Abstract The cable layout optimisation for floating offshore wind farms is a complex task due to the number of elements involved and their nature, such as dynamic cables with buoyant sections. first step defining model suspended that connect turbines between them or on seabed (risers). A lumped mass finite element method are used find static position mechanical stresses cables, keeping balance ...

We prove that the generic quantized coordinate ringOq(G) is Auslander-regular, Cohen-Macaulay, and catenary for every connected semisimple Lie group G. This answers questions raised by Brown, Lenagan, and the first author. We also prove that under certain hypotheses concerning the existence of normal elements, a noetherian Hopf algebra is Auslander-Gorenstein and Cohen-Macaulay. This provides a...

The trajectory of a rider slowly traversing a zipline of fixed length and endpoints is computed, as a one-dimensional illustration of the curving of spacetime by a mass. As the rider’s weight increases from 0 to ∞, the trajectories uniformly interpolate between a catenary and an ellipse. These results are obtained by balancing forces in the horizontal and vertical directions, so that the treatm...

Let us consider a 3-numerical semigroup S = 〈a, b,N 〉. Given m ∈ S, the triple (x, y, z) ∈ N3 is a factorization of m in S if xa+ yb+ zN = m. This work is focused on finding the full set of factorizations of any m ∈ S and as an application we compute the catenary degree of S. To this end, we relate a 2D tessellation to S and we use it as a main tool.

Problems involving chains of irreducible factorizations in atomic integral domains and monoids have been the focus of much recent literature. If S is a commutative cancellative atomic monoid, then the catenary degree of S (denoted c(S)) and the tame degree of S (denoted t(S)) are combinatorial invariants of S which describe the behavior of chains of factorizations. In this note, we describe met...

The purpose of this paper is to describe the possibilities of studying the influence of forces external variables on the stability of motion of dynamical systems modeled by systems of differential equations with periodic coefficients of stability. The method is applied to analyze the influence of external harmonic forces on the stability of motion of the pantograph couple contact wire electric ...

In this paper, by considering the notion of extended BCK-module, we define the concepts of free extended BCK-module, free object in category of extended BCK-modules and we state and prove some related results. Specially, we define the notion of idempotent extended BCK-module and we get some important results in free extended BCK-modules. In particular, in category of idempotent extended BCK-mod...

The theory of local homology modules was initiated by Matlis in 1974. It is a dual version of the theory of local cohomology modules. Mohammadi and Divaani-Aazar (2012) studied the connection between local homology and Gorenstein flat modules by using Gorenstein flat resolutions. In this paper, we introduce generalized local homology modules for complexes and we give several ways for computing ...

In this paper, a new contact force control technique, based on the modified Takagi-Sugeno model and parallel distributed compensation concept is developed to suppress vibrations between pantograph catenary by regulating reference value, thereby achieving stable current collection. The proposed method uses simple standard PID fuzzy controllers. two controllers guarantee designed system's robust ...

‎highest weight modules of the double affine lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎singular vectors of verma modules are‎ ‎determined using a similar condition with horizontal affine lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.