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21.
Uporaba Mathematice pri osnovah matematične analize : zbrano gradivo
Irena Kosi-Ulbl, 2011, učbenik za višje in visoke šole

Ključne besede: matematika, matematična analiza, visokošolski učbeniki
Objavljeno: 17.01.2011; Ogledov: 1507; Prenosov: 72
Celotno besedilo (3,96 MB)

22.
On dimension of inverse limits with upper semicontinuous set-vaulted bonding functions
Iztok Banič, 2007, izvirni znanstveni članek

Opis: We give results about the dimension of continua, obtained by combining inverselimits of inverse sequences of metric spaces and one-valued bonding maps with inverse limits of inverse sequences of metric spaces and upper semicontinuous set-valued bonding functions, by standard procedure introduced in [I. Banič, Continua with kernels, Houston J. Math. (2006) in press].
Ključne besede: mathematics, topology
Objavljeno: 31.05.2012; Ogledov: 873; Prenosov: 8
URL Povezava na celotno besedilo

23.
Inverse limits as limits with respect to the Hausdorff metric
Iztok Banič, 2007, objavljeni povzetek znanstvenega prispevka na konferenci

Ključne besede: mathematics, topology, continua, inverse limits, upper semicontinuous set-valued functions
Objavljeno: 31.05.2012; Ogledov: 699; Prenosov: 33
URL Povezava na celotno besedilo

24.
25.
Continua with kernels
Iztok Banič, 2008, izvirni znanstveni članek

Opis: In this article we introduce the concept of kernels of continua, obtained by combining inverse limits of inverse sequences of unit intervals and one-valued bonding maps with inverse limits of inverse sequences of unit intervals and upper semicontinuous set-valued bonding functions. We also show some of their properties, with special emphasis on arc-like continua.
Ključne besede: mathematics, kernels, arc-like continua
Objavljeno: 01.06.2012; Ogledov: 721; Prenosov: 22
URL Povezava na celotno besedilo

26.
27.
Fault-diameter of Cartesian product of graphs and Cartesian graph bundles
Iztok Banič, Janez Žerovnik, 2006

Opis: Cartesian graph bundles is a class of graphs that is a generalization of the Cartesian graph products. Let ▫$G$▫ be a ▫$k_G$▫-connected graph and ▫${mathcal{D}}_c(G)$▫ denote the diameter of ▫$G$▫ after deleting any of its ▫$c < k_G$▫ vertices. We prove that if ▫$G_1, G_2, dots, G_q$▫ are ▫$k_1$▫-connected, ▫$k_2$▫-connected,...,▫$k_q$▫-connected graphs and ▫$0 leq a_1 < k_1$▫, ▫$0 leq a_2 < k_2$▫,...,▫$0 leq a_q < k_q$▫ and ▫$a = a_1 + a_2 + dots + a_q + (q-1)$▫, then the fault diameter of ▫$G$▫, a Cartesian product of ▫$G_1$▫, ▫$G_2$▫,...,▫$G_q$▫, with ▫$a$▫ faulty nodes is ▫${mathcal{D}}_{a}(G) leq {mathcal{D}}_{a_1}(G_1)+{mathcal{D}}_{a_2}(G_2) + dots + {mathcal{D}}_{a_q}(G_q) + 1$▫. We also show that ▫${mathcal{D}}_{a+b+1}(G) leq {mathcal{D}}_a(F) + {mathcal{D}}_b(B) + 1$▫ if ▫$G$▫ is a graph bundle with fibre ▫$F$▫ over base ▫$B$▫, ▫$a leq k_F$▫, and ▫$b leq k_B$▫. As an auxiliary result we prove that connectivity of graph bundle ▫$G$▫ is at least ▫$k_F+k_B$▫.
Ključne besede: mathematics, graph theory, Cartesian graph bundles, Cartesian graph products, fault diameter, interconnection network
Objavljeno: 10.07.2015; Ogledov: 310; Prenosov: 13
URL Povezava na celotno besedilo

28.
Wide and fault diameters of Cartesian graph bundles
Janez Žerovnik, Iztok Banič, Rija Erveš, 2008, objavljeni povzetek znanstvenega prispevka na konferenci

Ključne besede: matematika, teorija grafov, kartezični produkt grafov
Objavljeno: 10.07.2015; Ogledov: 189; Prenosov: 6
URL Povezava na celotno besedilo

29.
Edge, vertex and mixed fault-diameters
Iztok Banič, Rija Erveš, Janez Žerovnik, 2008

Opis: Let ▫${mathcal{D}}^E_q(G)$▫ denote the diameter of a graph ▫$G$▫ after deleting any of its ▫$q$▫ edges, and ▫${mathcal{D}}^V_p(G)$▫ denote the diameter of ▫$G$▫ after deleting any of its ▫$p$▫ vertices. We prove that ▫${mathcal{D}}^E_a(G) le {mathcal{D}}^V_a(G) + 1$▫ a for all meaningful ▫$a$▫. We also define mixed fault diameter ▫${mathcal{D}}^M_{(p,q)}(G)$▫, where ▫$p$▫ vertices and ▫$q$▫ edges are deleted at the same time. We prove that for ▫$0 < l le a$▫, ▫${mathcal{D}}^E_a(G) le {mathcal{D}}^M_{(a-l,l)}(G) le {mathcal{D}}^V_a(G) + 1$▫, and give some examples.
Ključne besede: matematika, teorija grafov, povezanost, mathematics, (vertex)-connectivity, edge-connectivity, (vertex) fault-diameter, edge-fault diameter, interconnection network
Objavljeno: 10.07.2015; Ogledov: 282; Prenosov: 32
URL Povezava na celotno besedilo

30.
Paths through inverse limits
Iztok Banič, Matevž Črepnjak, Matej Merhar, Uroš Milutinović, 2009

Opis: In [I.Banič, M. Črepnjak, M. Merhar, U. Milutinović, Limits of inverse limits, Topology Appl. 157 (2010) 439-450] the authors proved that if a sequence of graphs of surjective upper semi-continuous set-valued functions ▫$f_n: X rightarrow 2^X$▫ converges to the graph of a continuous single-valued function ▫$f: X rightarrow X$▫, then the sequence of corresponding inverse limits obtained from ▫$f_n$▫ converges to the inverse limit obtained from ▫$f$▫. In this paper a more general result is presented in which surjectivity of ▫$f_n$▫ is not required. Also, the result is generalized to the case of inverse sequences with non-constant sequences of bonding maps. Finally, these new theorems are applied to inverse limits with tent maps. Among other applications it is shown that the inverse limits appearing in the Ingram conjecture (with a point added) form an arc.
Ključne besede: matematika, topologija, kontinuumi, limite, inverzne limite, navzgor polzvezne večlične funkcije, poti, loki, mathematics, topology, continua, limits, inverse limits, upper semi-continuous set-valued functions, paths, arcs
Objavljeno: 10.07.2015; Ogledov: 459; Prenosov: 15
URL Povezava na celotno besedilo

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