Cezar Lupu

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Research & Publications

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\blacklozenge Statement of research philosophy

\bullet \Huge{\mathbf{RESEARCH}} \Huge{\mathbf{PAPERS}}

1. Geodesics in the Heisenberg group revisited and the isoperimetric deficit for curves in \mathbb{R}^{2n}, in preparation.

2. A note on some rational zeta series representations of Glasser type for Apery and Catalan constants, in progress. (with Derek Orr)

3. Remarks on the evaluation of some multiple zeta values and multiple t-values, in progress.

4. Walker’s self-improvement inequality revisited, in progress.

5. Wallis ratio type series representations for Apery and Catalan constants, in progress, (with Tudorel Lupu)

6. Approximations of Apery’s constant \zeta(3) and rational series representations involving \zeta(2n), submitted. (with Derek Orr) arXiv

7. Another look at some new Cauchy-Schwarz type inner product inequalities, Applied Mathematics and Computation, vol. 231 (2014), 463–477. (with Dan Schwarz)

8. Mean value problems of Flett type for a Volterra operator, Electronic Journal of Differential Equations, vol. 2013, nr. 53/2013, 1-7.

9. Variational like inequality problems involving set-valued mappings and generalized monotonicity, Journal of Optimization Theory and Applications, vol. 155 (2012), 79-99. (with Nicusor Costea and Daniel Alexandru Ion)

10. Arithmetic functions, prime counting function and polynomials, Mathematical Inequalities and Applications, vol. 15 (2012), 549-558. (with Vlad Matei)

11. On a class of variational-hemivariational inequalities involving set-valued mappings, Advances in Pure and Applied Mathematics, vol. 1 (2010), 233-246. (with Nicusor Costea) arXiv

12. Mean value theorems for some linear integral operators, Electronic Journal of Differential Equations, vol. 2009, nr. 117/2009, 1-15. (with Tudorel Lupu)

\bullet \Huge{\mathbf{EXPOSITORY}} \Huge{\mathbf{AND}} \Huge{\mathbf{ELEMENTARY}} \Huge{\mathbf{PAPERS}}

1. Algebraic-geometric proofs for the Weitzenbock and Hadwiger-Finsler inequalities revisited, The Mathematical Gazette, in revision.

2. On an Erdos inscribed triangle inequality revisited, Elemente der Mathematik,  in revision. (with Stefan Spataru)

3. A new proof of the Finsler-Hadwiger inequality, American Mathematical Monthly, vol. 124, pp. 73.

4. Una aplicacion de la desigualidad isoperimetrica, Universo Math, vol. 2, no. 2/2015, art. 4. (with Razvan Gelca)

5. Matrix adjugates and additive commutators, Gazeta Matematica (A-series), vol. 24 (2011), 90-97.

6. Another trace inequality for unitary matrices, Gazeta Matematica (A-series), vol. 28, nr. 3-4/2010, 137-140

7. Improved Finsler-Hadwiger inequality revisited, Gazeta Matematica (A-series), vol. 28, nr. 3-4/2010, 130-133. (with Virgil Nicula)

8. Refinements of the Finsler-Hadwiger reverse inequality, Gazeta Matematica (A-series), vol. 28, nr. 1-2/2010, 49-53. (with Vlad Matei, Constantin Mateescu, Mihai Opincariu)

9. An olympiad problem: Zeros of functions in the image of a Volterra operator, Gazeta Matematica (A-series), vol. 27, nr. 3/2009, 209-213. (with Radu Gologan)

10. Sharpening the Hadwiger-Finsler inequality, Crux Mathematicorum with Math. Mayhem, vol. 34, nr.2/2008, 97-101. (with Cosmin Pohoata)

11. About a nice inequality, Mathematical Reflections, vol. 2, nr.1/2007, 1-5. (with Cosmin Pohoata)

\bullet \Huge{\mathbf{PROPOSED}} \Huge{\mathbf{PROBLEMS}} \Huge{\mathbf{IN}} \Huge{\mathbf{JOURNALS}}

I. AMERICAN MATHEMATICAL MONTHLY

1. Problem 11245 (vol. 113, October 2006, with Tudorel Lupu)
2. Problem 11290 (vol. 114, April 2007, with Tudorel Lupu)
3. Problem 11313 (vol. 114, October 2007, with Tudorel Lupu)
4. Problem 11341 (vol. 115, February 2008, with Tudorel Lupu)
5. Problem 11349 (vol. 115, March 2008)
6. Problem 11360 (vol. 115, April 2008, with Tudorel Lupu)
7. Problem 11375 (vol. 115, June-July 2008)
8. Problem 11417 (vol. 116, February 2009, with Tudorel Lupu)
9. Problem 11429 (vol. 116, April 2009, with Tudorel Lupu)
10. Problem 11458 (vol. 116, October 2009, with Vicentiu Radulescu)
11. Problem 11474 (vol. 117, January 2010, with Valentin Vornicu)
12. Problem 11486 (vol. 117, February 2010)
13. Problem 11496 (vol. 117, April 2010, with Benjamin Bogosel)
14. Problem 11517 (vol. 117, August-September 2010, with Tudorel Lupu)
15. Problem 11527 (vol. 117, October 2010)
16. Problem 11532 (vol. 117, November 2010, with Vicentiu Radulescu)
17. Problem 11542 (vol. 117, December 2010, with Vicentiu Radulescu)
18. Problem 11548 (vol. 118, January 2011, with Tudorel Lupu)
19. Problem 11561 (vol. 118, March 2011)
20. Problem 11626 (Vol. 119, February 2012)
21. Problem 11632 (Vol. 119, March 2012, with Dan Schwarz)
22. Problem 11647 (Vol. 119, May 2012, with Tudorel Lupu)
23. Problem 11667 (vol. 119, October 2012, with Dan Schwarz)
24. Problem 11680 (vol. 119, December 2012, with Benjamin Bogosel)
25. Problem 11692 (vol. 120, February 2013, with Stefan Spataru)
26. Problem 11748 (vol. 121, January 2014, with Tudorel Lupu)
27. Problem 11759 (vol. 121, February 2014, with Octavian Ganea)
28. Problem 11780 (vol. 121, May 2014, with Tudorel Lupu)
29. Problem 11814 (vol. 122, January 2015)
30. Problem 11819 (vol. 122, February 2015)
31. Problem 11855 (vol. 122, August-September 2015)
32. Problem 11871 (vol. 122, November 2015, with Stefan Spataru)
33. Problem 11884 (vol. 123, January 2016, with Tudorel Lupu)
34. Problem 11905 (vol. 123, April 2016)
35. Problem 11981 (vol. 124, May 2017)

II. COLLEGE MATHEMATICS JOURNAL

1. Problem 896 (vol. 40, March 2009, with Darij Grinberg)
2. Problem 901 (vol. 40, May 2009)
3. Problem 918 (vol. 41, January 2010)
4. Problem 925 (vol. 41, March 2010, with Tudorel Lupu)
5. Problem 927 (Vol. 41, May 2010, with Tudorel Lupu)
6. Problem 929 (Vol. 41, May 2010, with Vlad Matei)
7. Problem 932 (vol. 41, September 2010, with Tudorel Lupu)
8. Problem 936 (vol. 41, November 2010, with Tudorel Lupu)
9. Problem 939 (vol. 41, November 2010)
10. Problem 949 (vol. 42, March 2011)
11. Problem 975 (Vol. 43, March 2012)
12. Problem 990 (Vol. 43, November 2012, with \fbox{Ion Cucurezeanu})
13. Problem 999 (vol. 44, March 2013, with Stefan Spataru)
14. Problem 1008 (vol. 44, September 2013)

III. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS

1. Problem 2010-1 (vol. 2010, with Vicentiu Radulescu)
2. Problem 2011-1 (vol. 2010, with Vicentiu Radulescu)
3. Problem 2011-3 (vol. 2010, with Vicentiu Radulescu)

IV. GAZETA MATEMATICA (A-series)

1. Problem 287 (vol. 27, No. 3/2009, with Tudorel Lupu)
2. Problem 293 (vol. 27, No. 4/2009, with Tudorel Lupu)
3. Problem 300 (vol. 28, No. 1-2/2010, with Alin Galatan)
4. Problem 303 (vol. 28, No. 1-2/2010, with Tudorel Lupu)
5. Problem 312 (vol. 28, nr. 3-4/2010, with Cristinel Mortici)
6. Problem 316 (vol. 28, nr. 3-4/2010, with Andrei Deneanu)
7. Problem 327 (vol. 29, nr. 1-2/2011 with Tudorel Lupu)
8. Problem 333 (vol.29, nr. 1-2/2011, with Cristinel Mortici)
9. Problem 323 (vol. 29, nr. 3-4/2011, with Flavian Georgescu)
10. Problem 335 (vol. 29, nr. 3-4/2011, with Tudorel Lupu)
11. Problem 353 (vol. 30, nr. 1-2/2012, with Calin Popescu)
12. Problem 353 (vol. 30, nr. 1-2/2012, with Marius Cavachi)
13. Problem 388 (vol. 31, no. 1-2/2013, with Stefan Spataru)
14. Problem 395 (vol. 31, no. 3-4/2013, with Stefan Spataru)
15. Problem 402 (vol. 31, no. 3-4/2013)
16. Problem 414 (vol. 32, no. 1-2/2014)

V. MATHEMATICS MAGAZINE

1. Problem 1824 (vol. 82, January 2009)
2. Problem 1852 (vol. 83, September 2010, with Radu Gologan)
3. Problem 1857 (vol. 83, December 2010, with Tudorel Lupu)
4. Problem Q 1039 (vol. 87, April 2014)
5. Problem Q 1060 (vol. 89, April 2016)


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