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Wyniki wyszukiwania dla: EQUITABLE CHROMATIC NUMBER
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T-colorings, divisibility and circular chromatic number
PublikacjaLet T be a T-set, i.e., a finite set of nonnegative integers satisfying 0 ∈ T, and G be a graph. In the paper we study relations between the T-edge spans espT (G) and espd⊙T (G), where d is a positive integer and d ⊙ T = {0 ≤ t ≤ d (max T + 1): d |t ⇒ t/d ∈ T} . We show that espd⊙T (G) = d espT (G) − r, where r, 0 ≤ r ≤ d − 1, is an integer that depends on T and G. Next we focus on the case T = {0} and show that espd⊙{0} (G) =...
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Equitable colorings of some variation of corona products of cubic graphs
PublikacjaThe problem of determining the value of equitable chromatic number for multicoronas of cubic graphs is studied. We provide some polynomially solvable cases of cubical multicoronas and give simple linear time algorithms for equitable coloring of such graphs which use almost optimal number of colors in the remaining cases.
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Equitable coloring of corona multiproducts of graphs
PublikacjaWe give some results regarding the equitable chromatic number for l-corona product of two graphs: G and H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G.
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Equitable coloring of corona products of graphs
PublikacjaIn this paper we consider an equitable coloring of some corona products of graphs G and H in symbols, G o H). In particular, we show that deciding the colorability of G o H is NP-complete even if G is 4-regular and H is K_2. Next, we prove exact values or upper bounds on the equitable chromatic number of G o H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a path, a cycle or a complete graph.
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Eqiuitable coloring of corona products of cubic graphs is harder than ordinary coloring
PublikacjaA graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G. In this paper the problem of determinig the equitable coloring number for coronas of cubic graphs is studied. Although the problem of ordinary coloring of coronas...
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Total chromatic sum for trees
PublikacjaThe total chromatic sum of a graph is the minimum sum of colors (natural numbers) taken over all proper colorings of vertices and edges of a graph. We provide infinite families of trees for which the minimum number of colors to achieve the total chromatic sum is equal to the total chromatic number. We construct infinite families of trees for which these numbers are not equal, disproving the conjecture from 2012.
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Equitable and semi-equitable coloring of cubic graphs and its application in batch scheduling
PublikacjaIn the paper we consider the problems of equitable and semi-equitable coloring of vertices of cubic graphs. We show that in contrast to the equitable coloring, which is easy, the problem of semi-equitable coloring is NP- complete within a broad spectrum of graph parameters. This affects the complexity of batch scheduling of unit-length jobs with cubic incompatibility graph on three uniform processors to minimize...
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Infinite chromatic games
PublikacjaIn the paper we introduce a new variant of the graph coloring game and a new graph parameter being the result of the new game. We study their properties and get some lower and upper bounds, exact values for complete multipartite graphs and optimal, often polynomial-time strategies for both players provided that the game is played on a graph with an odd number of vertices. At the end we show that both games, the new and the classic...
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Equitable coloring of hypergraphs
PublikacjaA hypergraph is equitablyk-colorable if its vertices can be partitioned into k sets/colorclasses in such a way that monochromatic edges are avoided and the number of verticesin any two color classes differs by at most one. We prove that the problem of equitable 2-coloring of hypergraphs is NP-complete even for 3-uniform hyperstars. Finally, we apply the method of dynamic programming for designing a polynomial-time algorithm to...
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A 27/26-approximation algorithm for the chromatic sum coloring of bipartitegraphs
PublikacjaWe consider the CHROMATIC SUM PROBLEM on bipartite graphs which appears to be much harder than the classical CHROMATIC NUMBER PROBLEM. We prove that the CHROMATIC SUM PROBLEM is NP-complete on planar bipartite graphs with Delta less than or equal to 5, but polynomial on bipartite graphs with Delta less than or equal to 3, for which we construct an O(n(2))-time algorithm. Hence, we tighten the borderline of intractability for this...
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2-Coloring number revisited
Publikacja2-Coloring number is a parameter, which is often used in the literature to bound the game chromatic number and other related parameters. However, this parameter has not been precisely studied before. In this paper we aim to fill this gap. In particular we show that the approximation of the game chromatic number by the 2-coloring number can be very poor for many graphs. Additionally we prove that the 2-coloring number may grow...
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Equitable coloring of graphs. Recent theoretical results and new practical algorithms
PublikacjaIn this paper we survey recent theoretical results concerning conditions for equitable colorability of some graphs and recent theoretical results concerning the complexity of equitable coloring problem. Next, since the general coloring problem is strongly NP-hard, we report on practical experiments with some efficient polynomial-time algorithms for approximate equitable coloring of general graphs.
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Tight bounds on the complexity of semi-equitable coloring of cubic and subcubic graphs
PublikacjaWe consider the complexity of semi-equitable k-coloring, k>3, of the vertices of a cubic or subcubic graph G. In particular, we show that, given a n-vertex subcubic graph G, it is NP-complete to obtain a semi-equitable k-coloring of G whose non-equitable color class is of size s if s>n/3, and it is polynomially solvable if s, n/3.
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Relations between the domination parameters and the chromatic index of a graph
PublikacjaIn this paper we show bounds for the sum and the product of the domination parameters and the chromatic index of a graph. We alsopresent some families of graphs for which these bounds are achieved.
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Smartphones as tools for equitable food quality assessment
PublikacjaBackground: The ubiquity of smartphones equipped with an array of sophisticated sensors, ample processing power, network connectivity and a convenient interface makes them a promising tool for non-invasive, portable food quality assessment. Combined with the recent developments in the areas of IoT, deep learning algorithms and cloud computing, they present an opportunity for advancing wide-spread, equitable and sustainable food...
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Sharp bounds for the complexity of semi-equitable coloring of cubic and subcubic graphs
PublikacjaIn this paper we consider the complexity of semi-equitable k-coloring of the vertices of a cubic or subcubic graph. We show that, given n-vertex subcubic graph G, a semi-equitable k-coloring of G is NP-hard if s >= 7n/20 and polynomially solvable if s <= 7n/21, where s is the size of maximum color class of the coloring.
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Equitable and semi-equitable coloring of cubic graphs and its application in batch scheduling
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Equitable vertex coloring of graphs
PublikacjaW pracy podajemy wartości sprawiedliwej liczby chromatycznej dla niektórych klas grafów. Podajemy również dwa algorytmy heurystyczne dla sprawiedliwego kolorowania grafów z suboptymalna liczba koloru.
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Green and equitable analytical chemistry
PublikacjaGreen analytical chemistry introduces the ideas of reduction ofanalytical activities impact on the environment. However, to bemore sustainable, analytical chemistry should include socialaspects in greater manner. In this light‘equitable’analyticalprocedures, which are easily available in terms of price andapplicability by everyday user, are developed. These positivetrends are observed as many procedures, based on commonlyused for...
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Isolation Number versus Domination Number of Trees
PublikacjaIf G=(VG,EG) is a graph of order n, we call S⊆VG an isolating set if the graph induced by VG−NG[S] contains no edges. The minimum cardinality of an isolating set of G is called the isolation number of G, and it is denoted by ι(G). It is known that ι(G)≤n3 and the bound is sharp. A subset S⊆VG is called dominating in G if NG[S]=VG. The minimum cardinality of a dominating set of G is the domination number, and it is denoted by γ(G)....
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Chromatic scheduling in a cyclic open shop
PublikacjaPraca jest poświęcona złożoności obliczeniowej problemu cyklicznego szeregowania w systemie otwartym. Autorzy analizując wykazują, że problem jest NP-trudny dla 3 procesorów i konstruują algorytm dokładny dla przypadku dwóch procesorów.Ponadto analizowany jest zwarty wariant cyklicznego systemu otwartego. W tym przypadku autorzy pokazują, że już szeregowanie na dwóch procesorach prowadzi do problemu NP-trudnego.
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The complexity of equitable vertex coloring graphs
PublikacjaW artykule podajemy wzory na sprawiedliwą liczbę chromatyczną niektórych produktów grafowych. Ponadto przedstawiamy dwa algorytmy wielomianowe dla sprawiedliwego kolorowania grafów suboptymalną liczba kolorów.
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On trees with double domination number equal to total domination number plus one
PublikacjaA total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The total (double, respectively) domination number of a graph G is the minimum cardinality of a total (double,...
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On trees with double domination number equal to 2-domination number plus one
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A subset D subseteq V(G) is a 2-dominating set of G if every vertex of V(G)D is dominated by at least two vertices of D, while it is a double dominating set of G if every vertex of G is dominated by at least two vertices of D. The 2-domination (double domination, respectively) number of a graph G is the minimum cardinality of a 2-dominating (double dominating,...
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Chromatic cost coloring of weighted bipartite graphs
PublikacjaGiven a graph G and a sequence of color costs C, the Cost Coloring optimization problem consists in finding a coloring of G with the smallest total cost with respect to C. We present an analysis of this problem with respect to weighted bipartite graphs. We specify for which finite sequences of color costs the problem is NP-hard and we present an exact polynomial algorithm for the other finite sequences. These results are then extended...
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Bondage number of grid graphs
PublikacjaThe bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater than the domination number of G. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some strong product and direct product of two paths.
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Bounds on isolated scattering number
PublikacjaThe isolated scattering number is a parameter that measures the vulnerability of networks. This measure is bounded by formulas de- pending on the independence number. We present new bounds on the isolated scattering number that can be calculated in polynomial time.
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Bounds on isolated scattering number
PublikacjaThe isolated scattering number is a parameter that measures the vulnerability of networks. This measure is bounded by formulas de- pending on the independence number. We present new bounds on the isolated scattering number that can be calculated in polynomial time.
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Navier number and transition to turbulence
PublikacjaThe motivation behind this article is to explain a role of the Navier number (Na -dimensionless slip-length) in prediction of closures for laminar to turbulent transition undergoing via eddies detachment from the slip layer in nano-cannals. Additionally the role of the Navier number Na in universal modeling of phenomenon of enhanced mass flow rate reported in micro- and nano-channels has been explained. The Na number should be...
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On trees with double domination number equal to 2-outer-independent domination number plus one
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G is the minimum cardinality of a double dominating set of G. For a graph G=(V,E), a subset D subseteq V(G) is a 2-dominating set if every vertex of V(G)D has at least two neighbors...
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On domination multisubdivision number of unicyclic graphs
PublikacjaThe paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009), 622–628], we constructively characterize all connected unicyclic graphs with...
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Edge-chromatic sum of trees and bounded cyclicity graphs
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The circular chromatic index of some class 2 graphs
PublikacjaW artykule został wyznaczony cyrkularny indeks chromatyczny dla dwóch rodzin grafów klasy 2. Co więcej, podano nie trywialne oszacowania tego parametru dla snarków Isaacsa i Goldberga. Na koniec artykułu rozważana jest złożoność obliczeniowa problemów związanych z cyrkularnym kolorowaniem krawędzi.
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TOTAL DOMINATION MULTISUBDIVISION NUMBER OF A GRAPH
PublikacjaThe domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G. Similarly we define the total domination multisubdivision number msd_t (G) of a graph G and we show that for any connected graph G of order at least two, msd_t (G) ≤ 3. We show that for trees the total domination...
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Some variants of perfect graphs related to the matching number, the vertex cover and the weakly connected domination number
PublikacjaGiven two types of graph theoretical parameters ρ and σ, we say that a graph G is (σ, ρ)- perfect if σ(H) = ρ(H) for every non-trivial connected induced subgraph H of G. In this work we characterize (γw, τ )-perfect graphs, (γw, α′)-perfect graphs, and (α′, τ )-perfect graphs, where γw(G), τ (G) and α′(G) denote the weakly connected domination number, the vertex cover number and the matching number of G, respectively. Moreover,...
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The convex domination subdivision number of a graph
PublikacjaLet G = (V;E) be a simple graph. A set D\subset V is a dominating set of G if every vertex in V - D has at least one neighbor in D. The distance d_G(u, v) between two vertices u and v is the length of a shortest (u, v)-path in G. An (u, v)-path of length d_G(u; v) is called an (u, v)-geodesic. A set X\subset V is convex in G if vertices from all (a, b)-geodesics belong to X for any two vertices a, b \in X. A set X is a convex dominating...
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Similarities and Differences Between the Vertex Cover Number and the Weakly Connected Domination Number of a Graph
PublikacjaA vertex cover of a graph G = (V, E) is a set X ⊂ V such that each edge of G is incident to at least one vertex of X. The ve cardinality of a vertex cover of G. A dominating set D ⊆ V is a weakly connected dominating set of G if the subgraph G[D]w = (N[D], Ew) weakly induced by D, is connected, where Ew is the set of all edges having at least one vertex in D. The weakly connected domination number γw(G) of G is the minimum cardinality...
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Weakly convex domination subdivision number of a graph
PublikacjaA set X is weakly convex in G if for any two vertices a; b \in X there exists an ab–geodesic such that all of its vertices belong to X. A set X \subset V is a weakly convex dominating set if X is weakly convex and dominating. The weakly convex domination number \gamma_wcon(G) of a graph G equals the minimum cardinality of a weakly convex dominating set in G. The weakly convex domination subdivision number sd_wcon (G) is the minimum...
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Influence of edge subdivision on the convex domination number
PublikacjaWe study the influence of edge subdivision on the convex domination number. We show that in general an edge subdivision can arbitrarily increase and arbitrarily decrease the convex domination number. We also find some bounds for unicyclic graphs and we investigate graphs G for which the convex domination number changes after subdivision of any edge in G.
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On the super domination number of lexicographic product graphs
PublikacjaThe neighbourhood of a vertexvof a graphGis the setN(v) of all verticesadjacent tovinG. ForD⊆V(G) we defineD=V(G)\D. A setD⊆V(G) is called a super dominating set if for every vertexu∈D, there existsv∈Dsuch thatN(v)∩D={u}. The super domination number ofGis theminimum cardinality among all super dominating sets inG. In this article weobtain closed formulas and tight bounds for the super dominating number oflexicographic product...
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Equitable 4-coloring of cacti and edge-cacti in polynomial time
PublikacjaRozważono problem wyznaczania sprawiedliwej liczby chromatycznej kaktusów i drzew wielokątowych bez trójkątów i krawędzi wiszących. Podano wielomianowy algorytm wyznaczający pokolorowanie optymalne, oparty na paradygmacie programowania dynamicznego. Tym samym znaleziona została kolejna klasa grafów planarnych, dla której kolorowanie sprawiedliwe jawi się jako zagadnienie obliczeniowo łatwe.
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Coronas and Domination Subdivision Number of a Graph
PublikacjaIn this paper, for a graph G and a family of partitions P of vertex neighborhoods of G, we define the general corona G ◦P of G. Among several properties of this new operation, we focus on application general coronas to a new kind of characterization of trees with the domination subdivision number equal to 3.
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Graphs with isolation number equal to one third of the order
PublikacjaA set D of vertices of a graph G is isolating if the set of vertices not in D and with no neighbor in D is independent. The isolation number of G, denoted by \iota(G) , is the minimum cardinality of an isolating set of G. It is known that \iota(G) \leq n/3 , if G is a connected graph of order n, , distinct from C_5 . The main result of this work is the characterisation of unicyclic and block graphs of order n with isolating number...
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On trees attaining an upper bound on the total domination number
PublikacjaA total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. The total domination number of a graph G, denoted by γ_t(G), is the minimum cardinality of a total dominating set of G. Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International Journal of Graphs and Combinatorics 1 (2004), 69-75] established the following upper bound on the total domination...
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Equitable Coloring of Graphs. Recent Theoretical Results and New Practical Algorithms
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Block graphs with large paired domination multisubdivision number
PublikacjaThe paired domination multisubdivision number of a nonempty graph G, denoted by msdpr(G), is the smallest positive integer k such that there exists an edge which must be subdivided k times to increase the paired domination number of G. It is known that msdpr(G) ≤ 4 for all graphs G. We characterize block graphs with msdpr(G) = 4.
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On the independence number of some strong products of cycle-powers
PublikacjaIn the paper we give some theoretical and computational results on the third strong power of cycle-powers, for example, we have found the independence numbers alpha((C^2_10)^⊠3) = 30 and alpha((C^4 _14)^⊠3) = 14. A number of optimizations have been introduced to improve the running time of our exhaustive algorithm used to establish the independence number of the third strong power of cycle-powers. Moreover, our results establish...
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Comparison of the Efficiency of Turbo Codes with Mechanisms of Reducing the Number of Iterations
PublikacjaThe paper presents the construction of encoders and decoders turbo codes with different number of states. Simulation results of the transmission quality of the turbo codes were presented. Decoders for turbo codes have worked with a fixed number of iterations and with the mechanisms reducing the number of iterations. Data were transmitted in Outdoor to Indoor & Pedestrian B environment for data rate 384 kbps. The SOVA algorithm...
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Entanglement and Nonlocality are Inequivalent for Any Number of Parties
PublikacjaUnderstanding the relation between nonlocality and entanglement is one of the fundamental problems in quantum physics. In the bipartite case, it is known that these two phenomena are inequivalent, as there exist entangled states of two parties that do not violate any Bell inequality. However, except for a single example of an entangled three-qubit state that has a local model, almost nothing is known about such a relation in multipartite...
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Bounds on the vertex-edge domination number of a tree
PublikacjaA vertex-edge dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every edge of $G$ is incident with a vertex of $D$ or a vertex adjacent to a vertex of $D$. The vertex-edge domination number of a graph $G$, denoted by $\gamma_{ve}(T)$, is the minimum cardinality of a vertex-edge dominating set of $G$. We prove that for every tree $T$ of order $n \ge 3$ with $l$ leaves and $s$ support vertices we have $(n-l-s+3)/4...
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An Alternative Proof of a Lower Bound on the 2-Domination Number of a Tree
PublikacjaA 2-dominating set of a graph G is a set D of vertices of G such that every vertex not in D has a at least two neighbors in D. The 2-domination number of a graph G, denoted by gamma_2(G), is the minimum cardinality of a 2-dominating set of G. Fink and Jacobson [n-domination in graphs, Graph theory with applications to algorithms and computer science, Wiley, New York, 1985, 283-300] established the following lower bound on the 2-domination...
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Chromatic Scheduling of 1- and 2-Processor UET Tasks on Dedicated Machines with Availability Constraints
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Chromatic scheduling of 1- and 2-processor uet tasks on dedicated machines with availability constraints.
PublikacjaRozważono uogólnienie klasycznego szeregowania jednostkowych zadań jedno- i dwuprocesorowych na maszynach dedykowanych. Przyjęty model pozwala na naturalne wprowadzenie wszystkich klasycznych kryteriów optymalizacyjnych dla harmonogramów. Zaproponowano algorytmy wielomianowe dla systemów rzadkich.
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Impact of Cyclist Facility Availability at Work on the Number of Bike Commuters
PublikacjaThe article describes the results of research designed to establish whether cycle provision can influence the number of employees commuting by bike. To that end, employee surveys were conducted in three IT companies in 2012 and 2016. The questionnaire asked about travel behaviour and what the staff thought about their company’s provision of cyclist facilities. Since 2012 each of the companies has moved its head office and the...
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Paired domination versus domination and packing number in graphs
PublikacjaGiven a graph G = (V(G), E(G)), the size of a minimum dominating set, minimum paired dominating set, and a minimum total dominating set of a graph G are denoted by γ (G), γpr(G), and γt(G), respectively. For a positive integer k, a k-packing in G is a set S ⊆ V(G) such that for every pair of distinct vertices u and v in S, the distance between u and v is at least k + 1. The k-packing number is the order of a largest kpacking and...
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A lower bound on the total outer-independent domination number of a tree
PublikacjaA total outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V(G)D is independent. The total outer-independent domination number of a graph G, denoted by gamma_t^{oi}(G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every nontrivial tree T of order n with l leaves we have gamma_t^{oi}(T) >= (2n-2l+2)/3,...
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Chromatic monitoring technique for thickness measurementof thin transparent films.IV Workshopon Atomic and Molecular Physics.
PublikacjaW pracy opisano nową technikę monitorowania grubości cienkich warstw podczas procesu ich syntezy. Jest to optyczna metoda oparta na zdegenerowanej analizie widmowej tzw. modulacji chromatycznej. Umożliwia ona precyzyjny ciągły pomiar zmian grubości wzrastających warstw stosowanych w optyce.
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Mechanical exfoliation and layer number identification of single crystal monoclinic CrCl3
PublikacjaAfter the recent finding that CrI3, displays ferromagnetic order down to its monolayer, extensive studies have followed to pursue new two-dimensional (2D) magnetic materials. In this article, we report on the growth of single crystal CrCl3 in the layered monoclinic phase. The system after mechanical exfoliation exhibits stability in ambient air (the degradation occurs on a time scale at least four orders of magnitude longer than...
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An upper bound on the 2-outer-independent domination number of a tree
PublikacjaA 2-outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)D has a at least two neighbors in D, and the set V(G)D is independent. The 2-outer-independent domination number of a graph G, denoted by gamma_2^{oi}(G), is the minimum cardinality of a 2-outer-independent dominating set of G. We prove that for every nontrivial tree T of order n with l leaves we have gamma_2^{oi}(T) <= (n+l)/2,...
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An upper bound on the total outer-independent domination number of a tree
PublikacjaA total outer-independent dominating set of a graph G=(V(G),E(G)) is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V(G)D is independent. The total outer-independent domination number of a graph G, denoted by gamma_t^{oi}(G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every tree T of order n >= 4, with l leaves and s support vertices we have...
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Realistic noise-tolerant randomness amplification using finite number of devices
PublikacjaRandomness is a fundamental concept, with implications from security of modern data systems, to fundamental laws of nature and even the philosophy of science. Randomness is called certified if it describes events that cannot be pre-determined by an external adversary. It is known that weak certified randomness can be amplified to nearly ideal randomness using quantum-mechanical systems. However, so far, it was unclear whether randomness amplification...
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Application of Regression Line to Obtain Specified Number of Points in Reduced Large Datasets
PublikacjaModern measurement techniques like scanning technology or sonar measurements, provide large datasets, which are a reliable source of information about measured object, however such datasets are sometimes difficult to develop. Therefore, the algorithms for reducing the number of such sets are incorporated into their processing. In the reduction algorithms based on the...
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An upper bound for the double outer-independent domination number of a tree
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D, and the set V(G)\D is independent. The double outer-independent domination number of a graph G, denoted by γ_d^{oi}(G), is the minimum cardinality of a double outer-independent dominating set of G. We prove...
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total number and biomass of bacteria in drinking water distribution systems.
PublikacjaIn the vast water supply network using traditional methods of treatment it is often impossible to maintain a constant and acceptable microbiological quality of water. In Poland the main reason of bacterial re-growth is presence of organic matter and nutrients in the circulating water and prolonged water retention in the network systems due to the decrease of water consumption, which has been observed for the last 20 years. In the...
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Performance of data transmission in UMTS with turbo code about decreased number of states
PublikacjaIn the paper a structure of turbo encoder and decoder about decreased number of states has been described. The simulation results of transmission performance based on turbo coding without the reduction of the number of iterations for the uplink and downlink of WCDMA/FDD interface have been presented. The SOVA algorithm for turbo decoding has been used. The investigations have been carried out for Outdoor to Indoor & Pedestrian...
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A lower bound on the double outer-independent domination number of a tree
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D, and the set V(G)D is independent. The double outer-independent domination number of a graph G, denoted by gamma_d^{oi}(G), is the minimum cardinality of a double outer-independent dominating set of G. We...
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The outer-connected domination number of a graph
PublikacjaW pracy została zdefiniowana liczba dominowania zewnętrznie spójnego i przedstawiono jej podstawowe własności.
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On the total restrained domination number of a graph
PublikacjaW pracy przedstawione są ograniczenia i własności liczby dominowania podwójnie totalnego.
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On the doubly connected domination number of a graph
PublikacjaW pracy została zdefiniowana liczba dominowania podwójnie spójnego i przedstawiono jej podstawowe własności.
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Lower bound on the domination number of a tree.
PublikacjaW pracy przedstawiono dolne ograniczenie na liczbę dominowania w drzewach oraz przedstawiono pełną charakterystykę grafów ekstremalnych.
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Complexity Issues on of Secondary Domination Number
PublikacjaIn this paper we study the computational complexity issues of the problem of secondary domination (known also as (1, 2)-domination) in several graph classes. We also study the computational complexity of the problem of determining whether the domination and secondary domination numbers are equal. In particular, we study the influence of triangles and vertices of degree 1 on these numbers. Also, an optimal algorithm for finding...
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DO WE NEED NAVIER NUMBER? – FURTHER REMARKS AND COMPARISON WITH ANOTHER DIMENSIONLESS NUMBERS
PublikacjaThis paper presents a role of the Navier number (Na-dimensionless slip-length) in universal modelling of flow reported in micro- and nano-channels like: capillary biological flows, fuel cell systems, micro-electro-mechanical systems and nano-electro-mechanical systems. Similar to another bulk-like and surface-like dimensionless numbers, the Na number should be treated as a ratio of internal viscous to external viscous momentum...
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All graphs with paired-domination number two less than their order
PublikacjaLet G=(V,E) be a graph with no isolated vertices. A set S⊆V is a paired-dominating set of G if every vertex not in S is adjacent with some vertex in S and the subgraph induced by S contains a perfect matching. The paired-domination number γp(G) of G is defined to be the minimum cardinality of a paired-dominating set of G. Let G be a graph of order n. In [Paired-domination in graphs, Networks 32 (1998), 199-206] Haynes and Slater...
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Determination of the uncertainty of mass flow measurement using the orifice for different values of the Reynolds number
PublikacjaStandard orifice flowmeters are widely used in the chemical and energy industry. Therefore, it is essential to know how accurate the measurements made with these instruments are. The paper presents an estimation of measurement uncertainty of a liquid mass flow using the orifice plate. The authors will present the influence of ranges of the Reynolds number on the estimated uncertainty, obtained on the basis of simulation and laboratory...
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Optimum number of actuators to minimize the cross-sectional area of prestressable cable and truss structures
PublikacjaThis paper describes a new computational method for determining the optimum number of actuators to design the optimal and economic cross-sectional area of pin-jointed assemblies based on the conventional force method. The most active members are selected to be prestressed to redistribute stress in the whole structure, resulting in regulating the internal force of bars that face high stress. Reducing stress in critical members allows...
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Empirical Probability Distributions with Unknown Number of Components
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Non-standard binary weighted number systems
PublikacjaZdefiniowano szeroką klasę binarnych systemów wagowych. Wszystkie sa wzajemnie jednoznaczne ale mogą być zupełne lub niezupełne. Jeżeli wagi systemu są kolejnymi liczbami naturalnymi to system jest minimalny.Jesli wagi sa kolejnymi potęgami podstawy Z to system jest maksymalny. W przestrzeni między tymi systemami znajdują się inne systemy binarne. Kilka z nich przedstawiono w referacie.
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Lower bound on the paired domination number of a tree
PublikacjaW pracy przedstawione jest ograniczenie dolne dla liczby dominowania parami oraz scharakteryzowane są wszystkie drzewa ekstremalne.
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Graphs with convex domination number close to their order
PublikacjaW pracy opisane są grafy z liczbą dominowania wypukłego bliską ilości ich wierzchołków.
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Porównanie wydajności modyfikacji algorytmu Proof-number search uwzględniających wartości remisowe
PublikacjaProof-number search to znana rodzina algorytmów służących do wyznaczania wartości pozycji w nielosowych grach dwóch graczy z pełną informacją. W wersji podstawowej pn-search doskonale radzi sobie z wyszukiwaniem strategii wygrywającej jednego z graczy. Jednak istnieje wiele znanych gier, w których obydwaj gracze posiadają jedynie strategię remisującą (Młynek, Awari, Warcaby). W niniejszej pracy porównano wydajność dwóch modyfikacji...
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Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublikacjaLet M be a smooth compact and simply-connected manifold with simply-connected boundary ∂M, r be a fixed odd natural number. We consider f, a C1 self-map of M, preserving ∂M . Under the assumption that the dimension of M is at least 4, we define an invariant Dr(f;M,∂M) that is equal to the minimal number of r-periodic points for all maps preserving ∂M and C1-homotopic to f. As an application, we give necessary and sufficient...
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Estimation of the minimal number of periodic points for smooth self-maps of odd dimensional real projective spaces
PublikacjaLet f be a smooth self-map of a closed connected manifold of dimension m⩾3. The authors introduced in [G. Graff, J. Jezierski, Minimizing the number of periodic points for smooth maps. Non-simply connected case, Topology Appl. 158 (3) (2011) 276-290] the topological invariant NJD_r[f], where r is a fixed natural number, which is equal to the minimal number of r-periodic points in the smooth homotopy class of f. In this paper smooth...
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Computations of the least number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublikacjaLet $r$ be an odd natural number, $M$ a compact simply-connected smooth manifold, $\dim M\geq 4$, such that its boundary $\partial M$ is also simply-connected. We consider $f$, a $C^1$ self-maps of $M$, preserving $\partial M$. In [G. Graff and J. Jezierski, Geom. Dedicata 187 (2017), 241-258] the smooth Nielsen type periodic number $D_r(f;M,\partial M)$ was defined and proved to be equal to the minimal number of $r$-periodic points...
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Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds
PublikacjaLet M be a smooth closed simply-connected 4-dimensional manifold, f be a smooth self-map of M with fast grow of Lefschetz numbers and r be a product of different primes. The authors calculate the invariant equal to the minimal number of r-periodic points in the smooth homotopy class of f.
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Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers
PublikacjaLet f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math....
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Microbiological Survey in Two Arctic Fjords: Total Bacterial Number and Biomass Comparison of Hornsund and Kongsfjorden
PublikacjaTwo microbiological parameters: total bacterial number (TBN) and biomass (BBM) were studied in two Arctic fjords: Hornsund and Kongsfjorden. Samples were collected from three sampling points in each fjord, from various water depth layers: from the surface to 75 m depth. Total bacterial number and biomass were examined using the DAPI staining and direct count method. The greater amount of bacteria, as well as highest bacterial biomass...
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Microbiological Survey in Two Arctic Fjords: Total Bacterial Number and Biomass Comparison of Hornsund and Kongsfjorden
PublikacjaTwo microbiological parameters: total bacterial number (TBN) and biomass (BBM) were studied in two Arctic fjords: Hornsund and Kongsfjorden. Samples were collected from three sampling points in each fjord, from various water depth layers: from the surface to 75 m depth. Total bacterial number and biomass were examined using the DAPI staining and direct count method. The greater amount of bacteria, as well as highest bacterial biomass...
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improved noniterative residue division for small number ranges
Publikacjaw pracy zaprezentowano multiplikatywny algorytm dzielenia w systemie resztowym i projekt 12-bitowego dzielnika dla modułów 5-bitowych. w algorytmie zastosowano obliczanie przybliżonej odwrotności dzielnika i mnozenie przez dzielną. binarna reprezentacja dzielnika jest dekomponowana na dwa segmenty 6-bitowe, co umożliwia obliczenie w środowisku fpga poprzez odwzorowanie realizowane jako odczyt pamięci. w pracy podano udoskonalony...
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Lower bound on the weakly connected domination number of a tree
PublikacjaPraca dotyczy dolnego ograniczenia liczby dominowania słabo spójnego w drzewach (ograniczenie ze względu na ilość wierzchołków i ilość wierzchołków końcowych w drzewie).
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Nordhaus-Gaddum results for the convex domination number of a graph
PublikacjaPraca dotyczy nierówności typu Nordhausa-Gadduma dla dominowania wypukłego.
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Complex multiplier based on the polynomial residue number system
PublikacjaPrzedstawiono próbę zaprojektowania mnożnika zespolonego 4x4 opartego na algorytmie Skavantzosa i Stouraitisa. W algorytmie stosuje siękodowanie liczb n-bitowych jako wielomianów stopnia 7 w pierścieniu wielomianów modulo (x^8-1) z n/4-bitowymi współczynnikami. Mnożenie zespolone jest wykonywane jako 8-punktowy splot cykliczny. Podanoopóżnienie i złożoność sprzętową jak również porównanie ze standardowym.rozwiązaniem.
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Lower bound on the distance k-domination number of a tree
PublikacjaW artykule przedstawiono dolne ograniczenie na liczbę k-dominowania w drzewach oraz scharakteryzowano wszystkie grafy ekstremalne.
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Computation of the convolution with use of the polynomial residue number system.
PublikacjaPrzedstawiono użycie wielomianowych systemów resztowych do obliczania splotu w cyfrowych układach dużej skali integracji VLSI.
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Local Nusselt number evaluation in the case of jet impingement
PublikacjaJet impingement still is one of demanding cases regarding computational fluid dynamics, due to its highly turbulent behaviour, with occurrence of turbulent-laminar transition. Even recently developed methods exhibit some drawbacks – RANS based simulations lack accuracy, LES and DNS based ones require too much computational time. Hybrid methods also exist, but their development and validation is in progress. Nevertheless, CFD application...
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Combinatorial scheme of finding minimal number of periodic points for smooth self-maps of simply connected manifolds
PublikacjaLet M be a closed smooth connected and simply connected manifold of dimension m at least 3, and let r be a fixed natural number. The topological invariant D^m_r [f], defined by the authors in [Forum Math. 21 (2009), 491-509], is equal to the minimal number of r-periodic points in the smooth homotopy class of f, a given self-map of M. In this paper, we present a general combinatorial scheme of computing D^m_r [f] for arbitrary dimension...
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Torque Transmitted by Multi-plate Wet Clutches in Relation to Number of Friction Plates and Their Dimensions
PublikacjaIn the paper results of experimental tests on multi-plate wet clutch torque capacity for various diameters and numbers of friction plates are presented. Construction of an apparatus for laboratory tests of wet clutch engagement, drag torque and maximum torque is shown. Methodology of maximum torque capacity experiment and hydraulic circuit diagram, which supplies a motor and an actuator for the experiment are described. Analytically...
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Ocena poprawności działania algorytmu proof-number search na strukturze digrafu acyklicznego
PublikacjaAlgorytm proof-number search jest znanym algorytmem służącym do rozwiązywania gier logicznych. Rozwiązanie gry jest jednoznaczne ze znalezieniem optymalnej strategii i pozwala przeprowadzić rozgrywkę w sposób pozwalający na osiągnięcie najlepszego możliwego wyniku. Jedną z największych wad tego algorytmu, naturalnie pracującego na strukturze drzewa, jest wielokrotne rozwijanie identycznych poddrzew gry co prowadzi do nadmiarowego...
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DETERMINATION OF THE HYDROXYL NUMBER OF GROUND TIRE RUBBER PARTICLES VIA MODIFIED TEST METHOD FOR ISOCYANATE GROUPS
PublikacjaNowadays, considering the environmental trends and law regulations associated with the circular economy, it is very important to seek for the methods of by-products and waste utilization. The example of such material, which requires the attention and recycling method is ground tire rubber generated during recycling of post-consumer car tires. It can be introduced into various polymer matrices as a filler, but to enhance its effectivity...
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Uncertainty of mass flow measurement using centric and eccentric orifice for Reynolds number in the range 10,000 ≤ Re ≤ 20,000
PublikacjaThe article analyses the impact of the Reynolds number on the estimated uncertainty of the mass flow rate measurement using an orifice plate. The objects of the research were two types of orifices: centric (ISA) and eccentric, with the diameter ratio β = 0.5. Studies were performed by Monte Carlo simulation and experiments for Reynolds numbers in the range 10,000 ≤ Re ≤ 20,000. The obtained results have shown that for both orifice...
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Fast Calibration-Free Single-Anchor Indoor Localization Based on Limited Number of ESPAR Antenna Radiation Patterns
Publikacja— In this article, we investigate how the calibrationfree single-anchor indoor localization algorithm developed for base stations equipped with electronically steerable parasitic array radiator (ESPAR) antennas can further be improved. By reducing the total number of ESPAR antenna radiation patterns used in localization process, one can significantly reduce the time needed for an object localization. Performed localization measurements...