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Search results for: on-line ramsey number
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A NOTE ON ON-LINE RAMSEY NUMBERS FOR QUADRILATERALS
PublicationWe consider on-line Ramsey numbers defined by a game played between two players, Builder and Painter. In each round Builder draws an the edge and Painter colors it either red or blue, as it appears. Builder’s goal is to force Painter to create a monochromatic copy of a fixed graph H in as few rounds as possible. The minimum number of rounds (assuming both players play perfectly) is the on-line Ramsey number \widetilde{r}(H) of...
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On-line Ramsey Numbers of Paths and Cycles
PublicationConsider a game played on the edge set of the infinite clique by two players, Builder and Painter. In each round, Builder chooses an edge and Painter colours it red or blue. Builder wins by creating either a red copy of $G$ or a blue copy of $H$ for some fixed graphs $G$ and $H$. The minimum number of rounds within which Builder can win, assuming both players play perfectly, is the \emph{on-line Ramsey number} $\tilde{r}(G,H)$. In...
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Application of Regression Line to Obtain Specified Number of Points in Reduced Large Datasets
PublicationModern 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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Liczby Ramseya on-line dla różnych klas grafów
PublicationRozpatrujemy grę rozgrywaną na nieskończonej liczbie wierzchołków, w której każda runda polega na wskazaniu krawędzi przez jednego gracza - Budowniczego oraz pokolorowaniu jej przez drugiego gracza - Malarkę na jeden z dwóch kolorów, czerwony lub niebieski. Celem Budowniczego jest zmuszenie Malarki do stworzenia monochromatycznej kopii wcześniej ustalonego grafu H w jak najmniejszej możliwej liczbie ruchów. Zakładamy, że gracze...
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On some open questions for Ramsey and Folkman numbers
PublicationWe discuss some of our favorite open questions about Ramsey numbers and a related problem on edge Folkman numbers. For the classical two-color Ramsey numbers, we first focus on constructive bounds for the difference between consecutive Ramsey numbers. We present the history of progress on the Ramsey number R(5,5) and discuss the conjecture that it is equal to 43.
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Polyhedral Ramsey Numbers
PublicationGiven two polygons or polyhedrons P1 and P2, we can transform these figures to graphs G1 and G2, respectively. The polyhedral Ramsey number Rp(G1,G2) is the smallest integer n such that every graph, which represents polyhedron on n vertices either contains a copy of G1 or its complement contains a copy of G2. Using a computer search together with some theoretical results we have established some polyhedral Ramsey numbers, for example...
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On some Zarankiewicz numbers and bipartite Ramsey Numbers for Quadrilateral
PublicationThe Zarankiewicz number z ( m, n ; s, t ) is the maximum number of edges in a subgraph of K m,n that does not contain K s,t as a subgraph. The bipartite Ramsey number b ( n 1 , · · · , n k ) is the least positive integer b such that any coloring of the edges of K b,b with k colors will result in a monochromatic copy of K n i ,n i in the i -th color, for some i , 1 ≤ i ≤ k . If n i = m for all i , then we denote this number by b k ( m )....
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Shannon Capacity and Ramsey Numbers
PublicationRamsey-type theorems are strongly related to some results from information theory. In this paper we present these relations.
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Dataset of non-isomorphic graphs of the coloring types (K4,K4;n), 1<n<R(4,4)
Open Research DataFor K4 graph, a coloring type (K4,K4;n) is such an edge coloring of the full Kn graph, which does not have the K4 subgraph in the first color (representing by no edges in the graph) or the K4 subgraph in the second color (representing by edges in the graph).The Ramsey number R(4,4) is the smallest natural number n such that for any edge coloring of...
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Dataset of non-isomorphic graphs being coloring types (K5-e,Km-e;n), 2<m<5, 1<n<R(K5-e,Km-e)
Open Research DataFor K5-e and Km-e graphs, the type coloring (K5-e,Km-e;n) is such an edge coloring of the full Kn graph, which does not have the K5-e subgraph in the first color (no edge in the graph) or the Km-e subgraph in the second color (exists edge in the graph). Km-e means the full Km graph with one edge removed.The Ramsey number R(K5-e,Km-e) is the smallest...
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Dataset of non-isomorphic graphs being coloring types (K6-e,Km-e;n), 2<m<5, 1<n<R(K6-e,Km-e)
Open Research DataFor K6-e and Km-e graphs, the type coloring (K6-e,Km-e;n) is such an edge coloring of the full Kn graph, which does not have the K6-e subgraph in the first color (no edge in the graph) or the Km-e subgraph in the second color (exists edge in the graph). Km-e means the full Km graph with one edge removed. The Ramsey number R(K6-e,Km-e) is the smallest...
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Dataset of non-isomorphic graphs of the coloring types (K4,Km-e;n), 2<m<5, 1<n<R(K4,Km-e)
Open Research DataFor K4 and Km-e graphs, a coloring type (K4,Km-e;n) is such an edge coloring of the full Kn graph, which does not have the K4 subgraph in the first color (representing by no edges in the graph) or the Km-e subgraph in the second color (representing by edges in the graph). Km-e means the full Km graph with one edge removed.The Ramsey number R(K4,Km-e)...
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Jerzy Proficz dr hab. inż.
PeopleJerzy Proficz, Ph.D. is the director of the Centre of Informatics – Tricity Academic Supercomputer & networK (CI TASK) at Gdansk University of Technology, Poland. He earned his Ph.D. (2012) in HPC (High Performance Computing) in the subject of supercomputer resource provisioning and management for on-line data processing D.Sc. (2022) in the discipline: Information and Communication Technology. Author and co-author of over 50...
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Dataset of non-isomorphic graphs of the coloring types (K3,Km;n), 2<m<7, 1<n<R(3,m)
Open Research DataFor K3 and Km graphs, a coloring type (K3,Km;n) is such an edge coloring of the full Kn graph, which does not have the K3 subgraph in the first color (representing by no edges in the graph) or the Km subgraph in the second color (representing by edges in the graph).The Ramsey number R(3,m) is the smallest natural number n such that for any edge coloring...
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Dataset of non-isomorphic graphs of the coloring types (Km,K3-e;n), 4<m<8, 1<n<R(Km,K3-e)
Open Research DataFor Km and K3-e graphs, a coloring type (Km,K3-e;n) is such an edge coloring of the full Kn graph, which does not have the Km subgraph in the first color (representing by no edges in the graph) or the K3-e subgraph in the second color (representing by edges in the graph). K3-e means the full Km graph with one edge removed.The Ramsey number R(Km,K3-e)...
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Dataset of non-isomorphic graphs of the coloring types (K3,Km-e;n), 2<m<7, 1<n<R(K3,Km-e).
Open Research DataFor K3 and Km-e graphs, a coloring type (K3,Km-e;n) is such an edge coloring of the full Kn graph, which does not have the K3 subgraph in the first color (representing by no edges in the graph) or the Km-e subgraph in the second color (representing by edges in the graph). Km-e means the full Km graph with one edge removed.The Ramsey number R(K3,Km-e)...
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Dataset of non-isomorphic graphs being coloring types (K4-e,Km-e;n), 2<m<7, 1<n<R(K4-e,Km-e)
Open Research DataFor K4-e and Km-e graphs, the type coloring (K4-e,Km-e;n) is such an edge coloring of the full Kn graph, which does not have the K4-e subgraph in the first color (no edge in the graph) or the Km-e subgraph in the second color (exists edge in the graph). Km-e means the full Km graph with one edge removed.The Ramsey number R(K4-e,Km-e) is the smallest...
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A Note on Shannon Capacity for Invariant and Evolving Channels
PublicationIn the paper we discuss the notion of Shannon capacity for invariant and evolving channels. We show how this notion is involved in information theory, graph theory and Ramsey theory.
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Dataset of non-isomorphic graphs being coloring types (K3-e,Km-e;n), 2<m<8, 1<n<R(K3-e,Km-e)
Open Research DataFor K3-e and Km-e graphs, the type coloring (K3-e,Km-e;n) is such an edge coloring of the full Kn graph, which does not have the K3-e subgraph in the first color (no edge in the graph) or the Km-e subgraph in the second color (exists edge in the graph). Km-e means the full Km graph with one edge removed.The Ramsey number R(K3-e,Km-e) is the smallest...
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A survey on known values and bounds on the Shannon capacity
PublicationIn this survey we present exact values and bounds on the Shannon capacity for different classes of graphs, for example for regular graphs and Kneser graphs. Additionally, we show a relation between Ramsey numbers and Shannon capacity.
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Determination of non-steroidal anti-inflammatory drugs in natural waters using off-line and on-line SPE followed by LC coupled with DAD-MS
PublicationOpisano dwie metody pozwalające na jednoczesne oznaczanie zawartości niesterydowych leków przeciwzapalnych (difluisal, diklofenak, naproksen, tolmetin, fenoprofen, ibuprofen) w próbkach wodnych. Próbki przygotowywano do analizy z użyciem techniki ekstrakcji do fazy stałej (off-line i on-line). Natomiast oznaczeń końcowych dokonano z użyciem LC-DAD-MS. Sprawdzono kilka różnych kolumienek ekstrakcyjnych i wybrano RP-18 jako najlepsze...
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Usługi on-line w kontekście mobilnym - jakościowe badanie obserwacyjne
PublicationArtykuł przedstawia wyniki badania obserwacyjnego, majacego na celu zidentyfikowanie czynników kształtujących u użytkowników chęć skorzystania z usług on-line za pomocą urządzeń mobilnych takich jak smartfon, tablet lub laptop. Przeprowadzono badania obserwacyjne, w których użytkownicy (7 osób) przez 14 dni notowali swoją aktywność w zakresie korzystania z usług on-line z dostępnych urządzeń w powiązaniu z czynnikami uznawanymi...
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Kamila Kokot-Kanikuła mgr
PeopleKamila Kokot-Kanikuła is a digital media senior librarian at Gdańsk University of Technology (GUT) Library. She works in Digital Archive and Multimedia Creation Department and her main areas of interests include early printed books, digital libraries, Open Access and Open Science. In the Pomeranian Digital Library (PDL) Project she is responsible for creating annual digital plans, transferring files on digital platform, and promoting...
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Elipsometric data analysis used in on-line metal passivation monitoring
PublicationWykorzystano technikę elipsometrii monochromatycznej do opisu on-line warstw tlenkowych, elektroosadzanych na miedzi. Elipsometria jest w stanie dostarczyć informacji odnośnie grubości i współczynników załamania światła układów warstwowych, jednakże wymagane w tym celu jest zbudowanie matematycznego modelu odwzorowującego stałe optyczne układu badanego. W powyższej pracy przedyskutowane zostały różne metody dopasowywania modelu...
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Nowa metoda obliczania rozpływu prądów zwarciowych w przewodach odgromowych linii wysokiego napięcia
PublicationReferat przedstawia nowatorską metodę obliczania wartości prądów płynących w przewodach odgromowych w czasie zwarć, pozwalającą na dobór przewodów odgromowych pod względem wytrzymałości cieplnej. Proponowana metoda charakteryzuje się większą dokładnością i większą uniwersalnością niż powszechnie stosowane metody, pozwalając tym samym na dobór przewodów odgromowych z mniejszym ryzykiem niepewności. Prezentowana metoda obliczeniowa...
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Possibility of exact determination of thermal and flow degradation symptoms in on-line power objects diagnostics
PublicationPrzedyskutowano problem dokładności tworzenia symptomów degradacji dotyczących sprawności urządzeń składowych dużych obiektów energetycznych. W referacie zajęto się szczególnie metodami tworzenia wzorców sprawnej pracy w przypadku określania sprawności w układzie on-line i porównano ją z określeniem w systemie off-line. Do odtwarzania stanu referencyjnego zastosowano sieć neuronową statystyczną (SSN, ang. ANN) o nieskokowych funkcjach...
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OCENA UZIEMIEŃ SŁUPÓW LINII ELEKTROENERGETYCZNYCH ZWŁASZCZA POSADOWIONYCH NA GRUNTACH O WYSOKIEJ REZYSTYWNOŚCI
PublicationW artykule została omówiona problematyka pomiaru i oceny właściwości uziemień słupów linii elektroenergetycznych z wykorzystaniem przebiegów wolno-i szybkozmiennych. Uzyskanie odpowiednio niskiej wartości rezystancji uziemienia słupa posadowionego na gruncie o rezystywności powyżej 1000Ωm może być trudne. Praca zawiera analizę zmian właściwości statycznych i udarowych uziemień w funkcji rezystywności...
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Katalogi i inwentarze księgozbiorów Zygmunta Pusłowskiego
PublicationPrzedmiotem artykułu są katalogi i inwentarze księgozbioru hrabiego Zygmunta Pusłowskiego, wchodzące w skład rękopiśmiennego Archiwum Pusłowskich, znajdującego się w Bibliotece Jagiellońskiej. Praca ma na celu nakreślenie sylwetki twórcy tych spisów oraz przedstawicieli czarkowskiej linii rodu Pusłowskich, począwszy od Wojciecha i Józefy z Druckich-Lubeckich. Przedstawiony zostanie stan zachowanych spisów inwentarzowych zgrupowanych...
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On-Line Partitioning for On-Line Scheduling with Resource Conflicts
PublicationWithin this paper, we consider the problem of on-line partitioning the sequence of jobs which are competing for non-sharable resources. As a result of partitioning we get the subsets of jobs that form separate instances of the on-line scheduling problem. The objective is to generate a partition into the minimum number of instances such that the response time of any job in each instance is bounded by a given constant. Our research...
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Porównanie działania transformatora symetryzującego (zygzak) z aktywnym energoelektronicznym symetryzatorem prądów fazowych linii niskiego napięcia
PublicationNa potrzeby planowania sieci niskiego napięcia operatorzy systemów dystrybucyjnych (OSD) zakładają symetryczne warunki obciążenia linii. Z roku na rok, rośnie liczba rozproszonych systemów fotowoltaicznych (PV) zainstalowanych w sieciach niskiego napięcia, których większość to małe jednofazowe systemy dachowe. Dodatkowo, do niesymetrii obciążenia przyczyniają się instalowane masowo pompy ciepła i ładowane jednofazowo samochody...
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On-line ranking of split graphs
PublicationA vertex ranking of a graph G is an assignment of positive integers (colors) to the vertices of G such that each path connecting two vertices of the same color contains a vertex of a higher color. Our main goal is to find a vertex ranking using as few colors as possible. Considering on-line algorithms for vertex ranking of split graphs, we prove that the worst case ratio of the number of colors used by any on-line ranking algorithm...
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Arsalan Muhammad Soomar Doctoral Student
PeopleHi, I'm Arsalan Muhammad Soomar, an Electrical Engineer. I received my Master's and Bachelor's Degree in the field of Electrical Engineering from Mehran University of Engineering and Technology, Jamshoro, Sindh, Pakistan. Currently enrolled as a Doctoral student at the Gdansk University of Technology, Gdansk, Poland. Also worked in Yellowlite. INC, Ohio as a Solar Design Engineer. HEADLINE Currently Enrolled as a Doctoral...
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Badania eksperymentalne i symulacyjne dynamiki modelowego odcinka sieci trakcyjnej
PublicationW pracy przedstawiono główne założenia i strukturę opracowanego modelu matematycznego odcinka kolejowej górnej sieci trakcyjnej, opartego na metodzie energetycznej Lagrange’a. W celu wyznaczenia wybranych parametrów modelu, jak również dla oceny stopnia zgodności odwzorowania przez utworzony program symulacyjny stanów statycznych i dynamicznych sieci zbudowano laboratoryjny model odcinka sieci jezdnej z użyciem rzeczywistych jej...
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Isolation Number versus Domination Number of Trees
PublicationIf 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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Geoambiente On-line
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Kinematyczne pomiary GNSS na linii kolei wąskotorowej w Koszalinie
PublicationW artykule opisano metodę kinematycznych pomiarów geodezyjnych GNSS zastosowaną dla inwentaryzacji trasy kolejowej w terenie silnie zalesionym. W badaniach wskazano możliwości wykorzystania tej metody dla inwentaryzacji układu geometrycznego trasy kolei wąskotorowej w Koszalinie. Opisano najważniejsze różnice pomiędzy koleją o rozstawie szyn 1000 mm a 1435 mm oraz przyszłościowe zagadnienie planowanej rewitalizacji tego odcinka....
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On-line Search in Two-Dimensional Environment
PublicationWe consider the following on-line pursuit-evasion problem. A team of mobile agents called searchers starts at an arbitrary node of an unknown network. Their goal is to execute a search strategy that guarantees capturing a fast and invisible intruder regardless of its movements using as few searchers as possible. As a way of modeling two-dimensional shapes, we restrict our attention to networks that are embedded into partial grids:...
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On-line Search in Two-Dimensional Environment
PublicationWe consider the following on-line pursuit-evasion problem. A team of mobile agents called searchers starts at an arbitrary node of an unknown network. Their goal is to execute a search strategy that guarantees capturing a fast and invisible intruder regardless of its movements using as few searchers as possible. We require that the strategy is connected and monotone, that is, at each point of the execution the part of the graph...
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On some ramsey and turan-type numbers for paths and cycles
PublicationUdowodniono, że R(P_3,C_k,C_k)= R(C_k,C_k)= 2k - 1, dla nieparzystych k. Udowodniono, że R(P_4,P_4,C_k) = k + 2 oraz R(P_3,P_5,C_k) = k + 1 dla k > 2.
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Ramsey numbers for triangles versus almost-complete graphs.
PublicationPokazano, że w każdym krawędziowym pokolorowaniu dwoma kolorami grafu pełnego o 38 wierzchołkach występuje trójkąt w pierwszym kolorze lub podgraf izomorficzny z K_10 - e w drugim kolorze. Stąd otrzymujemy górne oszacowanie R(K_3, K_10 - e) <= 38. Przedstawiamy także pokolorowanie krawędziowe grafu K_36, którego istnienie dowodzi, że R(K_3, K_10 - e) >= 37.
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On trees with double domination number equal to 2-domination number plus one
PublicationA 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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On trees with double domination number equal to total domination number plus one
PublicationA 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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Bondage number of grid graphs
PublicationThe 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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2-Coloring number revisited
Publication2-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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Bounds on isolated scattering number
PublicationThe 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
PublicationThe 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
PublicationThe 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-line P-coloring of graphs
PublicationFor a given induced hereditary property P, a P-coloring of a graph G is an assignment of one color to each vertex such that the subgraphs induced by each of the color classes have property P. We consider the effectiveness of on-line P-coloring algorithms and give the generalizations and extensions of selected results known for on-line proper coloring algorithms. We prove a linear lower bound for the performance guarantee function...