732,118 research outputs found
Power Series Composition and Change of Basis
Efficient algorithms are known for many operations on truncated power series
(multiplication, powering, exponential, ...). Composition is a more complex
task. We isolate a large class of power series for which composition can be
performed efficiently. We deduce fast algorithms for converting polynomials
between various bases, including Euler, Bernoulli, Fibonacci, and the
orthogonal Laguerre, Hermite, Jacobi, Krawtchouk, Meixner and
Meixner-Pollaczek
On generating series of finitely presented operads
Given an operad P with a finite Groebner basis of relations, we study the
generating functions for the dimensions of its graded components P(n). Under
moderate assumptions on the relations we prove that the exponential generating
function for the sequence {dim P(n)} is differential algebraic, and in fact
algebraic if P is a symmetrization of a non-symmetric operad. If, in addition,
the growth of the dimensions of P(n) is bounded by an exponent of n (or a
polynomial of n, in the non-symmetric case) then, moreover, the ordinary
generating function for the above sequence {dim P(n)} is rational. We give a
number of examples of calculations and discuss conjectures about the above
generating functions for more general classes of operads.Comment: Minor changes; references to recent articles by Berele and by Belov,
Bokut, Rowen, and Yu are adde
Character formulas for the operad of two compatible brackets and for the bihamiltonian operad
We compute dimensions of the components for the operad of two compatible
brackets and for the bihamiltonian operad. We also obtain character formulas
for the representations of the symmetric groups and the group in these
spaces.Comment: 24 pages, accepted by Functional Analysis and its Applications, a few
typos correcte
The making of Britain’s first urban landscapes: the case of late Iron Age and Roman Essex
This paper presents preliminary research into the social and economic impact of early urban settlement in Britain, focusing on the case-study area of Late Iron Age to Roman Essex. Through fresh analysis of ceramic assemblages from Colchester and Heybridge, we describe hitherto unrecognised socio-cultural groupings and identities through subtle differences in the deposition of pottery in the generations before and after conquest. The concluding discussion concentrates on problems that we still have to address in describing the economic basis of early urban society in Britain
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Structural coupling and magnetic tuning in Mn2–x CoxP magnetocalorics for thermomagnetic power generation
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