Publications

Journal Papers (*Corresponding Author, Equal Contribution, Student Authors from Our Group Underlined)

  1. N. Wan, P. Zhang, Z. Liu, Z. Li, W. Niu, X. Rui, S. Wang, M. Seong, P. He, S. Liang, J. Zhou, R. Yang*, Sung- Liang Chen*, Implantable QR code subcutaneous microchip using photoacoustic and ultrasound microscopy for secure and convenient individual identification and authentication, Photoacoustics 31, 100504 (2023). Link is: https://www.sciencedirect.com/science/article/pii/S2213597923000575?via%3Dihub
  2. L. Wang, P. Zhang, Z. Liu, Z. Wang*, R. Yang*, “On-Chip Mechanical Computing: Status, Challenges, and Opportunities”, Chip (2023), doi.org/10.1016/j.chip.2023.100038. Link is: https://www.sciencedirect.com/science/article/pii/S2709472323000011
  3. B. Xu, P. Zhang, J. Zhu, Z. Liu, A. Eichler, X.-Q. Zheng, J. Lee, A. Dash, S. More, S. Wu, Y. Wang, H. Jia, A. Naik*, A. Bachtold, R. Yang*, P. X.-L. Feng*, Z. Wang*, “Nanomechanical Resonators: Toward Atomic Scale”, ACS Nano (2022). Link is: https://pubs.acs.org/doi/10.1021/acsnano.2c01673
  4. R. Yang*, S M Enamul Hoque Yousuf, Jaesung Lee, Pengcheng Zhang, Zuheng Liu, Philip X.-L. Feng*, “Raman Spectroscopic Probe for Nonlinear MoS2 Nanoelectromechanical Resonators”, Nano Letters 22, 5780-5787 (2022). Link is: https://pubs.acs.org/doi/10.1021/acs.nanolett.2c01250
  5. P. Zhang, Yueyang Jia, Maosong Xie, Zuheng Liu, Sheng Shen, Jianyong Wei, Rui Yang*,”Strain-Modulated Dissipation in Two-Dimensional Molybdenum Disulfide Nanoelectromechanical Resonators”, ACS Nano 16, 2261-2270 (2022). Link is: https://pubs.acs.org/doi/10.1021/acsnano.1c08380
  6. J. Zhu, P. Zhang, R. Yang*, Z. Wang*, “Analyzing electrostatic modulation of signal transduction efficiency in MoS2 nanoelectromechanical resonators with interferometric readout”, Science China Information Sciences 65, 122409 (2022). Link is: https://link.springer.com/article/10.1007/s11432-021-3297-x
  7. J. Fang, P. Zhang, R. Yang*, Z. Wang*, “A cantilever-based resonator for reconfigurable nanomechanical computing”, Journal of Micromechanics and Microengineering 31, 124003 (2021). Link is: https://iopscience.iop.org/article/10.1088/1361-6439/ac3466
  8. Z. Wang†,*, R. Yang, P. X.-L. Feng*, “Thermal Hysteresis Controlled Reconfigurable MoS2 Nanomechanical Resonators”, Nanoscale 13, 18089 (2021). Link is: https://pubs.rsc.org/en/content/articlelanding/2021/nr/d1nr03286k
  9. Z. Wang†,*, J. Fang, P. Zhang, R. Yang*, “Nanomechanics: Emerging Opportunities for Future Computing”, Science China Information Sciences 64, 206401 (2021). Link is: https://link.springer.com/article/10.1007/s11432-020-3241-9
  10. R. Yang, “In-Memory Computing with Ferroelectrics”, Nature Electronics 3, 237–238 (2020). (Invited News & Views Article) Link is: https://www.nature.com/articles/s41928-020-0411-2
  11. C. I. Evans, R. Yang, L. T. Gan, M. Abbasi, X. Wang, R. Traylor, J. A. Fan, D. Natelson, “Thermoelectric Response from Grain Boundaries and Lattice Distortions in Crystalline Gold Devices”, Proceedings of the National Academy of Sciences of the United States of America (PNAS) 117, 23350-23355 (2020). Link is: https://www.pnas.org/doi/10.1073/pnas.2002284117
  12. R. Yang*, J. Qian*, P. X.-L. Feng*, “Electrodynamic Force, Casimir Effect, and Stiction Mitigation in Silicon Carbide Nanoelectromechanical Switches”, Small 16, 2005594 (2020). Link is: https://onlinelibrary.wiley.com/doi/10.1002/smll.202005594
  13. R. Yang*, H. Li, K. K. H. Smithe, T. R. Kim, K. Okabe, E. Pop, J. A. Fan, H.-S. P. Wong, “Ternary Content-Addressable Memory with MoS2 Transistors for Massively Parallel Data Search”, Nature Electronics 2, 108-114 (2019). Link is: https://www.nature.com/articles/s41928-019-0220-7
  14. L. T. Gan, R. Yang, R. Traylor, W. Cai, W. D. Nix, J. A. Fan, “High-Throughput Growth of Microscale Gold Bicrystals for Single-Grain-Boundary Studies”, Advanced Materials 31, 1902189 (2019). Link is: https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201902189
  15. R. Yang, J. Lee, S. Ghosh, H. Tang, R. M. Sankaran, C. A. Zorman, P. X.-L. Feng, “Tuning Optical Signatures of Single-and Few-Layer MoS2 by Blown-Bubble Bulge Straining up to Fracture”, Nano Letters 17, 4568-4575 (2017). Link is: https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.7b00730
  16. R. Yang, A. Islam, P. X.-L. Feng, “Electromechanical Coupling and Design Considerations in Single-Layer MoS2 Suspended-Channel Transistors and Resonators”, Nanoscale 7, 19921-19929(2015). Link is: https://pubs.rsc.org/en/content/articlelanding/2015/nr/c5nr06118k#!
  17. R. Yang, T. He, M. A. Tupta, C. Marcoux, P. Andreucci, L. Duraffourg, P. X.-L. Feng, “Probing Contact-Mode Characteristics of Silicon Nanowire Electromechanical Systems with Embedded Piezoresistive Transducers”, Journal of Micromechanics and Microengineering 25, 095014 (2015). (Featured as Cover Article) Link is: https://iopscience.iop.org/article/10.1088/0960-1317/25/9/095014
  18. R. Yang, C. A. Zorman, P. X.-L. Feng, “High Frequency Torsional-Mode Nanomechanical Resonators Enabled by Very Thin Nanocrystalline Diamond Diaphragms”, Diamond and Related Materials 54, 19-25 (2015). Link is: https://www.sciencedirect.com/science/article/abs/pii/S0925963514002313
  19. R. Yang, Z. Wang, P. X.-L. Feng, “Electrical Breakdown of Multilayer MoS2 Field-Effect Transistors with Thickness-Dependent Mobility”, Nanoscale 6, 12383-12390 (2014). Link is: https://pubs.rsc.org/en/content/articlelanding/2014/nr/c4nr03472d
  20. R. Yang, X. Zheng, Z. Wang, P. X.-L. Feng, “Multilayer MoS2 Transistors Enabled by a Facile Dry-Transfer Technique and Thermal Annealing”, Journal of Vacuum Science and Technology B 32, 061203 (2014). (Featured as Cover Article, Editor’s Pick and Most Read Article) Link is: https://avs.scitation.org/doi/10.1116/1.4898117
  21. R. Yang, Z. Wang, J. Lee, K. Ladhane, D. J. Young, P. X.-L. Feng, “6H-SiC Microdisk Torsional Resonators in a “Smart-cut” Technology”, Applied Physics Letters 104, 091906 (2014). Link is: https://aip.scitation.org/doi/10.1063/1.4867866
  22. M. T. Kiani, L. T. Gan, R. Traylor, R. Yang, C. M. Barr, K. Hattar, J. A. Fan, X. W. Gu, “In Situ TEM Tensile Testing of Bicrystals with Tailored Misorientation Angles”, Acta Materialia 224, 117505 (2022).
  23. J. He, H. Liu, C. Huang, Y. Jia, K. Li, A. Mesli, R. Yang, Y. He, Y. Dan, “Analytical Transient Responses and Gain−Bandwidth Products of Low-Dimensional High-Gain Photodetectors”, ACS Nano 15, 20242-20252 (2021).
  24. Y. Lyu, Y. Zhang, Y. Liu, W. Chen, X. Zhang, W. Xu, C. Wu, L. Wang, H. Zeng, X. Sheng, R. Yang, Z. Wang, K. Kuang, W. Fei, “Analysis of Potential Disruptive Technologies in the Electronics and Information Field Towards the Intelligent Society”, Engineering 7, 1051-1056 (2021).
  25. C. I. Evans, L. T. Gan, R. Yang, M. Abbasi, X. Wang, R. Traylor, J. A. Fan, D. Natelson, “Detection of Trace Impurity Gradients in Noble Metals by the Photothermoelectric Effect”, The Journal of Physical Chemistry C 125, 17509-17517 (2021).
  26. H. Li, S. Wang, X. Zhang, W. Wang, R. Yang, Z. Sun, W. Feng, P. Lin, Z. Wang, L. Sun, and Y. Yao, “Memristive Crossbar Arrays for Storage and Computing Applications”, Advanced Intelligent Systems, 2100017, (2021).
  27. Y. Sun, C. Ma, Z. Li, Y. Zhao, J. Jiang, W. Qian, R. Yang, Z. He, L. Jiang, “Unary Coding and Variation-Aware Optimal Mapping Scheme for Reliable ReRAM-based Neuromorphic Computing”, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD) (Early Access) (2021).
  28. K. Zhang, X. B. Pitner, R. Yang, W. D. Nix, J. D. Plummer, J. A. Fan, “Single Crystal Metal Growth on Amorphous Insulating Substrates”, Proceedings of the National Academy of Sciences of the United States of America (PNAS) 115, 685-689 (2018).
  29. J. Lee, Z. Wang, K. He, R. Yang, J. Shan, P. X.-L. Feng, “Electrically Tunable Single- and Few-Layer MoS2 Nanoelectromechanical Systems with Broad Dynamic Range”, Science Advances 4: eaao6653 (2018).
  30. S. Doshay, D. Sell, J. Yang, R. Yang, J. A. Fan, “High-Performance Axicon Lenses based on High-Contrast, Multilayer Gratings”, APL Photonics 3, 011302 (2018).
  31. L. Ding, M. S. Ukhtary, M. Chubarov, T. H. Choudhury, F. Zhang, R. Yang, A. Zhang, J. Fan, M. Terrones, J. M. Redwing, T. Yang, M. Li, R. Saito, S. Huang, “Understanding Interlayer Coupling in TMD-hBN Heterostructure by Raman Spectroscopy”, IEEE Transactions on Electron Devices 65, 4059-4067 (2018).
  32. D. Sell, J. Yang, S. Doshay, R. Yang, J. A. Fan, “Large-Angle, Multifunctional Metagratings Based on Freeform Multimode Geometries”, Nano Letters 17, 3752-3757 (2017).
  33. Z. Wang, H. Jia, X. Zheng, R. Yang, G. J. Ye, X. H. Chen, P. X.-L. Feng, “Resolving and Tuning Mechanical Anisotropy in Black Phosphorus via Nanomechanical Multimode Resonance Spectromicroscopy”, Nano Letters 16, 5394-5400 (2016). 
  34. H. Jia, R. Yang, A. E. Nguyen, S. N. Alvillar, T. Empante, L. Bartels, P. X.-L. Feng, “Large-Scale Arrays of Single- and Few-Layer MoS2 Nanomechanical Resonators”, Nanoscale 8, 10677-10685 (2016). 
  35. J. Lee, F. Ye, Z. Wang, R. Yang, J. Hu, Z. Mao, J. Wei, P. X.-L. Feng, “Single- and Few-Layer WTe2 and Their Suspended Nanostructures: Raman Signatures and Nanomechanical Resonances”, Nanoscale 8, 7854-7860 (2016).
  36. S. Ghosh, E. Ostrowski, R. Yang, D. Debnath, P. X.-L. Feng, C. A. Zorman, R. M. Sankaran, “Atmospheric-Pressure Plasma Reduction of Metal Cation-Containing Polymer Films to Produce Electrically Conductive Nanocomposites by an Electrodiffusion Mechanism”, Plasma Chemistry and Plasma Processing 36, 295-307 (2016).
  37. Z. Wang, H. Jia, X. Zheng, R. Yang, G. J. Ye, X. H. Chen, J. Shan, P. X.-L. Feng, “Black Phosphorus Nanoelectromechanical Resonators Vibrating at Very High Frequencies”, Nanoscale 7, 877-884 (2015).
  38. Z. Wang, A. Islam, R. Yang, X. Zheng, P. X.-L. Feng, “Environmental, Thermal, and Electrical Susceptibility of Black Phosphorus Field Effect Transistors”, Journal of Vacuum Science and Technology B 33, 052202 (2015). (Featured as Editor’s Pick and Most Read Article)
  39. S. Ghosh, R. Yang, M. Kaumeyer, C. A. Zorman, S. J. Rowan, P. X.-L. Feng, R. M. Sankaran, “Fabrication of Electrically-Conductive Metal Patterns at the Surface of Polymer Films by Microplasma-Based Direct Writing”, ACS Applied Materials and Interfaces 6, 3099-3104 (2014).

Conference Papers

  1. Z. Liu, L. Wang, P. Zhang, M. Xie, Y. Jia, Y. Chen, H. Jia, Z. Wang*, R. Yang*, “Large-Scale Arrays of Tunable Monolayer MoS2 Nanoelectromechanical Resonators”, in Proc. 36th IEEE International Conference on Micro Electro Mechanical Systems (MEMS 2023), 281-284 (2023).
  2. Z. Liu, R. Yang*, “2D Transition Metal Dichalcogenide (TMDC) Nanoelectromechanical Resonators”, in Proc. 2022 IEEE Nanotechnology Materials & Devices Conference (NMDC 2022), DOI: 10.1109/NMDC46933.2022.10052223 (2022).
  3. P. Zhang, Y. Jia, Z. Liu, Y. Zhang, M. Xie, J. Wei, R. Yang*, “Nanoelectromechanical Memories based on Nonlinear 2D MoS2 Resonators”, in Proc. 35th IEEE International Conference on Micro Electro Mechanical Systems (MEMS 2022), 208-211 (2022).
  4. J. Zhu, P. Zhang, J. Li, B. Xu, S. Wu, F. Xiao, Y. Liang, T. Wen, F. Wang, R. Yang*, Z. Wang*, “Observation of Tunable Opto-Mechanical Responsivity in Two-Dimensional Semiconducting Nanoelectromechanical Resonators”, in Proc. Joint Conf. European Frequency and Time Forum & IEEE Int. Frequency Control Symposium (EFTF-IFCS 2021), Jul. 7-17 (2021).
  5. P. Zhang, Y. Jia, S. Shen, R. Yang*, “Strain-Modulated Equivalent Circuit Model and Dissipation Model for 2D MoS2 NEMS Resonators”, in Proc. 34th IEEE International Conference on Micro Electro Mechanical Systems (MEMS 2021), 658-661, Jan. 25-29 (2021).
  6. R. Yang, M. Xie, Y. Jia, L. Duraffourg, P. X.-L. Feng, “Hybrid Nanoelectromechanical Switch and Resistive Memory in Silicon Nanowires by VLSI NEMS,” in Proc. 34th IEEE International Conference on Micro Electro Mechanical Systems (MEMS 2021), 607-610, Jan. 25-29 (2021).
  7. R. Yang, H. Li, K. K. H. Smithe, T. R. Kim, K. Okabe, E. Pop, J. A. Fan, H.-S. P. Wong, “2D Molybdenum Disulfide (MoS2) Transistors Driving RRAMs with 1T1R Configuration”, in Tech. Digest, IEEE Int. Electron Devices Meeting (IEDM 2017), 477-480, Dec. 2-6(2017). Featured by IEEE Spectrum on Dec. 2017: “2D Material Integrates Digital Logic and Memory Into One Chip” https://spectrum.ieee.org/nanoclast/semiconductors/devices/2d-material-integrates-digital-logic-and-memory-into-one-chip
  8. R. Yang, C. Chen, J. Lee, D. A. Czaplewski, P. X.-L. Feng, “Local-Gate Electrical Actuation, Detection, and Tuning of Atomic-Layer MoS2 Nanoelectromechanical Resonators”, in Proc. 30th IEEE Int. Conf. on Micro Electro Mechanical Systems (MEMS 2017), 163-166, Jan. 22-26 (2017) (+talk, selection rate 10%).
  9. R. Yang, Z. Wang, P. X.-L. Feng, “All-Electrical Readout of Atomically Thin MoS2 Nanoelectromechanical Resonators in the VHF Band”, in 29th IEEE Int. Conf. on Micro Electro Mechanical Systems (MEMS 2016), 59-62, Jan. 24-28 (2016) (+talk, selection rate 8%).
  10. R. Yang, M. A. Tupta, C. Marcoux, P. Andreucci, L. Duraffourg, P. X.-L. Feng, “Capacitance-Voltage (CV) Characterization in Very Thin Suspended Silicon Nanowires for NEMS-CMOS Integration in 160nm Silicon-on-Insulator (SOI)”, in Proc. IEEE Int. Conf. on Nanotechnology (IEEE NANO 2015), 1175-1178, Jul. 27-30 (2015). 
  11. R. Yang, Z. Li, P. X.-L. Feng, “Molybdenum Disulfide (MoS2) Nanomechanical Resonators Integrated on Microchannels”, in Proc. ASME InterPACK 2015 & ICNMM 2015, Paper No. IPACK2015-48590, pp. V003T07A003, Jul. 6-9 (2015). 
  12. R. Yang, Z. Wang, P. X.-L. Feng, “Calibrating Temperature Coefficient of Frequency (TCf) and Thermal Expansion Coefficient (α) of MoS2 Nanomechanical Resonators”, in Proc. IEEE Int. Frequency Control Symposium & European Frequency and Time Forum (IFCS-EFTF 2015) 198-201, Apr. 12-16 (2015). 
  13. R. Yang, Z. Wang, P. Wang, R. Lujan, T. N. Ng, P. X.-L. Feng, “Two-Dimensional MoS2 Nanomechanical Resonators Freely-Suspended on Microtrenches on Flexible Substrate”, in Proc. 28th IEEE Int. Conf. on Micro Electro Mechanical Systems (MEMS 2015) 877-880, Jan. 18-22 (2015).
  14. R. Yang, Z. Wang, J. Lee, K. Ladhane, D. J. Young, P. X.-L. Feng, “Temperature Dependence of Torsional and Flexural Modes in 6H-SiC Microdisk Resonators”, in Proc. IEEE Int. Frequency Control Symposium (IFCS 2014) 618-620, May 19-22 (2014). 
  15. R. Yang, K. Ladhane, Z. Wang, J. Lee, D. J. Young, P. X.-L. Feng, “Smart-Cut 6H-Silicon Carbide (SiC) Microdisk Torsional Resonators with Sensitive Photon Radiation Detection”, in Proc. 27th IEEE Int. Conf. on Micro Electro Mechanical Systems (MEMS 2014) 793-796, Jan. 26-30 (2014).
  16. R. Yang, T. He, C. Marcoux, P. Andreucci, L. Duraffourg, P. X.-L. Feng, “Silicon Nanowire and Cantilever Electromechanical Switches with Integrated Piezoresistive Transducers”, in Proc. 26th IEEE Int. Conf. on Micro Electro Mechanical Systems (MEMS 2013) 229-232, Jan. 20-24 (2013) (+talk, selection rate 8%).
  17. R. Yang, J. Lee, Z. Wang, P. X.-L. Feng, “Multimode Characteristics in Mechanically-Coupled Silicon Carbide (SiC) Nanowire Array Resonators”, in Proc. IEEE Int. Frequency Control Symposium (IFCS 2013) 145-148, Jul. 21-25 (2013).
  18. Zongwu Wang, Zhezhi He, Rui Yang, Shiquan Fan, Jie Lin, Fangxin Liu, Yueyang Jia, Chenxi Yuan, Qidong Tang, Li Jiang, “Self-Terminating Write of Multi-Level Cell ReRAM for Efficient Neuromorphic Computing”, IEEE Design, Automation and Test in Europe Conference (DATE 2022), 1251-1256, Mar. 14–23 (2022).
  19. Fangxin Liu, Wenbo Zhao, Yongbiao Chen, Zongwu Wang, Zhezhi He, Rui Yang, Qidong Tang, Tao Yang, Cheng Zhuo, Li Jiang, “PIM-DH: ReRAM-based Processing-in-Memory Architecture for Deep Hashing Acceleration”, Design Automation Conference (DAC 2022), 1087–1092, Aug. 23 (2022).
  20. Z. Meng, W. Qian, Y. Zhao, Y. Sun, R. Yang, L. Jiang, “Digital Offset for RRAM-based Neuromorphic Computing: A Novel Solution to Conquer Cycle-to-cycle Variation,” IEEE Design, Automation and Test in Europe Conference (DATE 2021), Accepted. (Acceptance rate ~26%)
  21. C. Ma, Y. Sun, W. Qian, Z. Meng, R. Yang, L. Jiang, “Go Unary: A Novel Synapse Coding and Mapping Scheme for Reliable ReRAM-based Neuromorphic Computing,” IEEE Design, Automation and Test in Europe Conference (DATE 2020), March 2020. (Nominated for Best Paper Award) (Acceptance rate ~26%)
  22. H. Jia, R. Yang, A. E. Nguyen, S. N. Alvillar, S. Bobek, M. Wurch, C.-Y. Huang, L. Bartels, P. X.-L. Feng, “Single- and Few-Layer Transfer-Printed CVD MoS2 Nanomechanical Resonators with Enhancement by Thermal Annealing”, in Proc. IEEE Int. Frequency Control Symposium (IFCS 2016), May 9-12 (2016), DOI: 10.1109/FCS.2016.7546737.
  23. Z. Wang, R. Yang, A. Islam, P. X.-L. Feng, “Observation of Strong Temperature Hysteresis in Molybdenum Disulfide (MoS2) Vibrating Nanomechanical Resonators”, in Proc. IEEE Int. Frequency Control Symposium & European Frequency and Time Forum (IFCS-EFTF 2015) 783-786, Apr. 12-16 (2015).
  24. [Invited Paper] P. X.-L. Feng, Z. Wang, J. Lee, R. Yang, X. Zheng, K. He, J. Shan, “Two-Dimensional Nanoelectromechanical Systems (2D NEMS) via Atomically-Thin Semiconducting Crystals Vibrating at Radio Frequencies”, in Tech. Digest, Int. Electron Devices Meeting (IEDM 2014), 196-199, Dec. 15-17 (2014).
  25. [Invited Paper] S. Bhunia, V. Ranganathan, T. He, S. Rajgopal, R. Yang, M. Mehregany, P. X.-L. Feng, “Toward Ultralow-Power Computing at Extreme with Silicon Carbide (SiC) Nanoelectromechanical Logic”, in Proc. Design, Automation and Test in Europe Conference and Exhibition (DATE 2014) 1-6, Mar. 24-28 (2014).
  26. T. He, R. Yang, V. Ranganathan, S. Rajgopal, M. A. Tupta, S. Bhunia, M. Mehregany, P. X.-L. Feng, “Silicon Carbide (SiC) Nanoelectromechanical Switches and Logic Gates with Long Cycles and Robust Performance in Ambient Air and at High Temperature”, in Tech. Digest, Int. Electron Devices Meeting (IEDM 2013), 108-111, Dec. 9-11 (2013).
  27. T. He, V. Ranganathan, R. Yang, S. Rajgopal, S. Bhunia, M. Mehregany, P. X.-L. Feng, “Time-Domain AC Characterization of Silicon Carbide (SiC) Nanoelectromechanical Switches toward High Speed Operations”, in Tech. Digest, 17th Int. Conf. on Solid-State Sensors, Actuators and Microsystems (Transducers 2013) 669-672, Jun. 16-20 (2013).
  28. T. He, R. Yang, S. Rajgopal, S. Bhunia, M. Mehregany, P. X.-L. Feng, “Dual-Gate Silicon Carbide (SiC) Lateral Nanoelectromechanical Switches”, in Proc. 8th IEEE Int. Conf. on Nano/Micro Engineered and Molecular Systems (NEMS 2013) 554-557, Apr. 7-10 (2013). (Winner, Best Student Paper Award)
  29. T. He, R. Yang, S. Rajgopal, M. A. Tupta, S. Bhunia, M. Mehregany, P. X.-L. Feng, “Robust Silicon Carbide (SiC) Nanoelectromechanical Switches with Long Cycles in Ambient and High Temperature Conditions”, in Proc. 26th IEEE Int. Conf. on Micro Electro Mechanical Systems (MEMS 2013) 516-519, Jan. 20-24 (2013).