Seminar on Applied Mathematics

PROGRAM

Matematički Institut
Matematički fakultet
Fakultet organizacionih nauka
JUPIM

SEMINAR ZA PRIMENJENU I INDUSTRIJSKU MATEMATIKU

MI SANU, Knez Mihailova 35, sala 2

PLAN RADA SEMINARA ZA JUN 2007. GODINE

Utorak, 05.06.2007. u 14:15, Sala 2, MI SANU:

Domingos M. Cardoso, Departamento de Matemática, Universidade de Aveiro, Portugal (dcardoso@mat.ua.pt)
CONVEX QUADRATIC PROGRAMMING TECHNIQUES ON GRAPHS AND RELATED SPECTRAL RESULTS

Abstract. Convex quadratic programming upper bounds on the size of $k$-regular induced subgraphs are introduced and a necessary and sufficient for this upper bound be tight is presented. Some applications on extremal graph theory are explored. Related spectral upper bounds are deduced and an extension of the Hoffman bound for the stability number of regular graphs is obtained.

Utorak, 12.06.2007. u 14:15, SALA 2, MI SANU:

Katica (Stevanović) Hedrih, Mažinski fakultet, Niž
UPRAVLJANJE U NELINEARNIM SISTEMIMA SA TRIGEROM SPREGNUTIH SINGULARITETA

Sadrzaj: Dobitnica Povelje Jugoslovenskog udruzenja za primenjenu i industrijsku matematiku (JUPIM) za naucni rad ili naucnu monografiju publikovanu u 2006. godini izlozice svoje najznacajnije rezultate. Opis rezultata o kojima se govori u predavanju nalazi se u prilozenom .pdf dokumentu.

Nakon predavanja ce biti urucena nagrada.

Abstract. Let $R_+ = (0,\infty)$ and let ${\cal M}$ be the family of all mean values of two numbers in $R_+$ (some examples are the arithmetic, geometric and harmonic means). Given $m_1,m_2\in {\cal M}$; we say that a function $f : R_+ \to R_+$ is $(m_1,m_2)$-convex if $f(m_1(x,y)) \leq m_2(f(x), f(y))$ for all $x, y \in R_+$. The usual convexity is the special case when both mean values are arithmetic means. We study the dependence of the $(m_1,m_2)$-convexity on $m_1$ and $m_2$ and give sufficient conditions for the $(m_1,m_2)$-convexity of functions defined by Maclaurin series. The criteria involve the Maclaurin coefficients. Our results yield a class of new inequalities for several special functions such as the Gaussian hypergeometric function and a generalized Bessel function. The results will be published in a joint paper with G.D. Anderson and M. Vamanamurthy in J. Math. Anal. Appl. 2007.