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The swallowtail integral in the highly oscillatory region II. ETNA - Electronic Transactions on Numerical Analysis
No full textWe analyze the asymptotic behavior of the swallowtail integral \\int_{-\\infty}^\\infty e^{i(t^5 +xt^3+yt^2+zt)}dt for largevalues of and bounded values of and . We use the simplified saddle point method introducedin [López et al., J. Math. Anal. Appl., 354 (2009), pp. 347–359].With this method, the analysis is more straightforward than with the standard saddle point method,and it is possible to derive complete asymptotic expansions of the integral for large and fixed and .There are four Stokes lines in the sector that divide the complex -plane into four sectors inwhich the swallowtail integral behaves differently when is large. The asymptotic approximation is the sum oftwo asymptotic series whose terms are elementary functions of , , and .One of them is of Poincaré type and is given in terms of inverse powers of . The other one is given in terms of an asymptotic sequence whose terms are of the order of inverse powers of when , and it is multiplied by an exponential factor that behaves differently in the four mentioned sectors. Some numerical experiments illustrate the accuracy of the approximation
Nuragic Pottery from Hala Sultan Tekke: The Cypriot-Sardinian Connection
No full textThe present paper describes, for the first time, Cypriot evidence of Nuragic tableware from Sardinia discovered at Hala Sultan Tekke. This Late Bronze Age harbour and trade metropolis is situated near modern Larnaca on the southern littoral of Cyprus. The city’s exceptional wealth during the Late Bronze Age (1650–1050 BCE) was based on trade and cross-cultural connections with a vast area, including the entire Aegean, Anatolia, the Levant and Egypt. This is exemplified by the enormous amount of imported goods, most of which originated in the Mycenaean sphere of culture. Five handmade and burnished bowls of dark grey fabric with highly lustrous surfaces found at Hala Sultan Tekke were recently identified as imports from Sardinia. The main purpose of this article is to provide primary information about these exceptional finds and to place them in the context of trade between Sardinia and the eastern Mediterranean
