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The six-phase two-level voltage source inverter (SPTLVSI) fed the six-phase asymmetrical induction motor (SPAIM), which has a stator that splits the three-phase windings into two groups those are shifted electrically by 30 ∘ . It introduces significant current harmonics of the order of 6 k ± 1 k = 1 , 3 , 5 … , which can be mapped into the non-flux/torque producing X - Y sub-plane. These harmonics cause only losses in the motor winding as they do not take part in torque production. The authors propose a new space vector modulation technique named the 48-sector vector space decomposition-based space vector pulse-width modulation (C6 ϕ SVPWM48) technique, which has been verified using MATLAB (Matrix Laboratory) simulation and reported by the authors in the previous work, and the work is extended in this paper. This paper presents a contribution to compare the proposed technique with the 12-sector vector space decomposition-based space vector pulse-width modulation (C6 ϕ SVPWM12) based on CMV (Common mode voltage) , switching loss of the inverter, torque ripple, and stator current distortion. The C6 ϕ SVPWM48 technique has been implemented experimentally on the SPTLVSI fed a prototype of 200 V, 2 kW SPAIM. The C6 ϕ SVPWM48 technique is controlled using the ARM cortex M4 32-bit microcontroller (STM32F407VGT6) and the SPTLVSI during steady-state and dynamic operating conditions. The experimental results of the C6 ϕ SVPWM48 technique are discussed and presented. Furthermore, it reduces the harmonic current drawn by the machine to a large extent, consequently, the copper losses of the machine and also reducing the average switching loss.

In the present work, we introduce the notion of pseudo-seminorm, then we established, a criterion for the metrizability of a pseudo vector space with a pseudo topology . It is specified, that for the metrizability of is necessary and sufficient that is first countable. Moreover, a sufficient condition for existence a base for the filter of neighborhoods of zero is proved and demonstrated that this condition introduces a compatible pseudo topology with the algebraic vector space structures.

We consider the space of functions almost in Lp and endow it with the topology of asymptotic Lp -convergence. This yields a completely metrizable topological vector space which, on finite measure spaces, coincides with the space of measurable functions equipped with the topology of (local) convergence in measure. We investigate analogs of classical results such as dominated convergence and Vitali convergence theorems. For Rd as the underlying measure space, we establish results on approximation by smooth functions and separability. Further aspects, including local boundedness, local convexity, and duality are examined in the Rd setting, revealing fundamental differences from standard Lp spaces.

We construct in ZFC (the Zermelo-Fraenkel system with choice) an L topological vector space—a topological vector space that is an L space—and an L field—a topological field that is an L space. This generalizes earlier results in L spaces and L groups.

Traditional Web news media retrieval technology can only meet the specific requirements of customers. Because of its universal characteristics, it cannot meet the needs of different environments, different purposes, and different times simultaneously. Researchers have proposed a search method for online news media, which is used for computing the semantic grouping vector space model. The customer's interest model is analyzed through the characteristics of the user's different classification areas. In this paper, we propose a vector space model that performs semantic grouping based on feature words. The model divides four groups that are relatively independent in the meaning of feature words in a news report: time, place, person, and event, and then forms four vector spaces and calculates the weight value and similarity of each vector space. Theoretical analysis and experimental results show that the improved model is suitable for searching Web news information and improves the calibration rate, query speed, and calibration rate.

Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra.

A simplified space vector modulation (SVM) technique is proposed for the seven-level cascaded H-bridge (CHB) inverter. It is based on decomposing the seven-level space vector hexagon into a number of two-level space vector hexagons. The presented technique significantly reduces the calculation time and efforts involved in the SVM of a seven-level inverter; without any loss in the output voltage magnitude or increase in the total harmonic distortion content. A further simplified technique is also presented in this study, which significantly reduces the complexity and effort involved in the seven-level SVM. Simulation results for the seven-level CHB inverter using the proposed techniques are presented. The results are compared with results using sinusoidal pulse-width modulation (PWM) and third harmonic injection PWM to prove the validity of the proposed techniques. The proposed technique is perfectly general and can be applied to all types of multilevel inverters and extended to higher level inverters.

In this paper, the notions of (L,M)-fuzzy bornological convergence and separation in (L,M)-fuzzy bornological vector spaces are introduced. Some properties of (L,M)-fuzzy bornological convergence and separation are discussed. The relationships between (L,M)-fuzzy bornologial convergence and separation in (L,M)-fuzzy bornological vector spaces are proposed. Moreover, the relationships of bornological convergence and separation between the framework of (L,M)-fuzzy bornological vector spaces and L-bornological vector spaces are discussed.

An affine vector space partition of AG ( n , q ) is a set of proper affine subspaces that partitions the set of points. Here we determine minimum sizes and enumerate equivalence classes of affine vector space partitions for small parameters. We also give parametric constructions for arbitrary field sizes.

A bstract Twisted period integrals are ubiquitous in theoretical physics and mathematics, where they inhabit a finite-dimensional vector space governed by an inner product known as the intersection number. In this work, we uncover the associated tensor structures of intersection numbers and integrate them with the fibration method to develop a novel evaluation scheme. Companion matrices allow us to cast the computation of the intersection numbers in terms of a matrix operator calculus within the ambient tensor space. For illustrative purposes, our algorithm has been successfully applied to the numerical decomposition of a sample of two-loop integrals, coming from planar five-point massless functions, representing a significant advancement for the direct projection of Feynman integrals to master integrals via intersection numbers.