Golomb and Gaal [15] study the number of permutations on n objects with largest cycle length equal to k. They give explicit expressions on ranges n/(i + 1) < k ≤ n/ i for i = 1, 2, . . . , derive a general recurrence for the number of permutations of size n with largest cycle length equal to k, and provide the contribution of the ranges (n/(i + 1), n/ i] for i = 1, 2, . . . , to the expected le...

Abstract For a random binary noncoalescing feedback shift register of width $n$ , with all $2^{2^{n-1}}$ possible functions $f$ equally likely, the process long cycle lengths, scaled by dividing $N=2^n$ converges in distribution to same Poisson–Dirichlet limit as holds for permutations $\mathcal{S}_N$ $N!$ likely. Such behaviour was conjectured Golomb, Welch and Goldstein 1959.

In many industrial and non-industrial applications, it is necessary to identify the largest inscribed rectangle in a certain shape. The problem is studied for convex and non-convex polygons. Another criterion is the direction of the rectangle: axis aligned or general. In this paper a heuristic algorithm is presented for finding the largest axis aligned inscribed rectangle in a general polygon. ...

In this paper, we show that the largest signless Laplacian H-eigenvalue of a connected k-uniform hypergraph G, where k ≥ 3, reaches its upper bound 2∆(G), where ∆(G) is the largest degree of G, if and only if G is regular. Thus the largest Laplacian H-eigenvalue of G, reaches the same upper bound, if and only if G is regular and oddbipartite. We show that an s-cycle G, as a k-uniform hypergraph...

We report on the solar and interplanetary (IP) causes of third largest geomagnetic storm (2018 August 26) in cycle 24. The underlying coronal mass ejection (CME) originating from a quiescent filament region becomes 440 km/s magnetic cloud (MC) at 1 au after ~5 days. prolonged CME acceleration (for about 24 hrs) coincides with time profiles post-eruption arcade intensity reconnected flux. Chen e...

Electricity generation in thermal power plants as the largest producer of electricity in Iran is associated with greenhouse gas emissions. In this paper, using the Malmquist-Luenberger method, green productivity, and efficiency changes are measured for 31 thermal power plants (including 12 steam power plants, 13 gas power plants, and six combined cycle power plants) during 2009-2016. The result...

We solve an interesting optimization problem motivated by tolerancing metrology, paper position sensing, and facility location: What rectangle fits best a given set of points? This problem has relations to the minimum width annulus problem and also to the largest empty rectangle problem for both of which O(n log n) time solutions are not known. Nevertheless, for our problem there is a linear ti...