Derivations of decoder and beamforming vector for amplify—and—forward relays based on the Cauchy-Schwartz inequality

2009 ◽  
Author(s):  
Seokkwon Kim ◽  
Joontae Kim ◽  
Won-Chul Choi ◽  
Dong-Jo Park
Keyword(s):  
Schwartz Inequality

scholarly journals Refinements of Cauchy-Bunyakovsky-Schwartz inequality and Bergstrom inequality with applications

2020 ◽  
Vol 13(62) (1) ◽  
pp. 115-128
Author(s):  
Diana Georgiana Dragomir ◽  
Cristina Maria Pacurar ◽  
Keyword(s):  
Schwartz Inequality

scholarly journals Truncated V-fractional Taylor's Formula with Applications

2018 ◽  
Vol 19 (3) ◽  
pp. 525
Author(s):  
José Vanterler da Costa Sousa ◽  
Edmundo Capelas de Oliveira
Keyword(s):  
Fractional Integral ◽  
Taylor’S Formula ◽  
Variation Of Constants Formula ◽  
Variation Of Constants ◽  
Schwartz Inequality ◽  
Taylor's Formula

In this paper, we present and prove a new truncated V-fractional Taylor's formula using the truncated V-fractional variation of constants formula. In this sense, we present the truncated V-fractional Taylor's remainder by means of V-fractional integral, essential for analyzing and comparing the error, when approaching functions by polynomials. From these new results, some applications were made involving some inequalities, specifically, we generalize the Cauchy-Schwartz inequality.

scholarly journals Quantum Entanglement and its Quantification in a Two-Mode Cascade Laser

2021 ◽  
pp. 1-8
Author(s):  
Ebisa Mosisa Kanea ◽  
Keyword(s):  
Master Equation ◽  
Quantum Entanglement ◽  
Normal Ordering ◽  
Logarithmic Negativity ◽  
Squeezed Vacuum ◽  
Level Laser ◽  
Cavity Radiation ◽  
Schwartz Inequality ◽  
Correlation Properties ◽  
Degree Of Entanglement

In this paper, quantum entanglement of correlated two-mode light generated by a three-level laser coupled to a two-mode squeezed vacuum reservoir is thoroughly analyzed using different inseparability criteria, using the master equation, we obtain the stochastic dierential equation and the correlation properties of the noise forces associated with the normal ordering. Next, we study the photon entanglement by considering different inseparability criteria. In particular, the criteria applied are Duan-Giedke-Cirac-Zoller (DGCZ) criterion, logarithmic negativity, Hillery-Zubairy, and Cauchy-Schwartz inequality and we found that the presence of the squeezing parameter leads to an increase in the degree of entanglement. Moreover, the linear gain coecient significantly achieved the degree of entanglement for the cavity radiation

scholarly journals Absence of Non-Trivial Fuzzy Inner Product Spaces and the Cauchy–Schwartz Inequality

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 571
Author(s):  
Taechang Byun ◽  
Ji Eun Lee ◽  
Keun Young Lee ◽  
Jin Hee Yoon
Keyword(s):  
Real Number ◽  
Product Space ◽  
Positive Definiteness ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Schwartz Inequality ◽  
Linearity Condition

First, we show that the non-trivial fuzzy inner product space under the linearity condition does not exist, which means a fuzzy inner product space with linearity produces only a crisp real number for each pair of vectors. If the positive-definiteness is added to the condition, then the Cauchy–Schwartz inequality is also proved.

Sign in / Sign up

Export Citation Format

Share Document