On the rotordynamic stability of two-pole synchronous electric machinery considering different load cases

This paper discusses stationary rotordynamics of synchronous electric machinery, considering different load cases. The model comprises the electrical operation in a rigid network and in an isolated condition. The mechanical part is modelled as a Laval Rotor (Jeffcott Rotor) with a noncircular shaft, accounting for both static- and dynamic rotor eccentricities. The results show, that the machine's electrical operation may influence the occurence of mechanical vibrations significantly and therefore demonstrate the importance of analysing the electromechanical interaction. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A smoothing SQP method for nonlinear programs with?stability constraints arising from power systems

This paper investigates a new class of optimization problems arising from power systems, known as nonlinear programs with stability constraints (NPSC), which is an extension of ordinary nonlinear programs. Since the stability constraint is described generally by eigenvalues or norm of Jacobian matrices of systems, this results in the semismooth property of NPSC problems. The optimal conditions of both NPSC and its smoothing problem are studied. A smoothing SQP algorithm is proposed for solving such optimization problem. The global convergence of algorithm is established. A numerical example from optimal power flow (OPF) is done. The computational results show efficiency of the new model and algorithm.     

An asymptotic formula for the ranks of homotopy groups

Let X be a finite simply connected CW complex of dimension n. The loop space homology H_∗(ΩX;Q) is the universal enveloping algebra of a graded Lie algebra LX isomorphic with π∗−1(X)⊗Q. Let QX⊂LX be a minimal generating subspace, and set .Theorem: If dimLX=∞ and , then

     

A compactness result for Landau state in thin-film micromagnetics

We deal with a nonconvex and nonlocal variational problem coming from thin-film micromagnetics. It consists in a free-energy functional depending on two small parameters ε and η and defined over vector fields m:Ω⊂R²→S² that are tangent at the boundary ∂Ω. We are interested in the behavior of minimizers as ε,η→0. They tend to be in-plane away from a region of length scale ε (generically, an interior vortex ball or two boundary vortex balls) and of vanishing divergence, so that S¹-transition layers of length scale η (Néel walls) are enforced by the boundary condition. We first prove an upper bound for the minimal energy that corresponds to the cost of a vortex and the configuration of Néel walls associated to the viscosity solution, so-called Landau state. Our main result concerns the compactness of vector fields {mε,η}_ε,η↓0 of energies close to the Landau state in the regime where a vortex is energetically more expensive than a Néel wall. Our method uses techniques developed for the Ginzburg-Landau type problems for the concentration of energy on vortex balls, together with an approximation argument of S²-vector fields by S¹-vector fields away from the vortex balls.     

An Extremal Characterization of the Incidence Graphs of Projective Planes

Let G be a 4-cycle free, bipartite graph on 2n vertices with partitions of equal cardinality n. Let c₆(G) denote the number of cycles of length 6 in G. We prove that for n 3, c₆(G) , where , with equality if and only if G is the incidence point-line graph of a projective plane.     

Non-Autonomous Evolution Equations on Nonsmooth Domair

The solution of a stationary boundary value problem on a domain with conical points has singularities near these points. Here we first consider existence results in appropriate weighted Sobolev spaces in order to incorporate the singularities. We secondly use these results to prove existence, uniqueness and regularity of solutions of non-autonomous second order evolution equations on such domains.     

An Overview on Non-Ideal Vibrations

We analyze the dynamical coupling between energy sources and structural response that must not be ignored in real engineering problems, since real motors have limited output power.     

Isomorphism criterion for monomial graphs

Let q be a prime power, ??_q be the field of q elements, and k, m be positive integers. A bipartite graph G = G_q(k, m) is defined as follows. The vertex set of G is a union of two copies P and L of two‐dimensional vector spaces over ??_q, with two vertices (p₁, p₂) ∈ P and [ l₁, l₂] ∈ L being adjacent if and only if p₂ + l₂ = pl. We prove that graphs G_q(k, m) and G_q′(k′, m′) are isomorphic if and only if q = q′ and {gcd (k, q ? 1), gcd (m, q ? 1)} = {gcd (k′, q ? 1),gcd (m′, q ? 1)} as multisets. The proof is based on counting the number of complete bipartite INFgraphs in the graphs. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 322–328, 2005     

Multi-attribute group decision-making with multi-granularity linguistic assessment information: An improved approach based on deviation and TOPSIS

With respect to group decision-making problems with multi-granularity linguistic assessment information, a new approach is proposed. Firstly, the computational formulae are given in order to transform and unify the multi-granularity linguistic comparison matrices. Secondly, the method of standard and mean deviation is applied to determine the unknown attribute weights, and the weights of the decision makers will be determined by using the extended TOPSIS (technique for order preference by similarity to an ideal solution) method. Finally, based on the LWAA (linguistic weighted arithmetic averaging) operator, information on the preference provided by each decision maker is aggregated into the comprehensive evaluation value of each alternative, and the most desirable alternative is selected. The proposed approach expands the research in multi-attribute group decision-making with multi-granularity linguistic assessment information by both considering the weights of the attributes and decision makers, and objective weighting for them. A numerical example is given to illustrate the practicability and usefulness of the proposed approach.