Decomposition Of Space Research Articles

Testing Zero-Dimensionality of Varieties at a Point

Effective methods are introduced for testing zero-dimensionality of varieties at a point. The motivation of this paper is to compute and analyze deformations of isolated hypersurface singularities. As an application, methods for computing local dimensions are also described. For the case where a given ideal contains parameters, the proposed algorithms can output in particular a decomposition of a parameter space into strata according to the local dimension at a point of the associated varieties. The key of the proposed algorithms is the use of the notion of comprehensive Gröbner systems.

Minimizers of curl prescribed full trace

This paper concerns the minimization problem of L2 norm of curl of vector fields prescribed full trace on the boundary of a multiconnected bounded domain. The existence of the minimizers in H1 are shown by orthogonal decompositions of vector function spaces and a constructed auxiliary variational problem. And the H2 estimate of the type II divergence-free part of the minimizers is established by div-curl-gradient type estimates of vector fields.

Multiphase current imbalance localisation method applied to natural fault‐tolerant strategies

Multiphase machines are interesting options for high-reliability applications due to their inherent fault tolerance against open-circuit faults (OCFs). Moreover, if the regulation of the x–y currents is realised in open-loop mode using virtual voltage vectors (VVs), the mandatory post-fault control reconfiguration is avoided. The new reconfigurationless approach was recently defined as a natural/passive fault-tolerant strategy, offering good prospects for industry applications. This work extends the idea to the fault detection procedure and suggests new settings for the current imbalance localisation method. The proposal is based on the vector space decomposition approach that allows the joint detection of OCFs and stator resistances dissymmetry. Experimental results in a five-phase induction motor drive using VVs confirm the viability of the technique.

On ID*-superderivations of Lie superalgebras

Let L be a Lie superalgebra over a field of characteristic different from 2, 3 and write for the Lie superalgebra consisting of superderivations mapping L to and the central elements to zero. In this paper we first give an upper bound for the superdimension of by means of linear vector space decompositions. Then we characterize the -superderivation superalgebras for the nilpotent Lie superalgebras of class 2 and the model filiform Lie superalgebras by methods of block matrices.

Star partial order on $${\mathcal {B}}_{Id}({\mathcal {H}})$$

Let $${\mathcal {B}}_{Id}({\mathcal {H}})$$ be the set of all idempotents on a Hilbert space $${\mathcal {H}}.$$ We give characterizations of the star partial order on $${\mathcal {B}}_{Id}({\mathcal {H}})$$ with respect to a particular space decomposition, which is related to Halmos’ two projections theory. Using this, we investigate the lattice properties of $${\mathcal {B}}_{Id}({\mathcal {H}})$$ endowed with the star partial order.

Symmetries for J-projection

Let $$\mathcal{B}(\mathcal{H})$$ be the algebra of all bounded linear operators on a separable complex Hilbert space $$\mathcal{H}$$. We introduce the J-decomposition property for projections in $$\mathcal{B}(\mathcal{H})$$, and prove that the projection E in $$\mathcal{B}(\mathcal{H})$$ has J-decomposition property with respect to a particular space decomposition, which is related to Hal-mos’ two projections theory. Using this, we characterize symmetries J such that the projection E is a J-projection (or J-positive projection, or J-negative projection). Also, we give the explicit representations of the maximum and the minimum of symmetries J such that the projection E is J-positive (or J-negative).

An Improved Method for Reliability Evaluation of Two-Terminal Multistate Networks Based on State Space Decomposition

This article presents an improved state space decomposition (SSD) method for reliability evaluation of multistate networks. We observe that the decomposition process of the existing SSD is a sequential decomposition process. However, the SSD has the basis of parallel operations, as the decomposition process from each unspecified state is independent of each other. In addition, the existing SSD methods applied heuristic to select a proper minimal path vector (d-MP). When there is a tie during the process, the tie is broken arbitrarily. However, we find that different d-MPs with same function value of the current heuristic affect the efficiency of the decomposition procedure. Based on these observations, an improved SSD method is developed for reliability evaluation of multistate networks. First, a parallel mechanism is proposed and incorporated into the SSD algorithm. Second, several improved heuristics, namely R1, R2, R3, and R4, are developed to select a proper d-MP. The experimental results show that the proposed SSD method can improve the efficiency for reliability evaluation of multistate networks, which provides the reliability engineers and facility managers a more powerful tool for the design and maintenance of more complex multistate networks.

Current Regulator Design for Dual Y Shift 30 Degrees Permanent Magnet Synchronous Motor

This paper gives the current regulator design for a dual Y shift 30 degrees permanent magnet synchronous motor (DT_PMSM) based on the vector space decomposition (VSD). Current regulator design in α-β subspace is insufficient and designing additional controllers in x-y subspace is necessary to eliminate the harmonic currents due to the nonlinear characteristics of the inverter. A sliding mode controller based on an internal model is proposed in α-β subspace, which is robust to the parameter uncertainties and disturbances in current control loops. In order to eliminate the harmonic currents in x-y subspace, a resonant controller is employed based on a new synchronous rotating matrix. Three-phase decomposition space vector pulse width modulation (SVPWM) technique is illustrated for the purpose of synthesizing the voltage vectors in both subspaces simultaneously. The feasibility and efficiency of the suggested current regulator design are validated by a set of experimental results.

Spectral triples for higher-rank graph $C^*$-algebras

In this note, we present a new way to associate a spectral triple to the noncommutative $C^*$-algebra $C^*(\Lambda )$ of a strongly connected finite higher-rank graph Λ. Our spectral triple builds on an approach used by Consani and Marcolli to construct spectral triples for Cuntz-Krieger algebras. We prove that our spectral triples are intimately connected to the wavelet decomposition of the infinite path space of Λ which was introduced by Farsi, Gillaspy, Kang, and Packer in 2015. In particular, we prove that the wavelet decomposition of Farsi et al. describes the eigenspaces of the Dirac operator of our spectral triple. The paper concludes by discussing other properties of the spectral triple, namely, θ-summability and Brownian motion.

Central charges for the double coset

The state space of excited giant graviton brane systems is given by the Gauss graph operators. After restricting to the su(2|3) sector of the theory, we consider this state space. Our main result is the decomposition of this state space into irreducible representations of the su(2|2) ⋉ ℝ global symmetry. Excitations of the giant graviton branes are charged under a central extension of the global symmetry. The central extension generates gauge transformations so that the action of the central extension vanishes on physical states. Indeed, we explicitly demonstrate that the central charge is set to zero by the Gauss Law of the brane world volume gauge theory.

Scale balance for prototype-based binary quantization

Nowadays, prototype-based binary quantization (PBQ) is a promising solution for the approximate nearest neighbor search problem, which simultaneously preserves the affinity structures of prototypes in both Euclidean space as well as those of their codes in binary space. To learn longer binary codes, space decomposition based on product quantization is usually adopted. In practice, we find that the scale between Euclidean distance and Hamming distance usually varies across these decomposed subspaces, which degenerates the performance of PBQ based methods. We make an attempt to balance the scale of these subspaces via a joint optimization problem in the classic PBQ model, and present both an iterative and alternate algorithm for optimization. We conducted experiments on 6 public databases, and demonstrated that our scale balancing based methods SKMH and SABQ outperform state-of-the-art hashing methods including popular prototype-based binary quantization methods, with up to 81.62% relative performance gains when learning 256-bit binary codes.

Uncertainty propagation in dynamic sub-structuring by model reduction integrated domain decomposition

This paper addresses computational aspects in dynamic sub-structuring of built-up structures with uncertainty. Component mode synthesis (CMS), which is a model reduction technique, has been integrated within the framework of domain decomposition (DD), so that reduced models of individual sub-systems can be solved with smaller computational cost compared to solving the full (unreduced) system by DD. This is particularly relevant for structural dynamics applications where the overall system physics can be captured by a relatively low number of modes. The theoretical framework of the proposed methodology has been extended for application in stochastic dynamic systems. To limit the number of eigen-value analyses to be performed corresponding to the random realizations of input parameters, a locally refined high dimensional model representation model with stepwise least squares regression is presented. Effectively, a bi-level decomposition is proposed, one in the physical space and the other in the stochastic space. The geometric decomposition in the physical space by the proposed model reduction-based DD reduces the computational cost of a single analysis of the system and the functional decomposition in the stochastic space by the proposed meta-model lowers the number of simulations to be performed on the actual system. The results achieved by solving a finite-element model of an assembled beam structure and a 3D space frame illustrate good performance of the proposed methodology, highlighting its potential for complex problems.

Path to Stochastic Stability: Comparative Analysis of Stochastic Learning Dynamics in Games

Stochastic stability is an important solution concept for stochastic learning dynamics in games. However, a limitation of this solution concept is its inability to distinguish between different learning rules that lead to the same steady-state behavior. We identify this limitation and develop a framework for the comparative analysis of the transient behavior of stochastic learning dynamics. We present the framework in the context of two learning dynamics: Log-linear learning (LLL) and Metropolis learning (ML). Although both of these dynamics lead to the same steady-state behavior, they correspond to different behavioral models for decision making. In this article, we propose multiple criteria to analyze and quantify the differences in the short and medium-run behaviors of stochastic dynamics. We derive upper bounds on the expected hitting time of the set of Nash equilibria for both LLL and ML. For the medium to long-run behavior, we identify a set of tools from the theory of perturbed Markov chains that result in a hierarchical decomposition of the state space into collections of states called cycles. We compare LLL and ML based on the proposed criteria and develop invaluable insights into the behavior of the two dynamics.

Multi-Harmonic Currents Control Strategy for Five-Phase Permanent Magnet Machine with non-sinusoidal back-EMF

This paper describes an optimal torque per peak current control method for a five-phase permanent magnet (PM) machine considering both 3rd and 5th harmonic currents. These optimal ratios to the fundamental component are analytically derived to maximize the output torque. It is found that except for the 3rd harmonic current contributing to the output torque, the 5th harmonic current can also produce the additional positive torque. However, the 5th harmonic is zero sequence component for the five-phase machines, which does not exist in the phase windings. Hence, the neutral point is required to connect the middle point of the DC link capacitors for constructing flowing path. The conventional vector space decomposition (VSD) control is extended to zero sequence sub-plane, which can quantitatively control 5th harmonic current. For a prototype five-phase PM machine, the average torque can be increased by 21.4% with 3rd harmonic current injection. Meanwhile, 10.7% additional positive torque is achieved together with 3rd and 5th harmonic injection. The torque ripple remains similar to that without harmonics injection. Finally, the experiments are given to demonstrate the theoretical analysis.

Quality-Related Root Cause Diagnosis Based on Orthogonal Kernel Principal Component Regression and Transfer Entropy

This article is devoted to solving the problem of quality-related root cause diagnosis for nonlinear process. First, an orthogonal kernel principal component regression model is constructed to achieve orthogonal decomposition of feature space, such that quality-related and quality-unrelated faults can be separately detected in the subspaces of opposite correlations to the output, without any effect on each other. Then, in view of the high complexity of traditional nonlinear fault diagnosis methods, an efficient method of kernel sample equivalence replacement is established to replace the partial differential operations of the kernel gradient algorithm, which can convert nonlinear fault detection indicators into the standard quadratic forms of the original variable sample, thereby making it possible to solve the nonlinear fault diagnosis problem by linear manners. Furthermore, a transfer entropy algorithm is utilized to the new model to analyze the causality between the diagnosed candidate faulty variables to find out the accurate root cause of the fault. Finally, comparative studies between the latest result and the proposed one are carried out in the Tennessee Eastman process to verify the effectiveness and superiority of the new method.

The first cohomology of [formula omitted] with coefficients in χ-reduced Kac modules and simple modules

Over a field of characteristic p>2, the first cohomology of the special linear Lie superalgebra sl(2,1) with coefficients in all χ-reduced Kac modules and simple modules is determined by use of the weight space decompositions of these modules relative to the standard Cartan subalgebra of sl(2,1).

Convergence analysis of the Fast Subspace Descent method for convex optimization problems

Author(s): Chen, L; Hu, X; Wise, SM | Abstract: The full approximation storage (FAS) scheme is a widely used multigrid method for nonlinear problems. In this paper, a new framework to design and analyze FAS-like schemes for convex optimization problems is developed. The new method, the fast subspace descent (FASD) scheme, which generalizes classical FAS, can be recast as an inexact version of nonlinear multigrid methods based on space decomposition and subspace correction. The local problem in each subspace can be simplified to be linear and one gradient descent iteration (with an appropriate step size) is enough to ensure a global linear (geometric) convergence of FASD for convex optimization problems.

Spectrally accurate space–time solution of Manakov systems

In this paper, we study the numerical solution of Manakov systems by using a spectrally accurate Fourier decomposition in space, coupled with a spectrally accurate time integration. This latter relies on the use of spectral Hamiltonian Boundary Value Methods. The used approach allows to conserve all the physical invariants of the systems. Some numerical tests are reported.

Optimal Third-Harmonic Current Injection for Asymmetrical Multiphase Permanent Magnet Synchronous Machines

This article proposes a modeling approach and an optimization strategy to exploit a third-harmonic current injection for the torque enhancement in multiphase isotropic permanent magnet synchronous machines with nonsinusoidal back electromotive forces. The modeling approach is based on a proper vector space decomposition and on the associated rotational transformation, aimed to properly select a set of stator current space vectors to be controlled. It is presented for a generic (i.e., asymmetrical, with an arbitrary angular shift) winding configuration. The injection strategy is related to the choice of a constant synchronous current set aimed at minimizing the average stator winding losses for a given reference torque by using the first and the third spatial harmonics of the air-gap flux density. The optimal solution has been found analytically and has been developed in detail for a selected set of asymmetrical winding configurations. Both the numerical and experimental results are in good agreement with the theoretical analysis.

Hardy space estimates for bi-parameter Littlewood-Paley square functions

Suppose that g(f) are bi-parameter Littlewood-Paley square functions which were introduced by H. Martikainen. It is known that the L2(ℝn × ℝm) boundedness and the H1 (ℝn × ℝm)-L1(ℝn × ℝm) boundedness of g(f) have been proved by H. Martikainen and by Z. Li and Q. Xue, respectively. In this paper, we apply the vector-valued theory, the atomic decomposition of product Hardy spaces, and Journe’s covering lemma to show that g(f) are bounded from Hp(ℝn × ℝm) to Lp(ℝn × ℝm) with p smaller than 1.