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Abstract:

In this research, we compared the Bayesian estimators when estimating the scale parameter for the exponential distribution by using different loss functions under Jeffrey and Gamma priors, as most of the available symmetric and asymmetric loss functions were used, also the balanced and unbalanced loss functions. The simulation results proved the advantage of balanced loss functions with the Gamma prior, and the effectiveness of the balanced loss functions when using Jeffrey prior especially if the value of the weighted coefficient is equal to 0.5, so it is possible to use initial estimators as maximum likelihood estimator to compensate for the lack of prior information around the parameter to be estimated, also the advantage of the balanced general entropy loss function and the balanced weighted square error loss function under Jeffrey prior when the value of the scale parameter for the exponential distribution is less than 1, the preference of the balanced weighted square error loss function and the balanced K loss function if the value of the scale parameter for the exponential distribution is equal to 1, and the preference for the AL-Sayyad balanced loss function and the balanced AL-Bayyati loss function if the value of the scale parameter for the exponential distribution is greater or equal to 2.

Keywords:

Bayes Method,Unbalanced Loss Functions,Balanced Loss Functions,Exponential Distribution,

Refference:

I. AL-Badran, M., (2010). “Bayes Estimation under Balanced Loss Functions”. Journal of Administration & Economics, (42)119, PP.108-120.

II. Al-Bayyati, (2002). “Comparing methods of estimating Weibull failure models using simulation”. Ph.D. Thesis, College of Administration and Economics, Baghdad University, Iraq.
III. Ali, S., Aslam, M. , Kazmi, A., (2013). “A study of the effect of the loss function on Bayes Estimate, posterior risk and hazard function for Lindley distribution”. Applied Mathematical Modelling, 37, PP. 6068–6078.

IV. Calabria, R., Pulcini, G., (1996) “Point estimation under asymmetric loss functions for left-truncated exponential samples”, Communications in Statistics – Theory and Methods, (25)3, PP.585-600.

V. Casella G., Berger R., (2002).”Statistical Inference”, 2nd ed. USA,Duxbury.

VI. Dey, D., Ghosh, M., Strawderman, E. (1999).” On estimation with balanced loss functions”. Statistics & Probability Letters, 45, PP.97-101.

VII. El–Sayyad, M., (1967). “Estimation of the parameter of an exponential distribution”, Royal Statistical Society, Ser. B., (29)4, PP.525–532.

VIII. Norstrom, J.,(1996).”The use of precautionary loss functions in risk analysis”. IEEE Transactions on Reliability, (45)3, PP. 400-403.

IX. Rodrigues, J., Zellner, A. (1994). “Weighted balanced loss function and estimation of the mean time to failure”. Communications in Statistics: Theory and Methods, 23, 3609-3616.

X. Wasan, T., “Parametric Estimation”, McGraw-Hill Book Company, New York, 1970.

XI. Zellner, A. (1994). “Bayesian and Non-Bayesian estimation using balanced loss functions Statistical”, Decision Theory and Methods, New York: Springer, PP.337-390.

XII. Zellner, A., (1971). “Bayesian and non-Bayesian analysis of the log-normal distribution and log normal regression”. Journal of the American Statistical Association, 66, PP.327-330.

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Abstract:

The present numerical investigation deals with the laminar natural convection flow of a nanofluid along an isothermal vertical plate. As indicated by the Boungiorno model [V], nanofluid is considered a two-part combination (base liquid in addition to nanoparticles) where the impacts of Brownian movement and thermophoresis are significant. The boundary condition on the fluid flow is new: the nanoparticle volume fraction at the plate is passively controlled by assuming that its flux there is zero. The outcome of the present study with this new boundary condition is in better agreement with the practical applications of nanofluids.

Keywords:

Isothermal Vertical Plate,Natural Convection,NanoFluid,Brownian Motion,Thermophoresis,

Refference:

I. A. Bejan, Convection Heat Transfer, Wiley, New York, NY, 1984.
II. A.V. Kuznetsov and D. A. Nield, Natural convective boundary-layer flow of a nanofluid past a vertical plate, Int. J. Thermal Sciences, 49, (2010) 243–247.
III. D.A. Nield, A.V. Kuznetsov, Thermal instability in a porous medium layer saturated by a nanofluid, Int. J. Heat Mass Transf, 52 (2009) 5796–5801.
IV. J. Buongiorno, Convective transport in nanofluids, ASME J. Heat Transf. 128 (2006) 240–250.
V. S. Choi, Enhancing thermal conductivity of fluids with nanoparticle in: D.A. Siginer, H.P. Wang (Eds.), Developments and Applications of Non-Newtonian Flows, ASME MD 231 and FED 66, 1995, pp. 99–105.
VI. W. A. Khan and A. Aziz Natural convection flow of a nanofluid over a vertical plate with uniform surface heat flux, International Journal of Thermal Sciences, 50 (2011) 1207-1214.

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Abstract:

In this paper, we present an all-optical multiplexer based on a Terahertz Optical Asymmetric Demultiplexer (TOAD) device. The TOAD is used as a nonlinear optical switch to selectively route optical signals based on their wavelength or frequency, allowing for the multiplexing of multiple optical channels onto a single fiber optic cable. We describe the design and implementation of the TOAD-based multiplexer, including the optical components and signal processing algorithms used to achieve high-speed, low-error-rate operation. We also present experimental results demonstrating the performance of the multiplexer, including its ability to maintain signal quality over long distances and under various noise and interference conditions. Our results show that the TOAD-based multiplexer offers a promising approach to all-optical multiplexing for high-speed, high-capacity optical communications systems.

Keywords:

Optical Multiplexer,Nonlinear optics,Optical communications,TOAD-based switches.,

Refference:

I. C. Ni et al., “Bandwidth allocation based on priority and excess-bandwidth-utilized algorithm in WDM/TDM PON,”AEU – International Journal of Electronics and Communications, Volume 69, Issue 11, Pages 1659-1666 November 2015.
II. El-Hageen, Hazem M., Alatwi, Aadel M. and Zaki Rashed, Ahmed Nabih. “High-speed signal processing and wide band optical semiconductor amplifier in the optical communication systems”, Journal of Optical Communications, pp. 000010151520200070, 2020.
III. H. Furukawa et al., “Demonstration of 10 Gbit Ethernet/Optical-Packet Converter for IP Over Optical Packet Switching Network,” in Journal of Lightwave Technology, vol. 27, no. 13, pp. 2379-2380, July1, 2009.
IV. I. S. Choi, Jongseon Park, Hoon Jeong, Ji Won Kim, Min Yong Jeon, and Hong-Seok Seo, “Fabrication of 4 × 1 signal combiner for high-power lasers using hydrofluoric acid,” Opt. Express 26, 30667-30677, 2018.
V. J. H. Huh, H. Homma, H. Nakayama and Y. Maeda, “All optical switching triode based on cross-gain modulation in semiconductor optical amplifier,” 2007 Photonics in Switching, San Francisco, CA, USA, pp. 73-74, 2007.
VI. J. M. Tang, P. S. Spencer, P. Rees and K. A. Shore, “Pump-power dependence of transparency characteristics in semiconductor optical amplifiers,” in IEEE Journal of Quantum Electronics, vol. 36, no. 12, pp. 1462-1467, Dec. 2000.
VII. J. P. Sokoloff, P. R. Prucnal, I. Glesk and M. Kane, “A terahertz optical asymmetric demultiplexer (TOAD),” in IEEE Photonics Technology Letters, vol. 5, no. 7, pp. 787-790, July 1993.
VIII. K. Christodoulopoulos, I. Tomkos and E. Varvarigos, “Dynamic bandwidth allocation in flexible OFDM-based networks,” Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference, Los Angeles, CA, USA, 2011, pp. 1-3 2011.
IX. Lei Xu, I. Glesk, V. Baby and P. R. Prucnal, “All-optical wavelength conversion using SOA at nearly symmetric position in a fiber-based sagnac interferometric loop,” in IEEE Photonics Technology Letters, vol. 16, no. 2, pp. 539-541, Feb. 2004.
X. M. F. C. Stephens, M. Asghari, R. V. Penty and I. H. White, “Demonstration of ultrafast all-optical wavelength conversion utilizing birefringence in semiconductor optical amplifiers,” in IEEE Photonics Technology Letters, vol. 9, no. 4, pp. 449-451, April 1997.
XI. M. S. Salleh, A. Aris, R. Mohamad and K. Dimyati, “Modeling of a step and linear shared buffer using an OOP for optical packet switch,” 8th International Conference Advanced Communication Technology, Phoenix Park, Korea (South), pp. 6 pp.-1073, 2006.
XII. N. Bai, Ezra Ip, Yue-Kai Huang, Eduardo Mateo, Fatih Yaman, Ming-Jun Li, Scott Bickham, Sergey Ten, Jesús Liñares, Carlos Montero, Vicente Moreno, Xesús Prieto, Vincent Tse, Kit Man Chung, Alan Pak Tao Lau, Hwa-Yaw Tam, Chao Lu, Yanhua Luo, Gang-Ding Peng, Guifang Li, and Ting Wang, “Mode-division multiplexed transmission with inline few-mode fiber amplifier,” Opt. Express 20, 2668-2680, 2012.
XIII. P. S. Cho, D. Mahgerefteh and J. Coldhar, “All-optical 2R regeneration and wavelength conversion at 20 Gb/s using an electroabsorption modulator,” in IEEE Photonics Technology Letters, vol. 11, no. 12, pp. 1662-1664, Dec. 1999.
XIV. S. A. Hamilton, Bryan S. Robinson, Thomas E. Murphy, Shelby Jay Savage, and Erich P. Ippen, “100 Gb/s Optical Time-Division Multiplexed Networks,” J. Lightwave Technol. 20, 2086-, 2002.
XV. S. Soysouvanh, Phongsanam, P., Mitatha, S. et al. Ultrafast all-optical ALU operation using a soliton control within the cascaded InGaAsP/InP microring circuits. Microsyst Technol 25, 431–440, 2019.
XVI. V. M. Menon et al., “All-optical wavelength conversion using a regrowth-free monolithically integrated Sagnac interferometer,” in IEEE Photonics Technology Letters, vol. 15, no. 2, pp. 254-256, Feb. 2003.
XVII. V. Sasikala, Chitra, K. All optical switching and associated technologies: a review. J Opt 47, 307–317, 2018.
XVIII. Y. Liu, E. Tangdiongga, Z. Li, Shaoxian Zhang, Huug de Waardt, G. D. Khoe, and H. J. S. Dorren, “Error-Free All-Optical Wavelength Conversion at 160 Gb/s Using a Semiconductor Optical Amplifier and an Optical Bandpass Filter,” J. Lightwave Technol. 24, 230-,2006.
XIX. Y. Xiao, F. Brunet, M. Kanskar, M. Faucher, A. Wetter, and N. Holehouse, “1-kilowatt CW all-fiber laser oscillator pumped with wavelength-beam-combined diode stacks,” Opt. Express 20, 3296-3301, 2012.
XX. Z. F. Chaykandi, Bahrami, A. & Mohammadnejad, S. MMI-based all-optical multi-input XOR and XNOR logic gates using nonlinear directional coupler. Opt Quant Electron 47, 3477–3489, 2015.

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