oppressed under Byzantine rule. Sultan Orhan gave them permission to build the Etz ha-Hayyim (Tree of Life) synagogue which remained in service until nineteen forties.Early in the 14th century, when the Ottomans had established their capital at Edirne, Jews from Europe, including Karaites, migrated there.
In fact, from the early 15th century on, the Ottomans actively encouraged Jewish immigration.
Double continuum wave functions and threshold law for electron atom ionisation, Physics Review A. In 1537 the Jews expelled from Apulia (Italy) after the city fell under Papal control, in 1542 those expelled from Bohemia by King Ferdinand found a safe haven in the Ottoman Empire. Half a century later, 8070 Jewish houses were listed in the city.The Life of Ottoman Jews For 300 years following the expulsion, the prosperity and creativity of the Ottoman Jews rivalled that of the Golden Age of Spain.
Another Portuguese Marrano, Alvaro Mendes, was named Duke of Mytylene in return of his diplomatic services to the Sultan.Salamon ben Nathan Eskenazi arranged the first diplomatic ties with the British Empire. As a result, leadership of the community began to shift away from the religious figure to secular forces.,,World War I brought to an end the glory of the Ottoman Empire.
In 1926, on the eve of Turkey's adoption of the Swiss Civil Code, the Jewish Community renounced its minority status on personal rights.During the tragic days of World War II, Turkey managed to maintain its neutrality. As early as 1933 Ataturk invited numbers of prominent German Jewish professors to flee Nazi Germany and settle in Turkey. Before and during the war years, these scholars contributed a great deal to the development of the Turkish university system.
During World War II Turkey served as a safe passage for many Jews fleeing the horrors of the Nazism. While the Jewish communities of Greece were wiped out almost completely by Hitler, the Turkish Jews remained secure.
The vast majority live in Istanbul, with a community of about 2.500 in Izmir and other smaller groups located in Adana, Ankara, Antakya, Bursa, Canakkale, Kirklareli etc.
There are about 100 Karaites, an independent group who does not accept the authority of the Chief Rabbi.Turkish Jews are legally represented, as they have been for many centuries, by the Hahambasi, the Chief Rabbi. Fifty Lay Counsellors look after the secular affairs of the Community and an Executive Committee of fourteen runs the daily matters.
Representatives of Jewish foundations and institutions meet four times a year as a so-called ??think tank?? Some of them are very old, especially Ahrida Synagogue in the Balat area, which dates from middle15th century.
The 15th and 16th century Haskoy and Kuzguncuk cemeteries in Istanbul are still in use today.,??The Museum of Turkish Jews?? Additionally, the Community maintains in Istanbul a school complex including elementary and secondary schools for around 700 students. Turkish is the language of instruction, and Hebrew is taught 3 to 5 hours a week.,While younger Jews speak Turkish as their native language, the over-70-years-old generation is more at home speaking in French or Judeo-Spanish (Ladino). Graetz, History of the JewsJewish communities in Anatolia flourished and continued to prosper through the Turkish conquest.



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