Constantin Buse

Email: c.buse@sms.edu.pk

Course: Mathematical Analysis, Differential Equations

Publications

1. Didactic Publications-Selected Papers

[DP1] C. Bu»se, Gabriela Bu»se, An elementary evaluation of the Euler constant, V^alcea School Journal of Mathematics No.4-5 (2005), 3-4 (in Romanian).

[DP2] C. Bu»se, G. Bu»se, and V. Vulcanov, About of class of functions which admits primitive functions, Octogon Mathematical Maga- zine, Vol. 9 (2001), 380-385 (in English), Mathematics Didactic Data-
base, 2003f05391.

[DP3] C. Bu»se, About of some competition problem, The Mathemat- ical Journal of Craiova, VIII, (1), 1997-1998 (in Romanian).

[DP4] A. B¸al¸a»sel, C. Bu»se, C. T. Drugan, V. Cuc, and M. Megan, Problems for disciples and teachers, Publishing House{ Almarom-Rm. V^alcea(1997){ISBN 973-98053-3-3, 260 pages (in Romanian).

[DP5] M. Megan, C. Bu»se, D. R. Lat»cu, Mathematical Analysis, for 9-12 classes, Publishing House{ Amarcord-Timi»soara(1995){ ISBN 973-97051-1-4-6, 277 pages (in Romanian).

[DP6] C. Drugan, C. Bu»se, The solutions of the problems given of math's competition in 1988, Mathematic for Disciples(1988), Slatina Olt County, 17 pages (in Romanian).

[DP7] C. Bu»se, F. Dumitrel, Calculus of natural powers of some quadratic matrix with distinct proper values and the solved of certain systems of recursions, Mathematic for Disciples (1987), Slatina-Olt County, 7 pages (in Romanian).

[DP8] C. Bu»se, C. T. Drugan, Methods and Techniques for the solved of certain problems on geometrical place, The V^alcea School(1986), Rm. V^alcea, 7 pages (in Romanian).

2 Research Monographs

[RM2] Constantin Bu»se, Linear semigroups on Banach spaces and evolution semigroups on the space of almost periodic functions, Pub- lishing House EUBEEA and EUROSTAMPA, Timi»soara, (2003), 172 pages, ISBN 973-673-005-0, (in Romanian);

[RM1] Constantin Bu»se, Asymptotic behavior of evolutionary processes Publishing House SEDONA, Timi»soara, (1998), 172 pages, ISBN 973- 9345-14-X, (in Romanian);

3 Selected Research Papers

[RP46] N.S. Barnett, C. Bu»se, P. Cerone and S.S. Dragomir, Some GrÄus type inequalities for vector-valued functions in Banach spaces and applications (submitted).

[RP45] (ISI-journal) C. Bu»se, P. Cerone, S.S. Dragomir, and A. Sofo, Uniform asymptotic stability of periodic discrete systems in Banach spaces, Journal of Difference Equations and Applications Vol. 11, No. 12, October 2005, 1081-1088.

[RP44] (ISI-journal) C. Bu»se, P. Cerone, S.S. Dragomir, and J. Roumeliotis, A refinement of GrÄuss inequality for the Bochner integral of vector-valued functions in Hilbert spaces and applications, accepted for publication in Journal of the Korean Mathematical Society.

[RP43](ISI-journal) C. Bu»se, N. S. Barnett, P. Cerone, S. S. Dragomir, Integral characterizations for exponential stability of semigroups and evolution families on Banach spaces, accepted (27 November 2004) for publication in Bulletin of the Belgian Mathematical Society-Simon Stevin, to appear in 2006.

[RP42] (ISI-journal) C. Bu»se, C. P. Niculescu, and J. Pecaric, Asymptotic stability and integral inequalities for solutions of linear systems on Radon-Nikodym spaces, Mathematical Inequalities and Applications, Volume 8, Number 2(2005), 347-356, Zbl:02212040, Reviewer: Dagmar Medkova (Praha).

[RP41](ISI-journal) C. Bu»se, S. S. Dragomir, A Kallman-Rota Inequality for Evolution Semigroups, Mathematical Inequality and Applications, Volume 7, Number 1, January 2004, 95-101, MR 2035353: Reviewer: Gaston Mandata N'Guerekata.

[RP40] Sorina B^arz¸a, Constantin Bu»se, & Josip Pecaric, New characterizations of asymptotic stability for evolution families on Banach spaces, Electron. J. Di®. Equations., Vol. 2004 (2004), No. 38, pp. 1-9. MR:2005b:34112, Reviewer: Roland Schnaubelt. Zbl: 02100279, Reviewer: Andras Batkai(Roma)

[RP39] C. Bu»se, A characterization of exponential stability for periodic evolution families in terms of lower semi-continuous functionals, Electronic Journal of Qualitative Theory of Di®erential Equations, Proc. 7th Coll. QTDE (2004), No. 5 1-7; http://www.math.u-szeged.hu/ejqtde/, Zbl:02186185, Reviewer: Gen Qi Xu (Tianjin)

[RP38] C. P. Niculescu, C. Bu»se, The Hardy- Landau-Littlewood Inequalities with Less Smoothness, Journal of Inequalities in Pure and Applied Mathematics, Vol. 4, Issue 3 (GI8), 2003, Article 51, pp. 1-8, http://jipam.vu.edu.au, Zbl:02107619, Reviewer: Hans F. GÄunzler.

[RP37] C. Bu»se& V. Lupulescu, Exponential stability of linear and almost periodic systems on Banach spaces, Electron. J. Di®. Equations., Vol.2003(2003), No. 125, pp. 1-7. MR:2004i:47076, Reviewer: Olu- sola Akinydele.

[RP36] Constantin Bu»se, Gheorghe C¸ainiceanu and Ciprian Preda, A class of exponentially stable semigroups on Banach spaces, International Journal of Di®erential Equations and Applications, Academic Publications, vol. 7, No. 1(2003), 43-48. MR: 1991458.

[RP35] Constantin Bu»se & Oprea Jitianu, A new theorem on exponen tial stability of evolution families on Banach spaces, Electronic Journal of Di®erential Equations, USA, Vol. 2003(2003), No. 14, pp.1-10. Zbl: 0189.6914; MR: 2003k:47050, Reviewer: Ralph Chill. Zbl: 105347034, Reviewer: Miklavz Mastinsek (Maribor)

[RP34] C. Bu»se and O. Jitianu, Datko-Pazy type theorems for strongly continuous semigroups, IJPAM, International Journal of Pure and Ap- plied Mathematics, Academic Publications, 2 (2002), no. 3, 281-286.
Zbl: 0181.0497.

[RP33] C. Bu»se, O. Jitianu and C. Preda, Exponential Stability for Solutions of Linear Di®erential Equations with Periodic Coe±cients, International Journal of Differential Equations and Applications, Aca- demic Publications, vol.5, No.1 (2002), 45-54. MR: 2003d:34114.

[32] (ISI-journal) N. S. Barnett, C. Bu»se, P. Cerone and S. S. Dragomir, Ostrowski's Inequality for Vector-Valued Functions and Applications, Computers and Mathematics with Applications, (Pergamon-Elsevier), USA, 44(2002), 559-572;
MR:2003h:26025.

[RP31] C. Bu»se, The Spectral Mapping Theorem for Evolution Semi- groups on the space of Asymptotically Almost Periodic Functions defined on the Half Line, Electronic Journal of Di®erential Equations, USA, Vol. 2002(2002), No. 70, pp. 1-11. Zbl: 1010.47027, Reviewer: Boris Rubin; MR: 2003h:47078, Reviewer: C.J.K. Batty.

[RP30] C. Bu»se, S. S. Dragomir and A. Sofo, On the Ostrowski i nequality for vector-valued functions of bounded semi-variation and applications, New Zealand Journal of Mathematics, Vol. 31(2002), 137- 152. Zbl: 0189.4480, Reviewer: Gheorghe Toader; MR: 2003j:26013, Reviewer:E. Thandapani.

[RP29] N. S. Barnett, C. Bu»se, P. Cerone and S. S. Dragomir, On Weighted Ostrowski Type Inequalities for Operators and Vector-valued functions, Journal of Inequalities in Pure and Applied Mathematics, Melbourne, Australia, vol. 3, Number 1 (2002), Paper 12. Zbl: 0992.26016, Reviewer: C.P. Niculescu; MR:2002m: 26022, Reviewer: Javier Soria.

[RP28] (ISI-journal) C. Bu»se, S. S. Dragomir, A Theorem of Rolewicz's type on Solid Function Spaces, Glasgow Mathematical Journal, 44(2002), 125-135 Zbl: 017.47475; MR: 2003a:47088, Reviewer: Min He.

[RP27] C. Bu»se and C.T. Drugan, The numerical indexes associated to a q-periodic evolution families and integral characterizations for ex ponential stability Di®erential Equations and Applications vol2 (2002), Y. J. Cho, J. K. Kim, K. S. Ha (eds.), Nova Science Publishers, Hunt ington, New-York, 29-41, USA.

[RP26] (ISI-journal) C. Bu»se, S. S. Dragomir, J. Roumeliotis and
A. Sofo, Generalized trapezoid type inequalities for vector-valued functions and applications, Mathematical Inequalities & Applications, Vol ume 5, Number 3 (2002), 435-450, Croatia. Zbl: 1008.26018, Reviewer: J. Sandor; MR: 2003d:26025, Reviewer: Vania D. Mascioni.

[RP25] C. Bu»se, S. S. Dragomir, V. Lupulescu, Characterizations of Stability for Strongly Continuous Semigroups by Convolutions, Inter national Journal of Di®erential Equations and Applications, Academic Publications, Vol. 2, No.1 (2001), 103-109. MR:2004f:47053, Reviewer: Min He.

[RP24] C. Bu»se, S. S. Dragomir, A Rolewicz's type Theorem. An evolution semigroup approach, Electonic Journal Di®erential Equations, Vol. 2001(2001), No.45, 1-5, Texas, USA; Zbl: 0991.47024, MR: 2002i:47047, Reviewer: Roland Schnaubelt.

[RP23] C. Bu»se and S. S. Dragomir, A Rolewicz's type Theorem for strongly measurable evolution families of bounded linear operators on Banach spaces, Electronic Journal of Di®erential Equations, Vol. 2001(2001), No. 70, pp. 1-5, Texas, USA; Zbl: 0985.47031, Reviewer: Yang Dachun, MR: 2002j:47069, Reviewer: R.F.Datko.

[RP22] C. Bu»se, A. Pogan, Individual Exponential Stability for Evolution Families of Linear and Bounded Operators, New Zealand Journal of Mathematics, Vol. 30(2001), 15-24. Zbl: 0990.35020, Reviewer: Catalin Badea, MR: 2002c:93147, Reviewer: Brigit Jacob.

[RP21] S. S. Dragomir, C. Bu»se, M.V. Boldea and L. Br¸aescu, A gene ralisation of the trapezoidal rule for the Riemann-Stieltejes integral and applications, Nonlinear Analysis Forum, South Korea, 6(2), 337-351, (2001). Zbl: 01777.438; MR: 2003e:26024, Reviewer: D. Acu.

[RP20] S. S. Dragomir, J. Sunde, C. Bu»se, Some new inequalities for Je®reys divergence measure in information theory, Tamsui Oxford Journal of Math. Sciences, 16, No.2 (2000), 295-309, Taipei, Taiwan. Zbl: 0994.94017, Reviewer: Puspha N. Rathie; MR: 2002:94024, Reviewer: L. Losonczi.

[RP19] D. Barbu, C. Bu»se, Z. Peter, Global Problems in the space of Matrices, Octagon Mathematical Magazine, Bra»sov, Vol. 8, Nr.2, 297-305 (2000).

[RP18] C. Bu»se, Perron Conditions and its Connection with Exponential Stability of Solutions for Integro-Di®erential Equations on the half line, International Journal of Di®erential Equations and Applications , (invited paper) 1, 1A, (2000), 23-30. Zbl: 1005.47038, Reviewer: Wilfried Hazod; MR: 2001f:47068, Reviewer: Qing Rong Liu.

[RP17] C. Bu»se, Exponential Stability for Periodic Evolution Families of Bounded Linear Operators, Rend. Sem. Matematico. Univers. Pol. Torino., Vol. 59(1)(2001), 17-22. MR:1967496.

[RP16] M. Reghi»s, C. Bu»se, On the Perron-Bellman theorem for C0-se- migroups and periodic evolutionary processes in Banach spaces, Italian Journal of Pure and Applied Mathematics, Nr. 4 (1998), 155-166. Zbl: 0981.47030, Reviewer: Nguyen Hong Thai, MR: 2001b:47067.

[RP15] C. Bu»se, On nonuniform asymptotic stability of impulse differential equations, Demonstratio Mathematica, Poland, Vol. 31, No. 3 (1998), 485-497. Zbl: 0928.34011, Reviewer: S. Kostadinov, 99m:3417, Reviewer: O.S. Chernikova.

[RP14] C. Bu»se, On the Perron-Bellman theorem for evolutionary processes with exponential growth in Banach spaces, New Zealand Journal of Mathematics, Auckland, Vol. 27(1998), 183-190. Zbl: 0972.47027, Reviewer: Robert Alicki, MR: 2001b:47063.

[RP13] C. Bu»se, D. Barbu, Some remarks about the Perron condition for C0- semigroups, Analele Universit¸at»ii din Timi»soara, vol.35, fasc. 1 (1997), 3-8. Zbl: 1003.93043, MR: 1875631.

[RP12] C. Bu»se, D. Barbu, The Lyapunov equations and nonuniform exponential stability, Mathematical Reports, Bucure»sti, 49, 1-2 (1997), 25-31. Zbl: 0893.93031, Reviewer: V. Wihstutz; MR: 99k:47084, Reviewer: O. Akinye.le.

[RP11] C. Bu»se, Asymptotic Stability of Evolutors and Normed Function Spaces, Rend. Sem. Mat. Univ. Pol. Torino, 55, (2), 1997, 109- 122. Zbl: 0959.93030, Reviewer: A.V. Balakrishnan; MR: 2000c:47077, Reviewer: Timothy Randolph.

[RP10] C. Bu»se, Nonuniform exponential stability and Orlicz func tions, Annales Societatis Mathematicae Polonae, Series I: Commenta- tiones Mathematicae, 36 (1996), 47-55. Zbl: 0871.34036, MR: 98g:34083, Reviewer: O. Akinye.le.

[RP9] C. Bu»se, S.S. Dragomir, D. Barbu, The convergence of some sequences connected to Hadamard's inequality, Demonstratio Mathe- matica, Poland, 29,(1), 1996, 53-59. Zbl:0860.26010, Reviewer: Josip Pecaric, MR: 97d:26016.

[RP8](ISI-journal) S.S. Dragomir and C. Bu»se, Re¯nements of Hadamard's inequality for Multiple Integrals, Utilitas Mathematica, Canada, 47, 1995, 193-198. Zbl: 0838.26013, Reviewer: I. Ra»sa, MR: 96b:26023.

[RP7] C. Bu»se, Admissibility and exponential stability of evolution operators, Annals of Univ. Timi»soara, 33, (1), 1995, (3-17). Zbl: 087834053, MR: 1975305.

[RP6] C. Bu»se, On nonuniform exponential stability of evolutionary processes, Rend. Sem. Mat. Univers. Pol. Torino, 52,(4), 1994, 395-406. Zbl: 0836.47047, MR: 96i:47071, Reviewer: Angelo Favini.

[RP5] M. Megan and C. Bu»se, Dichotomies and Lyapunov functions in Banach spaces, Bull. Math. Soc. Sci. Math. Rumanian, 37, (85), 3-4, 1993, 103-113. Zbl: 0845.47031; MR: 97j:34069.

[RP4] D. Barbu, S.S. Dragomir, C. Bu»se, A probabilistic argument for the convergence of some sequences associated to Hadamard's inequality, Studia Math., Cluj-Napoca, 38, (1), 1993, 29-33. Zbl: 0829.26009, Reviewer: J. Sandor, MR: 1863680.

[RP3] M. Megan and C. Bu»se, On uniform exponential dichotomy of observable evolution operators, Rend. Sem. Univers. Pol. Torino, 50,(2), 1992, 183-194. Zbl: 0835.47028; MR: 95a:34068, Reviewer: R. F. Datko.

[RP2] P. Preda and C. Bu»se, On uniform N-dichotomy for evolutionary processes in Banach spaces, Annals of Univ. Timi»soara, 30, (1), 1992, 105-117. Zbl: 0821.34054; MR: 96a:47072, Reviewer: R.F. Datko.

[RP1] C. Bu»se and M.Megan, On uniform exponential stability of ob- servable evolutionary processes, Annals of Univ. Timi»soara, 29 (1), (1991), 29-32. Zbl: 0787.34042; MR: 1336196.

LIST OF RECENT PAPERS OF BOOKS WHERE MY (JOINTLY) WORK WAS BEEN QUOTED:

a) David N. Cheban, Asymptotically Almost Periodic Solutions of Differential Equations, World Scientific Publishing Company, in press;

b) Inder Jeet Taneya, Refinement inequalities among symmetric divergence measures, the Australian Journal of Mathematical Analysis and Applications, Vol.2, Issue 1, Article 8, pp.1-23(2005);

c) Adina Luminita Sasu, Admisibilitate si proprietati asimptotice ale cociclilor, Colectia Matematici Moderne, Editura Politehnica, Timisoara (2005);

d) Bogdan Sasu, Comportari asimptotice ale sistemelor autonome, Colectia Matematici Moderne, Editura Politehnica, Timisoara (2005);

e) (ISI-journal) Adina Luminita Sasu, New criteria for exponential stability of variational difference equations, Applied Mathematics Letters (2005), to appear;

f) Inder Jeet Taneja, Generalized Symmetric Divergence Measures and Inequalities, Arxiv Preprint Math. ST/0501301(2005)-arxiv.org.

g) Inder Jeet Taneja, Bounds on non-symmetric divergence measures in terms of symmetric divergence measures, Arxiv math. PR/0506256 (2005) arxiv.org.

h) I. J. Taneja, Bounds on triangular discrimination, harmonic mean and symmetric chi-square divergences, Arxiv preprint math. PR/0505238 (2005) arxiv. org;

i) I. J. Taneja, P. Kumar, Generalised non-symmetric divergence measures and inequalities, Arxiv Preprint math. PR/0505238 (2005) arxiv.org.

j) P. Kumar, I. J. Taneja, On unified generalizations of relative Jensen-Shannon and arithmetic-geometric divergence, Arxiv Preprint math. PR/0501299 (2005) arxiv.org.

k) D. S. Mitrinovici, J. Pecaric, J. Kraljevici, On Landau’s theorems, Glas. Math. Ser. III, 39(59), 2004, no. 2, 257-264;

l) S.S. Dragomir, A Sequence of Mappings Associated with the Hermite-Hadamard Inequalities and Applications, Applications of Mathematics (Springer), Vol. 49(2) (2004), 123-140;

m) P. Cerone, Y. J. Cho, S.S. Dragomir, J. K. Kim, S. S. Kim, Norm estimates for the difference between Bochner’s integral and the convex continuation of function’s values, Austral. J. Math. Anal. And Applications, 1(2) 2004, article 8;

n) S.S. Dragomir, C.I. Preda, Some Landau Type inequalities for functions whose derivatives are Holder continuous, Nonlinear Analysis Forum, 9 (2004) no.1, 25-31;

o) Ujevici Nenad, Error inequalities for a corrected interpolating polynomial, New York Journal Math. 10(2004), 69-81;

p) Abdelader Elkoutri and Mohamed Aziz Taoudi, Spectral inclusions and stability results for strongly continuous semi-groups, International Journal of Mathematical Sciences IJMMS 2003:37(2003), 2379-2387

q) (ISI-journal) Cerone P. Dragomir S. S Roumeliotis J., Gruss inequality in terms of Delta semi-norms and applications, Integral Transforms Special Functions 14(2003), no.3, 205-216.

r) Dragomir S. S, Properties of Some Sequences of Mappings associated to the Hermite-Hadamard Inequality, SUT-journal of Mathematics (Japan), Vol. 38 No.1 (2002), 1-16.

s) Dragomir S. S., A refinement of Ostrowski inequality for absolutely continuous functions and applications, Acta Math. Vietnam, 27(2002), no.2, 203-217.

t) D. Cruz-Uribe and C.J. Neugebauer, Sharp Error Bounds for the trapezoidal rule and Simpson’s rule, Journal of Inequalities in Pure and Applied Mathematics, vol. 3, issue 4, article 49(2002);

u) Mohamed Akkouchi, A result on the mapping H of S.S. Dragomir with applications, Facta Universitatis (Nis), Ser Math. Inform. 17(2002), 5-12.

v) (ISI-journal) Gou-Sheng Yang and Kuei-Lin Tseng, On certain multiple integral inequalities related to Hermite-Hadamard inequality, Utilitas Mathematica, Vol. 62(2002), 131-142;

w) David N. Cheban, Uniform Exponential Stability of Linear Periodic Systems in Banach Spaces, Electronic Journal of Differential Equations, Vol. 2001(2001) No. 03. 1-12;

x) (ISI-journal) Dragomir S. S., On the Hadamard’s inequality for convex functions on the coordinates in a rectangle plane, Taiwanese Journal Math. 5(2001), no.4 775-788.

y) Roland Schnaubelt, Well posed-ness and asymptotic behavior of non-autonomous linear evolution equations, Evolutionequations semi-groups and functional analysis (Milano-2000), 318-338, Prog. Non-linear Differential Equations Appl. Birkhauser-Basel (2002);

z) (ISI-journal) Steve Clark, Yuri Latushkin S. Montgomery-Smith and Timothy Randolph, Stability Radius and Internal Versus External Stability in Banach spaces: An Evolution Semi-group Approach, SIAM Journal of Control and Optimization 38(6), 2000 1757-1793.

aa) Carmen Chicone and Yuri Latushkin Evolution Semi-groups in Dynamical Systems and Differential Equations, Mathematical Surveys and Monographs, Vol. 70, American Mathematical Society , Providence R.I. (1999);

bb) (ISI-journal) Nguyen Van Minh, Frank Rabiger and Roland Schnaubelt, Exponential Stability, Exponential Expansive-ness and Exponential Dichotomy of Evolution Equations on the Half-Line Integral Equatio