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21,497
result(s) for
"Vector spaces"
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Metrizability of Pseudo Topological Vector Spaces
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.
Journal Article
Experimental Realization of a Novel 48-Sector Space Vector Decomposition-Based SVPWM Technique for A Six-Phase Two-Level VSI-Fed Six-Phase Asymmetrical Induction Motor
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.
Journal Article
Distance Functions in Some Class of Infinite Dimensional Vector Spaces
This paper considers the problem of measuring technical efficiency in some class of normed vector spaces. Specifically, the paper focuses on preordered and partially ordered vector spaces by proposing a suitable encompassing netput formulation of the production possibility set. Duality theorems extending some earlier results are established in the context of infinite dimensional spaces. The paper considers directional and normed distance functions and analyzes their relationships. Among other things, overall efficiency can be derived from technical efficiency under a suitable preordered vector space structure. More importantly, it is shown that the existence of core points in partially ordered vector spaces guarantees the comparison of production vectors using the directional distance function. Although the interior of the positive cone may be empty in infinite dimensional vector spaces, it is shown that normed distance functions can also be used to measure efficiency in such spaces by providing them with a suitable preorder structure.
Journal Article
Blaschke-Minkowski Homomorphisms in Complex Vector Spaces
Abstract-This article extends the concept of Blaschke-Minkowski homomorphisms operator in n-dimensional Euclidean space to complex vector space, and establishes some important geometric inequalities for this purpose. Moreover, the Shephard-type problem of complex Blaschke-Minkowski homomorphisms is also studied.
Journal Article
The Intrinsic Core and Minimal Faces of Convex Sets in General Vector Spaces
Intrinsic core generalises the finite-dimensional notion of the relative interior to arbitrary (real) vector spaces. Our main goal is to provide a self-contained overview of the key results pertaining to the intrinsic core and to elucidate the relations between intrinsic core and facial structure of convex sets in this general context. We gather several equivalent definitions of the intrinsic core, cover much of the folklore, review relevant recent results and present examples illustrating some of the phenomena specific to the facial structure of infinite-dimensional sets.
Journal Article
A quest for convergence: exploring series in non-linear environments
This note presents an extension of a result within the concept of
S
-lineability, originally due to Bernal-González, Conejero, Murillo-Arcila, and Seoane-Sepúlveda. Additionally, we provide a characterization of lineability in the context of complements of unions of closed subspaces in
F
-spaces in terms of
ℓ
∞
-lineability. We also present a negative result in both normed spaces and
p
-Banach spaces. These findings contribute to the understanding of linearity within exotic settings in vector spaces.
Journal Article
CONTRACTIVE SEMIGROUPS IN TOPOLOGICAL VECTOR SPACES, ON THE 100TH ANNIVERSARY OF STEFAN BANACH’S CONTRACTION PRINCIPLE
Celebrating 100 years of the Banach contraction principle, we prove some fixed point theorems having all ingredients of the principle, but dealing with common fixed points of a contractive semigroup of nonlinear mappings acting in a modulated topological vector space. This research follows the ideas of the author’s recent papers [‘On modulated topological vector spaces and applications’, Bull. Aust. Math. Soc. 101 (2020), 325–332, and ‘Normal structure in modulated topological vector spaces’, Comment. Math. 60 (2020), 1–11]. Modulated topological vector spaces generalise, among others, Banach spaces and modular function spaces. The interest in modulars reflects the fact that the notions of ‘norm like’ but ‘noneuclidean’ (and not even necessarily convex) constructs to measure a level of proximity between complex objects are frequently used in science and technology. To prove our fixed point results in this setting, we introduce a new concept of Opial sets using analogies with the norm-weak and modular versions of the Opial property. As an example, the results of this work can be applied to spaces like
$L^p$
for
$p> 0 $
, variable Lebesgue spaces
$L^{p(\\cdot )}$
where
$1 \\leq p(t) < + \\infty $
, Orlicz and Musielak–Orlicz spaces.
Journal Article
Banach’s isometric subspace problem in dimension four
We prove that if all intersections of a convex body B⊂R4 with 3-dimensional linear subspaces are linearly equivalent then B is a centered ellipsoid. This gives an affirmative answer to the case n=3 of the following question by Banach from 1932: Is a normed vector space V whose n-dimensional linear subspaces are all isometric, for a fixed 2≤n
Journal Article
Constructing new Segal topological algebras from existing ones
In this paper, we examine the properties of Segal topological algebras, looking at ways to construct new objects from existing ones. Equipped with the example of algebras (in the sense of vector spaces equipped with multiplication), we consider two approaches: one via a direct product of an arbitrary family of Segal topological algebras and another using the Dorroh extensions of the underlying topological algebras.
Journal Article