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Journal articles on the topic 'Scalar product'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Bose, Subrata. "Privacy preserving computation of scalar product and sign of scalar product." International Journal of Internet Technology and Secured Transactions 9, no. 1/2 (2019): 112. http://dx.doi.org/10.1504/ijitst.2019.098164.

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2

Bose, Subrata. "Privacy Preserving Computation of Scalar Product and Sign of Scalar Product." International Journal of Internet Technology and Secured Transactions 9, no. 1-2 (2019): 1. http://dx.doi.org/10.1504/ijitst.2019.10013024.

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3

Shundong, LI, ZHANG Mengyu, and XU Wenting. "Secure Scalar Product Protocols." Chinese Journal of Electronics 30, no. 6 (2021): 1059–68. http://dx.doi.org/10.1049/cje.2021.07.018.

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4

Droz-Vincent, Philippe. "Modules with scalar product." Letters in Mathematical Physics 9, no. 4 (1985): 271–76. http://dx.doi.org/10.1007/bf00397753.

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5

GUNARA, BOBBY E., FREDDY P. ZEN, FIKI T. AKBAR, AGUS SUROSO, and ARIANTO. "SOME ASPECTS OF SPHERICAL SYMMETRIC EXTREMAL DYONIC BLACK HOLES IN 4D N = 1 SUPERGRAVITY." International Journal of Modern Physics A 28, no. 18 (2013): 1350084. http://dx.doi.org/10.1142/s0217751x1350084x.

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In this paper, we study several aspects of extremal spherical symmetric black hole solutions of four-dimensional N = 1 supergravity coupled to vector and chiral multiplets with the scalar potential turned on. In the asymptotic region, the complex scalars are fixed and regular which can be viewed as the critical points of the black hole and the scalar potentials with vanishing scalar charges. It follows that the asymptotic geometries are of a constant and nonzero scalar curvature which are generally not Einstein. These spaces could also correspond to the near horizon geometries which are the pr

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6

Gosselin, J. R. "76.6 On the Scalar Triple Product and Determinantal Products." Mathematical Gazette 76, no. 476 (1992): 280. http://dx.doi.org/10.2307/3619144.

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7

Siburg, Karl Friedrich, and Pavel A. Stoimenov. "A scalar product for copulas." Journal of Mathematical Analysis and Applications 344, no. 1 (2008): 429–39. http://dx.doi.org/10.1016/j.jmaa.2008.02.045.

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8

Lin, T. Y., E. M. Drakakis, and A. J. Payne. "Vector-scalar-product circuit concept." Electronics Letters 36, no. 20 (2000): 1676. http://dx.doi.org/10.1049/el:20001235.

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9

Çolakoğlu, Harun Barış, İskender Öztürk, Oğuzhan Çelik, and Mustafa Özdemir. "Generalized Galilean Rotations." Symmetry 16, no. 11 (2024): 1553. http://dx.doi.org/10.3390/sym16111553.

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In this article, we give rotational motions on any straight line or any parabola in a scalar product space. To achieve this goal, we first define the generalized Galilean scalar product and determine the generalized Galilean skew symmetric and orthogonal matrices. Then, using the well-known Rodrigues, Cayley, and Householder maps, we produce the generalized Galilean rotation matrices. Finally, we show that these rotation matrices can also be used to determine parabolic rotational motion.

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10

Aloui, Foued, and Ibrahim Al-Dayel. "Einstein Doubly Warped Product Poisson Manifolds." Symmetry 17, no. 3 (2025): 342. https://doi.org/10.3390/sym17030342.

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In this paper, we study Einstein doubly warped product Poisson manifolds. First, we provide necessary and sufficient conditions for a doubly warped product manifold (M=Bf×bF,g,Π), equipped with a Poisson structure Π to be a contravariant Einstein manifold. Additionally, under certain conditions on the base space B, we prove that if M is an Einstein doubly warped product Poisson manifold with non-positive scalar curvature, then M is simply a singly warped product Poisson manifold. We also investigate the existence and non-existence of the warping function on the base space B associated with con

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11

Clifford, Frank. "73.40 Applications of the Scalar Product." Mathematical Gazette 73, no. 465 (1989): 231. http://dx.doi.org/10.2307/3618452.

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12

Mackey, D. Steven, Niloufer Mackey, and Françoise Tisseur. "Structured Factorizations in Scalar Product Spaces." SIAM Journal on Matrix Analysis and Applications 27, no. 3 (2005): 821–50. http://dx.doi.org/10.1137/040619363.

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13

Greco, Frank A. "How is the scalar product derived?" Mathematical Gazette 103, no. 557 (2019): 357–58. http://dx.doi.org/10.1017/mag.2019.75.

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14

Viskov, O. V. "Schwinger's formula for the scalar product." Russian Mathematical Surveys 60, no. 2 (2005): 380–81. http://dx.doi.org/10.1070/rm2005v060n02abeh000831.

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15

GIBILISCO, PAOLO, and TOMMASO ISOLA. "A CHARACTERISATION OF WIGNER–YANASE SKEW INFORMATION AMONG STATISTICALLY MONOTONE METRICS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 04, no. 04 (2001): 553–57. http://dx.doi.org/10.1142/s0219025701000644.

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Let [Formula: see text] be the space of n × n complex matrices endowed with the Hilbert–Schmidt scalar product, let Sn be the unit sphere of Mn and let Dn⊂ Mn be the space of strictly positive density matrices. We show that the scalar product over Dn introduced by Gibilisco and Isola3 (that is the scalar product induced by the map [Formula: see text]) coincides with the Wigner–Yanase monotone metric.

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16

Ceno, Stela. "Some properties of the superior and inferior semi inner product function associated to the 2-norm." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 5 (2016): 6254–60. http://dx.doi.org/10.24297/jam.v12i5.322.

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Special properties that the scalar product enjoys and its close link with the norm function have raised the interest of researchers from a very long period of time. S.S. Dragomir presents concrete generalizations of the scalar product functions in a normed space and deals with the interesting properties of them. Based on S.S. Dragomirs idea in this paper we treat generalizations of superior and inferior scalar product functions in the case of semi-normed spaces and 2-normed spaces.

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17

Tsmots, Ivan, Yurii Opotyak, and Bohdan Shtohrinets. "Method of Synthesis of Devices for Parallel Stream Calculation of Scalar Product in Real Time." Vìsnik Nacìonalʹnogo unìversitetu "Lʹvìvsʹka polìtehnìka". Serìâ Ìnformacìjnì sistemi ta merežì 14 (December 26, 2023): 248–66. http://dx.doi.org/10.23939/sisn2023.14.248.

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A graph scheme of a generalized algorithm for parallel stream calculation of the scalar product was developed. The proposed algorithm uses the same type of operations for forming a partial product that is calculated starting from the lowest digits of the multipliers. The developed algorithm of parallel stream calculation of the scalar product is performed with the use of operations for forming partial products, calculating the macro-partial product, and adding it to the partial result shifted to the right by the number of digits that were used in the formation of partial products. It is sugges

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18

Nurjaman, Jajang. "Perbandingan Optimasi Query Menggunakan Query Scalar, Correlated Dan Kombinasi." Jurnal Bangkit Indonesia 6, no. 2 (2017): 22. http://dx.doi.org/10.52771/bangkitindonesia.v6i2.26.

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Optimasi query merupakan suatu pola penulisan SQL yang mengacu pada standar SQL. Optimasi query ini sangat penting untuk dapat dipelajari karena dengan optimasi query ini kita dapat memaksimalkan kecepatan dan efisiensi dari eksekusi suatu program. Ada dua jenis pendekatan yang umum pada optimasi query ini yaitu pendekatan heuristic dan cost-base.dalam pendekatan cost base terdapat dua model optimasi query yaitu cross product dan subquery. Pada subquery sendiri terdapat tiga jenis query yaitu scalar, correlated dan kombinasi (cross product-scalar dan multi scalar). Ketiga jenis query dari subq

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19

Ehrlich, Paul E., Jung Yoon-Tae, and Seon-Bu Kim. "Constant scalar curvatures on warped product manifolds." Tsukuba Journal of Mathematics 20, no. 1 (1996): 239–56. http://dx.doi.org/10.21099/tkbjm/1496162996.

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20

Dehghan, O. R. "Sum and scalar product of fuzzy subhyperspaces." Journal of Discrete Mathematical Sciences and Cryptography 23, no. 4 (2019): 841–60. http://dx.doi.org/10.1080/09720529.2019.1624061.

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21

I-Cheng Wang, Chih-hao Shen, J. Zhan, Tsan-sheng Hsu, Churn-Jung Liau, and Da-Wei Wang. "Toward Empirical Aspects of Secure Scalar Product." IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews) 39, no. 4 (2009): 440–47. http://dx.doi.org/10.1109/tsmcc.2009.2016430.

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22

Marangoz, Ata, and Salim Yüce. "Matrix Theory on Lorentz-Minkowski Scalar Product." Azerbaijan Journal of Mathematics, no. 02 (2024): 65. http://dx.doi.org/10.59849/2218-6816.2024.2.65.

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23

Savvidy, George. "Invariant scalar product on extended Poincaré algebra." Journal of Physics A: Mathematical and Theoretical 47, no. 5 (2014): 055204. http://dx.doi.org/10.1088/1751-8113/47/5/055204.

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24

Galloway, Gregory J., and Hyun Chul Jang. "Some scalar curvature warped product splitting theorems." Proceedings of the American Mathematical Society 148, no. 6 (2020): 2617–29. http://dx.doi.org/10.1090/proc/14922.

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25

Asanov, G. S. "Finsleroid space with angle and scalar product." Publicationes Mathematicae Debrecen 67, no. 1-2 (2005): 209–52. http://dx.doi.org/10.5486/pmd.2005.3146.

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26

Blaga, Adara. "On warped product gradient η-Ricci solitons". Filomat 31, № 18 (2017): 5791–801. http://dx.doi.org/10.2298/fil1718791b.

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If the potential vector field of an ?-Ricci soliton is of gradient type, using Bochner formula, we derive from the soliton equation a nonlinear second order PDE. In a particular case of irrotational potential vector field we prove that the soliton is completely determined by f . We give a way to construct a gradient ?-Ricci soliton on a warped product manifold and show that if the base manifold is oriented, compact and of constant scalar curvature, the soliton on the product manifold gives a lower bound for its scalar curvature.

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27

Bossi, Hannah, and Shreyashi Chakdar. "A Symmetric Two Higgs Doublet Model." Journal of Nepal Physical Society 7, no. 3 (2021): 34–40. http://dx.doi.org/10.3126/jnphyssoc.v7i3.42189.

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In the light of ongoing experimental search efforts for the dark matter and the post-Higgs Beyond the Standard Model (BSM) null results at the Large Hadron Collider (LHC), the Electroweak sector demands to be investigated for possible new scalar states discoverable at the LHC fulfilling the role of the dark matter. In this work we present a symmetric two Higgs doublet model with a discrete interchange symmetry among the two Higgs doublets (Φ1 ↔ Φ2). Apart from the Standard Model (SM)-like scalar state (h) with mh = 125 GeV, the model has several distinguishing features including the pseudoscal

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28

Cherkas, Sergey L., and Vladimir L. Kalashnikov. "Scalar Product for a Version of Minisuperspace Model with Grassmann Variables." Universe 9, no. 12 (2023): 508. http://dx.doi.org/10.3390/universe9120508.

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Grassmann variables are used to formally transform a system with constraints into an unconstrained system. As a result, the Schrödinger equation arises instead of the Wheeler–DeWitt one. The Schrödinger equation describes a system’s evolution, but a definition of the scalar product is needed to calculate the mean values of the operators. We suggest an explicit formula for the scalar product related to the Klein–Gordon scalar product. The calculation of the mean values is compared with an etalon method in which a redundant degree of freedom is excluded. Nevertheless, we note that a complete cor

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29

Wang, Jinmin, and Zhizhang Xie. "Scalar curvature rigidity of degenerate warped product spaces." Transactions of the American Mathematical Society, Series B 12, no. 1 (2025): 1–37. https://doi.org/10.1090/btran/206.

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In this paper we prove the scalar curvature extremality and rigidity for a class of warped product spaces that are possibly degenerate at the two ends. The leaves of these warped product spaces can be any closed Riemannian manifolds with nonnegative curvature operators and nonvanishing Euler characteristics, flat tori, round spheres and their direct products. In particular, we obtain the scalar curvature extremality and rigidity for certain degenerate toric bands and also for round spheres with two antipodal points removed. This answers positively the corresponding questions of Gromov in all d

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30

Pal, Buddhadev, and Pankaj Kumar. "Compact Einstein multiply warped product space with nonpositive scalar curvature." International Journal of Geometric Methods in Modern Physics 16, no. 10 (2019): 1950162. http://dx.doi.org/10.1142/s0219887819501627.

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In this paper, we characterize the Einstein multiply warped product space with nonpositive scalar curvature. As a result, it is shown that, if [Formula: see text] is Einstein multiple-warped product spaces with compact base and nonpositive scalar curvature, then [Formula: see text] is simply a Riemannian manifold. Next, we apply our result on Generalized Robertson–Walker space-time and Generalized Friedmann–Robertson–Walker space-time.

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31

Cieśliński, Jan L., and Artur Kobus. "On the Product Rule for the Hyperbolic Scator Algebra." Axioms 9, no. 2 (2020): 55. http://dx.doi.org/10.3390/axioms9020055.

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Scator set, introduced by Fernández-Guasti and Zaldívar, is endowed with a very peculiar non-distributive product. In this paper we consider the scator space of dimension 1 + 2 and the so called fundamental embedding which maps the subset of scators with non-zero scalar component into 4-dimensional space endowed with a natural distributive product. The original definition of the scator product is induced in a straightforward way. Moreover, we propose an extension of the scator product on the whole scator space, including all scators with vanishing scalar component.

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32

Huang, C. "Notes on Screw Product Operations in the Formulations of Successive Finite Displacements." Journal of Mechanical Design 119, no. 4 (1997): 434–39. http://dx.doi.org/10.1115/1.2826387.

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Geometrical interpretations of two line-based formulations of successive finite displacements, Dimentberg’s formulation and a linear formulation, are discussed in this paper. The interpretations are based on the fact that the pitch of the screw product of two unit line vectors is consistent with Parkin’s definition of pitch. Finite twists in Dimentberg’s formulation are shown to be the screw product of unit line vectors divided by the scalar product of unit line vectors. On the other hand, Finite twists in the linear formulation are interpreted as the screw product of unit line vectors divided

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33

Kirby, R. "83.12 The Scalar Product from a Different Direction." Mathematical Gazette 83, no. 496 (1999): 117. http://dx.doi.org/10.2307/3618700.

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34

Kyrov, V. A. "The Analytic Embedding of Geometries with Scalar Product." Siberian Advances in Mathematics 31, no. 1 (2021): 27–39. http://dx.doi.org/10.1134/s105513442101003x.

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35

Zhang, Yaqian, and Zhifang Zhang. "Scalar MSCR Codes via the Product Matrix Construction." IEEE Transactions on Information Theory 66, no. 2 (2020): 995–1006. http://dx.doi.org/10.1109/tit.2019.2934114.

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36

Belliard, S., N. A. Slavnov, and B. Vallet. "Scalar product of twisted XXX modified Bethe vectors." Journal of Statistical Mechanics: Theory and Experiment 2018, no. 9 (2018): 093103. http://dx.doi.org/10.1088/1742-5468/aaddac.

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37

Galleas, W. "Scalar Product of Bethe Vectors from Functional Equations." Communications in Mathematical Physics 329, no. 1 (2014): 141–67. http://dx.doi.org/10.1007/s00220-014-1976-2.

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38

Falceto, F., K. Gawȩdzki, and A. Kupiainen. "Scalar product of current blocks in WZW theory." Physics Letters B 260, no. 1-2 (1991): 101–8. http://dx.doi.org/10.1016/0370-2693(91)90975-v.

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39

Leroy, L. "Operator product expansion in supersymmetric scalar field theories." Physics Letters B 187, no. 1-2 (1987): 97–105. http://dx.doi.org/10.1016/0370-2693(87)90079-7.

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40

Yang, Bo, Yong Yu, and Chung-Huang Yang. "A Secure Scalar Product Protocol Against Malicious Adversaries." Journal of Computer Science and Technology 28, no. 1 (2013): 152–58. http://dx.doi.org/10.1007/s11390-013-1319-3.

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41

Lukic, Katarina. "The Jacobi-orthogonality in indefinite scalar product spaces." Publications de l'Institut Math?matique (Belgrade) 115, no. 129 (2024): 33–44. http://dx.doi.org/10.2298/pim2429033l.

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We generalize the property of Jacobi-orthogonality to indefinite scalar product spaces. We compare various principles and investigate relations between Osserman, Jacobi-dual, and Jacobi-orthogonal algebraic curvature tensors. We show that every quasi-Clifford tensor is Jacobi-orthogonal. We prove that a Jacobi-diagonalizable Jacobi-orthogonal tensor is Jacobi-dual whenever JX has no null eigenvectors for all nonnull X. We show that any algebraic curvature tensor of dimension 3 is Jacobi-orthogonal if and only if it is of constant sectional curvature. We prove that every 4-dimensional Jacobidia

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42

BECKERS, JULES, NATHALIE DEBERGH, JOSÉ F. CARIÑENA та GIUSEPPE MARMO. "NON-HERMITIAN OSCILLATOR-LIKE HAMILTONIANS AND λ-COHERENT STATES REVISITED". Modern Physics Letters A 16, № 02 (2001): 91–98. http://dx.doi.org/10.1142/s021773230100295x.

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Previous λ-deformed non-Hermitian Hamiltonians with respect to the usual scalar product of Hilbert spaces dealing with harmonic oscillator-like developments are (re)considered with respect to a new scalar product in order to take into account their property of self-adjointness. The corresponding deformed λ-states lead to new families of coherent states according to the DOCS, AOCS and MUCS points of view.

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43

Baesler, Malte, Sven-Ole Voigt, and Thomas Teufel. "A Decimal Floating-Point Accurate Scalar Product Unit with a Parallel Fixed-Point Multiplier on a Virtex-5 FPGA." International Journal of Reconfigurable Computing 2010 (2010): 1–13. http://dx.doi.org/10.1155/2010/357839.

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Decimal Floating Point operations are important for applications that cannot tolerate errors from conversions between binary and decimal formats, for instance, commercial, financial, and insurance applications. In this paper, we present a parallel decimal fixed-point multiplier designed to exploit the features of Virtex-5 FPGAs. Our multiplier is based on BCD recoding schemes, fast partial product generation, and a BCD-4221 carry save adder reduction tree. Pipeline stages can be added to target low latency. Furthermore, we extend the multiplier with an accurate scalar product unit for IEEE 754

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44

OVCHINNIKOV, A. A. "CONSTRUCTION OF MONODROMY MATRIX IN THE F-BASIS AND SCALAR PRODUCTS IN SPIN CHAINS." International Journal of Modern Physics A 16, no. 12 (2001): 2175–93. http://dx.doi.org/10.1142/s0217751x01003743.

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We present in a simple terms the theory of the factorizing operator introduced recently by Maillet and Sanches de Santos for the spin-1/2 chains. We obtain the explicit expressions for the matrix elements of the factorizing operator in terms of the elements of the monodromy matrix. We use this results to derive the expression for the general scalar product for the quantum spin chain. We comment on the previous determination of the scalar product of Bethe eigenstate with an arbitrary dual state. We also establish the direct correspondence between the calculations of scalar products in the F-bas

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45

Blei, Ron C. "An Extension Theorem Concerning Frechet Measures." Canadian Mathematical Bulletin 38, no. 3 (1995): 278–85. http://dx.doi.org/10.4153/cmb-1995-041-0.

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AbstractAn F-measure on a Cartesian product of algebras of sets is a scalar-valued function which is a scalar measure independently in each coordinate. It is demonstrated that an F-measure on a product of algebras determines an F-measure on the product of the corresponding σ-algebras if and only if its Fréchet variation is finite. An analogous statement is obtained in a framework of fractional Cartesian products of algebras, and a measurement of p-variation of F-measures, based on Littlewood-type inequalities, is discussed.

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46

Du, Qizhen, ChengFeng Guo, Qiang Zhao, Xufei Gong, Chengxiang Wang, and Xiang-yang Li. "Vector-based elastic reverse time migration based on scalar imaging condition." GEOPHYSICS 82, no. 2 (2017): S111—S127. http://dx.doi.org/10.1190/geo2016-0146.1.

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The scalar images (PP, PS, SP, and SS) of elastic reverse time migration (ERTM) can be generated by applying an imaging condition as crosscorrelation of pure wave modes. In conventional ERTM, Helmholtz decomposition is commonly applied in wavefield separation, which leads to a polarity reversal problem in converted-wave images because of the opposite polarity distributions of the S-wavefields. Polarity reversal of the converted-wave image will cause destructive interference when stacking over multiple shots. Besides, in the 3D case, the curl calculation generates a vector S-wave, which makes i

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47

Fassari, Silvestro, Manuel Gadella, Luis M. Nieto, and Fabio Rinaldi. "On Hermite Functions, Integral Kernels, and Quantum Wires." Mathematics 10, no. 16 (2022): 3012. http://dx.doi.org/10.3390/math10163012.

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In this note, we first evaluate and subsequently achieve a rather accurate approximation of a scalar product, the calculation of which is essential in order to determine the ground state energy in a two-dimensional quantum model. This scalar product involves an integral operator defined in terms of the eigenfunctions of the harmonic oscillator, expressed in terms of the well-known Hermite polynomials, so that some rather sophisticated mathematical tools are required.

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48

BERTOLAMI, ORFEU. "NONCOMMUTATIVE SCALAR FIELD MINIMALLY COUPLED TO GRAVITY." Modern Physics Letters A 20, no. 17n18 (2005): 1359–69. http://dx.doi.org/10.1142/s0217732305017810.

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A model for noncommutative scalar fields coupled to gravity based on the generalization of the Moyal product is proposed. Solutions compatible with homogeneous and isotropic flat Robertson-Walker spaces to first non-trivial order in the perturbation of the star-product are presented. It is shown that in the context of a typical chaotic inflationary scenario, at least in the slow-roll regime, noncommutativity yields no observable effect.

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49

Pahan, Sampa, Pal Buddhadev, and Arindam Bhattacharyya. "On Compact Super Quasi-Einstein Warped Product with Nonpositive Scalar Curvature." Zurnal matematiceskoj fiziki, analiza, geometrii 13, no. 4 (2017): 353–63. http://dx.doi.org/10.15407/mag13.04.353.

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50

Razon, A., and L. P. Horwitz. "Uniqueness of the scalar product in the tensor product of quaternion Hilbert modules." Journal of Mathematical Physics 33, no. 9 (1992): 3098–104. http://dx.doi.org/10.1063/1.529528.

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