We define the complex powers of a densely defined operator A whose resolvent exists in a suitable region of the complex plane. Generally, this region is strictly contained in an angle and there exists α ∈ [0,∞) such that the resolvent of A is bounded by O((1 + |λ|)α) there. We prove that for some particular choices of a fractional number b, the negative of the fractional power (−A)b is the c.i....

We consider the problem of recovering l-adic representations from a knowledge of the character values at the Frobenius elements associated to l-adic representations constructed algebraically out of the original representations. These results generalize earlier results in [Ra] concerning refinements of strong multiplicity one for l-adic represntations, and a result of Ramakrishnan [DR] recoverin...

The extended power construction can be used to create new framed manifolds out of old. We show here how to compute the effect of such operations in the Adams spectral sequence, extending partial results of Milgram and the author. This gives the simplest method of proving that Jones’ 30manifold has Kervaire invariant one, and allows the construction of manifolds representing Mahowald’s classes η...

The aim of this paper was to present an optimized method in order to use maximum capacity of the photovoltaic panels. In this regard, we presented a method for the maximum power point tracking in the photovoltaic systems by using the neural networks and adaptive controller. In the proposed system, we estimated an error by using neural network. If this error is lower than the allowable systems e...

With deregulation and growth of the power industry, many power system elements such as generators, transmission lines, are driven to operate near their maximum capacity, especially those serving heavy load centres. Wide Area Controllers (WACs) using wide area or global signals can provide remote auxiliary control signals to local controllers such as automatic voltage regulators, power system st...

In general in an organisation whose system of governance involves weighted voting, a member's weight in terms of the number of votes and the formal power it represents differ. Power indices provide a means of analysing this difference. The paper uses new algorithms for computing power indices for large games. Three analyses are carried out: (1) the distribution of Banzhaf voting power among mem...

We construct all possible orthogonally intersecting S-brane solutions in 11-dimensions corresponding to standard supersymmetric M-brane intersections. It is found that the solutions can be obtained by multiplying the brane and the transverse directions with appropriate powers of two hyperbolic functions of time. This is the S-brane analog of the " harmonic function rule ". The transverse direct...

Introduction. The sums formed from the set of non-negative powers of 2 are just the non-negative integers. It is easy to obtain “abelian” results to the effect that if a set is distributed like the powers of 2, then the sum set will be distributed like Dhe non-negative integers. We will be concerned here with converse, or “Tauberian” results. The main theme of this paper is t’he following quest...

We examine the problem of writing every sufficiently large even number as the sum of two primes and at most K powers of 2. We outline an approach that only just falls short of improving the current bounds on K. Finally, we improve the estimates in other Waring–Goldbach problems.

In this paper we study the exact orders of lacunary sums of binomial coefficients. It is remarkable that the periodic patterns evolving from powers of 2 differ markedly from those of other prime powers. For the latter ones the pattern is transparent and is determined by the first term. For the former ones multisected generating functions are used to obtain the exact order or lower bounds on it.