**Seminar on Applied Mathematics**

**PROGRAM**

Matematički fakultet

Fakultet organizacionih nauka

JUPIM

MI SANU, Knez Mihailova 35, sala 2

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** 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. **

__Utorak, 19.06.2006. u 14:15, sala 2 MI SANU:__

* Slavik Jablan, Radmila Sazdanović, Matematički institut SANU * KNOT THEORY PROGRAM "LINKNOT"

Abstract: The Mathematica-based knot theory program LinKnot is the extension of the program Knot2000 (K2K) written by M.Ochiai and N.Imafuji. LinKnot is the knot theory program that works with knots and links (KLs) given in the Conway notation. Conway symbols are the input used for creating Dowker codes or P-data (the main input for K2K functions). Instead of a graphical input or Dowker codes, for the first time in a computer program you can use human-comprehensive Conway notation of KLs represented as a Mathematica string and work with links, and not only with knots. For all KLs there is no restriction on the number of crossings. The program provides also the complete data base of alternating KLs with at most 12 crossings, and non-alternating KLs with at most 11 crossings, and the data base of basic polyhedra with at most 20 crossings. More datailed abstract you can find in the attached .pdf file.

__Utorak, 26.06.2007. u 14:15, sala 2, MI SANU:__

* Matti Vuorinen, University of Turku, Finland vuorinen@utu.fi *

GENERALIZED CONVEXITY AND INEQUALITIES

** 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. **

** RUKOVODIOCI SEMINARA **

** Vera Kovačević-Vujčić Milan Dražić **