Glasnik Matematicki 

About: Glasnik Matematicki is an academic journal published by University of Zagreb. The journal publishes majorly in the area(s): Diophantine equation & Mathematics. It has an ISSN identifier of 0017-095X. Over the lifetime, 680 publications have been published receiving 4294 citations.

Compact embeddings of vector valued Sobolev and Besov spaces

Abstract: The main result of this paper is a generalization and sharpening of the Aubin-Dubinskii lemma concerning compact subsets in vectorvalued Lebesque spaces. In addition, there are given some new embedding results for vector valued Besov spaces.

Solution of the Ulam stability problem for quartic mappings

Abstract: In 1940 S. M. Ulam proposed at the University of Wisconsin the problem: "Give conditions in order for a linear mapping near an approximately linear mapping to exist." In 1968 S. Jvl. Ulam proposed the general problem: "When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?" In 1978 P. 1\1. Gruber proposed the Ulam type problem: "Suppose a mathematical object satisfies a certain property approximately. Is it then possible to approximate this object by objects, satisfying the property exactly?" According to P. lvl. Gruber this kind of stability problems is of particular interest in probability theory and in the case of functional equations of different types. In 1982-1998 we solved the above Ulam problem, or equivalently the Ulam type problem for linear mappings and also established analogous stability problems for quadratic and cubic mappings. In this paper we introduce the new quartic mappings F : X ---t Y , satisfying the new quartic functional equation F(XI + 2X2) + F(XI 2X2) + 6F(Xl) "" 4 [F(XI + X2) + F(XI X2) + 6F(X2)] for a1l2-dimensional vectors (Xl,X2) E X2, with X a linear space (Y: "" a real complete linear space), and then solve the Ulam stability problem for the above mappings F. 1. QUARTIC FUNCTIONAL EQUATION DEFINITION 1.1. Let X be a linear space and let Y be a real complete linear space. Then a mapping F : X --t Y, is called quartic, if the new quartic 1991 Mathematics Subject Classification. 39B.

One-dimensional flow of a compressible viscous micropolar fluid: a local existence theorem

Abstract: An initial-boundary value problem for one-dimensional flow of a compressible viscous heat-conducting micropolar fluid is considered. It is assumed that the fluid is thermodinamicaly perfect and politropic. A global-in-time existence theorem is proved. The proof is based on a local existence theorem, obtained in the previous paper [4]. 1. Statement of the problem and the main result In this paper we consider an initial-boundary value problem for one-dimensional flow of a compressible viscous heat-conducting micropolar fluid, being in thermodinamical sense perfect and politropic (see [4] and references therein). Let p, v, 01 and e denotes respectively the mass density, velocity, microrotation velocity and temperature in the Lagrangean description. Then the problem that we consider has the formulation as follows: op 20V _ 0 ot + p ox , ov 0 (OV) 0 t = ox P ox K ox(pe), pow =A[P~(pOW) _ 01], ot ox ox oe 2 OV 2(OV)2 2(001)2 2 0 ( oe) PEii = -Kp e ox + p ox + p ox + 01 + Dp ox P x (1.4) in ]0, l[xR+, v(O, t) = v(l, t) = 0, 01(0, t) = 01(1, t) = 0, oe oe ox (0, t) = ox (1, t) = 0, for t E R+, p(x, 0) = Po(x), v(x, 0) = vo(x), (1.5) (1.6) (1. 7)

Some Rational Diophantine Sextuples

Abstract: A famous problem posed by Diophantus was to find sets of distinct positive rational numbers such that the product of any two is one less than a rational square. Some sets of six such numbers are presented and the computational algorithm used to find them is described. A classification of quadruples and quintuples with examples and statistics is also given.

Topologies generated by discrete subspaces

Abstract: A topological space X is called discretely generated if for ev- ery subset A X we have A=(fD:D A and D is a discrete subspace of Xg. We say that X is weakly discretely generated if A X and A6A implies DnA6; for some discrete D A. It is established that sequential spaces, mono- tonically normal spaces and compact countably tight spaces are discretely generated. We also prove that every compact space is weakly discretely generated and under the Continuum Hypothesis any dyadic discretely gen- erated space is metrizable.