On the Hodge conjecture for quasi-smooth intersections in toric varieties

We establish the Hodge conjecture for some subvarieties of a class of toric varieties. First we study quasi-smooth intersections in a projective simplicial toric variety, which is a suitable notion to generalize smooth complete intersection subvarieties in the toric environment, and in particular quasi-smooth hypersurfaces. We show that under appropriate conditions, the Hodge conjecture holds for a very general quasi-smooth intersection subvariety, generalizing the work on quasi-smooth hypersurfaces of the first author and Grassi in Bruzzo and Grassi (Commun Anal Geom 28: 1773–1786, 2020). We also show that the Hodge Conjecture holds asymptotically for suitable quasi-smooth hypersurface in the Noether–Lefschetz locus, where “asymptotically” means that the degree of the hypersurface is big enough, under the assumption that the ambient variety PΣ2k+1 has Picard group Z. This extends to a class of toric varieties Otwinowska’s result in Otwinowska (J Alg Geom 12: 307–320, 2003)

Active and reactive power conditioning using SMES devices with PMW-CSC: A feedback nonlinear control approach

The active and reactive power conditioning using superconducting magnetic energy storage (SMES) systems for low-voltage distribution networks via feedback nonlinear control is proposed in this paper. The SMES system is interconnected to ac grid using a pulsed-width modulated current source converter (PWM-CSC). The dynamical model of the system exhibits a nonlinear structure, which is eliminated by the application of a nonlinear feedback controller based of the expected behavior of the closed-loop system. The steady state analysis under time-domain reference frame to verify the stability properties on the proposed controller is used. The general control rules allow improving different objectives. The robustness and applicability of the proposed controller is tested considering unbalance and harmonic distortion in the voltage provided by the ac grid. It is also considered the possibility to use the SMES system with the proposed controller to compensate the active power oscillations of a wind-generator system. © 2019 The AuthorsDepartamento Administrativo de Ciencia, Tecnología e Innovación, COLCIENCIAS, Department of Science, Information Technology and Innovation, Queensland Governmen

Efficient Tensor-Product Spectral-Element Operators with the Summation-by-Parts Property on Curved Triangles and Tetrahedra

We present an extension of the summation-by-parts (SBP) framework to tensor-product spectral-element operators in collapsed coordinates. The proposed approach enables the construction of provably stable discretizations of arbitrary order which combine the geometric flexibility of unstructured triangular and tetrahedral meshes with the efficiency of sum-factorization algorithms. Specifically, a methodology is developed for constructing triangular and tetrahedral spectral-element operators of any order which possess the SBP property (i.e. satisfying a discrete analogue of integration by parts) as well as a tensor-product decomposition. Such operators are then employed within the context of discontinuous spectral-element methods based on nodal expansions collocated at the tensor-product quadrature nodes as well as modal expansions employing Proriol-Koornwinder-Dubiner polynomials, the latter approach resolving the time step limitation associated with the singularity of the collapsed coordinate transformation. Energy-stable formulations for curvilinear meshes are obtained using a skew-symmetric splitting of the metric terms, and a weight-adjusted approximation is used to efficiently invert the curvilinear modal mass matrix. The proposed schemes are compared to those using non-tensorial multidimensional SBP operators, and are found to offer comparable accuracy to such schemes in the context of smooth linear advection problems on curved meshes, but at a reduced computational cost for higher polynomial degrees.Comment: 26 pages, 5 figure

Nonlinear analysis and control of a reaction wheel pendulum: Lyapunov-based approach

This paper presents a nonlinear analysis, control, and comparison of controllers based on the dynamical model of the reaction wheel pendulum (RWP) in a tutorial style. Classical methodologies such as proportional integral derivative (PID) control and state variables feedback control are explored. Lyapunov's method is proposed to analyze the stability of the proposed nonlinear controllers, and it is also used to design control laws guaranteeing globally asymptotically stability conditions in closed-loop. A swing up strategy is also included to bring the pendulum bar to the desired operating zone at the vertical upper position from an arbitrary initial location. Simulation results show that it is possible to obtain the same dynamical behavior of the RWP system adjusting the control gains adequately. All simulations were conducted via MATLAB Ordinary Differential Equation packages. © 2019 Karabuk Universit

Active and reactive power conditioning using SMES devices with PMW-CSC: A feedback nonlinear control approach

The active and reactive power conditioning using superconducting magnetic energy storage (SMES) systems for low-voltage distribution networks via feedback nonlinear control is proposed in this paper. The SMES system is interconnected to ac grid using a pulsed-width modulated current source converter (PWM-CSC). The dynamical model of the system exhibits a nonlinear structure, which is eliminated by the application of a nonlinear feedback controller based of the expected behavior of the closed-loop system. The steady state analysis under time-domain reference frame to verify the stability properties on the proposed controller is used. The general control rules allow improving different objectives. The robustness and applicability of the proposed controller is tested considering unbalance and harmonic distortion in the voltage provided by the ac grid. It is also considered the possibility to use the SMES system with the proposed controller to compensate the active power oscillations of a wind-generator system. © 2019 The AuthorsDepartamento Administrativo de Ciencia, Tecnología e Innovación, COLCIENCIAS Department of Science, Information Technology and Innovation, Queensland GovernmentThis work was partially supported by the National Scholarship Program Doctorates of the Administrative Department of Science, Technology and Innovation of Colombia ( COLCIENCIAS ), by calling contest 727-2015

Restructurable Controls

Restructurable control system theory, robust reconfiguration for high reliability and survivability for advanced aircraft, restructurable controls problem definition and research, experimentation, system identification methods applied to aircraft, a self-repairing digital flight control system, and state-of-the-art theory application are addressed

Codimension bounds for the Noether–Lefschetz components for toric varieties

For a quasi-smooth hypersurface X in a projective simplicial toric variety PΣ, the morphism i∗: Hp(PΣ) → Hp(X) induced by the inclusion is injective for p= dim X and an isomorphism for p< dim X- 1. This allows one to define the Noether–Lefschetz locus NL β as the locus of quasi-smooth hypersurfaces of degree β such that i∗ acting on the middle algebraic cohomology is not an isomorphism. We prove that, under some assumptions, if dim PΣ= 2 k+ 1 and kβ- β= nη, n∈ N, where η is the class of a 0-regular ample divisor, and β is the anticanonical class, every irreducible component V of the Noether–Lefschetz locus quasi-smooth hypersurfaces of degree β satisfies the bounds n+1⩽codimZ⩽hk-1,k+1(X)

Alternative power flow method for direct current resistive grids with constant power loads: A truncated Taylor-based method

The power flow in electrical system permits analyzing and studying the steady-state behavior of any grid. Additionally, the power flow helps with the proper planning and management of the system. Therefore, it is increasingly necessary to propose power flows with fast convergence and high efficiency in their results. For this reason, this paper presents an alternative power flow approach for direct current networks with constant power loads based on a truncated Taylor-based approximation. This approach is based on a first-order linear approximation reformulated as a recursive, iterative method. It works with a slope variable concept based on derivatives, which allow few iterations and low processing times. Numerical simulations permit identifying the best power flow approaches reported in the specialized literature for radial and mesh dc grids, including the proposed approach. All the simulations were conducted in MATLAB 2015a. © Published under licence by IOP Publishing Ltd.Universidad Tecnológica de Pereira, UTP: C2018P020 Department of Science, Information Technology and Innovation, Queensland Government, DSITI: ColcienciasThis work was supported in part by the Administrative Department of Science, Technology and Innovation of Colombia (Colciencias) through the National Scholarship Program under Grant 727-2015 and in part by the Universidad Tecnológica de Bolívar under Project C2018P020

Optimal power flow studies in direct current grids: An application of the bio-inspired elephant swarm water search algorithm

Colombian power system is experienced important changes due to the large scale integration of renewable power generation based on solar and wind power; added to the fact that direct current networks have taken important attention, since they are efficient in terms of power loss and voltage profile at distribution or transmission levels For addressing this problem, this paper presents the application of an emerging bio-inspired metaheuristic optimization technique known as elephant swarm water search algorithm to the optimal power flow problem in direct current networks. A master-slave hybrid optimization strategy for optimal power flow analysis is addressed in this paper by decoupling this problem in two optimizing issues. The first problem corresponds to the selection of the power generated by all non-voltage controlled distributed generators; While the second problem lies in the solution of the classical power flow equations in direct current networks. The solution of the master problem (first problem) is made by applying the elephant swarm water search algorithm, while the second problem (slave problem) is solved by a conventional Gauss-Seidel numerical method. The proposed hybrid methodology allows solving the power flow problem by using any basic programming language with minimum computational effort and well-precision when is compared with optimizing packages such as general algebraic modeling system/CONOPT solver and conventional metaheuristic techniques such as genetic algorithms. © Published under licence by IOP Publishing Ltd.Universidad Tecnológica de Pereira, UTP: C2018P020 Department of Science, Information Technology and Innovation, Queensland Government, DSITI: ColcienciasThis work was supported in part by the Administrative Department of Science, Technology and Innovation of Colombia (Colciencias) through the National Scholarship Program under Grant 727-2015 and in part by the Universidad Tecnológica de Bolívar under Project C2018P020