## Article

# A Decentralized Event-Based Model Predictive Controller Design Method for Large-Scale Systems

^{1}Department of Instrumentation and Industrial Automation, Petroleum University of Technology, Ahwaz, Iran

*Automatic Control and Information Sciences*.

**2014**, 2(1), 26-31

**DOI:**10.12691/acis-2-1-5

**Copyright © 2014 Science and Education Publishing**

**Cite this paper:**

Karim Salahshoor, Mohsen Hadian. A Decentralized Event-Based Model Predictive Controller Design Method for Large-Scale Systems.

*Automatic Control and Information Sciences*. 2014; 2(1):26-31. doi: 10.12691/acis-2-1-5.

Correspondence to: Mohsen Hadian, Department of Instrumentation and Industrial Automation, Petroleum University of Technology, Ahwaz, Iran. Email: m.hadian@put.ac.ir

## Abstract

## Keywords

## References

[[[[[[[[[[[[[[[[1] | K.-E. Årzén, “A simple event-based PID controller,” in Proc. 14th IFAC World Congress, 1999, vol. 18, pp. 423-428. | ||

[[2] | W. Heemels, R. J. A. Gorter, A. van Zijl, P. P. J. Van den Bosch, S. Weiland, W. H. A. Hendrix, and M. R. Vonder, “Asynchronous measurement and control: a case study on motor synchronization,” Control Eng. Pract., vol. 7, no. 12, pp. 1467-1482, 1999. | ||

[[3] | W. Heemels, J. H. Sandee, and P. P. J. Van Den Bosch, “Analysis of event-driven controllers for linear systems,” Int. J. Control, vol. 81, no. 4, pp. 571-590, 2008. | ||

[[4] | M. Mazo and P. Tabuada, “On event-triggered and self-triggered control over sensor/actuator networks,” in Decision and Control, 2008. CDC 2008. 47th IEEE Conference on, 2008, pp. 435-440. | ||

[[5] | J. H. Sandee, W. P. M. H. Heemels, and P. P. J. van den Bosch, “Event-driven control as an opportunity in the multidisciplinary development of embedded controllers,” Proc. 2005, Am. Control Conf. 2005., pp. 1776-1781, 2005. | ||

[6] | D. V Dimarogonas and K. H. Johansson, “Event-triggered control for multi-agent systems,” in Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on, 2009, pp. 7131-7136. | ||

[7] | X. Wang and M. D. Lemmon, “Event-triggered broadcasting across distributed networked control systems,” in American Control Conference, 2008, 2008, pp. 3139-3144. | ||

[8] | R. Fletcher, Practical methods of optimization. John Wiley & Sons, 2013. | ||

[9] | E. Camacho and C. Bordons, Model predictive control. 2004, pp. 1-78. | ||

[10] | D. Q. Mayne, J. B. Rawlings, C. V Rao, and P. O. M. Scokaert, “Constrained model predictive control: Stability and optimality,” Automatica, vol. 36, no. 6, pp. 789-814, 2000. | ||

[11] | S. J. Qin and T. A. Badgwell, “A survey of industrial model predictive control technology,” Control Eng. Pract., vol. 11, no. 7, pp. 733-764, 2003. | ||

[12] | L. Magni and R. Scattolini, “Stabilizing decentralized model predictive control of nonlinear systems,” Automatica, vol. 42, no. 7, pp. 1231-1236, 2006. | ||

[13] | R. M. Hermans, M. Lazar, A. Jokic, and P. van den Bosch, “Almost decentralized model predictive control of power networks,” in MELECON 2010-2010 15th IEEE Mediterranean Electrotechnical Conference, 2010, pp. 1551-1556. | ||

[14] | A. Damoiseaux, A. Jokic, M. Lazar, A. Alessio, P. P. J. Van den Bosch, I. Hiskens, and A. Bemporad, “Assessment of decentralized model predictive control techniques for power networks,” in 16th Power Systems Computation Conference, Glasgow, Scotland, 2008, vol. 210. | ||

[15] | A. Alessio and A. Bemporad, “Decentralized model predictive control of constrained linear systems,” Aiche J., vol. 48, pp. 2813-2818, 2007. | ||

[16] | J. Liu, X. Chen, D. Muñoz de la Peña, and P. D. Christofides, “Sequential and iterative architectures for distributed model predictive control of nonlinear process systems,” AIChE J., vol. 56, no. 8, pp. 2137-2149, 2010. | ||

[17] | H. Ganji, J. S. Ahari, A. Farshi, and M. Kakavand, “Modelling and simulation of benzene alkylation process reactors for production of ethylbenzene,” Pet. Coal, vol. 46, pp. 55-63, 2004. | ||

[18] | C. Perego and P. Ingallina, “Combining alkylation and transalkylation for alkylaromatic production,” Green Chem., vol. 6, no. 6, pp. 274-279, 2004. | ||

[19] | D. Lehmann, E. Heriksson, and K. H. Johansson, “Event-Triggered Model Predictive Control of Discrete-Time Linear Systems Subject to Disturbances,” in European Control Conference, 2013. | ||

## Article

# Some Identities of Subjective Analysis Derived on the Basis of the Subjective Entropy Extremization Principle by Professor V.A. Kasianov

^{1}Mechanics Department, Mechanical-Energetical Faculty, Aero-Space Institute, National Aviation University, Kyiv, Ukraine

*Automatic Control and Information Sciences*.

**2014**, 2(1), 20-25

**DOI:**10.12691/acis-2-1-4

**Copyright © 2014 Science and Education Publishing**

**Cite this paper:**

Andriy Viktorovich Goncharenko. Some Identities of Subjective Analysis Derived on the Basis of the Subjective Entropy Extremization Principle by Professor V.A. Kasianov.

*Automatic Control and Information Sciences*. 2014; 2(1):20-25. doi: 10.12691/acis-2-1-4.

Correspondence to: Andriy Viktorovich Goncharenko, Mechanics Department, Mechanical-Energetical Faculty, Aero-Space Institute, National Aviation University, Kyiv, Ukraine. Email: andygoncharenco@yahoo.com

## Abstract

## Keywords

## References

[[[[[[[[[[[[[[[1] | Ma, F.C., Lv, P.H., and Ye, M., “Study on Global Science and Social Science Entropy Research Trend”, 2012 IEEE fifth International Conference on Advanced Computational Intelligence (ICACI), October 18-20, 2012 Nanjing, Jiangsu, China. 238-242. 2012. | ||

[[2] | Kasianov, V.A., Subjective analysis: monograph, National Aviation University, Kyiv, Ukraine, 2007, 512 | ||

[[3] | Kasianov, V.A., Goncharenko, A.V., Light and shadow. Proportions of shadow economy. Entropy approach: monograph, Kafedra, Kyiv, Ukraine, 2013, 86. | ||

[[4] | Kasyanov, V.O., Goncharenko, A.V., “Variational principle in the problem of ship propulsion and power plant operation with respect to subjective preferences”, Scientific proceedings of Kherson state maritime academy: Scientific journal, 2 (7). 56-61. Dec. 2012. | ||

[[5] | Goncharenko, A.V., “Mathematical modeling of the ship’s main engine random operational process” , Internal combustion engines: Scientifically-engineering journal, 2. 117-125. Dec. 2012. | ||

[6] | Goncharenko, A.V., “Measures for estimating transport vessels operators’ subjective preferences uncertainty”, Scientific proceedings of Kherson state maritime academy: Scientific journal, 1 (6). 59-69. Jun. 2012. | ||

[7] | Kasianov, V., Subjective entropy of preferences. Subjective analysis: monograph, Institute of aviation, Warsaw, Poland, 2013, 644. | ||

[8] | Kasianov, V.A., Elements of subjective analysis: monograph, National Aviation University, Kyiv, Ukraine, 2003, 224. | ||

[9] | Golitsyn, G.A., Levich, A.P., “Variational principles in the scientific knowledge”, Philosophy sciences, 1. 105-136. 2004. | ||

[10] | Jaynes, E.T., “Information theory and statistical mechanics”, Physical review, 106 (4). 620-630. 1957. | ||

[11] | Jaynes, E.T., “Information theory and statistical mechanics. II”, Physical review, 108 (2). 171-190. 1957. | ||

[12] | Stratonovich, R.L., Theory of information, Sovetskoe radio, Moscow, Russia, 1975, 424. | ||

[13] | Golitsyn, G.A., Petrov, V.M., Information and biological principles of optimality: Harmony and algebra of alive, Book house “LIBROKOM”, Moscow, Russia, 2010, 128.] | ||

[14] | Golitsyn, G.A., “Information maximum principle in the evolution of matter”, Phenomenon and noumenon of time, 1(1). 16-19. 2004. | ||

[15] | “Weber-Fechner law”, Wikipedia, the free encyclopedia. [Online]. Available: http://en.wikipedia.org/wiki/Weber–Fechner_law. [Accessed Apr. 8, 2013]. | ||

[16] | “Weber-Fechner law”, Wikiznanie.ru.. [Online]. Available: http://www.wikiznanie.ru/ru-wz/index.php/Закон_Вебера-Фехнера. [Accessed Apr. 8, 2013]. | ||

[17] | Ufimtsev, R., “Prologue 61. Information and Weber-Fechner law”, Cognitivist.ru. [Online]. Available: http://www.cognitivist.ru/er/kernel/prologi_61_weber_fechner.xml. [Accessed Apr. 8, 2013]. | ||

[18] | [Kasianov, V.A., Flight modelling: monograph, National Aviation University, Kyiv, Ukraine, 2004, 400. | ||

## Article

# Further Results on Stability of Singular Time Delay Systems in the Sense of Non-Lyapunov: A New Delay Dependent Conditions

^{1}Department of Control Eng., University of Belgrade, School of Mechanical Engineering, Belgrade, Serbia

^{2}Faculty of Technology, University of Nis, Serbia

^{3}University of Belgrade, School of Mechanical Engineering, Innovation Centre, Belgrade, Serbia

*Automatic Control and Information Sciences*.

**2014**, 2(1), 13-19

**DOI:**10.12691/acis-2-1-3

**Copyright © 2014 Science and Education Publishing**

**Cite this paper:**

Dragutin Lj. Debeljkovic, Sreten B. Stojanovic, Goran V. Simeunovic, Nebojsa J. Dimitrijevic. Further Results on Stability of Singular Time Delay Systems in the Sense of Non-Lyapunov: A New Delay Dependent Conditions.

*Automatic Control and Information Sciences*. 2014; 2(1):13-19. doi: 10.12691/acis-2-1-3.

Correspondence to: Dragutin Lj. Debeljkovic, Department of Control Eng., University of Belgrade, School of Mechanical Engineering, Belgrade, Serbia. Email: ddebeljkovic@yahoo.com

## Abstract

## Keywords

## References

[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[1] | Campbell, S. L., “Singular Systems of Differential Equations”, Pitman, Marshfield, MA, 1980. | ||

[[2] | Müller, P.C., “Stability of Linear Mechanical Systems with Holonomic Constraints”, Applied Mechanics Review, 46 (11). 160-164. 1993. | ||

[[3] | Campbell, S.L., Meyer, C.D., Rose, N.J. “Application of Drazin Inverse to Linear Systems of Differential Equations”, SIAM J. Appl. Math., 31. 411-425. 1976. | ||

[[4] | Luenberger, D.G., “Dynamic Equations in Descriptor Form”, IEEE Trans. Automat. Cont., 22 (3). 312-321. 1977. | ||

[[5] | La Salle, Lefschet, S., “Stability by Lyapunov’s Direct Method”, Academic Press, New York, 1961. | ||

[6] | Weiss, L., Infante, E.F., “On the Stability of Systems Defined over a Finite Time Interval”, Proc. National Acad. Sci., 54. 44-48. 1965. | ||

[7] | Weiss, L., Infante, E.F., “Finite Time Stability under Perturbing Forces and on Product Spaces”, IEEE Trans. Automat. Cont., 12. 54-59. 1967. | ||

[8] | Debeljkovic, D., Owens, H., “On practical stability of singular systems”, Proc. MELECON Conf. 85, Madrid, Spain, 103-105. 1985. | ||

[9] | Debeljkovic, D.Lj., Bajic, V.B., Gajic, Z., Petrovic, B., “Boundedness and existence of solutions of regular and irregular singular systems", Publications of the Faculty of Electrical Eng, Belgrade, Automatic Control, 1. 69-78. 1993. | ||

[10] | Debeljkovic, D.Lj., Lazarevic, M.P., Koruga, Đ., Tomasevic, S., “Finite time stability of singular systems operating under perturbing forces: Matrix measure approach”, Proc. AMSE Conference, Melbourne Australia, 447-450. October 29-31. 1997. | ||

[11] | Kablar, N.A., Debeljkovic, D.Lj., “Non - Lyapunov stability of linear singular systems: Matrix measure approach”, MNTS - Mathematical Theory of Networks and Systems, Presented lecture, also in Proc. of Ext. Abstracts, TM7, Padova, Italy, July 6-10, 1998. | ||

[12] | Kablar, N.A., Debeljkovic, D.Lj., “Non - Lyapunov stability of linear singular systems: Matrix measure approach”, Preprints 5th IFAC Symposium on Low Cost Automation, Shenyang, China, September 8-10, TS13. 16-20, 1998. | ||

[13] | Kablar, N.A., Debeljkovic, D.Lj., “Finite time stability of time varying singular systems”, Proc. IEEE CDC 98, Florida, USA, pp.3831-3836, December 10-12, 1998. | ||

[14] | Debeljkovic, D.Lj., Kablar, N.A., “On necessary and sufficient conditions of linear singular systems stability operating on finite time interval”, Proc. XII CBA, Uberlandia, Brazil, IV. 1241-1246. September 14 -18. 1998. | ||

[15] | Kablar, N.A., Debeljkovic, D.Lj., “Finite time instability of time varying linear singular systems”, Proc. IEEE ACC 99, San Diego, USA, 1796-1800. June 2-4. 1999. | ||

[16] | Debeljkovic, D.Lj., Kablar, N.A., “Finite time stability of linear singular systems: Bellman-Gronwall approach”, Proc. ACC 99, San Diego, USA, 1803-1806. June 2-4. 1999. | ||

[17] | Yang, C.Y., Zhang, Q.L., Lin, Y.P., “Practical Stability of Descriptor Systems“, Dynamics of Continuous, Discrete and Impulsive Systems, Series B: 12.b. 44-57. 2005. | ||

[18] | Nie, Y.Y., Debeljkovic, D.Lj., “Non–Lyapunov Stability of Linear Singular Systems: A Quite new Approach in Time Domain”, Dynamics of Continuous, Discrete and Impulsive Systems, Vol.11, Series A: Math. Analysis, No. 5-6, pp.751-760., 2004. | ||

[19] | Yang, C.Y., Zhang, Q.L., Zhou, L., “Practical Stabilization and Controllability of Descriptor Systems“, International Journal of Information and System Science, 1 (3-4). 455-466. 2005. | ||

[20] | Jun-E, F., Zhen, W., Jia-Bing, S., “Finite-Time Control of Linear Singular Systems with Parametric Uncertainties and Disturbances”, Acta Automatica Sinica, 31(4). 634-637. 2005 | ||

[21] | Feng, H.H., Hunsarg, J., “Stabilization of Nonlinear Singularly Perturbed Multiple Time Delay Systems by Dither”, Trans. ASME J. of Dynamic Systems, Measurement and Control, 118 (3). 177-181. 1996. | ||

[22] | Debeljkovic, D.Lj., Nenadic, Z..Lj., Milinkovic, S.A., Jovanovic, M.B., “On Practical and Finite-Time Stability of Time-Delay Systems”, Proc. ECC 97, Brussels, Belgium, 307-311. July 2-6. 1997. | ||

[23] | Debeljkovic, D.Lj., Nenadic, Z.Lj., Milinkovic, S.A., Jovanovic, M.B. “On the Stability of Linear Systems with Delayed State Defined over Finite Time Interval”, Proc. IEEE CDC 97, San Diego, California, USA, 2771-2772. December 21-23. 1997. | ||

[24] | Nenadic, Z.Lj., Debeljkovic, D.Lj., Milinkovic, S.A., “On Practical Stability of Time Delay Systems”, Proc. IEEE American Control Conference, Albuquerque, USA, 3235-3235. June 4-6. 1997. | ||

[25] | Debeljkovic, D.Lj., Koruga, Đ., Milinkovic, S.A., Jovanovic, M. B., Jacic, Lj. “Further Results on Non-Lyapunov Stability of Time Delay Systems”, Proc. MELECON 98, Tel-Aviv, Israel, 1. 509-512. May 18-20. 1998. | ||

[26] | Debeljkovic, D.Lj., Lazarevic, M.P., Milinkovic, S.A., Jovanovic, M.B., “Finite Time Stability Analysis of Linear Time Delay Systems: Bellman-Gronwall Approach”, Proc. 1st IFAC Workshop on Linear Time Delay Systems, Grenoble, France, 171-175. July 6-7. 1998. | ||

[27] | Debeljkovic, D.Lj., Lazarevic, M.P., Nenadic, Z.Lj., Milinkovic, S.A., “Finite Time Stability of Time Delay Systems” IMA J. Math. Control and Info., 16 (3). 101-109. 1999. | ||

[28] | Debeljkovic, D.Lj., Visnjic, N.S., Pjescic, M., “The Stability of Linear Continuous Singular Systems over the Finite Time Interval: An Overview”, International Journal of Information & System Science, 4 (4). 560-584. 2008. | ||

[29] | Debeljkovic, D.Lj., Lazarevic, M.P., Koruga, Đ., Milinkovic, S.A., Jovanovic, M.B., “Further results on the stability of linear nonautonomous systems with delayed state defined over finite time interval”, Proc. IEEE ACC 2000, Chicago, Illinois, USA, 1450-1451. June 28-30. 2000. | ||

[30] | Yang, C., Zhang, Q., Lin, Y., Zhou, L., “Practical stability of descriptor systems with time-delay in terms of two measurements”, Journal of the Franklin Institute, 343 (6). 635-646. 2006. | ||

[31] | Debeljkovic, D.Lj, Stojanovic, S.B., Aleksendric, M.S., “Stability of Singular Time Delay Systems in the Sense of Non-Lyapunov: Classical and Modern Approach”, Hemijska Industrija, 61 (5). 193-202. 2013. | ||

[32] | Owens, D.H., Debeljkovic, D.Lj., “Consistency and Lyapunov Stability of Linear Descriptor Systems: a Geometric Analysis”, IMA Journal of Math. Control and Information, 2. 139-151. 1985. | ||

[33] | Su, J.H., “Further results on the robust stability of linear systems with single time delay”, Systems & Control Letters 23 (5). 375-379. 1994. | ||

[34] | Debeljkovic, D.Lj., Buzurovic, I.M., Nestorovic, T., Popov, D., “A New Approach to Stability of Singular Time Delay Systems in the sense of Non-Lyapunov: Delay Independent Conditions”, Proc. 2011 IEEE ICCA (International Conference on Control and Automation, Santiago (Chile), December 19-21. 312-317. 2011. | ||

[35] | Xu, S. Dooren, P.V., Stefan, R., Lam, J., “Robust Stability and Stabilization for Singular Systems with State Delay and Parameter Uncertainty”, IEEE Trans. Automat. Control, 47 (7). 1122-1128. 2002. | ||

[36] | Debeljkovic, D.Lj., Buzurovic, I.M., Nestorovic, T., Popov, D.,“On Finite and Practical Stability of Time Delayed Systems: Lyapunov-Krassovski Approach: Delay Dependent Criteria”, Proc. The 23 ^{rd}, Chinese Control and Decision Conference CCDC 2011, Mianyang, (China), 23-25. 331-337. 2011. | ||

## Article

# Decoding of the Triple-Error-Correcting Binary Quadratic Residue Codes

^{1}Department of Computer Science and Information Engineering, Fortune Institute of Technology, Kaohsiung, ROC

*Automatic Control and Information Sciences*.

**2014**, 2(1), 7-12

**DOI:**10.12691/acis-2-1-2

**Copyright © 2014 Science and Education Publishing**

**Cite this paper:**

Hung-Peng Lee, Hsin-Chiu Chang. Decoding of the Triple-Error-Correcting Binary Quadratic Residue Codes.

*Automatic Control and Information Sciences*. 2014; 2(1):7-12. doi: 10.12691/acis-2-1-2.

Correspondence to: Hung-Peng Lee, Department of Computer Science and Information Engineering, Fortune Institute of Technology, Kaohsiung, ROC. Email: hpl@fotech.edu.tw

## Abstract

## Keywords

## References

[[[[[[[[[[1] | Chien, R.T., “Cyclic decoding procedure for the Bose-Chaudhuri-Hocquenghem codes,” IEEE Trans. Inform. Theory, 10(4). 357-363. Oct. 1964. | ||

[[2] | Chen, Y.H., Chien, C.H., Huang, C.H., Truong, T.K., and Jing, M.H., “Efficient decoding of systematic (23, 12, 7) and (41, 21, 9) quadratic residue codes,” J. Inform. Sci. and Eng., 26(5). 1831-1843. Sept. 2010. | ||

[[3] | Elia, M., “Algebraic decoding of the (23, 12, 7) Golay codes,” IEEE Trans. Inform. Theory, 33(1). 150-151. Jan. 1987. | ||

[[4] | Golay, M.J.E., “Notes on digital coding,” Proc. IRE, 37, 657. 1949. | ||

[[5] | Lee, C.D., “Weak general error locator polynomials for triple-error-correcting binary Golay code,” IEEE Comm. Letters, 15(8). 857-859. Aug. 2011. | ||

[6] | Lin, T.C., Chang, H.C., Lee, H.P., Chu, S.I, and Truong, T.K., “Decoding of the (31, 16, 7) quadratic residue code,” J. Chinese Institute of Engineers, 33(4). 573-580. June 2010. | ||

[7] | Lin, T.C., Chang, H.C., Lee, H.P., and Truong, T.K., “On the decoding of the (24, 12, 8) Golay code,” Inform. Sci., 180(23). 4729-4736. Dec. 2010. | ||

[8] | Lin, T.C., Lee, H.P., Chang, H.C., Chu, S.I, and Truong, T.K., “High speed decoding of the binary (47, 24, 11) quadratic residue code,” Inform. Sci., 180(20). 4060-4068. Oct. 2010. | ||

[9] | Lin, T.C., Lee, H.P., Chang, H.C., and Truong, T.K., “A cyclic weight algorithm of decoding the (47, 24, 11) quadratic residue code,” Inform. Sci., 197. 215-222. Aug. 2012. | ||

[10] | Reed, I.S., Shih, M.T., and Truong, T.K., “VLSI design of inverse-free Berlekamp-Massey algorithm,” IEE Proc. Comput. Digit. Tech., 138(5). 295-298. Sept. 1991. | ||

[11] | Reed, I.S., Yin, X., and Truong, T.K., “Algebraic decoding of the (32, 16, 8) quadratic residue code,” IEEE Trans. Inform. Theory, 36 (4). 876-880. July 1990. | ||

[12] | Reed, I.S., Yin, X., Truong, T.K., and Holmes, J.K., “Decoding the (24, 12, 8) Golay code,” IEE Proc. Comput. Digit. Tech., 137(3). 202-206. May 1990. | ||

[13] | Wicker, S.B. Error control systems for digital communication and storage, Prentice Hall, New Jersey, 1995. | ||

## Article

# Evaluating the Partial Derivatives of Four Types of Two-Variables Functions

^{1}Department of Management and Information, Nan Jeon University of Science and Technology, Tainan City, Taiwan

*Automatic Control and Information Sciences*.

**2014**, 2(1), 1-6

**DOI:**10.12691/acis-2-1-1

**Copyright © 2014 Science and Education Publishing**

**Cite this paper:**

Chii-Huei Yu. Evaluating the Partial Derivatives of Four Types of Two-Variables Functions.

*Automatic Control and Information Sciences*. 2014; 2(1):1-6. doi: 10.12691/acis-2-1-1.

Correspondence to: Chii-Huei Yu, Department of Management and Information, Nan Jeon University of Science and Technology, Tainan City, Taiwan. Email: chiihuei@nju.edu.tw

## Abstract

## Keywords

## References

[[[[[[[[[[[[1] | T-W, Ma, “Higher chain formula proved by combinatorics,” The Electronic Journal of Combinatorics, Vol. 16, #N21, 2009. | ||

[[2] | C. H., Bischof, G. Corliss, and A. Griewank, “Structured second and higher-order derivatives through univariate Taylor series,” Optimization Methods and Software, Vol. 2, pp. 211-232, 1993. | ||

[[3] | L. E. Fraenkel, “Formulae for high derivatives of composite functions,” Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 83, pp. 159-165, 1978. | ||

[[4] | D. N. Richard, “ An efficient method for the numerical evaluation of partial derivatives of arbitrary order,” ACM Transactions on Mathematical Software, Vol. 18, No. 2, pp. 159-173, 1992. | ||

[[5] | A. Griewank and A. Walther, Evaluating derivatives: principles and techniques of algorithmic differentiation, 2nd ed., SIAM, Philadelphia, 2008. | ||

[6] | C. -H. Yu, “Using Maple to evaluate the partial derivatives of two-variables functions, ” International Journal of Computer Science and Mobile Computing, Vol. 2, Issue. 6, pp. 225-232, 2013. | ||

[7] | C.-H. Yu, “Using Maple to study the partial differential problems,” Applied Mechanics and Materials, in press. | ||

[8] | C. -H. Yu, “Evaluating partial derivatives of two-variables functions by using Maple,” Proceedings of the 6th IEEE/International Conference on Advanced Infocomm Technology, Taiwan, pp. 23-27, 2013. | ||

[9] | C.-H. Yu, “Application of Maple: taking the partial differential problem of some types of two-variables functions as an example,” Proceedings of the International Conference on e-Learning, Taiwan, pp. 337-345, 2013. | ||

[10] | C.-H. Yu, “Application of Maple on the partial differential problem of four types of two-variables functions,” Proceedings of the International Conference on Advanced Information Technologies, Taiwan, No. 87, 2013. | ||

[11] | C.-H., Yu, “Application of Maple: taking the partial differential problem of two-variables functions as an example,” Proceedings of 2013 Business Innovation and Development Symposium, Taiwan, B20130113001, 2013. | ||

[12] | C. -H. Yu and B. -H. Chen, “The partial differential problem,” Computational Research, Vol. 1, No. 3, pp. 53-60, 2013. | ||

[13] | C. -H. Yu, “Partial derivatives of some types of two-variables functions,” Pure and Applied Mathematics Journal, Vol. 2, No. 2, pp. 56-61, 2013. | ||

[14] | R. V. Churchill and J. W. Brown, Complex variables and applications, 4th ed., McGraw-Hill, New York, p 62, 1984. | ||

[15] | T. M. Apostol, Mathematical analysis, 2nd ed., Addison-Wesley, Boston, p 230, 1975. | ||

## Latest News

## Statistics of This Journal

**Article Downloads:**
22838

**Article Views:**
62905

## Most popular papers

## Sponsors, Associates, and Links

To list your link on our website, please
click here
or
contact us

20th Congress of the International Organization for Mycoplasmology