Conservation laws for multidimensional systems and related linear algebra problems

We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order t-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for existence of higher conservation laws in terms of the system's symbol. For systems that violate this condition we give an effective upper bound on the order of conservation laws. Using this result, we completely describe conservation laws for viscous transonic equations, for the Brusselator model, and the Belousov-Zhabotinskii system. To achieve this, we solve over an arbitrary field the matrix equations SA=A^tS and SA=-A^tS for a quadratic matrix A and its transpose A^t, which may be of independent interest.Comment: 12 pages; proof of Theorem 1 clarified; misprints correcte

Combining Relative Chronology and AMS 14C Dating to Contextualize ‘Megasites’, Serial Migrations and Diachronic Expressions of Material Culture in the Western Tripolye Culture, Ukraine

Scholarship regarding the Eneolithic Cucuteni-Tripolye cultural complex of Romania, Moldova and Ukraine has recently focused on ‘megasites’ of the Western Tripolye culture (WTC) in Central Ukraine. However, in order to properly contextualize such unusual phenomena, we must explore the broader typo-chronology of the WTC, which is suggestive of a high degree of mobility and technological transfer between regions. We report 28 new AMS 14C dates from sites representing diagnostic types and propose a high-resolution chronological sequence for the WTC’s development. Our results support the relative chronology and offer an opportunity to propose a new chronological synthesis for the WTC