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Journal articles on the topic 'Zero-order hold'

Author: Grafiati

Published: 5 June 2025

Last updated: 15 July 2025

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1

Helmicki, A. J., C. A. Jacobson, and C. N. Nett. "On zero-order hold equivalents of distributed parameter systems." IEEE Transactions on Automatic Control 37, no. 4 (1992): 488–91. http://dx.doi.org/10.1109/9.126582.

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2

A., Abdelmgeid, Tarek A., Al-Hussien Seddik, and Shaimaa M. "New Image Steganography Method using Zero Order Hold Zooming." International Journal of Computer Applications 133, no. 9 (2016): 27–31. http://dx.doi.org/10.5120/ijca2016908016.

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3

Goodwin, G. C., and G. J. Adams. "Multi-Rate Techniques in Non-Zero-Order Hold Identification." IFAC Proceedings Volumes 27, no. 8 (1994): 1087–92. http://dx.doi.org/10.1016/s1474-6670(17)47853-0.

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4

Ugalde, Unai, Rafael Bárcena, and Koldo Basterretxea. "Generalized sampled-data hold functions with asymptotic zero-order hold behavior and polynomic reconstruction." Automatica 48, no. 6 (2012): 1171–76. http://dx.doi.org/10.1016/j.automatica.2012.03.004.

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5

Shan, Hong Tao, and Bin Zhou. "The Effect of Digital Process of Single-Phase Photovoltaic Grid Connected Inverter." Advanced Materials Research 1070-1072 (December 2014): 60–63. http://dx.doi.org/10.4028/www.scientific.net/amr.1070-1072.60.

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Digital control possesses evident advantages and has become a mainstream control of photovoltaic grid connected inverter.The mathematical model and parameter setting of the single phase photovoltaic grid connected inverter with L filter was introduced in the paper.It was analysed on the effect on system stability of digital process from the two aspects which were the zero-order-hold and one-step-delay control. The bode diagram was verified the theoretical analysis on system stability.The conclusions were made that the introduction of digital control reduces the critical stable gain of photovol

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6

H., Shashidhara, and Usha B. "Video Steganography using Zero Order Hold Method for Secured Data Transmission." International Journal of Computer Applications 176, no. 5 (2017): 44–48. http://dx.doi.org/10.5120/ijca2017915587.

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7

Tóth, R., F. Felici, P. S. C. Heuberger, and P. M. J. Van den Hof. "Crucial Aspects of Zero-Order Hold LPV State-Space System Discretization." IFAC Proceedings Volumes 41, no. 2 (2008): 4952–57. http://dx.doi.org/10.3182/20080706-5-kr-1001.00832.

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8

Ou, Minghui, Zhiyong Yang, Zhenjie Yan, et al. "Stability of Zeros for Sampled-Data Models with Triangle Sample and Hold Implemented by Zero-Order Hold." Machines 10, no. 5 (2022): 386. http://dx.doi.org/10.3390/machines10050386.

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This paper deals with the stability characteristics of zeros for sampled-data models with a class of triangle sample and hold realized by a traditional zero-order hold. For any controlled models in the modern industrial system, using a digital control strategy has been shown to provide the means to achieve the assigned objectives. In this process, one must utilize the sample and hold device to obtain the sampled-data models. Previous studies have shown that the triangle sample and hold can improve the stability properties of zeros of a sampled-data control system compared with zero-order hold.

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9

Shan, Hong Tao, Yong Kang, Xue Juan Kong, and Yu Zhang. "Research on the Stability Affected by Digital Process of SPWM Inverter." Advanced Materials Research 347-353 (October 2011): 564–67. http://dx.doi.org/10.4028/www.scientific.net/amr.347-353.564.

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Digital controlled SPWM inverter has become main-stream in development of SPWM inverter control strategy. But the traditional PID control strategy realized in digital control can’t achieve better performance than in analog control. Process of the zero-order hold & one-step-delay control were researched the effect of zero-order hold & one-step-delay control on the stability of digital control SPWM inverter with quantitative analysis in this paper. Finally relevant simulations and experiments were verified the validity of the theoretical analysis.

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10

Hashemzadeh, Farzad, Amin Rezaei Pish-Robat, and Parviz Jabehdar-Maralani. "A New Fractional Order Hold and Its Capability in Frequency Response and Zero Placement." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/157292.

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This paper introduces a new holder with application on digital control systems. This holder is a combination of fractional order hold (FROH) and zero-order hold (ZOH) that has the capability of both holders and a frequency response better than both of ZOH and FROH. For the stability of zeros of the sampled system two theorems are stated and proved with the assumption that the sampling period is very small. Also simulation results are studied to show the effectiveness of the proposed holder and better performance results in comparison with ZOH and FROH.

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11

Olkkonen, J. T., and H. Olkkonen. "Sampling and Reconstruction of Zero-Order Hold Signals by Parallel RC Filters." Wireless Engineering and Technology 02, no. 03 (2011): 153–56. http://dx.doi.org/10.4236/wet.2011.23022.

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12

PAOR, A. M. DE, and M. J. O'MALLEY. "The zero-order hold equivalent transfer function for a time-delayed process." International Journal of Control 61, no. 3 (1995): 657–65. http://dx.doi.org/10.1080/00207179508921922.

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13

Sagara, S., Zi-Zhang Yang, K. Wada, and T. Tsuji. "Parameter Identification and Adaptive Control of Continuous Systems with Zero-Order Hold." IFAC Proceedings Volumes 26, no. 2 (1993): 629–32. http://dx.doi.org/10.1016/s1474-6670(17)49203-2.

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14

Bernal, Dionisio. "The zero-order hold in time domain identification: An unnecessary operating premise." Structural Control and Health Monitoring 18, no. 5 (2010): 510–18. http://dx.doi.org/10.1002/stc.383.

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15

Karampetakis, Nicholas P., and Rallis Karamichalis. "Discretization of singular systems and error estimation." International Journal of Applied Mathematics and Computer Science 24, no. 1 (2014): 65–73. http://dx.doi.org/10.2478/amcs-2014-0005.

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Abstract This paper proposes a discretization technique for a descriptor differential system. The methodology used is both triangular first order hold discretization and zero order hold for the input function. Upper bounds for the error between the continuous and the discrete time solution are produced for both discretization methods and are shown to be better than any other existing method in the literature.

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16

Gao, Shian. "A further result on the complex oscillation theory of periodic second order linear differential equations." Proceedings of the Edinburgh Mathematical Society 33, no. 1 (1990): 143–58. http://dx.doi.org/10.1017/s0013091500028959.

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We prove the following: Assume that , where p is an odd positive integer, g(ζ is a transcendental entire function with order of growth less than 1, and set A(z) = B(ezz). Then for every solution , the exponent of convergence of the zero-sequence is infinite, and, in fact, the stronger conclusion holds. We also give an example to show that if the order of growth of g(ζ) equals 1 (or, in fact, equals an arbitrary positive integer), this conclusion doesn't hold.

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17

Ma, Junpeng, Xiongfei Wang, Frede Blaabjerg, Lennart Harnefors, and Wensheng Song. "Accuracy Analysis of the Zero-Order Hold Model for Digital Pulse Width Modulation." IEEE Transactions on Power Electronics 33, no. 12 (2018): 10826–34. http://dx.doi.org/10.1109/tpel.2018.2799819.

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18

Zhang, Xian-Ming, and Qing-Long Han. "Output feedback stabilization of networked control systems with a logic zero-order-hold." Information Sciences 381 (March 2017): 78–91. http://dx.doi.org/10.1016/j.ins.2016.11.009.

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19

Armitage, AK, M. Dixon, BE Frost, DC Mariner, and NM Sinclair. "The Effect of Inhalation Volume and Breath-Hold Duration on the Retention of Nicotine and Solanesol in the Human Respiratory Tract and on Subsequent Plasma Nicotine Concentrations During Cigarette Smoking." Beiträge zur Tabakforschung International/Contributions to Tobacco Research 21, no. 4 (2004): 240–49. http://dx.doi.org/10.2478/cttr-2013-0786.

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AbstractThe influence of inhalation depth and breath-hold duration on the retention of nicotine and solanesol in the human respiratory tract and on nicotine uptake was studied in ten cigarette smokers. In a first series of experiments, the subjects took seven puffs from a 10 mg ‘tar’ yield, test cigarette and a fixed volume of air (0, 75, 250, 500 or 1000 mL, as required by the protocol) was inhaled after each puff in order to give a controlled ‘depth’ of inhalation. The inhalation was drawn from a bag containing the required volume of air. Following a 2 s breath-hold, subjects exhaled normall

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20

Lysov, V. E., Ya I. Peshev, and A. V. Banartseva. "Determining the Quantization Frequency of a Zero-Order Hold in a Digital Positioning System." Russian Engineering Research 41, no. 2 (2021): 149–52. http://dx.doi.org/10.3103/s1068798x2102012x.

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21

Konaka, Eiji. "Stability of Networked Control System with Dynamic Quantizer and Data-Driven Zero-Order Hold." IEEJ Transactions on Electronics, Information and Systems 129, no. 1 (2009): 46–52. http://dx.doi.org/10.1541/ieejeiss.129.46.

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22

Momani, Mu’taz A., and Mehdi Hosseinzadeh. "Adaptive gain design for Zero-Order Hold discrete-time implementation of explicit reference governor." Control Engineering Practice 152 (November 2024): 106042. http://dx.doi.org/10.1016/j.conengprac.2024.106042.

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23

Konaka, Eiji. "Stability of networked control system with dynamic quantizer and data-driven zero-order hold." Electronics and Communications in Japan 94, no. 2 (2011): 1–8. http://dx.doi.org/10.1002/ecj.10329.

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24

Spencer, Joel. "Zero-one laws with variable probability." Journal of Symbolic Logic 58, no. 1 (1993): 1–14. http://dx.doi.org/10.2307/2275320.

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One of this author's favorite theorems has long been the Zero-One law discovered independently by Glebskii et al. [12] and Ron Fagin [10]. Let A be any first-order property of graphs and let µn(A) be the proportion of labelled graphs on n vertices for which A holds. ThenThis result has inspired much work by logicians, generally in the direction of showing (1) for some powerful languages. Thus it is known [5] that (1) holds when A is a sentence in fixed point logic and it is known [13] that (1) does not always hold when A is a sentence in second-order monadic logic. Here, however, we explore re

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25

Ortigueira, Manuel Duarte, and José Tenreiro Machado. "A Review of Sample and Hold Systems and Design of a New Fractional Algorithm." Applied Sciences 10, no. 20 (2020): 7360. http://dx.doi.org/10.3390/app10207360.

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Digital systems require sample and hold (S&H) systems to perform the conversion from analog to digital and vice versa. Besides the standard zero and first order holds, we find in the literature other versions, namely the fractional and exponential order holds, involving parameters that can be tuned to produce a superior performance. This paper reviews the fundamental concepts associated with the S&H and proposes a new fractional version. The systems are modeled both in the time and Laplace domains. The new S&H stemming from fractional calculus generalizes these devices. The differe

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26

Kruglov, Sergey Il’ich. "Thermodynamics of Magnetic Black Holes with Nonlinear Electrodynamics in Extended Phase Space." Universe 10, no. 7 (2024): 295. http://dx.doi.org/10.3390/universe10070295.

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We study Einstein’s gravity in AdS space coupled to nonlinear electrodynamics. Thermodynamics in extended phase space of magnetically charged black holes is investigated. We compute the metric and mass functions and their asymptotics, showing that black holes may have one or two horizons. The metric function is regular, f(0)=1, and corrections to the Reissner–Nordström solution are in the order of O(r−3) when the Schwarzschild mass is zero. We prove that the first law of black hole thermodynamics and the generalized Smarr relation hold. The magnetic potential and vacuum polarization conjugated

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27

Li, Xiu Yun, Cheng Zeng, Tong Zhou, Yan Jun Ren, and Yu Xuan Li. "Asymptotic Properties of Sampling Zero Dynamics for Nonlinear Systems in the Case of Time Delay and Relative Degree Two." Advanced Materials Research 1061-1062 (December 2014): 893–98. http://dx.doi.org/10.4028/www.scientific.net/amr.1061-1062.893.

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It is well-known that stability of zero dynamics is often inevitable to the controller design. And most real world plants often involve a time delay. This paper investigates the zero dynamics, as the sampling period tends to zero, of a sampled-data model composed of a zero-order hold (ZOH), a continuous-time plant with a time delay and a sampler in cascade. We first present how an approximate sampled-data model can be obtained for the nonlinear system with relative degree two, and the local truncation error between the output of obtained model and the true system output is of order , where T i

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28

de la Sen, M., and A. Bilbao-Guillerna. "Fractional hold circuits versus positive realness of discrete transfer functions." Discrete Dynamics in Nature and Society 2005, no. 3 (2005): 373–78. http://dx.doi.org/10.1155/ddns.2005.373.

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The appropriate use of fractional-order holds (β-FROH) of correcting gainsβ∈[−1,1]as an alternative to the classical zero-and first-order holds (ZOHs, FOHs) is discussed related to the positive realness of the associate discrete transfer functions obtained from a given continuous transfer function. It is proved that the minimum direct input/output gain (i.e., the quotient of the leading coefficients of the numerator and denominator of the transfer function) needed for discrete positive realness may be reduced by the choice ofβcompared to that required for discretization via ZOH.

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29

Khairudin, M. "Comparison Methods for Converting a Spindle Plant to Discrete System." Indonesian Journal of Electrical Engineering and Computer Science 1, no. 3 (2016): 575. http://dx.doi.org/10.11591/ijeecs.v1.i3.pp575-582.

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This study presents comparison methods in the conversion of a spindle plant in order to obtain an accurate discrete system when compared to a continuous system of spindle. The accurate conversion results of the continuous system into discrete form are required for implementing the control system of spindle. Comparison methods that will be conducted to convert the continuous system of spindle plant into discrete system through zero-order hold (ZOH), first-order hold (FOH), impulse invariant dicretisation, tustin (bilinear), and pole-zero matching methods. The performances of each method in the

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30

Kim, Daehan, Kunhee Ryu, and Juhoon Back. "Zero-Dynamics Attack on Wind Turbines and Countermeasures Using Generalized Hold and Generalized Sampler." Applied Sciences 11, no. 3 (2021): 1257. http://dx.doi.org/10.3390/app11031257.

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Most wind turbines are monitored and controlled by supervisory control and data acquisition systems that involve remote communication through networks. Despite the flexibility and efficiency that network-based monitoring and control systems bring, these systems are often threatened by cyberattacks. Among the various kinds of cyberattacks, some exploit the system dynamics so that the attack cannot be detected by monitoring system output, the zero-dynamics attack is one of them. This paper confirms that the zero-dynamics attack is fatal to wind turbines and the attack can cause system breakdown.

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31

Zeng, Cheng, and Shan Liang. "Zero dynamics of sampled-data models for nonlinear multivariable systems in fractional-order hold case." Applied Mathematics and Computation 246 (November 2014): 88–102. http://dx.doi.org/10.1016/j.amc.2014.08.001.

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32

Lysov, Vladimir E., and Vasilij A. Polyakov. "Analysis of the influence of the discrete period of the zero-order hold of the digital automatic control system on dynamic indicators of control quality." Vestnik of Samara State Technical University. Technical Sciences Series 31, no. 1 (2023): 34–46. http://dx.doi.org/10.14498/tech.2023.1.3.

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The issue of increasing the accuracy of reproduction of the master signal in a digital system for automatic control of an electric drive in the presence of a zero-order extrapolator in the block diagram is considered. The formation of discreteness in a control system with a zero-order extrapolator is considered. The analysis of the influence of the extrapolator discreteness on the dynamic indicators of the system control quality is carried out. As indicators of the quality of control direct indicators: overshoot and time of the transition process. The necessary relationship between the zero-or

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33

Grunau, H. Ch, and G. Sweers. "Sharp estimates for iterated Green functions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 132, no. 1 (2002): 91–120. http://dx.doi.org/10.1017/s0308210500001542.

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Optimal pointwise estimates from above and below are obtained for iterated (poly)harmonic Green functions corresponding to zero Dirichlet boundary conditions. For second-order elliptic operators, these estimates hold true on bounded C1,1 domains. For higher-order elliptic operators we have to restrict ourselves to the polyharmonic operator on balls. We will also consider applications to non-cooperatively coupled elliptic systems and to the lifetime of conditioned Brownian motion.

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34

Ikechukwu I. Udema. "Derivation of steady-state first-order rate constant equations for enzyme-substrate complex dissociation, as well as zero-order rate constant equations in relation to background assumptions." GSC Biological and Pharmaceutical Sciences 21, no. 3 (2022): 175–89. http://dx.doi.org/10.30574/gscbps.2022.21.3.0482.

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The maximum velocity (Vmax) of catalysis and the substrate concentration ([ST]) at half the Vmax, the KM, are regarded as steady-state (SS) parameters even though they are the outcomes of zero-order kinetics (ZOK). The research was aimed at disputing such a claim with the following objectives: To: 1) carry out an overview of issues pertaining to the validity of assumptions; 2) derive the needed steady-state (SS) equations distinct from Michaelian equations that can be fitted to both experimental variables and kinetic parameters; 3) calculate the SS first-order rate constant for the dissociatio

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35

Zeng, Cheng, Shan Liang, Jiaqi Zhong, and Yingying Su. "Improvement of the Asymptotic Properties of Zero Dynamics for Sampled-Data Systems in the Case of a Time Delay." Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/817534.

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It is well known that the existence of unstable zero dynamics is recognized as a major barrier in many control systems, and deeply limits the achievable control performance. When a continuous-time system with relative degree greater than or equal to three is discretized using a zero-order hold (ZOH), at least one of the zero dynamics of the resulting sampled-data model is obviously unstable for sufficiently small sampling periods, irrespective of whether they involve time delay or not. Thus, attention is here focused on continuous-time systems with time delay and relative degree two. This pape

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36

Friedenberg, Abraham. "Aliasing and zero-order hold reconstruction error in the modulation transfer function of a sampled signal." Journal of the Optical Society of America A 13, no. 7 (1996): 1477. http://dx.doi.org/10.1364/josaa.13.001477.

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37

Sun, Xi-Ming, Guo-Ping Liu, Wei Wang, and David Rees. "$L_{2}$-Gain of Systems With Input Delays and Controller Temporary Failure: Zero-Order Hold Model." IEEE Transactions on Control Systems Technology 19, no. 3 (2011): 699–706. http://dx.doi.org/10.1109/tcst.2010.2050320.

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38

Nishi, Masatoshi, and Mitsuaki Ishitobi. "Sampled-data models for affine nonlinear systems using a fractional-order hold and their zero dynamics." Artificial Life and Robotics 15, no. 4 (2010): 500–503. http://dx.doi.org/10.1007/s10015-010-0852-1.

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39

Yu, Xinghuo, and Renfrey B. Potts. "Computer-controlled variable-structure systems." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 34, no. 1 (1992): 1–17. http://dx.doi.org/10.1017/s0334270000007335.

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AbstractA theory is developed for the computer control of variable-structure systems, using periodic zero-order-hold sampling. A simple two-dimensional system is first analysed, and necessary and sufficient conditions for the occurrence of pseudo-sliding modes are discussed. The method is then applied to a discrete model of a cylindrical robot. The theoretical results are illustrated by computer simulations.

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40

Mosleh, Mosaad, and Amier Al-Ali. "Discrete Speed Controller Design of a Marine Diesel Engine Including Sampling Effects due to Fuel Injection." Journal of Vibration and Control 8, no. 5 (2002): 659–71. http://dx.doi.org/10.1177/1077546029294.

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A linear time invariant (LTI) model of a marine diesel engine is presented. The effect of the discontinuity of the fuel injection into the cylinders and the injection period is considered. The proposed discrete model consists of a sampler and zero-order-hold mechanism, representing the fuel injection process. The design of the discrete controller is based on the pole assignment of the characteristic polynomial of the closed-loop transfer function with the goal of achieving zero steady-state error, and satisfying other design specifications. A numerical example illustrating the characteristic p

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41

Lamichhane, Basu Dev, Amiya Bhaumik, and Achyut Gnawali. "The Changing Landscape: Sustainability of Nepalese Microfinance Institutions (MFIs)." Interdisciplinary Journal of Management and Social Sciences 4, no. 2 (2023): 18–28. http://dx.doi.org/10.3126/ijmss.v4i2.57219.

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The primary goal of this research is to identify changing landscapes Nepalese microfinance institutions (MFIs) in order to achieve outreach and sustainability. This is a descriptive research design. Typically, a microfinance program is designed to assist the poor and marginalized Nepalese women who are unable to access government and institutional financial services by focusing on modest loans with short terms, no collateral, and monthly payments. MFIs, on the other hand, have major challenges in terms of social and economic transformation, as well as long-term viability. In the Nepalese scena

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42

Yu, Mei, Lijuan Li, Guangming Xie, and Hong Shi. "Average Consensus in Multiagent Systems with the Problem of Packet Losses When Using the Second-Order Neighbors’ Information." Mathematical Problems in Engineering 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/304126.

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This paper mainly investigates the average consensus of multiagent systems with the problem of packet losses when both the first-order neighbors’ information and the second-order neighbors’ information are used. The problem is formulated under the sampled-data framework by discretizing the first-order agent dynamics with a zero-order hold. The communication graph is undirected and the loss of data across each communication link occurs at certain probability, which is governed by a Bernoulli process. It is found that the distributed average consensus speeds up by using the second-order neighbor

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43

Ikechukwu, I. Udema. "Derivation of steady-state first-order rate constant equations for enzyme-substrate complex dissociation, as well as zero-order rate constant equations in relation to background assumptions." GSC Biological and Pharmaceutical Sciences 21, no. 3 (2022): 175–89. https://doi.org/10.5281/zenodo.7654125.

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The maximum velocity (<em>V</em><sub>max</sub>) of catalysis and the substrate concentration ([<em>S</em><sub>T</sub>]) at half the <em>V</em><sub>max</sub>, the <em>K</em><sub>M</sub><em>,</em> are regarded as steady-state (SS) parameters even though they are the outcomes of zero-order kinetics (ZOK). The research was aimed at disputing such a claim with the following objectives: To: 1) carry out an overview of issues pertaining to the validity of assumptions; 2) derive the needed steady-state (SS) equations distinct from Michaelian equations that can be fitted to both experime

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44

Karafyllis, I., and M. Krstic. "Nonlinear Stabilization Under Sampled and Delayed Measurements, and With Inputs Subject to Delay and Zero-Order Hold." IEEE Transactions on Automatic Control 57, no. 5 (2012): 1141–54. http://dx.doi.org/10.1109/tac.2011.2170451.

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45

Friedenberg, Abraham. "Aliasing and zero-order hold reconstruction error in the modulation transfer function of a sampled signal: errata." Journal of the Optical Society of America A 14, no. 4 (1997): 941. http://dx.doi.org/10.1364/josaa.14.000941.

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46

Zhang, Daxi, and Yulin Zhang. "PySCP: A Multiple-Phase Optimal Control Software Using Sequential Convex Programming." International Journal of Aerospace Engineering 2022 (April 13, 2022): 1–18. http://dx.doi.org/10.1155/2022/2969809.

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Optimal control problems are common in aerospace engineering. A Python software program called PySCP is described for solving multiple-phase optimal control problems using sequential convex programming methods. By constructing a series of approximated second-order cone programming subproblems, PySCP approaches to the solution of the original optimal control problem in an iterative way. The key components of the software are described in detail, including convexification, discretization, and the adaptive trust region method. The convexification of the first-order differential dynamic equation i

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47

Su, Wu-Chung, Sergey V. Drakunov, and U¨mit O¨zgu¨ner. "A Sampled-Data Formulation for Boundary Control of a Longitudinal Elastic Bar." Journal of Vibration and Acoustics 123, no. 2 (2000): 245–49. http://dx.doi.org/10.1115/1.1350568.

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The sampled-data boundary control problem for a longitudinal flexible bar is formulated as a linear discrete-time control problem in an infinite-dimensional state space. With zero-order-hold applied to the control channel, the system is lifted into an infinite sequence of constant control problems. The finite-dimensional approximation of the discrete-time system is controllable-observable if the sampling period satisfies some inequality constraints, which are related to the associated eigenvalues.

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48

Zhang, Ruyu, Dongling Ouyang, and Liangpeng Xiong. "Coefficient Problems of Quasi-Convex Mappings of Type B on the Unit Ball in Complex Banach Spaces." Mathematica Slovaca 73, no. 5 (2023): 1207–16. http://dx.doi.org/10.1515/ms-2023-0089.

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ABSTRACT In this paper, the sharp solutions of Fekete-Szegö problems are provided for class of quasi-convex mappings f 1 of type B and class of quasi-convex mappings f 2 of type B and order α defined on the unit ball in a complex Banach space, respectively, where x = 0 is a zero of order k + 1 of fi (x) − x (i = 1, 2). Compare with some recent works, our main theorems hold without additional restrictive conditions. Also, the proof of our main theorems are more simple than those given in the previous results.

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49

Lesser, Omri, and Yuval Oreg. "Majorana zero modes induced by superconducting phase bias." Journal of Physics D: Applied Physics 55, no. 16 (2022): 164001. http://dx.doi.org/10.1088/1361-6463/ac4a37.

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Abstract Majorana zero modes in condensed matter systems have been the subject of much interest in recent years. Their non-Abelian exchange statistics, making them a unique state of matter, and their potential applications in topological quantum computation, earned them attention from both theorists and experimentalists. It is generally understood that in order to form Majorana zero modes in quasi-one-dimensional topological insulators, time-reversal symmetry must be broken. The straightforward mechanisms for doing so—applying magnetic fields or coupling to ferromagnets—turned out to have many

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Ou, Minghui, Shan Liang, Zhiyong Yang, Cheng Zeng, and Fei Liu. "Stabilization of a Class of Robot Systems in Fractional-Order Hold Case via Sampling Zero Dynamic Stable Approach." IEEE Access 7 (2019): 129770–77. http://dx.doi.org/10.1109/access.2019.2936605.

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