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Journal articles on the topic 'Space Vector'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Jordá, Enrique. "Weighted Vector-Valued Holomorphic Functions on Banach Spaces." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/501592.

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We study the weighted Banach spaces of vector-valued holomorphic functions defined on an open and connected subset of a Banach space. We use linearization results on these spaces to get conditions which ensure that a functionfdefined in a subsetAof an open and connected subsetUof a Banach spaceX, with values in another Banach spaceE, and admitting certain weak extensions in a Banach space of holomorphic functions can be holomorphically extended in the corresponding Banach space of vector-valued functions.

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Arai, Kenichi, and Hiroyuki Okazaki. "N-Dimensional Binary Vector Spaces." Formalized Mathematics 21, no. 2 (2013): 75–81. http://dx.doi.org/10.2478/forma-2013-0008.

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Summary The binary set {0, 1} together with modulo-2 addition and multiplication is called a binary field, which is denoted by F2. The binary field F2 is defined in [1]. A vector space over F2 is called a binary vector space. The set of all binary vectors of length n forms an n-dimensional vector space Vn over F2. Binary fields and n-dimensional binary vector spaces play an important role in practical computer science, for example, coding theory [15] and cryptology. In cryptology, binary fields and n-dimensional binary vector spaces are very important in proving the security of cryptographic s

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Madhu, Ram, and Davvaz Bijan. "Super quasi-topological and paratopological vector spaces versus topological vector spaces." Divulgaciones Matemáticas 23-24, no. 1-2 (2024): 1–11. https://doi.org/10.5281/zenodo.11515886.

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In this paper, we introduce the idea of super quasi-topological vector space which is an extension of the concept of topological vector space and investigate some of its basic properties. We extend the existing notion of quasi-topological vector space to all complex vector spaces and investigate the relationship of super quasi-topological vector spaces with paratopological and quasi-topological vector spaces.

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4

Friantika, Khasnah Aris, Harina O. L. Monim, and Rium Hilum. "MATRIKS BAKU UNTUK TRANSFORMASI LINIER PADA RUANG VEKTOR DIMENSI TIGA." Jurnal Natural 15, no. 2 (2019): 88–93. http://dx.doi.org/10.30862/jn.v15i2.140.

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The linear transformation is a function relating the vector ke . If , then the transformation is called a linear operator. Several examples of linear operators have been introduced since SMA such as reflexive, rotation, compression and expansion and shear. Apart from being introduced in SMA, these linear operators were also introduced to the linear algebra course. Linear transformations studied at the university level include linear transformation in finite dimension vector spaces . The discussion includes how to determine the standard matrix for reflexive linear transformations, rotation, com

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Amin, B. "Space phasor or space vector?" European Transactions on Electrical Power 4, no. 1 (2007): 69–72. http://dx.doi.org/10.1002/etep.4450040111.

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BAU, SHENG, and YIMING LEI. "BISECTORS IN VECTOR GROUPS OVER INTEGERS." Bulletin of the Australian Mathematical Society 100, no. 3 (2019): 353–61. http://dx.doi.org/10.1017/s0004972719000807.

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We present an example of an isometric subspace of a metric space that has a greater metric dimension. We also show that the metric spaces of vector groups over the integers, defined by the generating set of unit vectors, cannot be resolved by a finite set. Bisectors in the spaces of vector groups, defined by the generating set consisting of unit vectors, are completely determined.

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Guan, Yifei. "Research on the Vector Space and Its Linearity." Highlights in Science, Engineering and Technology 94 (April 26, 2024): 119–23. http://dx.doi.org/10.54097/cqd2x842.

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A vector space is an abelian group over a field. From the viewpoint of group theory, the tangent space is a theoretical concept. Tangent space is similar to a vector space, particularly in terms of linearity. From a field's perspective, a subfield is a subset of the original field that shares the same properties as the original field. Subfield is logically similar to a subspace of a vector space. A vector is an element of a vector space. Weight vectors can be used to describe motion, which can be applied in pattern recognition. A linear combination of weight vectors can describe a sequence of

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Folch-Gabayet, Magali, Martha Guzmán-Partida, and Salvador Pérez-Esteva. "Lipschitz measures and vector-valued Hardy spaces." International Journal of Mathematics and Mathematical Sciences 25, no. 5 (2001): 345–56. http://dx.doi.org/10.1155/s0161171201004549.

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We define certain spaces of Banach-valued measures called Lipschitz measures. When the Banach space is a dual spaceX*, these spaces can be identified with the duals of the atomic vector-valued Hardy spacesHXp(ℝn),0<p<1. We also prove that all these measures have Lipschitz densities. This implies that for every real Banach spaceXand0<p<1, the dualHXp(ℝn)∗can be identified with a space of Lipschitz functions with values inX*.

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9

Moumita Chiney and S. K. Samanta. "Multi vector space." ANNALS OF FUZZY MATHEMATICS AND INFORMATICS 13, no. 5 (2017): 553–62. http://dx.doi.org/10.30948/afmi.2017.13.5.553.

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10

Ismail, Shimaa, Tarek EL Shishtawy, and Abdelwahab Kamel Alsammak. "A New Alignment Word-Space Approach for Measuring Semantic Similarity for Arabic Text." International Journal on Semantic Web and Information Systems 18, no. 1 (2022): 1–18. http://dx.doi.org/10.4018/ijswis.297036.

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This work presents a new alignment word-space approach for measuring the similarity between two snipped texts. The approach combines two similarity measurement methods: alignment-based and vector space-based. The vector space-based method depends on a semantic net that represents the meaning of words as vectors. These vectors are lemmatized to enrich the search space. The alignment-based method generates an alignment word space matrix (AWSM) for the snipped texts according to the generated semantic word spaces. Finally, the degree of sentence semantic similarity is measured using some proposed

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11

Abbas, Fadhil, and Hassan A. Alhayo. "Fuzzy ideal topological vector spaces." Mathematica Slovaca 72, no. 4 (2021): 993–1000. http://dx.doi.org/10.1515/ms-2022-0069.

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Abstract In this paper, we introduce the concept of fuzzy ideal topological vector spaces and study the basic properties of fuzzy-I-open and fuzzy-I-closed sets in fuzzy ideal topological vector spaces. Also, we study the properties of fuzzy-I-Hausdorff and fuzzy-I-compact in fuzzy ideal topological vector spaces. Furthermore, we introduce the concepts of fuzzy-I-homogenous space, fuzzy-I-monomorphism space, fuzzy-I-isomorphism space and fuzzy-I-automorphism space. Finally, we introduce the concepts of fuzzy-I-bounded set, fuzzy-I-balanced set, fuzzy-I-symmetric set and study their properties

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12

Rodríguez, José. "Spaces of vector functions that are integrable with respect to vector measures." Journal of the Australian Mathematical Society 82, no. 1 (2007): 85–109. http://dx.doi.org/10.1017/s1446788700017481.

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AbstractWe study the normed spaces of (equivalence classes of) Banach space-valued functions that are Dobrakov,S* or McShane integrable with respect to a Banach space-valued measure, where the norm is the natural one given by the total semivariation of the indefinite integral. We show that simple functions are dense in these spaces. As a consequence we characterize when the corresponding indefinite integrals have norm relatively compact range. On the other hand, we also determine when these spaces are ultrabornological. Our results apply to conclude, for instance, that the spaces of Birkhoff (

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13

Obukhov, V. V. "Classification of Petrov Homogeneous Spaces." Symmetry 16, no. 10 (2024): 1385. http://dx.doi.org/10.3390/sym16101385.

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In this paper, the final stage of the Petrov classification is carried out. As it is known, the Killing vector fields specify infinitesimal transformations of the group of motions of space V4. In the case where the group of motions G3 acts in a simply transitive way in the homogeneous space V4, the geometry of the non-isotropic hypersurface is determined by the geometry of the transitivity space V3 of the group G3. In this case, the metric tensor of the space V3 can be given by a nonholonomic reper consisting of three independent vectors ℓ(a)α, which define the generators of the group G3 of fi

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Wong, S. K. M., and Wojciech Ziarko. "On Generalized Vector Space Model in Information Retrieval." Fundamenta Informaticae 8, no. 2 (1985): 253–67. http://dx.doi.org/10.3233/fi-1985-8207.

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In information retrieval, it is common to model index terms and documents as vectors in a suitably defined vector space. The main difficulty with this approach is that the explicit representation of term vectors is not known a priori. For this reason, the vector space model adopted by Salton for the SMART system treats the terms as a set of orthogonal vectors. In such a model it is often necessary to adopt a separate, corrective procedure to take into account the correlations between terms. In this paper, we propose a systematic method (the generalized vector space model) to compute term corre

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Elshenhab, Ahmed M., Osama Moaaz, Ioannis Dassios, and Ayman Elsharkawy. "Motion Along a Space Curve with a Quasi-Frame in Euclidean 3-Space: Acceleration and Jerk." Symmetry 14, no. 8 (2022): 1610. http://dx.doi.org/10.3390/sym14081610.

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The resolution of the acceleration and jerk vectors of a particle moving on a space curve in the Euclidean 3-space is considered. By applying this resolution and Siacci’s theorem, alternative resolutions of acceleration and jerk vectors are derived based on the quasi-frame. In the osculating plane, the acceleration vector is resolved as the sum of its tangential and radial components. In addition, in the osculating and rectifying planes, the jerk vector is resolved along the tangential direction and two special radial directions. The maximum permissible speed on a space curve at all trajectory

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16

ISIDRO, JOSÉ M. "QUANTUM STATES FROM TANGENT VECTORS." Modern Physics Letters A 19, no. 31 (2004): 2339–52. http://dx.doi.org/10.1142/s0217732304015634.

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We argue that tangent vectors to classical phase space give rise to quantum states of the corresponding quantum mechanics. This is established for the case of complex, finite-dimensional, compact, classical phase spaces [Formula: see text], by explicitly constructing Hilbert-space vector bundles over [Formula: see text]. We find that these vector bundles split as the direct sum of two holomorphic vector bundles: the holomorphic tangent bundle [Formula: see text], plus a complex line bundle [Formula: see text]. Quantum states (except the vacuum) appear as tangent vectors to [Formula: see text].

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17

Okhotkin, Grigory P., and Ivan I. Ivanchin. "SPACE VECTOR PWM IN A MULTILEVEL VOLTAGE CONVERTER." Vestnik Chuvashskogo universiteta, no. 1 (March 30, 2022): 107–14. http://dx.doi.org/10.47026/1810-1909-2022-1-107-114.

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The present article considers the voltage forming by multilevel converters. Multilevel converters are widely used in industry applications with medium voltages up to 20 kV. An example is the oil industry, where multilevel converters are installed in electric drives of pumping units on pipeline systems. The location of the pipelines in isolated areas implies weak net connections for power system and expects increased requirements for the efficiency of the use of electricity. In this regard, for a multilevel voltage converter, an energy-efficient vector method of pulse-width modulation is propos

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18

Kankarej, Manisha M., and Jai P. Singh. "Fractional Vector Cross Product in Euclidean 3-Space." International Journal of Analysis and Applications 21 (May 9, 2023): 44. http://dx.doi.org/10.28924/2291-8639-21-2023-44.

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In this research a new definition of fractional vector cross product of two vectors in Euclidean 3-space is presented. Using this new definition the formulae for Euclidean norm, fractional triple vector cross product, curl and divergence of fractional vector cross product of an electromagnetic vector field is discussed. In particular cases, all the properties satisfy definition of standard vector cross product for standard orthogonal basis of R3. The new definition has application in radiation characteristic in micro-strip antenna and can be applied in other branches of mathematics and physics

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19

NISHIMURA, Ryota, Miho HIGAKI, and Norihide KITAOKA. "Mapping Acoustic Vector Space and Document Vector Space by RNN-LSTM." Journal of Japan Society for Fuzzy Theory and Intelligent Informatics 30, no. 4 (2018): 628–33. http://dx.doi.org/10.3156/jsoft.30.4_628.

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20

Depenbrock, M., and V. Staudt. "Hyper space vectors: A new four-quantity extension of space-vector theory." European Transactions on Electrical Power 8, no. 4 (2007): 241–48. http://dx.doi.org/10.1002/etep.4450080404.

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21

Zhao, Wen Bin, and Zheng Xu Zhao. "Voronoi Diagram Based Retrieval Method for the Internet of Things." Advanced Materials Research 472-475 (February 2012): 3420–24. http://dx.doi.org/10.4028/www.scientific.net/amr.472-475.3420.

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In the Internet of Things, search service is that information which is corresponding to entities in real world is retrieve so as to help people achieve information that they need. From the angle of visualization, this paper study the search service in the Internet of Things. With the Vector-Space Model, entities' information is expressed as entity vectors, and a Voronoi diagram based Vector-Space Model visualization method is presented. According to similarity between entity vectors, entity vectors' position in two-dimensional plane is calculated and this plane is divided into Voronoi diagram

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22

Rizkallah, Sandra, Amir F. Atiya, and Samir Shaheen. "New Vector-Space Embeddings for Recommender Systems." Applied Sciences 11, no. 14 (2021): 6477. http://dx.doi.org/10.3390/app11146477.

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In this work, we propose a novel recommender system model based on a technology commonly used in natural language processing called word vector embedding. In this technology, a word is represented by a vector that is embedded in an n-dimensional space. The distance between two vectors expresses the level of similarity/dissimilarity of their underlying words. Since item similarities and user similarities are the basis of designing a successful collaborative filtering, vector embedding seems to be a good candidate. As opposed to words, we propose a vector embedding approach for learning vectors

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23

Franchi, Massimo, and Paolo Paruolo. "Cointegration, Root Functions and Minimal Bases." Econometrics 9, no. 3 (2021): 31. http://dx.doi.org/10.3390/econometrics9030031.

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This paper discusses the notion of cointegrating space for linear processes integrated of any order. It first shows that the notions of (polynomial) cointegrating vectors and of root functions coincide. Second, it discusses how the cointegrating space can be defined (i) as a vector space of polynomial vectors over complex scalars, (ii) as a free module of polynomial vectors over scalar polynomials, or finally (iii) as a vector space of rational vectors over rational scalars. Third, it shows that a canonical set of root functions can be used as a basis of the various notions of cointegrating sp

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24

Ramasamy, Palanisamy, Ramkumar Ravindran, Neetu Gupta, et al. "Simulation of 3D-space vector modulation for neutral point clamped inverters." Bulletin of Electrical Engineering and Informatics 12, no. 2 (2023): 719–26. http://dx.doi.org/10.11591/eei.v12i2.4502.

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This paper gives an idea to simulation of three-dimensional space vector modulation for neutral point clamped multilevel inverter. Three dimensional-space vector modulation (3D-SVM) algorithm is progressed method of two dimensional-space vector modulation (2D-SVM) algorithm; it leads to reduce the complexity in reference vector identification and switching time calculation, also it includes the various advantages of 2D-SVM like minimized total harmonic distortion, reduced EMI issues. A simple system for the assortment of switching state vectors to track the reference voltage vectors without us

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25

Giannakoulias, Efstathios. "Some properties of vector measures taking values in a topological vector space." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 43, no. 2 (1987): 224–30. http://dx.doi.org/10.1017/s1446788700029360.

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AbstractIn this paper we study some properties of vector measures with values in various topological vector spaces. As a matter of fact, we give a necessary condition implying the Pettis integrability of a function f: S → E, where S is a set and E a locally convex space. Furthermore, we prove an iff condition under which (Q, E) has the Pettis property, for an algebra Q and a sequentially complete topological vector space E. An approximating theorem concerning vector measures taking values in a Fréchet space is also given.

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26

Nguyen, Hien D., Chiaki Sakama, Taisuke Sato, and Katsumi Inoue. "An efficient reasoning method on logic programming using partial evaluation in vector spaces." Journal of Logic and Computation 31, no. 5 (2021): 1298–316. http://dx.doi.org/10.1093/logcom/exab010.

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Abstract In this paper, we introduce methods of encoding propositional logic programs in vector spaces. Interpretations are represented by vectors and programs are represented by matrices. The least model of a definite program is computed by multiplying an interpretation vector and a program matrix. To optimize computation in vector spaces, we provide a method of partial evaluation of programs using linear algebra. Partial evaluation is done by unfolding rules in a program, and it is realized in a vector space by multiplying program matrices. We perform experiments using artificial data and re

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27

Palanisamy, Ramasamy, Ravindran Ramkumar, Gupta Neetu, et al. "Simulation of 3D-space vector modulation for neutral point clamped inverters." Bulletin of Electrical Engineering and Informatics 12, no. 2 (2023): 719~726. https://doi.org/10.11591/eei.v12i2.4502.

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This paper gives an idea to simulation of three-dimensional space vector modulation for neutral point clamped multilevel inverter. Three dimensional-space vector modulation (3D-SVM) algorithm is progressed method of two dimensional-space vector modulation (2D-SVM) algorithm; it leads to reduce the complexity in reference vector identification and switching time calculation, also it includes the various advantages of 2DSVM like minimized total harmonic distortion, reduced EMI issues. A simple system for the assortment of switching state vectors to track the reference voltage vectors without usi

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28

K. Anuradha, Et al. "An Overview of the Different Kinds of Vector Space Partitions." International Journal on Recent and Innovation Trends in Computing and Communication 11, no. 9 (2023): 3907–18. http://dx.doi.org/10.17762/ijritcc.v11i9.9696.

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In a finite vector space V (n,q), where V is n-dimensional over a finite field with q elements, a collection P of subspaces is called a vector space partition. The property of this set P is that any vector that is not zero may be found in exactly one element of P. Partitions of vector spaces have strong ties to design theory, error-correcting algorithms, and finite projective planes. The first portion of my talk will focus on the mathematical fields that share common ground with vector space partitions. The rest of the lecture will go over some of the most well-known results on vector sp

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29

Ameri, Reza, M. Hamidi, and A. Samadifam. "Topological Vector Spaces Derived From Topological Hypervector Spaces." PROOF 3 (October 6, 2023): 50–57. http://dx.doi.org/10.37394/232020.2023.3.7.

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We introduce topological hypervector spaces on a topological field, in the sense of Tallini, and study some basic properties of this hyperspaces. In this regards we study the relationship between the topology on a hypervector spaces and its complete part. In particular we show that if every open subset of a topological hypervector space is a complete part then its fundamental vector space induced is a topological vector space. Finally, we study the quotient space of topological hypervector spaces and the derived topological space of a topological hypervector space with respect its fundamental

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30

Prabowo, Yulius Denny, Tedi Lesmana Marselino, and Meylisa Suryawiguna. "Pembentukan Vector Space Model Bahasa Indonesia Menggunakan Metode Word to Vector." Jurnal Buana Informatika 10, no. 1 (2019): 29. http://dx.doi.org/10.24002/jbi.v10i1.2053.

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Extracting information from a large amount of structured data requires expensive computing. The Vector Space Model method works by mapping words in continuous vector space where semantically similar words are mapped in adjacent vector spaces. The Vector Space Model model assumes words that appear in the same context, having the same semantic meaning. In the implementation, there are two different approaches: counting methods (eg: Latent Semantic Analysis) and predictive methods (eg Neural Probabilistic Language Model). This study aims to apply Word2Vec method using the Continuous Bag of Words

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31

Haas, Ruth. "Module and vector space bases for spline spaces." Journal of Approximation Theory 65, no. 1 (1991): 73–89. http://dx.doi.org/10.1016/0021-9045(91)90113-o.

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32

Siegl, E. "A free convenient vector space for holomorphic spaces." Monatshefte f�r Mathematik 119, no. 1-2 (1995): 85–97. http://dx.doi.org/10.1007/bf01292771.

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33

Moradi, Hamid Reza. "Bounded and Semi Bounded Inverse Theorems in Fuzzy Normed Spaces." International Journal of Fuzzy System Applications 4, no. 2 (2015): 47–55. http://dx.doi.org/10.4018/ijfsa.2015040104.

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In this paper, the author introduces the notion of the complete fuzzy norm on a linear space. And the author considers some relations between the fuzzy completeness and ordinary completeness on a linear space, moreover a new form of fuzzy compact spaces, namely b-compact spaces, b-closed space is introduced. Some characterization of their properties is obtained. Also some basic properties for linear operators between fuzzy normed spaces are further studied. The notions of fuzzy vector spaces and fuzzy topological vector spaces were introduced in Katsaras and Liu (1977). These ideas were modifi

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34

Moumita Chiney and S. K. Samanta. "Soft topological vector space." ANNALS OF FUZZY MATHEMATICS AND INFORMATICS 13, no. 2 (2017): 153–74. http://dx.doi.org/10.30948/afmi.2017.13.2.153.

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35

Fischer, H. D. "Generalized space vector transformation." Electrical Engineering (Archiv fur Elektrotechnik) 82, no. 6 (2000): 279–84. http://dx.doi.org/10.1007/s002020000044.

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36

Latif, Raja Mohammad. "M – STAR – Irresolute Topological Vector Spaces." International Journal of Pure Mathematics 7 (February 8, 2021): 20–36. http://dx.doi.org/10.46300/91019.2020.7.4.

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In 2016 A. Devika and A. Thilagavathi introduced a new class of sets called M*-open sets and investigated some properties of these sets in topological spaces. In this paper, we introduce and study a new class of spaces, namely M*-irresolute topological vector spaces via M*-open sets. We explore and investigate several properties and characterizations of this new notion of M*-irresolute topological vector space. We give several characterizations of M*-Hausdorff space. Moreover, we show that the extreme point of the convex subset of M*-irresolute topological vector space X lies on the boundary.

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Ravindran, R. Malathi, and Dr Antony Selvadoss Thanamani. "K-Means Document Clustering using Vector Space Model." Bonfring International Journal of Data Mining 5, no. 2 (2015): 10–14. http://dx.doi.org/10.9756/bijdm.8076.

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38

Michael, Prawin Angel. "FPGA Implementation of Multilevel Space Vector PWM Algorithms." International Journal of Engineering and Technology 1, no. 3 (2009): 208–12. http://dx.doi.org/10.7763/ijet.2009.v1.39.

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39

Njagi, L., B. M. Nzimbi, and S. K. Moindi. "On Finite Dimensional Hilbert Space Frames, Dual and Normalized Frames and Pseudo-inverse of the Frame Operator." Journal of Advance Research in Mathematics And Statistics (ISSN: 2208-2409) 5, no. 11 (2018): 11–14. http://dx.doi.org/10.53555/nnms.v5i11.528.

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In this research paper we do an introduction to Hilbert space frames. We also discuss various frames in the Hilbert space. A frame is a generalization of a basis. It is useful, for example, in signal processing. It also allows us to expand Hilbert space vectors in terms of a set of other vectors that satisfy a certain condition. This condition guarantees that any vector in the Hilbert space can be reconstructed in a numerically stable way from its frame coe?cients. Our focus will be on frames in ?nite dimensional spaces.

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40

Iwaszkiewicz, Jan, Adam Muc, and Agata Bielecka. "Polar Voltage Space Vectors of the Six-Phase Two-Level VSI." Energies 15, no. 8 (2022): 2763. http://dx.doi.org/10.3390/en15082763.

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The paper recommends polar voltage space vectors of the six-phase and two-level inverter as a useful mathematical tool for vector control of the inverter. The inverter model is described using three mathematical tools: analytic expressions, voltage state, and space vectors. The analytic formulas allow for the determination of elementary physical inverter quantities: current and voltage. The state voltage vectors make it easy to define phase voltage distribution in every possible state of the inverter and voltage space vectors are the most important tool used for inverters’ control. The space v

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41

Tambayong, Chrisanty Y., Jullia Titaley, and Rinancy Tumilaar. "EKSISTENSI RUANG VEKTOR ATAS LAPANGAN TERHADAP MODUL BEBAS." JURNAL ILMIAH SAINS 19, no. 1 (2019): 37. http://dx.doi.org/10.35799/jis.19.1.2019.22536.

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EKSISTENSI RUANG VEKTOR ATAS LAPANGANTERHADAP MODUL BEBAS ABSTRAKModul merupakan perluasan dari ruang vektor. Suatu Ruang vektor atas lapangan merupakan suatu himpunan vektor – vektor dengan dua operasi yaitu penjumlahan dan perkalian dengan skalar. Sebarang ruang vektor atas lapangan dapat dipandang sebagai modul atas ring Tetapi tidak semua modul dapat dinyatakan sebagai ruang vektor atas lapangan. Tujuan penelitian ini adalah untuk memberikan counter example bahwa tidak semua modul merupakan ruang vektor atas lapangan. Dari hasil penelitian dapat disimpulkan bahwa setiap modul yang memiliki

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Li, Gui San. "Quaternions and Vector Mapping in Three-Dimensional Space." Applied Mechanics and Materials 235 (November 2012): 101–6. http://dx.doi.org/10.4028/www.scientific.net/amm.235.101.

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On the basis of analyzing the relations between vector operation and properties of multiplication operation of quaternions, the geometric representation and mapping of quaternions and vectors defined in three-dimensional space are established. The mathmatic operation of space vector, in addition to any space unit vector, rotating around three coordinate axises is carried based on the utilization of quaternions.The main purpose of this paper is to solve the issues of mathmatic tools introduced in spatial mechanism analysises and integrations by making use of quatnions.

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Kumar, Nand Kishor, and Dipendra Prasad Yadav. "Topological Quasi-vector Space and It’s Characteristics." Perspectives on Higher Education 14 (December 31, 2024): 67–80. https://doi.org/10.3126/phe.v14i1.76568.

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This article discusses fundamental concepts and examples related to topological vector spaces. The primary goal of this article is to investigate topological quasi-vector spaces and their properties. This research endeavor begins with the discovery of various features of (topological) quasi-vector spaces that remain invariant under some kind of transformation. Any such transformation should be built in such a way that it can preserve the full quasi-vector spaces - structure. The features of quasi-vector space are used to characterize specific (topological) quasi-vector spaces that play an impo

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İsabeyoǧlu, Zeynep, Tülay Erişir, and Ayşe Zeynep Azak. "Spinor Equations of Smarandache Curves in E3." Mathematics 12, no. 24 (2024): 4022. https://doi.org/10.3390/math12244022.

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This study examines the spinor representations of TN (tangent and normal), NB (normal and binormal), TB (tangent and binormal) and TNB (tangent, normal and binormal)–Smarandache curves in three-dimensional Euclidean space E3. Spinors are complex column vectors and move on Pauli spin matrices. Isotropic vectors in the C3 complex vector space form a two-dimensional surface in the C2 complex space. Additionally, each isotropic vector in C3 space corresponds to two vectors in C2 space, called spinors. Based on this information, our goal is to establish a relationship between curve theory in differ

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Zhu, Jenny. "Beyond the finite: An exploration of infinite-dimensional vector spaces." Theoretical and Natural Science 30, no. 1 (2024): 29–37. http://dx.doi.org/10.54254/2753-8818/30/20241017.

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In this paper, we delve deeply into the intricacies of linear algebra, with a focus on the progression from finite to infinite-dimensional vector spaces. Starting with the foundational concepts, we define vectors, vector spaces, linear combinations, and basis. The importance of infinite-dimensional vector spaces is emphasized, particularly their role in better understanding and modeling complex mathematical phenomena. Through well-illustrated examples, we guide the reader on how to validate if a given set can be classified as a vector space. Additionally, the methodology to identify bases for

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Iwаszkiewicz, Jаn, and Adam Muc. "The active filtering of the inverter output voltage by use of orthogonal vectors’ control strategy." Renewable Energy and Power Quality Journal 20 (September 2022): 817–21. http://dx.doi.org/10.24084/repqj20.446.

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he paper proposes a creative control method permitting to filter output voltage waveforms of the inverter. The main idea is based on the assumption that the total inverter output space vector is carefully chosen as a composition of two space vectors generated by 2 two-level inverters. The total built-up inverter is assembled of two standard three-phase inverters: a main inverter (MI) and an auxiliary one (AI) serving as an active filter. The output voltage space vector of the built-up inverter is composed of one or two space vectors generated by the respective inverters. The space vectors of t

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Heijungs, Reinout. "Revisiting the Definition of Vectors—From ‘Magnitude and Direction’ to Abstract Tuples." Foundations 5, no. 2 (2025): 12. https://doi.org/10.3390/foundations5020012.

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Vectors are almost always introduced as objects having magnitude and direction. Following that idea, textbooks and courses introduce the concept of a vector norm and the angle between two vectors. While this is correct and useful for vectors in two- or three-dimensional Euclidean space, these concepts make no sense for more general vectors, that are defined in abstract, non-metric vector spaces. This is even the case when an inner product exists. Here, we analyze how several textbooks are imprecise in presenting the restricted validity of the expressions for the norm and the angle. We also stu

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Lin, C. S. "A-bilinear forms and generalised A-quadratic forms on unitary left A-modules." Bulletin of the Australian Mathematical Society 39, no. 1 (1989): 49–58. http://dx.doi.org/10.1017/s0004972700027970.

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In this paper we shall define a generalised A-quadratic form and prove that in some way this form and an A-bilinear form are equivalent to each other. Our result characterises that of Vukman in the sense that we use any n vectors for a fixed n ≥ 2, instead of any two vectors. Consequently, a new generalisation of an inner product space among vector spaces is obtained. This also leads to a new relationship between a 2-inner product space and a 2-normed space.

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AIZPURU, ANTONIO, and FRANCISCO J. GARCÍA-PACHECO. "A NOTE ON L2-SUMMAND VECTORS IN DUAL SPACES." Glasgow Mathematical Journal 50, no. 3 (2008): 429–32. http://dx.doi.org/10.1017/s0017089508004308.

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AbstractIt is shown that every L2-summand vector of a dual real Banach space is a norm-attaining functional. As consequences, the L2-summand vectors of a dual real Banach space can be determined by the L2-summand vectors of its predual; for every n ∈ , every real Banach space can be equivalently renormed so that the set of norm-attaining functionals is n-lineable; and it is easy to find equivalent norms on non-reflexive dual real Banach spaces that are not dual norms.

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DOGRA, SHOVAN, and MADHUMANGAL PAL. "Picture Fuzzy Subspace of a Crisp Vector Space." Kragujevac Journal of Mathematics 47, no. 4 (2003): 577–97. http://dx.doi.org/10.46793/kgjmat2304.577d.

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In this paper, the notion of picture fuzzy subspace of a crisp vector space is established and some related properties are explored on the basis of some basic operations (intersection, Cartesian product, union, (θ, ϕ, ψ)-cut etc.) on picture fuzzy sets. Direct sum of two picture fuzzy subspaces is initiated here over the direct sum of two crisp vector spaces. Also, the concepts of picture fuzzy linear transformation and picture fuzzy linearly independent set of vectors are introduced and some corresponding results are presented. Isomorphism between two picture fuzzy subspaces is developed here

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