Wind turbines are often controlled to harvest the maximum power from wind, which corresponds operation at top of bell-shaped coefficient graph. Such a mode may be achieved implementing an extremum seeking data-based strategy, is invasive technique that requires injection harmonic disturbances. Another approach based on knowledge analytic expression function, information usually unreliably provi...

The spectral problem where the field satisfies Dirichlet conditions on one part of the boundary of the relevant domain and Neumann on the remainder is discussed. It is shown that there does not exist a classical asymptotic expansion for short time in terms of fractional powers of t with locally computable coefficients. MSC Classification: 58G25

We prove universal recursive formulas for Branson’s Q-curvature of order eight in terms of lower-order Q-curvatures, lower-order GJMSoperators and holographic coefficients. The results confirm a special case of a conjecture in [On conformally covariant powers of the Laplacian, arXiv:0905.3992v3].

1 . Sequences of positive integers with the consecutive integer property. Consider a sequence of k positive integers {ai} = a,, . . ., a k with the following properties : (i) ai < k for all i, (ü) (the consecutive integer property) There is an n such that ai is the quotient when n + i is cleared of all its prime factors greater than k . Or, for each prime p k, the pattern of that prime and its ...

We introduce and study elliptic zeta values, a two-parameter deformation of the values of Riemann’s zeta function at positive integers. They are essentially Taylor coefficients of the logarithm of the elliptic gamma function, and share the SL(3,Z) modular properties of this function. Elliptic zeta values at even integers are related to Eisenstein series and thus to sums of odd powers of divisor...

Suppose f(x, y) is a binary form of degree d with coefficients in a field K ⊆ C. The K-rank of f is the smallest number of d-th powers of linear forms over K of which f is a K-linear combination. We prove that for d ≥ 5, there always exists a form of degree d with at least three different ranks over various fields. The K-rank of a form f (such as x3y2) may depend on whether -1 is a sum of two s...

For a pseudodifferential boundary operator A of order ν ∈ Z and class 0 (in the Boutet de Monvel calculus) on a compact n-dimensional manifold with boundary, we consider the function Tr(AB−s), where B is an auxiliary system formed of the Dirichlet realization of a second order strongly elliptic differential operator and an elliptic operator on the boundary. We prove that Tr(AB−s) has a meromorp...