A null-space approach for large-scale symmetric saddle point systems with a small and non zero (2, 2) block

Null-space methods have long been used to solve large sparse n × n symmetric saddle point systems of equations in which the (2, 2) block is zero. This paper focuses on the case where the (1, 1) block is ill conditioned or rank deficient and the k × k (2, 2) block is non zero and small (k ≪ n). Additionally, the (2, 1) block may be rank deficient. Such systems arise in a range of practical applications. A novel null-space approach is proposed that transforms the system matrix into a nicer symmetric saddle point matrix of order n that has a non zero (2, 2) block of order at most 2k and, importantly, the (1, 1) block is symmetric positive definite. Success of any null-space approach depends on constructing a suitable null-space basis. We propose methods for wide matrices having far fewer rows than columns with the aim of balancing stability of the transformed saddle point matrix with preserving sparsity in the (1, 1) block. Linear least squares problems that contain a small number of dense rows are an important motivation and are used to illustrate our ideas and to explore their potential for solving large-scale systems.

Unconstrained off-shell superfield formulation of 4D, $$ \mathcal{N} $$ = 2 supersymmetric higher spins

We present, for the first time, the complete off-shell 4D,$$ \mathcal{N} $$ N = 2 superfield actions for any free massless integer spin s ≥ 2 fields, using the $$ \mathcal{N} $$ N = 2 harmonic super-space approach. The relevant gauge supermultiplet is accommodated by two real analytic bosonic superfields $$ {h}_{\alpha \left(s-1\right)\dot{\alpha}\left(s-1\right)}^{++} $$ h α s − 1 α ̇ s − 1 + + , $$ {h}_{\alpha \left(s-2\right)\dot{\alpha}\left(s-2\right)}^{++} $$ h α s − 2 α ̇ s − 2 + + and two conjugated complex analytic spinor superfields $$ {h}_{\alpha \left(s-1\right)\dot{\alpha}\left(s-1\right)}^{+3} $$ h α s − 1 α ̇ s − 1 + 3 , $$ {h}_{\alpha \left(s-2\right)\dot{\alpha}\left(s-1\right)}^{+3} $$ h α s − 2 α ̇ s − 1 + 3 , where α(s) := (α1. . . αs),$$ \dot{\alpha} $$ α ̇ (s) := ($$ \dot{\alpha} $$ α ̇ 1. . .$$ \dot{\alpha} $$ α ̇ s). Like in the harmonic superspace formulations of $$ \mathcal{N} $$ N = 2 Maxwell and supergravity theories, an infinite number of original off-shell degrees of freedom is reduced to the finite set (in WZ-type gauge) due to an infinite number of the component gauge parameters in the analytic superfield parameters. On shell, the standard spin content (s,s−1/2,s−1/2,s−1) is restored. For s = 2 the action describes the linearized version of “minimal” $$ \mathcal{N} $$ N = 2 Einstein supergravity.

State-Space Approach for SPMSM Sensorless Passive Algorithm Tuning

Sensorless algorithms for Permanent Magnet Synchronous Motors (PMSM) have achieved increasing interest in the technical literature over the last few years. They can be divided into active methods and passive methods: the first inject high-frequency signals exploiting rotor anisotropy, whereas the second are based on observers. Recently, a sensorless control based on a rotor flux observer has been presented in the technical literature, which gives very accurate results in terms of rotor position estimation and robustness. In this paper, the aforementioned observer is considered and a procedure for choosing stabilizing gains of the observer is proposed. The contribution of the paper is three-fold: the mathematical modelling of the rotor flux observer, the methodology for the definition of the observer gains, and the presentation of the experimental results.

Blind orphanage with blind space approach in Jakarta

There are still people with disabilities in society who consider them a burden. However, in fact, every child with special needs such as a blind people has the right to have a decent life like any other community. So, we need an orphanage for the blind people with a blind space approach that aims to provide social services to blind children by helping and guiding them towards reasonable personal development and having work skills, so that they can be independent, live properly and have responsibility, both for himself, his family, and society. This research used a qualitative descriptive method by collecting literature studies from national and international journal articles regarding the blind orphanage, collecting data related to the research location and conducting a comparative study of similar buildings in Central Jakarta. This research resulted in a blind orphanage design with a blind space in Jakarta approach that provides disability facilities for visually impaired people, educational facilities, and activity facilities for visually impaired people. It is hoped that the design of the Blind Orphanage can accommodate the activities of the Blind people in Jakarta.