CV and List of publications

CURRICULUM VITAE


PERSONAL INFORMATION

 

Surname (Last):             Luca (married Tudorache)

Given name (First):        Rodica                      

 

Business Address :  Department of  Mathematics, "Gheorghe Asachi" Technical University of Iasi, 

                             11 Blvd. Carol  I, Iasi 700506, Romania

 

Birthdate:            May 18, 1962

Place of Birth:      Iasi, Romania

Phone:                 (004)0232278680 int.1623

E-mail:                 rlucatudor(at)yahoo.com  ;   rluca(at)math.tuiasi.ro


Primary Field of Speciality for Business Index:  SCIENCE (MATHEMATICS)

Current Position:   PROFESSOR

Company/University:   "GHEORGHE ASACHI" TECHNICAL UNIVERSITY OF IASI, ROMANIA

Hirsch Index Web of Science: 12 (see  the file Web of Science.pdf  at the bottom of the page)

Hirsch Index Scopus: 12 (see the file Scopus.pdf at the bottom of the page)

Hirsch Index Google Scholar: 16 (see the file Google academic.pdf at the bottom of the page)  


EDUCATION

Habilitation Certificate in Mathematics, School of Advanced Studies of the Romanian Academy, Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucuresti, 2017.

Ph.D. in Mathematics, "Alexandru Ioan Cuza" University, Iasi, 1996.

Degree in mathematics (graduated),  "Alexandru Ioan Cuza" University, Iasi, 1984.

 

CAREER POSITIONS

       1.     Professor, Department of Mathematics, "Gheorghe Asachi" Technical University, Iasi, 2008 up to the present.

       2.     Associate professor, Department of Mathematics, "Gheorghe Asachi" Technical University, Iasi, 2001-2008.

       3.     Lecturer  ( 'lector universitar'  in Romanian) , Department of Mathematics, "Gheorghe Asachi" Technical University, Iasi, 1994-2001.

       4.     Assistant professor, Department of Mathematics, "Gheorghe Asachi" Technical University, Iasi, 1988-1994.

       5.     Mathematician,  Institute of scientific research and technological engineering for technique of calculus and informatics Bucuresti, office Iasi, 1986-1988.

       6.     High school professor, Pascani, County Iasi, 1984-1986.

 

Organizations Professional (memberships)

     1) American Mathematical Society (since 2006)

     2) European Mathematical Society  (since 2005)

     3) International Society of Difference Equations (since 2015)

     4) International Federation of Nonlinear Analysts, USA (2003-2010)

     5) Mathematical Association of America (2007, 2008)

     6) Research Group in Mathematical Inequalities and Applications, Australia (since 2009)

     7) International Society for Development and Sustainability, Japan (since 2017)

     8) Societatea de Ştiinte Matematice din România (Society of Mathematical Sciences from Romania) (since 2001)

     9) Societatea Română de Matematică Aplicată şi Industrială (Romanian Society of Applied and Industrial Mathematics) (since 2005)

     10) Seminarul Matematic „Al. Myller” („Al. Myller” Mathematical Seminar), Iaşi (since 1986)

     11) Asociaţia „Recreaţii Matematice”(Mathematical Recreations Association), Iaşi (since 2005).


Honors:

I received 16 awards from ANCS-CNCS, UEFISCDI, in the "National Plan for Research, Development and Innovation, Human Resources Program, Awarding of research results" program ("Planul National de Cercetare, Dezvoltare şi Inovare, Programul Resurse Umane, Premierea rezultatelor cercetarii") for my  papers. 

My biographical sketch is presented in:

   - „Who’s Who in the World” (2016, 2015, 2014, 2010, 2009, 2008, 2007 Editions), „Who’s Who in America” (2009, 2007 Editions), „Who’s Who in Science and Engineering” (2008-2009, 2006-2007, 2005-2006, 2003-2004 Editions);

   - „Dictionary of International Biography” (2015, 2014, 2013, 2011), „World Who’s Who of Women” (2011), „2000 Outstanding Intellectuals of the 21st Century” (2015, 2014, 2011, 2009/10, 2008, 2007, 2004), „The Cambridge Blue Book of Foremost International Scientists” (2008), „2000 Outstanding Scientists” (2008/2009), „Outstanding Scientists of the 21st Century” (2007), „2000 Outstanding Scientists of the 21st Century” (2004), publications of International Biographical Centre, Cambridge, England;

     - "International Dictionary of Professionals” (2012), "Great minds of the 21st Century"  (2011), "Great Women of the 21-st Century" (2005 Edition), publications of American Biographical Institute.


Scientific domains in Mathematics

Ordinary differential equations, partial differential equations, finite difference equations, fractional differential equations.

 

Others competences:      

       I am a referee for the ISI mathematical journals: 

      "Advances in Difference Equations",

    “Advances in Mathematical Physics”,

    "Analele Ştiintifice ale Universităţii Ovidius Constanţa",

    “Annales Polonici Mathematici”,

    “Applied Mathematics and Computation”,

    "Applied Mathematics Letters",

    "Boundary Value Problems",

    "Carphatian Journal of Mathematics",

    “Chaos, Solitons & Fractals”,

    "Discrete and Continuous Dynamical Systems_ B",

    "Discrete Dynamics in Nature and Society",

    "Electronic Journal of Differential Equations”,

    "Electronic Journal of Qualitative Theory of Differential Equations",

    “European Physical Journal Special Topics”

    "Filomat",

    “Fixed Point Theory”,

    "Fractional Calculus and Applied Analysis",

    "Journal of Applied Analysis and Computation",

    "Journal of Difference Equations and Applications",

    “Journal of Fixed Point Theory and Applications”,

    "Journal of Function Spaces",

    "Journal of Inequalities and Applications",

    "Journal of International Equations and Applications",

    “Journal of Mathematics and Computer Science”,

    "Journal of Nonlinear Functional Analysis",

    "Journal of Nonlinear Sciences and Applications",   

    "Lithuanian Mathematical Journal",

    "Mathematica Slovaca",

    "Mathematical Communications",

    “Mathematical Methods in the Applied Sciences”,

    "Mathematical Modelling and Analysis",

    "Mathematical Problems in Engineering",

    "Nonlinear Analysis: Modelling and Control",

    "Nonlinear Dynamics",

    "Proceedings of the Edinburg Mathematical Society",

    "Proceedings of the Indian Academy of Sciences - Mathematical Sciences",

    “Revista Matematica Complutense”,

    “Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales”,

    "Topological Methods in Nonlinear Analysis",

    "Turkic World Mathematical Society - Journal of Applied and Engineering Mathematics”

   and for the mathematical journals (in international databases):

     "Abstract and Applied Analysis" (ex ISI), 

     "Advances in Pure and Applied Mathematics",

     "African Journal of Mathematics and Mathematical Sciences",

     "American Journal of Applied Mathematics",

     "Archirum Mathematicum",

     "British Journal of Mathematics & Computer Science",

     "Buletinul Institutului Politehnic din Iaşi, Secţia: Matematică, Mecanică Teoretică, Fizică”.

     "Bulletin of International Mathematical Virtual Institute",

     "Chinese Journal of Mathematics",

     "Collectanea Mathematica",   

     "Communications in Applied Analysis",

     "Contemporary Analysis and Applied Mathematics",

     "Creative Mathematics and Informatics",  

     "Differential Equations and Applications",

     "Differential Equations and Dynamical Systems",

     “Dynamics of Continuous, Discrete and Impulsive Systems - Series A”,

     "Fractional Differential Calculus",

     "Indian Journal of Mathematics",

     "International Journal of Dynamical Systems and Differential Equations",

     "International Scholarly Research Notices",  

     “Journal of Applied Analysis”,

     "Journal of Applied Mathematics" (ex ISI),

     "Journal of Applied Mathematics and Computing",

     "Journal of Computational Methods in Sciences and Engineering",

     "Journal of Contemporary Mathematical Analysis - Armenian Academy of Sciences",

     “Journal of King Saud University”

     "Journal of Mathematical Research with Applications",

      "Kragujevac Journal of Mathematics",

     "Matematichki Bilten",    

     "Modern Applied Science",

     "Nonlinear Studies",

     “Open Journal of Applied Sciences”,

     “Opuscula Mathematica”,

     "Romai Journal"

     "Tamkang Journal of Mathematics",

     "Vietnam Journal of Mathematics".

  

     I am a reviewer for Databases: Zentralblatt fur Mathematik (from Germany, Hungary, Italy, China, Czech Republic, Slovakia and Romania) (since 2001) and Mathematical Reviews (since 2005).

     I am a project expert estimator in CNCSIS Romania (National council of scientific research in university education from Romania) and in ARACIS Romania (The Romanian Agency for Quality Assurance in Higher Education).

      I am member of Editorial board of the journals:

   "Journal of Mathematics and Computer Science" - ISI journal (http://www.isr-publications.com/jmcs),

   "Journal of Advances in Mathematics and Computer Science" (Past name: "British Journal of Mathematics & Computer Science"),

   "Open Journal of Applied Sciences",

   "Asian Journal of Mathematics and Computer Research",

    "American Journal of Applied Mathematics",  

   "International Journal of Transformation in Applied Mathematics & Statistics", 

   "Buletinul Institutului Politehnic din Iaşi, Sectia: Matematică, Mecanică Teoretică, Fizică".

     I was member of "Asian Council of Science Editors" (2015).

     I am member of Editorial Board of "London Journals Press". 

    I had contributed talks at 53 international conferences (among which 35 in other countries: Bratislava, Slovakia, 2017; Chisinau, Moldova, 2017; Berlin, Germany, 2016; Riga, Latvia, 2016; Dubai, UAE, 2016; Beijing, China, 2015; Lyon, France, 2015; Amadora-Lisabona, Portugal, 2015; Dallas, USA, 2015; San Antonio, USA, 2015; Madrid, Spain, 2014; Catania, Italy, 2014; Side, Antalya, Turkey, 2014; Baltimore, USA, 2014; Rhodes, Greece, 2013; Prague, Czech Republic, 2013, Leiden, Netherlands, 2013; Ankara, Turkey, 2012; Kos, Greece, 2012; Patras, Greece, 2012; Chisinau, Moldova, 2012; Boston, USA, 2012; Loughborough, United Kingdom, 2011; Poitiers, France, 2010; Istanbul, Turkey, 2009; Brno, Czech Republic, 2009; Amsterdam, Netherlands, 2008 (poster); Orlando, Florida USA, 2008; Bremen, Germany, 2008; Plovdiv, Bulgaria, 2007; Zurich, Switzerland, 2007; Chambery, France, 2006; Chişinău, Moldova, 2006, 1996; Han sur Lesse, Belgium, 1991) and I had contributed talks at 23 national conferences.


    October 30, 2017

  

LIST OF PUBLICATIONS

 

(I)  BOOKS

Monographs


1.      Johnny Henderson, Rodica Luca, "Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions", ELSEVIER, Amsterdam, 2016 (2015 in Elsevier), (322 pag.), ISBN: 978-0-12-803652-5.

https://www.elsevier.com/books/boundary-value-problems-for-systems-of-differential-difference-and-fractional-equations/henderson/978-0-12-803652-5

2.      Rodica Luca-Tudorache, „Nonlinear Evolution Problems in Hilbert Spaces”, Publishing House Performantica, Iasi, 2007 (148 pag.) (in Romanian).

3.      Rodica Luca-Tudorache, "Boundary Value Problems for Nonlinear Hyperbolic Systems and Applications”, Publishing House Venus, Iasi, 2003 (236 pag.) (in Romanian).


Courses and Collections of problems for students


1.      Nicoleta Breaz, Lucia Căbulea, Ariana Pitea, Ioan Rasa, Rodica Tudorache, Gheorghiţă Zbăganu, “Probability and statistics”, 2013, Publishing House StudIS, Vatra-Dornei, 2013 (304 pag.) (in Romanian).

2.      Rodica Luca-Tudorache, "Problems of Mathematical Analysis. Integral Calculus”, Publishing House Venus, Iasi, 2007 (381 pag.) (in Romanian).

3.      Rodica Luca-Tudorache, "Problems of Mathematical Analysis. Differential Calculus", Publishing House Performantica, Iasi, 2006 (346 pag.) (in Romanian).

4.      Rodica Luca-Tudorache, "Problems of  probability theory",  Publishing House Tehnopress, Iasi, 2006 (100 pag.) (in Romanian).

5.      Rodica Luca-Tudorache, "Mathematical Analysis. Differential Calculus”, Publishing House Tehnopress, Iasi, 2005 (321 pag.) (in Romanian).

6.      Rodica Tudorache, "Collection of problems of mathematical analysis, Vol.II, Integral Calculus”, Publishing House of  „Gh. Asachi” Technical University, Iasi, 2001 (364 pag.) (in Romanian).

7.      Rodica Tudorache, "Collection of problems of mathematical analysis, Vol.I, Differential Calculus", Publishing House of „Gh. Asachi” Technical University, Iasi, 2000 (318 pag.) (in Romanian).

8.   Eugen Popa, Iulian Haimovici, Rodica Luca et al , "Problems of algebra for highschool”, Publishing House of  „Al.I.Cuza” University, Iasi, 1982 (134 pag.) (in Romanian).


(II)  PAPERS

             A. In ISI mathematical journals

1. Johnny Henderson, Rodica Luca, Positive solutions for a system of singular second-order integral boundary value problems, Fixed Point Theory, ISSN: 1583-5022, accepted for publication.

2. Johnny Henderson, Rodica Luca, Alexandru Tudorache, Existence and nonexistence of positive solutions to a discrete boundary value problem, Carpathian Journal of Mathematics, 2017, 33 (2), 181-190, ISSN: 1584 – 2851.

3. Bashir Ahmad, Rodica Luca,  Existence of solutions for a sequential fractional integro-differential system with coupled integral boundary conditions, Chaos, Solitons and Fractals, 2017, 104, 378–388, ISSN: 0960-0779.

4. Rodica Luca, Positive solutions for a system of Riemann-Liouville fractional differential equations with multi-point fractional boundary conditions, Boundary Value Problems, 2017, 2017:102, pp. 1-35, ISSN: 1687-2770.

5. Johnny Henderson, Rodica Luca, Systems of Riemann-Liouville fractional equations  with multi-point boundary conditions, Applied Mathematics and Computation, 2017, 309, 303-323, ISSN:  0096-3003.

6. Johnny Henderson, Rodica Luca, Positive solutions for an impulsive second-order nonlinear boundary value problem, Mediterranean Journal of Mathematics,  2017, 14:93, pp. 1-16, ISSN: 1660-5446.

7. Johnny Henderson, Rodica Luca, Existence of nonnegative solutions for a fractional integro-differential equation, Results in Mathematics,  2017, 72, 747-763, ISSN: 1422-6383.

8. Johnny Henderson, Rodica Luca, Existence of positive solutions for a singular fractional boundary value problem,  Nonlinear Analysis: Modelling and Control, 2017, 22(1), 99-114, ISSN: 1392-5113.

9. Johnny Henderson, Rodica Luca, Existence and multiplicity of positive solutions for a system of difference equations with coupled boundary conditions, Journal of Applied Analysis and Computation, 2017, 7 (1), 134-146, ISSN: 2156-907X.

10. Johnny Henderson, Rodica Luca, Alexandru Tudorache, Existence and nonexistence of positive solutions for coupled Riemann-Liouville fractional boundary value problems, Discrete Dynamics in Nature and SocietyVolume 2016, Article ID 2823971, pp. 1-12, ISSN: 1026-0226.

11Johnny Henderson, Rodica Luca, Existence of positive solutions for a system of semipositone fractional boundary value problemsElectronic Journal of Qualitative Theory of Differential Equations, 2016, No. 22, pp. 1-28, ISSN: 1417-3875.

12. Johnny Henderson, Rodica Luca, Positive solutions for a system of semipositone coupled fractional boundary value problems, Boundary Value Problems, 2016, 2016:61, pp. 1-23, ISSN: 1687-2770.

13. Johnny Henderson, Rodica Luca, Positive solutions for a system of difference equations with coupled multi-point boundary conditions, Journal of Difference Equations and Applications, 2016, 22 (2), 188-216, ISSN: 1023-6198.

14. Johnny Henderson, Rodica Luca, Positive solutions for systems of second-order difference equations, Discrete Dynamics in Nature and Society, 2015, Volume 2015, Article ID 468648, pp. 1-8, ISSN: 1026-0226.

15. Johnny Henderson, Rodica Luca, Nonexistence of positive solutions for a system of coupled fractional boundary value problems, Boundary Value Problems, 2015, 2015:138, pp. 1-12, ISSN: 1687-2770.

16. Johnny Henderson, Rodica Luca, Alexandru Tudorache, On a system of fractional differential equations with coupled integral boundary conditions, Fractional Calculus and Applied Analysis, 2015, 18 (2), 361-386, ISSN: 1311-0454.

17. John Graef, Johnny Henderson, Rodica Luca, Yu Tian, Boundary value problems for third order Lipschitz ordinary differential equations, Proceedings of  the Edinburg Mathematical Society, 2015, 58 (1), 183-197, ISSN: 0013-0915, EISSN: 1464-3839.

18. Johnny Henderson, Rodica Luca, Positive solutions for a system of fractional differential equations with coupled integral boundary conditions,  Applied Mathematics and Computation, 2014, 249, 182-197, ISSN:  0096-3003.

19. Johnny Henderson, Rodica Luca, Positive solutions for systems of nonlinear second-order multi-point boundary value problems, Mathematical Methods in the Applied Sciences, 2014, 37, 2502-2516, ISSN: 0170-4214.

20. Rodica Luca, Alexandru Tudorache, Positive solutions to a system of semipositone fractional boundary value problems, Advances in Difference Equations, 2014, 2014:179, pp.1-11, ISSN: 1687-1847.

21. Mouffak Benchohra, Johnny Henderson, Rodica Luca, Abdelghani Ouahab, Boundary data smoothness for solutions of second order ordinary differential equations with integral boundary conditions, Dynamic Systems and Applications, 2014, 23, 133-144, ISSN 1056-2176.

22. Johnny Henderson, Rodica Luca, On a second-order nonlinear discrete multi-point eigenvalue problem, Journal of Difference Equations and Applications, 2014, 20 (7), 1005-1018, ISSN: 1023-6198, ISSN: 1023-6198.

23. Johnny Henderson, Rodica Luca, Existence and multiplicity of positive solutions for a system of fractional boundary value problems, Boundary Value Problems, 2014, 2014:60, pp. 1-17, ISSN: 1687-2770.

24. Johnny Henderson, Rodica Luca, Positive solutions for systems of second-order integral boundary value problems, Electronic Journal of Qualitative Theory of Differential Equations, 2013, No. 70, pp. 1-21, ISSN: 1417-3875

25. Johnny Henderson, Rodica Luca, Existence of positive solutions for a system of second-order multi-point discrete boundary value problems, Journal of Difference Equations and Applications, 2013, 19 (11), 1889-1906, ISSN: 1023-6198.

26. Johnny Henderson, Rodica Luca, Positive solutions for a system of nonlocal fractional boundary value problems, Fractional Calculus and Applied Analysis, 2013, 16 (4), 985-1008, ISSN: 1311-0454.

27. Johnny Henderson, Rodica Luca, Positive solutions for a system of second-order nonlinear multi-point eigenvalue problems, Applied Mathematics and Computation, 2013, 223, 197-208.

28. Johnny Henderson, Rodica Luca, Positive solutions for singular systems of higher-order multi-point boundary value problems, Mathematical Modelling and Analysis, 2013, 18 (3), 309-324. ISSN: 1392-6292.

29. Johnny Henderson, Rodica Luca, Existence and multiplicity for positive solutions of a system of higher-order multi-point boundary value problems, Nonlinear Differential Equations and Applications NoDEA, 2013, 20 (3), 1035-1054, ISSN:  1021-9722.

30. Johnny Henderson, Rodica Luca, Positive solutions for singular systems of multi-point boundary value problems, Mathematical Methods in the Applied Sciences, 2013, 36 (7), 814-828, ISSN: 0170-4214.

31. Johnny Henderson, Rodica Luca, On a multi-point discrete boundary value problem, Journal of Difference Equations and Applications, 2013, 19 (4), 690-699, ISSN: 1023-6198.

32. Johnny Henderson, Rodica Luca, Existence and multiplicity for positive solutions of a second-order multi-point discrete boundary value problem, Journal of Difference Equations and Applications, 2013, 19 (3), 418-438, ISSN: 1023-6198.

33. Johnny Henderson, Rodica Luca, Existence of positive solutions for a system of higher-order multi-point boundary value problems,  Applied Mathematics and Computation, 2012, 219 (8), 3709-3720, ISSN: 0096-3003.

34. Johnny Henderson, Rodica Luca, On a system of higher-order multi-point boundary value problems, Electronic Journal of Qualitative Theory of Differential Equations, 2012, No. 49, 1-14, ISSN: 1417-3875.

35. Johnny Henderson, Rodica Luca, On a system of second-order multi-point boundary value problems, Applied Mathematics Letters, 2012, 25, 2089-2094, ISSN: 0893-9659.

36. Johnny Henderson, Rodica Luca, Positive solutions for a system of second-order multi-point discrete boundary value problems, Journal of Difference Equations and Applications, 2012, 18 (9), 1575-1592, ISSN: 1023-6198.

37. Rodica Luca, Existence of positive solutions for a second-order m+1-point discrete boundary value problem, Journal of Difference Equations and Applications, 2012, 18 (5), 865-877, ISSN: 1023-6198.

38. Johnny Henderson, Rodica Luca, Existence and multiplicity for positive solutions of a multi-point boundary value problem, Applied Mathematics and Computation, 2012, 218, 10572-10585, ISSN: 0096-3003.

39. Rodica Luca, Positive solutions for a higher-order m-point boundary value problem, Mediterranean Journal of Mathematics, 2012, 9(2), 381-394, ISSN: 1660-5446.

40. Rodica Luca, On a higher-order m-point boundary value problem, Fixed Point Theory, 2012, 13 (1), 137-145, ISSN: 1583-5022.

41. Johnny Henderson, Rodica Luca, Positive solutions for a system of second-order multi-point boundary value problems, Applied Mathematics and Computation, 2012, 218, 6083-6094, ISSN: 0096-3003.

42. Johnny Henderson, Rodica Luca, Positive solutions for a system of higher-order multi-point boundary value problems, Computers and Mathematics with Applications, 2011, 62, 3920-3932, ISSN: 0898-1221.

43. Rodica Luca, Existence and uniqueness of solutions for a second-order nonlinear hyperbolic system, Electronic Journal of Differential Equations, Vol. 2011 (2011), No. 78, pp. 1-11, ISSN: 1072-6691.

44. Rodica Luca, Positive solutions of m-point boundary value problems for systems of nonlinear second-order differential equations, Analele Ştiinţifice ale Universităţii “Alexandru Ioan Cuza” din Iaşi, Secţia Matematică, 2011, Tom LVII, Supliment, 161-174, ISSN: 1221-8421.

45. Rodica Luca, Boundary value problems for nonlinear systems with generalized second-order differences, Carpathian Journal of Mathematics, 27 (1), 2011, 95-104, ISSN: 1584 – 2851.

46. Rodica Luca, Existence of positive solutions for a class of higher-order m-point boundary value problems, Electronic Journal of Qualitative Theory of Differential Equations, 2010, No. 74, 1-15, ISSN: 1417-3875.

47. Rodica Luca, Nonlinear differential problems with first- or second-order differences in Hilbert spaces, Nonlinear Analysis, Theory Methods and Applications, 2009, 71, e81-e97 (special issue for Proceedings of the “Fifth World Congress of Nonlinear Analysts”, Orlando, Florida, USA, July 2-9, 2008), ISSN:  0362-546X.

48. Rodica Luca,Time periodic solutions for a class of nonlinear boundary value problems, Fixed Point Theory, 2008, 9 (1), 173-187, ISSN: 1583-5022.

49. Rodica Luca, On a nonlinear differential problem with second-order differences, Analele Ştiinţifice ale Universităţii “Alexandru Ioan Cuza” din Iaşi, Secţia Matematică, 2008,Tom LIV, f.2, 261-277, ISSN: 1221-8421.

50. Rodica Luca, Existence and uniqueness for a nonlinear discrete hyperbolic system, Nonlinear Analysis, Theory Methods and Applications, 2007, 67, 2433-2446, ISSN 0362-546X.

51. Rodica Luca, On a nonlinear discrete hyperbolic system, Asymptotic Analysis, 2007, 51 (3-4), 289-302, ISSN: 0921-7134.

52. Rodica Luca, Existence and asymptotic behaviour for a discrete hyperbolic system, Journal of Mathematical Analysis and Applications, 2007, 329, 191-205, ISSN: 0022-247X.

53. Rodica Luca, Existence for a class of discrete hyperbolic problems, Advances in Difference Equations, 2006 Vol. 2006,  Article ID89260, 14 pag., ISSN: 1687-1839 (Print) ISSN: 1687-1847 (Online).

54. Rodica Luca, On a class of nonlinear hyperbolic systems, Nonlinear Analysis, Theory Methods and Applications, 2002, 49,  841-860, ISSN 0362-546X.

55. Rodica Luca, Time periodic solutions for a nonlinear hyperbolic system, Nonlinear Analysis, Theory Methods and Applications,  2001, 45, 801-815, ISSN 0362-546X.

56. Rodica Luca, On a class of nonlinear hyperbolic systems with non-local boundary conditions, Journal of Mathematical Analysis and Applications, 2001, 256, 375-404, ISSN: 0022-247X.

        B.  In Proceedings of international conferences (ISI)

57. Johnny Henderson, Rodica Luca, Alexandru Tudorache, Existence of positive solutions for a system of fractional boundary value problems, in „ Differential and Difference Equations with Applications”, ICDDEA, Amadora, Portugal, May 2015, Selected Contributions, Editors: Sandra Pinelas, Zuzana Dosla, Ondrej Dosly, Peter E. Kloeden, (451 pag.), Springer, 2016, pag. 349-357, ISBN: 978-3-319-32855-3.

58. Johnny Henderson, Rodica Luca, Multiple positive solutions for a second-order multi-point discrete boundary value problem, AIP Conference Proceedings "11th International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2013", September 21-27, 2013, Rhodes, Greece, Vol. 1558, Editors: Theodore Simos, Georgios Psihoyios and Charalambos Tsitouras, pp. 391-394 (2013), ISBN: 978-0-7354-1184-5.

59. Johnny Henderson, Rodica Luca, Positive solutions for second-order multi-point discrete boundary value problems, AIP Conference Proceedings, 1479, pp. 565-567, "Numerical Analysis and Applied Ma5thematics ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics", 19–25 September 2012,  Kos, Greece, Editors: T.E. Simos, G. Psihoyios, C. Tsitouras, Z. Anastassi, 2012, ISBN-10: 0735410917, ISBN-13: 978-0-7354-1091-6.

60. Rodica Luca, Gheorghe Morosanu, Nonlinear boundary value problems for a class of hyperbolic systems, în „Evolution Equations, Control Theory and Biomathematics”, 1993, Vol. 155, New York-Basel-Hong Kong, 327-336, Proceedings of „The Third International Workshop – Conference on Evolution Equations, Control Theory and Biomathematics”, October 20-26, 1991, Han sur Lesse, Belgia, ISBN: 0-8247-8885-0.

61. Rodica Luca, Gheorghe Morosanu, Asymptotic properties of solutions to evolution equations, în „Optimization, Optimal Control and Partial Differential Equations”, International Series of Numerical Mathematics, 1992, Vol. 107, Basel- Boston-Berlin, 53-62, Proceedings of the „First Franco-Romanian Conference on Optimization, Optimal Control, Partial Differential Equations”, September 7-11, 1992, Iaşi, România, ISBN: 3-7643-2788-X, ISBN: 0-8176-2788-X. 

      C . In other international mathematical journals (in international databases)

62. Rodica Luca, Alexandru Tudorache, Existence and nonexistence of positive solutions for a system of higher-order differential equations with integral boundary conditions, British Journal of Mathematics & Computer Science, 2016, 19 (3), 1-10, ISSN: 2231-0851.

63. Johnny Henderson, Rodica Luca, Alexandru Tudorache, Positive solutions for a system of second-order differential equations with integral boundary conditions, International Journal of Applied Physics and Mathematics, 2016, 6 (3), 138-149, ISSN: 2010-362X.

64.  Johnny Henderson, Rodica Luca, On a system of Riemann-Liouville fractional boundary value problems, Communications on Applied Nonlinear Analysis, 2016, 23 (2), 1-19, ISSN: 1074-133X.

65. Johnny Henderson, Rodica Luca, Alexandru Tudorache, Positive solutions for systems of coupled fractional boundary value problems, Open Journal of Applied Sciences, 2015, 5, 600-608, ISSN: 2165-3917.

66. Johnny Henderson, Rodica Luca, Charles Nelms Jr., Aijun Yang, Positive solutions for a singular third order boundary value problem, Differential Equations & Applications, 2015, 7 (4), 437-447, ISSN: 1847-120X (print), 1848-9605 (online).

67. Rodica Luca, Alexandru Tudorache, Existence of positive solutions to a system of higher-order semipositone integral boundary value problems, Communications in Applied Analysis, 2015, 19, 589-604, ISSN: 1083-2564.

68. Johnny Henderson, Rodica Luca, Alexandru Tudorache, Positive solutions for a fractional boundary value problem, Nonlinear Studies, 2015, 22 (1), 1-13, ISSN: 1359-8678.

69. Johnny Henderson, Rodica Luca, Alexandru Tudorache, Multiple positive solutions for a multi-point discrete boundary value problem, Communications, Faculty of Sciences, University of Ankara, Series A1: Mathematics and Statistics, 2014, 63 (2), 59-70, ISSN: 1303-6991.

70. Johnny Henderson, Rodica Luca, Comparison of smallest eigenvalues for certain third order boundary value problems, PanAmerican Mathematical Journal, 2014, 24 (3), 75-81, ISSN: 1064-9735.

71. Johnny Henderson, Rodica Luca, Positive solutions for systems of multi-point nonlinear boundary value problems, Communications on Applied Nonlinear Analysis, 2014, 21 (3), 1-12, ISSN: 1074-133X.

72. Johnny Henderson, Rodica Luca, Positive solutions for systems of singular higher-order multi-point boundary value problems, British Journal of Mathematics & Computer Science, 2014, 4 (4), 460-473, ISSN: 2231-0851.

73. Johnny Henderson, Rodica Luca, Existence and multiplicity of positive solutions for a system of higher-order multi-point boundary value problems, Advances in Dynamical Systems and Applications, 2013, 8 (2), 233-245, ISSN: 0973-5321. 

74. Rodica Luca, On a class of m-point boundary value problems, Mathematica Bohemica, 2012, 137 (2), 187-194, ISSN: 0862-7959.

75. Rodica Luca, Positive solutions for a second-order m-point boundary value problem, Dynamics of Continuous, Discrete and Impulsive Systems - A, 2011, 18, 161-176, ISSN: 1201-3390.

76. Rodica Luca, Existence of positive solutions for a discrete boundary value problem,  The Journal of Mathematics, Physics and Astronomy, New Series, Faculty of Science, University of Istanbul, 2008-2009, 3, 119-126, ISSN: 1300-0713.

77. Rodica Luca, Positive solutions for m+1-point discrete boundary value problems, Libertas Mathematica, 2009, XXIX, 65-82, ISSN: 0278-5307.

78. Rodica Luca, On a class of nonlinear differential systems in Hilbert spaces, International Journal of Pure and Applied Mathematics, 2009, 51, No.1, 125-140, ISSN: 1311-8080.

79. Rodica Luca, Differential systems with second-order differences in Hilbert spaces, PanAmerican Mathematical Journal, 2008, 18, Number 3, 59-67, ISSN: 1064-9735.

80. Rodica Luca, On a differential system with first-order differences, International Journal of Pure and Applied Mathematics, 2008, 46, No.1, 73-81, ISSN: 1311-8080.

81. Rodica Luca, Existence of time almost-periodic solutions for a higher order nonlinear hyperbolic problem, Nonlinear Studies, 2008, 15, Number 1, 15-25, ISSN: 1359-8678.

82. Rodica Luca, Existence and uniqueness results for a class of nonlinear differential systems, International Journal of Pure and Applied Mathematics, 2007, 40, No. 3, 367-372, ISSN: 1311-8080.

83. Rodica Luca, Existence and uniqueness results for a class of nonlinear differential problems, Buletinul Academiei de Ştiinţe a Republicii Moldova, Matematica, 2007, 53, Nr.1, 46-58, ISSN: 1024-7696.

84. Rodica Luca, Monotone boundary conditions for a class of nonlinear hyperbolic systems, International Journal of Pure and Applied Mathematics, 2006, 32, No.1, 83-103, ISSN: 1311-8080.

85. Rodica Luca, Time almost-periodic solutions for a class of nonlinear hyperbolic problems, Communications on Applied Nonlinear Analysis, 2006, 13, Nr.1, 1-14, ISSN: 1074-133X.

86. Rodica Luca, An asymptotic result for the solutions of a higher order hyperbolic problem, PanAmerican Mathematical Journal, 2004, 14, Nr.3, 99-109, ISSN 1064-9735.

87. Rodica Luca, Boundary value problems for a second-order nonlinear hyperbolic system, Communications in Applied Analysis, 2004, 8, 305-321, ISSN: 1083-2564.

88. Rodica Luca, Asymptotic behaviour of solutions to a nonlinear hyperbolic problem, Libertas Mathematica, 2001, XXI, 41-51, ISSN: 0278-5307.

89. Rodica Luca, Time periodic solutions for a higher order nonlinear hyperbolic system, Libertas Mathematica, 1999, XIX, 83-93, ISSN: 0278-5307.

90. Rodica Luca, An existence result for a nonlinear hyperbolic system, Differential and Integral Equations, 1995, 8, 887-900, ISSN: 0893-4983.

      D.  In other international mathematical journals

91. Rodica Luca, Boundedness conditions for a class of nonlinear partial differential problems, Global Journal of Mathematics and Mathematical Sciences, 2005, Vol.1, No.1, 88-95, ISSN: 0972-9836.

92. Rodica Luca, Asymptotic behaviour of solutions to a higher order nonlinear hyperbolic system, Scripta Scientiarum Mathematicarum, 2001, Tom II, Fasc.I, 76-86, ISBN: 9975-63-073-1.

      E.  In Proceedings of international conferences (in international databases)

93. Johnny Henderson, Rodica Luca, Positive solutions for a system of difference equations with coupled boundary conditions, Proceedings of the 4th Conference of Mathematical Society of Moldova CMSM4’2017, June 28-July 2, 2017, Chisinau, Republic of Moldova, 285-288, ISBN 978-9975-71-915-5.

94. Johnny Henderson, Rodica Luca, Existence of positive solutions for a system of nonlinear second-order integral boundary value problems, Discrete and Continuous Dynamical Systems, 2015, Supplement, Dynamical Systems, Differential Equations and Applications, AIMS Proceedings 2015, Proceedings of the 10th AIMS International Conference (Madrid, Spain, 2014), Editors: Manuel de León, Wei Feng, Zhaosheng Feng, Julian Lopez-Gomez, Xin Lu, J.M. Martell, Javier Parcet, Daniel Peralta-Salas and Weihua Ruan, 596-604, DOI:10.3934/proc.2015.0596.

95. Rodica Luca-Tudorache, Time periodic solutions to a nonlinear second-order partial differential problem, Proceedings of the “Sixth Congress of Romanian Mathematicians”,  Bucharest, România, June 28-July 4, 2007, Editors L. Beznea et al., Vol. 1, Scientific Contributions, Editura Academiei Române, Bucuresti, 2009, 261-268, ISBN: 978-973-27-1781-3,  978-973-27-1780-6.

96. Rodica Luca-Tudorache, Existence and uniqueness results for a class of nonlinear differential systems with second-order differences, Proceedings in Applied Mathematics and Mechanics PAMM Volume 8 Issue 1, 2008, Special Issue: “79th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)”, Bremen 2008, pp. 10741-10742, ISSN: 1617-7061.

97. Rodica Luca-Tudorache, Existence and uniqueness results for a nonlinear differential system, Proceedings in Applied Mathematics and Mechanics PAMM,  Volume 7, Issue 1, 2007, Special Issue: “Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting”, Zürich 2007, pp. 2030023-2030024, ISSN: 1617-7061.

98. Rodica Luca-Tudorache, An existence result for a class of nonlinear differential systems, in „Applied Analysis and Differential Equations”, Proceedings of International Conference on Applied Analysis and Differential Equations”, Iaşi, Romania, September 4-9, 2006, Editors O. Cârjă and I.I. Vrabie, World Scientific, 2007, 185-198, ISBN-13: 978-981-270-594-5, ISBN-10: 981-270-594-5.

99. Rodica Luca-Tudorache, Time periodic solutions for a nonlinear hyperbolic boundary value problem, In Proceedings of the scientific communications meeting of the “Aurel Vlaicu" University of Arad. Edition IV-a. “25 years of high level technical education in Arad", Gheorghe Halic (ed.) et al., Arad, Romania, October 30-31, 1997. Vol. I: Mathematics. Arad: “Aurel Vlaicu" University of Arad Publishing House, 173-180, ISBN: 973-98365-1-8.

100. Rodica Luca, Nonlinear monotone boundary conditions for hyperbolic systems, “Symposium Septimum Tiraspolense Generalis Topologiae et Suae Applicationum”, 1996, Editura  Tehnică", U.T.M. Chişinău, 136-139, ISBN: 9975-910-06-8.

      F.  In Romanian mathematical journals (in international databases)

101. Johnny Henderson, Rodica Luca, Alexandru Tudorache, Multiple positive solutions for a second-order multi-point boundary value problem, Romai Journal, 2014, v.10, no.1, 71-80, ISSN 1841-5512.

102. Rodica Luca, Ciprian Deliu, Nonexistence of positive solutions for a system of higher-order multi-point  boundary value problems, Romai Journal, 2013, 9 (1), 69-77, ISSN 1841-5512.

103. Johnny Henderson, Rodica Luca, Existence of positive solutions for a nonlinear higher-order multi-point boundary value problem, Bulletin of the Transilvania University of Brasov, Series III: Mathematics, Informatics, Physics, Vol. 5(54) 2012, 167-178 (Special issue for Proceedings of the Seventh Congress of Romanian Mathematicians,  Brasov,  România, June 29 - July 5, 2011), ISSN 2065-2151.

104. Rodica Luca, Ciprian Deliu, Existence of positive solutions for a higher-order multi-point boundary value problem, Romai Journal, 2012, v. 8, no.2, 143-152, ISSN 1841-5512.

105. Rodica Luca, On a class of third-order difference problems, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2010, Tom LVI (LX), Fasc.2, 1-12.

106. Rodica Luca, Boundary value problems for a class of third-order difference systems, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2009, Tom LV (LIX), Fasc.4, 9-18.

107. Rodica Luca, On a nonlinear system with generalized second-order differences, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2009, Tom LV (LIX), Fasc.3, 23-30.

108. Rodica Luca, On an infinite differential system with second-order differences, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2008, Tom LIV (LVIII), Fasc.4, 29-35.

109. Rodica Luca, On a class of nonlinear differential problems, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2008, Tom LIV (LVIII), Fasc.3, 25-34.

110.  Rodica Luca, A fractional step scheme for a nonlinear hyperbolic problem, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2008, Tom LIV (LVIII), Fasc.2, 21-26.

111. Rodica Luca, Periodic solutions to a class of nonlinear boundary value problems, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2007, Tom LIII (LVII), Fasc.3-4, 9-18.

112. Rodica Luca, A nonlinear Volterra integrodifferential system of higher order PDE, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2007, Tom LIII (LVII), Fasc.1-2, 29-41.

113. Rodica Luca-Tudorache, Existence results for a class of nonlinear Volterra integro-differential problem, Romai Journal, 2006, Vol.2, Nr.1, 127-134, ISSN 1841-5512.

114. Rodica Luca, On some nonlinear boundary value problems, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2006, Tom LII (LVI), Fasc.3-4, 15-25.

115. Rodica Luca, On a Volterra integrodifferential problem, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2006, Tom LII (LVI), Fasc.1-2, 35-46.

116. Rodica Luca-Tudorache, Existence for a class of nonlinear differential systems, Studii si Cercetări Ştiinţifice, Seria Matematică, 2006, 16, Supplement, 311-323, ISSN: 1224-2519.

117. Rodica Luca, Nonlinear boundary value problems for a higher-order partial differential system, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică,  2005, Tom. LI (LV), Fasc.3-4, 13-19.

118. Rodica Luca, On a nonlinear higher-order partial differential problem, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2005, Tom LI (LV), Fasc.1-2,  11-16.

119. Rodica Luca, Remarks on a third-order boundary value problem, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2004, Tom L (LIV), Fasc.3-4,  17-23.

120. Rodica Luca, On some integral and discrete inequalities, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2004, Tom L (LIV), Fasc.1-2, 55-59.

121. Rodica Luca, Almost-periodic solutions to a nonlinear hyperbolic system of higher-order P.D.E., Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2003, Tom XLIX (LIII), Fasc.3-4, 49-55.

122. Rodica Luca, Almost-periodic solutions to a nonlinear hyperbolic problem, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2003, Tom XLIX (LIII), Fasc.3-4, 43-48.

123. Rodica Luca, On a nonlinear second-order partial differential system, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2003, Tom XLIX (LIII), Fasc.1-2, 27-36.

124. Rodica Luca, Nonlinear boundary value problems for second order partial differential systems, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2002, Tom XLVIII (LII), Fasc.3-4, 19-28.

125. Rodica Luca, Asymptotic behavior of solutions to a linear hyperbolic problem, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2002, Tom XLVIII (LII), Fasc.1-2, 45-50.

126. Rodica Luca, An iterative method for the solutions of a hyperbolic problem, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2001, Tom XLVII (LI), Fasc.3-4, 7-14.

127. Rodica Luca, Remarks on the nonaccretivity of a hyperbolic operator in some spaces, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2001, Tom XLVII (LI), Fasc.1-2, 25-37.

128. Rodica Luca, Periodic solutions of a hyperbolic system, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2000, Tom XLVI (L), Fasc.3-4, 43-49.

129. Rodica Luca, An existence result for a nonlinear parabolic problem, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 2000, Tom XLVI (L), Fasc.1-2, 47-59.

130. Rodica Luca, Existence and uniqueness results for a higher order hyperbolic system, Mathematical Reports (Studii şi Cercetări Matematice), 1999, Vol. 1 (51), No.4, 551-571, ISSN: 1582-3067.

131. Rodica Luca, An existence result for a nonlinear Volterra integrodifferential system, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 1999, Tom XLV (XLIX), Fasc.3-4, 61-69.

132. Rodica Luca, Periodic and almost-periodic solutions to a higher order nonlinear hyperbolic system, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică,  1999, Tom XLV (XLIX), Fasc.1-2, 67-77.

133. Rodica Luca, Nonlinear hyperbolic systems with non-local boundary conditions, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 1998, Tom XLIV (XLVIII), Fasc.3-4, 29-36.

134. Rodica Luca, Observations on a nonlinear hyperbolic problem, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 1997, Tom XLIII (XLVII), Fasc.1-2, 53-58.

135. Rodica Luca, Periodic and almost-periodic solutions for a class of nonlinear hyperbolic systems, Analele Ştiinţifice ale Universităţii “Alexandru Ioan Cuza” din Iaşi, Secţia Matematică,  1996, Tom XLII, 405-417, ISSN: 1221-8421.

136. Rodica Luca-Tudorache, Asymptotic behaviour of solutions to a class of hyperbolic systems,  Buletinul Ştiinţific al Universităţii Baia Mare, Seria B Matematică-Informatică, 1996, vol. XII, 71-76, ISSN: 1224-3221.

137. Rodica Luca-Tudorache, Mixed problems for a class of nonlinear hyperbolic systems, Buletinul Ştiinţific al Universităţii Baia Mare, Seria B Matematică-Informatică, 1996, vol. XII, 77-84, ISSN: 1224-3221.

138. Rodica Luca-Tudorache, Hyperbolic problems associated to integrated circuits modeling, Buletinul Ştiinţific al Universităţii Baia Mare, Seria B Matematică-Informatică, 1993, Vol. IX, 123-128, (in Romanian, ISSN: 1224-3221.

139. Rodica Luca-Tudorache, The asymptotic behaviour of the solutions of a class of nonlinear hyperbolic systems, Buletinul Ştiinţific al Universităţii Baia Mare, Seria B Matematică-Informatică, 1993, Vol. IX, 33-38, (in Romanian), ISSN: 1224-3221.

140. Rodica Luca, Gheorghe Morosanu, Hyperbolic problems in integrated circuits modelling, Mathematical Reports (Studii şi Cercetări Matematice), 1992, Tom 44, Nr.5, 355-373, ISSN: 1582-3067.

141. Rodica Luca, Gheorghe Morosanu, On a class of nonlinear hyperbolic systems, Memoriile Secţiilor Ştiinţifice ale Academiei Române, 1991, Seria IV, Tom XIV, Nr.2, 219-237, ISSN 1224-1407.

142. Rodica Luca, Theoretical studies on the equation of semi-infinite rod. The stationary case, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 1991, Tom XXXVII (XLI), Fasc.1-4, 59-65.

143. Rodica Luca, Oscillatory solutions for equations with deviating arguments, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 1990, Tom XXXVI (XL), Fasc.1-4, 41-46.

144. Rodica Luca, Observations on a Hamilton-Jacobi equation, Buletinul Institutului Politehnic din Iaşi, Secţia Matematică. Mecanică Teoretică. Fizică, 1989, Tom XXXV (XXXIX), Fasc.3-4,  45-50.


    October 30, 2017

Ċ
Rodica Luca Tudorache,
30 oct. 2017, 14:07
Ċ
Rodica Luca Tudorache,
30 oct. 2017, 14:40
Ċ
Rodica Luca Tudorache,
30 oct. 2017, 14:27