For a vertex v of a connected graph G and a subset S of V (G), the distance between v and S is d(v, S) = min{d(v, x)|x ∈ S}. For an ordered k-partition Π = {S1, S2, · · · , Sk} of V (G), the representation of v with respect to Π is the k-vector r(v|Π) = (d(v, S1), d(v, S2), · · · , d(v, Sk)). The k-partition Π is a resolving partition if the k-vectors r(v|Π), v ∈ V (G), are distinct. The minimu...

In this paper we consider several generalizations of the skew t-normal distribution, and some of their properties. Also, we represent several theorems for constructing each generalized skew t-normal distribution. Next, we illustrate the application of the proposed distribution studying the ratio of two heavy metals, Nickel and Vanadium, associated with crude oil in Shadgan wetland in the south-...

Despite many advantages of BrushLess DC motor, torque pulsation is one of the most important disadvantages of it. At first, an optimum primary design of BLDC motor is done using PSO algorithm. Then, other parameters for reducing the torque pulsation are considered by finite element method. It is shown that fractional slot structure has many advantages than conventional one. Both cogging and rip...

In this paper, we introducte a family of univariate Birnbaum-Saunders distributions arising from the skew-normal-t  distribution. We obtain several properties of this distribution such as its moments, the maximum likelihood estimation procedure via an EM-algorithm and a method to evaluate standard errors using the EM-algorithm. Finally, we apply these methods to a real data set to demonstr...

Clock skew is an increasing concern for high-speed circuit designers. Circuit designers use transparent latches and skew-tolerant domino circuits to hide clock skew from the critical path and take advantage of shared portions of the clock network to budget less skew between nearby elements than across the entire die, but current timing analysis algorithms do not handle correlated clock skews. T...

Let the sign of a skew standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. We examine how the sign property is transferred by the skew Robinson-Schensted correspondence invented by Sagan and Stanley. The result is a remarkably simple generalization of the ordinary non-skew formula. The sum of the signs of all standard tableaux ...

We obtain a near-tight bound of O(n), for any ε > 0, on the complexity of the overlay of the minimization diagrams of two collections of surfaces in four dimensions. This settles a long-standing problem in the theory of arrangements, most recently cited by Agarwal and Sharir [3, Open Problem 2], and substantially improves and simplifies a result previously published by the authors [17]. Our bou...

Two skew cyclic codes can be equivalent for the Hamming metric only if they have the same length, and only the zero code is degenerate. The situation is completely different for the rank metric, where lengths of codes correspond to the number of outgoing links from the source when applying the code on a network. We study rank equivalences between skew cyclic codes of different lengths and, with...