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Search results for: RESUDUE NUMBERS
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Similarities and Differences Between the Vertex Cover Number and the Weakly Connected Domination Number of a Graph
PublicationA 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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High-speed fpga pipelined binary-to-residue converter
Publicationw pracy przedstawiono architekturę przepływowego konwertera z systemu z uzupełnieniem do 2 z systemu binarnego. zastosowano segmentację słowa wejściowego ze wstępną inwersją dla liczb ujemnych. reszty liczb reprezentowanych przez poszczególne segmenty są obliczane poprzez odczyt z pamięci adresowanej binarną reprezentacją segmentu. otrzymane reszty sumowane są w wielooperandowym sumatorze modulo z korekcją reszty dla liczb ujemnych.pracę...
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FPGA realization of the high-speed binary-to-residue converter
Publicationprzedstawiono architekturę i realizację w technologii fpga konwertera z systemu binarnego do systemu resztowego. algorytm konwertera oparty jest na podziale słowa wejściowego na segmenty 4-bitowe i następnie obliczeniu reszty liczby reprezentowanej przez dany segment, sumowaniu binarnym przy zastosowaniu csa i redukcji modulo w układzie dwuoperandowego sumatora modulo.
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High-speed binary-to-residue converter with improved architecture.
PublicationPrzedstawiono ulepszoną architekturę szybkiego konwertera liczb z systemu binarnego do systemu resztowego dla liczb ze znakiem w kodzie U2. Algorytm konwertera oparty jest o segmentację słowa wejsciowego nasegmenty 4-bitowe. Reszty liczb reprezentowanych przez segmenty sąobliczane poprzez odwzorowanie. Wielooperandowe sumowanie modulo jest realizowane przy użyciu drzewa Wallace'a z segmentacją wektorów wyjściowych oraz finalnego...
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Effective residue-to-binary converter with the Chinese Remainder Theorem
PublicationKonwersja liczb z systemu resztowego do systemu binarnego jest podstawową operacją we wszystkich układach cyfrowego przetwarzania sygnałów, które wykorzystują system resztowy. W niniejszej pracy zaproponowano nową metodę konwersji opartą o chińskie twierdzenie o resztach dla modułów 5- i 6-bitowych. Specyficzną cechą nowej metody jest sposób obliczania tzw. współczynnika nadmiaru w formule chińskiego twierdzenia o resztach, co...
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Residue-to-two's complement converter based on core function
PublicationW artykule przedstawiono układową realizację konwertera z systemu resztowego do systemu binarnego bazującego na funkcji jądra. Zastosowanie funkcji jądra powoduje zmniejszenie wymagań sprzętowych przy realizacji konwertera. W publikacji omówiono problem dektekcji znaku oraz realizacje ukłądową konwertera w środowisku FPGA.
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Implementation of discrete convolution using polynomial residue representation
PublicationConvolution is one of the main algorithms performed in the digital signal processing. The algorithm is similar to polynomial multiplication and very intensive computationally. This paper presents a new convolution algorithm based on the Polynomial Residue Number System (PRNS). The use of the PRNS allows to decompose the computation problem and thereby reduce the number of multiplications. The algorithm has been implemented in Xilinx...
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Implementation of discrete convolution using polynomial residue representation
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Chromogenic azomacrocycles with imidazole residue: Structure vs. properties
PublicationNew diazo macrocycles linked by hydrocarbon chain bearing imidazole or 4-methylimidazole residue have been synthetized with satisfactory yield (24–55%). The structure of macrocycles was confirmed by X-ray analysis and spectroscopic methods (1H NMR, MS, FTIR). Metal cation complexation studies were carried out in acetonitrile and acetonitrile-water system. It was found that azomacrocyles form triple-decker complexes with lead(II)....
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Communications in Number Theory and Physics
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International Journal of Number Theory
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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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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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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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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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P-Adic Numbers Ultrametric Analysis and Applications
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Trees with equal restrained domination and total restrained domination numbers
PublicationW publikacji scharakteryzowano wszystkie drzewa, w których liczby dominowania powściągniętego oraz podwójnie totalnego są sobie równe.
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On trees with equal domination and total outer-independent domination numbers
PublicationFor a graph G=(V,E), a subset D subseteq V(G) is a dominating set if every vertex of V(G)D has a neighbor in D, while it is a total outer-independent dominating set if every vertex of G has a neighbor in D, and the set V(G)D is independent. The domination (total outer-independent domination, respectively) number of G is the minimum cardinality of a dominating (total outer-independent dominating, respectively) set of G. We characterize...
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Weakly convex and convex domination numbers of some products of graphs
PublicationIf $G=(V,E)$ is a simple connected graph and $a,b\in V$, then a shortest $(a-b)$ path is called a $(u-v)$-{\it geodesic}. A set $X\subseteq V$ is called {\it weakly convex} in $G$ if for every two vertices $a,b\in X$ exists $(a-b)$- geodesic whose all vertices belong to $X$. A set $X$ is {\it convex} in $G$ if for every $a,b\in X$ all vertices from every $(a-b)$-geodesic belong to $X$. The {\it weakly convex domination number}...
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On trees with double domination number equal to 2-outer-independent domination number plus one
PublicationA 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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Determination of antibiotic residues in honey
PublicationHoney produced by honeybees is a valuable food product. The presence of xenobiotics in honey may harm its quality and constitute a danger to human health. Antibiotics are commonly applied by beekeepers to eliminate disease among honeybees. Moreover, ubiquitous administration of antibiotics may cause bacteria to become resistant to many drugs and spread antibioticresistant strains of bacteria. Appropriate sample preparation and...
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High-speed binary-to-residue converter with the reduced input layer
Publicationprzedstawiono architekturę szybkiego konwertera z systemu binarnego do systemu resztowego dla modułów 5-bitowych. Algorytm konwersji oparty jest na dodawaniu binarnym reszt potęg liczby 2 obliczonych modulo m i redukcji modulo m sumy dla poszczególnych modułów bazy systemu resztowego. Warstwa wejciowa konwertera jest redukowana poprzez wykorzystanie wspólnych elementów układu dla odpowiednio zestawionych par modułów.
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High-speed residue-to-binary converter based on the Chinese RemainderTheorem.
PublicationPrzedstawiono szybki konwerter z systemu resztowego do systemu binarnego dla modułów 5-bitowych oparty o chińskie twierdzenie o resztach. Projekcje ortogonalne są generowane przy użyciu odwzorowania realizowanego przy zastosowaniu funkcji logicznych pięciu zmiennych. Wartość wyjściowa jest obliczana przy użyciu drzewaWallace'a z segmentacją wektorów wyjściowych i redukcją do 2M, M zakres liczbowy systemu oraz efektywny finalny...
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Novel Diazocrowns with Pyrrole Residue as Lead(II) Colorimetric Probes
PublicationNovel 18- and 23-membered diazomacrocycles were obtained with satisfactory yields by diazocoupling of aromatic diamines with pyrrole in reactions carried under high dilution conditions. X-ray structure of macrocycle bearing five carbon atoms linkage was determined and described. Compounds were characterized as chromogenic heavy metal ions receptors. Selective color and spectral response for lead(II) was found in acetonitrile and...
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Some variants of perfect graphs related to the matching number, the vertex cover and the weakly connected domination number
PublicationGiven 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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On domination multisubdivision number of unicyclic graphs
PublicationThe 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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Coronas and Domination Subdivision Number of a Graph
PublicationIn 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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The outer-connected domination number of a graph
PublicationW 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
PublicationW pracy przedstawione są ograniczenia i własności liczby dominowania podwójnie totalnego.
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Lower bound on the domination number of a tree.
PublicationW pracy przedstawiono dolne ograniczenie na liczbę dominowania w drzewach oraz przedstawiono pełną charakterystykę grafów ekstremalnych.
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TOTAL DOMINATION MULTISUBDIVISION NUMBER OF A GRAPH
PublicationThe 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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On the doubly connected domination number of a graph
PublicationW pracy została zdefiniowana liczba dominowania podwójnie spójnego i przedstawiono jej podstawowe własności.
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The convex domination subdivision number of a graph
PublicationLet 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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Complexity Issues on of Secondary Domination Number
PublicationIn 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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Fast rns scaling of signed numbers based on the chinese remainder theorem
PublicationPrzedstawiono architekturę szybkiego skalera resztowego dla liczb ze znakiem dla modułów 5-bitowych opartego na chińskim twierdzeniu o resztach. W architekturze zastosowano wyznaczanie projekcji ortogonalnych przy użyciu funkcji logicznych 5 zmiennych, sumator kodulo m/k oraz wejściowy konwerter do systemu resztowego. Operacja modulo m/k jest wykonywana przy zastosowaniu drzewa 4-operandowych sumatorów modulo 2m/k i końcowego...
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Unicyclic graphs with equal total and total outer-connected domination numbers
PublicationLet G = (V,E) be a graph without an isolated vertex. A set D ⊆ V (G) is a total dominating set if D is dominating and the in- duced subgraph G[D] does not contain an isolated vertex. The total domination number of G is the minimum cardinality of a total domi- nating set of G. A set D ⊆ V (G) is a total outer–connected dominating set if D is total dominating and the induced subgraph G[V (G)−D] is a connected graph. The total outer–connected...
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On trees with equal 2-domination and 2-outer-independent domination numbers
PublicationFor 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 in D, while it is a 2-outer-independent dominating set if additionally the set V(G)\D is independent. The 2-domination (2-outer-independent domination, respectively) number of G, is the minimum cardinality of a 2-dominating (2-outer-independent dominating, respectively) set of G. We characterize all trees...
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FPGA computation of magnitude of complex numbers using modified CORDIC algorithm
PublicationIn this work we present computation of the magnitude of complex numbers using a modified version of the CORDIC algorithm that uses only five iterations. The relationship between the computation error and the number of CORDIC iterations are presented for floating-point and integer arithmetics. The proposed modification of CORDIC for integer arithmetic relies upon the introduction of correction once basic computations are performed...
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Validation of the HS-GC-FID method for the determination of athanol residue in tablets
PublicationW pracy opisano proces walidacji metody oznaczania zawartości pozostałości etanolu w tabletkach. W pomiarach wykorzystano technikę HS-GC-FID. Wyznaczono następujące parametry walidacyjne:- selektywność- liniowość- poprawność- precyzję (powtarzalność i precyzję pośrednią)- granice wykrywalności i oznaczalności- zakres pomiarowy- niepewność
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Strength and Compressibility of Ammonia-Soda Residue from the Solvay Sodium Plant
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Validation of the HS-GC-FID method for the determination of ethanol residue in tablets
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Solvent residue determination in Uncaria Tomentosa Bark by HS-GC technique
PublicationPrzedstawiono wyniki oznaczeń pozostałości rozpuszczalników organicznych w preparacie uzyskanym z kory liany U. Tomentosa, wykorzystywanej do produkcji farmaceutyków i dodatków do żywności. 1,1,2-trichloroeten oraz dichlorometan są powszechnie stosowane do usunięcia z kory kilku grup alkaloidów o znanych właściwościach biologicznych, co umożliwia zbadanie pozostałych jej związków. Ilościowe oznaczanie tych rozpuszcalników jest...
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Notes on Number Theory and Discrete Mathematics
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Moscow Journal of Combinatorics and Number Theory
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On the ratio between 2-domination and total outer-independent domination numbers of trees
PublicationA 2-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. A 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 2-domination (total outer-independent domination, respectively) number of a graph G is the minimum cardinality of a 2-dominating (total...
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Numbers, Please: Power- and Voltage-Related Indices in Control of a Turbine-Generator Set
PublicationThis paper discusses the proper selection and interpretation of aggregated control performance indices values mirroring the quality of electrical energy generation by a turbine-generator set cooperating with a power system. Typically, a set of basic/classical and individual indices is used in energy engineering to ensure the mirroring feature and is related to voltage, frequency and active or reactive power deviations from their...
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T-colorings, divisibility and circular chromatic number
PublicationLet 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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Non-standard binary weighted number systems
PublicationZdefiniowano 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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Empirical Probability Distributions with Unknown Number of Components
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