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Search results for: STRONG PRODUCT GRAPHS
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Colorings of the Strong Product of Circulant Graphs
PublicationGraph coloring is one of the famous problems in graph theory and it has many applications to information theory. In the paper we present colorings of the strong product of several circulant graphs.
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Average distance is submultiplicative and subadditive with respect to the strong product of graphs
PublicationWe show that the average distance is submultiplicative and subadditive on the set of non-trivial connected graphs with respect to the strong product. We also give an application of the above-mentioned result.
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Strong weakly connected domination subdivisible graphs
PublicationArtykuł dotyczy wpływu podziału krawędzi na liczbę dominowania słabo spójnego. Charakteryzujemy grafy dla których podział dowolnej krawędzi zmienia liczbę dominowania słabo spójnego oraz grafy dla których podział dowolnych dwóch krawędzi powoduje zmianę liczby dominowania słabo spójnego.
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On the metric dimension of corona product graphs
PublicationWe give several results on the metric dimension of corona product graphs.
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On the super domination number of lexicographic product graphs
PublicationThe 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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Domination-Related Parameters in Rooted Product Graphs
PublicationAbstract A set S of vertices of a graph G is a dominating set in G if every vertex outside of S is adjacent to at least one vertex belonging to S. A domination parameter of G is related to those sets of vertices of a graph satisfying some domination property together with other conditions on the vertices of G. Here, we investigate several domination-related parameters in rooted product graphs.
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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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Product Graph Invariants with Applications in the Theory of Information
PublicationThere are a large number of graph invariants. In the paper, we consider some of them, e.g. the independence and chromatic numbers. It is well know that we cannot efficiently calculate these numbers for arbitrary graphs. In the paper we present relations between these invariants and concepts from the theory of information. Concepts such as source coding and transmission over a noisy channel with zero probability of error are modeled...
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Eqiuitable coloring of corona products of cubic graphs is harder than ordinary coloring
PublicationA 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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Equitable coloring of corona multiproducts of graphs
PublicationWe 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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The impact of end-user participation in IT projects on product usability
PublicationMany companies implementing new IT projects encounter numerous problems with ensuring good final product usability. The strong market competition they experience often results in necessity of undertaking difficult decisions with regard to cost minimization. This may force cuts in usability expertise and consulting, most often by limiting end-user participation in the project. However, it may also result in serious consequences...
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Approximation algorithms for job scheduling with block-type conflict graphs
PublicationThe problem of scheduling jobs on parallel machines (identical, uniform, or unrelated), under incompatibility relation modeled as a block graph, under the makespan optimality criterion, is considered in this paper. No two jobs that are in the relation (equivalently in the same block) may be scheduled on the same machine in this model. The presented model stems from a well-established line of research combining scheduling theory...
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Relations between the domination parameters and the chromatic index of a graph
PublicationIn 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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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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How to meet when you forget: log-space rendezvous in arbitrary graphs
PublicationTwo identical (anonymous) mobile agents start from arbitrary nodes in an a priori unknown graph and move synchronously from node to node with the goal of meeting. This rendezvous problem has been thoroughly studied, both for anonymous and for labeled agents, along with another basic task, that of exploring graphs by mobile agents. The rendezvous problem is known to be not easier than graph exploration. A well-known recent result...
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Cobalt(II) and Cobalt(III) Tri‐tert‐butoxysilanethiolates. Synthesis, Properties, Crystal and Molecular Structures of [Co{μ‐SSi(OBut)3}{SSi(OBut)3}(NH3)]2 and [Co{SSi(OBut)3}2(NH3)4][SSi(OBut)3] Complexes
PublicationThe heteroleptic neutral tri‐tert‐butoxysilanethiolate of cobalt(II) incorporating ammonia as additional ligand (1) has been prepared by the reaction of a cobalt(II) ammine complex with tri‐tert‐butoxysilanethiol in water. Complex 1, dissolved in hexane, undergoes oxidation in an ammonia saturated atmosphere to the ionic cobalt(III) compound 2. Molecular and...
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The complexity of minimum-length path decompositions
PublicationWe consider a bi-criteria generalization of the pathwidth problem, where, for given integers k, l and a graph G, we ask whether there exists a path decomposition P of G such that the width of P is at most k and the number of bags in P, i.e., the length of P, is at most l. We provide a complete complexity classification of the problem in terms of k and l for general graphs. Contrary to the original pathwidth problem, which is fixed-parameter...
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A facile structural manipulation strategy to prepare ultra-strong, super-tough, and thermally stable polylactide/nucleating agent composites
PublicationPolylactide (PLA) is a biodegradable thermoplastic widely used in diferent felds, but it should be adequately modifed considering high-performance applications. However, the current processes for developing PLA materials achieve high strength at the expense of toughness or ductility of the materials. Therefore, there is need to develop new strategies for generation of PLA materials with high strength, great toughness, good ductility,...
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Pączkowanie - metoda rozwoju interoperacyjnych komponentów dla systemów rozproszonych = Budding – the software development method of interoperable components for distributed systems
PublicationPrzedstawiono 2 współczesne metody wytwarzania oprogramowania: iteracyjno-przyrostową oraz techniki zwinne, ich zalety i wady w kontekście budowy interoperacyjnych platform i środowisk rozproszonych. Zaprezentowano metodę rozwoju oprogramowania przez pączkowanie, jej założenia, zalety i wady. Przedstawiono technologie, na bazie których działa metodologia wytwarzania oprogramowania przez pączkowanie: Software Product Line, Enterprise...
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Fractional Order Circuit Elements Derived from Electromagnetism
PublicationIn this paper, derivations of fractional-order (FO) circuit-element equations from electromagnetism are presented. Whilst many papers are devoted to FO modelling of electrical circuits, there are no strong foundations for such an approach. Therefore, we investigate relations between the FO electromagnetism and the FO circuit theory. Our derivations start from quasi-static (QS) approximations of Maxwell's equations in media with...
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LIGHT POLLUTION IN THE CONTEXT OF THREATS TO THE WILDLIFE CORRIDORS
PublicationAccess to remote sensing night-time imagery allows for modeling of light pollution Increasingly, data on the propagation of artificial light are a source of interesting information for different fields of science and affect the planning of economic development. The article presents the problem of light pollution in the context of threats to the wildlife corridors in Poland. Wildlife corridors are areas that allow safe migration...
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Synthesis of Combretastatin A-4 Analogs and their Biological Activities
PublicationCombretastatin A-4 (CA-4) is a natural product, which consists of two phenyl rings, linked by an ethylene bridge. CA-4, inhibitor of polymerization of tubulin to microtubules, possesses a strong antitumor and anti-vascular properties both in vitro and in vivo. Previous studies showed that disodium phosphate salt of CA-4, a water-soluble prodrug is well tolerated at therapeutically useful doses. However, it should be noted that...
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Total Domination Versus Domination in Cubic Graphs
PublicationA dominating set in a graph G is a set S of vertices of G such that every vertex not in S has a neighbor in S. Further, if every vertex of G has a neighbor in S, then S is a total dominating set of G. The domination number,γ(G), and total domination number, γ_t(G), are the minimum cardinalities of a dominating set and total dominating set, respectively, in G. The upper domination number, \Gamma(G), and the upper total domination...
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Dynamic F-free Coloring of Graphs
PublicationA problem of graph F-free coloring consists in partitioning the vertex set of a graph such that none of the resulting sets induces a graph containing a fixed graph F as an induced subgraph. In this paper we consider dynamic F-free coloring in which, similarly as in online coloring, the graph to be colored is not known in advance; it is gradually revealed to the coloring algorithm that has to color each vertex upon request as well...
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User -friendly E-learning Platform: a Case Study of a Design Thinking Approach Use
PublicationE-learning systems are very popular means to support the teaching process today. These systems are mainly used by universities as well as by commercial training centres. We analysed several popular e-learning platforms used in Polish universities and find them very unfriendly for the users. For this reason, the authors began the work on the creation of a new system that would be not only useful, but also usable for students, teachers...
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Reactive imines: Addition of 2-aminopyrimidine to the imine bond and isolation of the aminal from the equilibrium mixture aminal/imine
PublicationThe reaction between o-vanillin and 2-aminopyrimidine leads to the formation of a single crystalline product: aminal, 1, which results from the reaction of the initially formed imine with 2-aminopyrimidine. The reaction was followed by the NMR spectroscopy. VT NMR studies prove that in solution two major species are observed: aminal and imine and their ratio depends on the time or/and temperature with the imine content increasing...
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Distillery Fusel Oil as an Alternative Carbon Source for Denitrification – from Laboratory Experiments to Full-Scale Applications
PublicationIndustrial waste products may be a viable alternative to commercial external carbon sources, such as ethanol. In this study, the properties of fusel oil (distillery waste product) were investigated in terms of temperature dependency of denitrification, acclimation period, and the effects on NO2-N and PO4-P behavior. Furthermore, results obtained during three different full-scale trials were used to verify similarities and differences...
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Implementing Smart Virtual Product Development (SVPD) to Support Product Manufacturing
PublicationThis paper illustrates the concept of providing the manufacturing knowledge during early stages of product life cycle to experts working on product development. The aim of this research is to enable a more collaborative product development environment by using Smart Virtual Product Development (SVPD) system, which is powered by Set of Experience Knowledge Structure (SOEKS) and Decisional DNA (DDNA). It enhances the industrial product...
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Visual Attention Distribution Based Assessment of User's Skill in Electronic Medical Record Navigation
PublicationCurrently, the most precise way of reflecting the skills level is an expert’s subjective assessment. In this paper we investigate the possibility of the use of eye tracking data for scalar quantitative and objective assessment of medical staff competency in EMR system navigation. According to the experiment conducted by Yarbus the observation process of particular features is associated with thinking. Moreover, eye tracking is...
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Distillery Fusel Oil as an Alternative Carbon Source for Denitrification – from Laboratory Experiments to Full-Scale Applications
PublicationIndustrial waste products may be a viable alternative to commercial external carbon sources. In this study, the properties of fusel oil (distillery waste product) were investigated in terms of temperature dependency of denitrification and acclimation period. Furthermore, results obtained during three different full-scale trials were used to verify similarities and differences with the results obtained under laboratory-scale conditions....
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Smart Virtual Product Development (SVPD) to Enhance Product Manufacturing in Industry 4.0
PublicationThis paper presents a system capable of enhancing product development process for industrial manufactured products. This system is known as Smart Virtual Product Development (SVPD), and it helps in decision making by using explicit knowledge of formal decision events. It stores and reuses the past decisional events or sets of experiences related to different activities involved in industrial product development process i.e. product...
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Market knowledge and new product performance: the mediating effects of new product performance
PublicationMarket knowledge is recognised as an important predictor of new product performance, which existing studies have proven. However, a missing link in this relationship is creativity, and specifically, as a natural process in product innovation. This study aims to examine a model that includes two mediating mechanisms between market knowledge scope and two new product outcomes, respectively: a new product’s competitive advantage and...
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Changes in the Global Competitiveness Index 4.0 Methodology: The Improved Approach of Competitiveness Benchmarking
PublicationThe Global Competitiveness Index (GCI) developed by the World Economic Forum (WEF) is used as a standard for measuring a country’s competitiveness. However, in literature, the GCI has been accused of numerous methodological flaws. Consequently, in 2018, the WEF introduced significant methodological changes. This study aims to examine whether the methodological modifications in the GCI’s structure increase its ability to capture...
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Strategic balance in graphs
PublicationFor a given graph G, a nonempty subset S contained in V ( G ) is an alliance iff for each vertex v ∈ S there are at least as many vertices from the closed neighbourhood of v in S as in V ( G ) − S. An alliance is global if it is also a dominating set of G. The alliance partition number of G was defined in Hedetniemi et al. (2004) to be the maximum number of sets in a partition of V ( G ) such that each set is an alliance. Similarly,...
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Dynamic coloring of graphs
PublicationDynamics is an inherent feature of many real life systems so it is natural to define and investigate the properties of models that reflect their dynamic nature. Dynamic graph colorings can be naturally applied in system modeling, e.g. for scheduling threads of parallel programs, time sharing in wireless networks, session scheduling in high-speed LAN's, channel assignment in WDM optical networks as well as traffic scheduling. In...
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Smart Virtual Product Development (SVPD) System to Support Product Inspection Planning in Industry 4.0
PublicationThis paper presents the idea of supporting product inspection planning process during the early stages of product life cycle for the experts working on product development. Aim of this research is to assist a collaborative product development process by using Smart Virtual Product Development (SVPD) system, which is based on Set of Experience Knowledge Structure (SOEKS) and Decisional DNA (DDNA). The proposed system is developed...
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Some variations of perfect graphs
PublicationWe consider (ψk−γk−1)-perfect graphs, i.e., graphs G for which ψk(H) =γk−1(H) for any induced subgraph H of G, where ψk and γk−1 are the k -path vertex cover number and the distance (k−1)-domination number, respectively. We study (ψk−γk−1)-perfect paths, cycles and complete graphs for k≥2. Moreover, we provide a complete characterisation of (ψ2−γ1)-perfect graphs describing the set of its forbidden induced subgraphs and providing...
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Independent Domination Subdivision in Graphs
PublicationA set $S$ of vertices in a graph $G$ is a dominating set if every vertex not in $S$ is adjacent to a vertex in~$S$. If, in addition, $S$ is an independent set, then $S$ is an independent dominating set. The independent domination number $i(G)$ of $G$ is the minimum cardinality of an independent dominating set in $G$. The independent domination subdivision number $\sdi(G)$ is the minimum number of edges that must be subdivided (each...
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Systematic Assessment of Product Quality
PublicationThe article describes an innovative metrizable idea for systemic assessments of product quality within the baking industry. Complex product quality analysis requires the employment of metrizability criteria for factors that impact the quality of the product, and these are called determinants. Therefore, such analysis is only possible with the use of systems engineering. A system represents the potential of a manufacturing process,...
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Enhancing Product Manufacturing through Smart Virtual Product Development (SVPD) for Industry 4.0
PublicationABSTRACT This paper proposes the Smart Virtual Product Development (SVPD) system, which enhances the industrial product manufacturing processes. The proposed system comprises of three main modules: design knowledge management (DKM), manufacturing capability analysis and process planning (MCAPP), and product inspection planning (PIP). Smart virtual product development system collects, stores, and uses experiential knowledge from...
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Smart Virtual Product Development (SVPD): Experience Based Product Development System for Industry 4.0
PublicationThis chapter presents the concept of smart virtual product development (SVPD) system capable of supporting industrial product development. It enhances the decision making process during various activities involved in product development i.e. product design, manufacturing, and inspection planning. This is achieved by using the explicit knowledge of past formal decision events, which are captured, stored, and recalled in the form...
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Double bondage in graphs
PublicationA vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G=(V,E) 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, denoted by gamma_d(G), is the minimum cardinality of a double dominating set of G. The double bondage number of G, denoted by b_d(G), is the minimum cardinality among all sets...
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Interval incidence coloring of bipartite graphs
PublicationIn this paper we study the problem of interval incidence coloring of bipartite graphs. We show the upper bound for interval incidence coloring number (χii) for bipartite graphs χii≤2Δ, and we prove that χii=2Δ holds for regular bipartite graphs. We solve this problem for subcubic bipartite graphs, i.e. we fully characterize the subcubic graphs that admit 4, 5 or 6 coloring, and we construct a linear time exact algorithm for subcubic...
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Global edge alliances in graphs
PublicationIn the paper we introduce and study a new problem of finding a minimum global edge alliance in a graph which is related to the global defensive alliance (Haynes et al., 2013; Hedetniemi, 2004) and the global defensive set (Lewoń et al., 2016). We proved the NP-completeness of the global edge alliance problem for subcubic graphs and we constructed polynomial time algorithms for trees. We found the exact values of the size of the...
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Some Progress on Total Bondage in Graphs
PublicationThe total bondage number b_t(G) of a graph G with no isolated vertex is the cardinality of a smallest set of edges E'⊆E(G) for which (1) G−E' has no isolated vertex, and (2) γ_t(G−E')>γ_t(G). We improve some results on the total bondage number of a graph and give a constructive characterization of a certain class of trees achieving the upper bound on the total bondage number.
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Algorithms for testing security in graphs
PublicationIn this paper we propose new algorithmic methods giving with the high probability the correct answer to the decision problem of security in graphs. For a given graph G and a subset S of a vertex set of G we have to decide whether S is secure, i.e. every subset X of S fulfils the condition: |N[X] \cap S| >= |N[X] \ S|, where N[X] is a closed neighbourhood of X in graph G. We constructed a polynomial time property pseudotester based...
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2-bondage in graphs
PublicationA 2-dominating set of a graph G=(V,E) is a set D of vertices of G such that every vertex of V(G)D has 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. The 2-bondage number of G, denoted by b_2(G), is the minimum cardinality among all sets of edges E' subseteq E such that gamma_2(G-E') > gamma_2(G). If for every E' subseteq E we have...
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Overview of new product development strategies and models
PublicationMotivation: The motivation for the overview presented in this article is to provide a starting point for considering whether existing new product development methodology and its level of detail allows product teams to develop high-quality and business-effective product concepts. Aim: The aim of this article is recognise the current state of research into new product development methodology and to present the strategies and models...
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Strategies for Dealing With Software Product Management Challenges
PublicationSoftware product management, which involves multiple processes and responsibilities and links to many activities within the organisation, increases the success rate of IT projects. However, the adoption of product management activities and the implementation of the software product manager role itself varies between companies. This research explores the topic of software product managers’ strategies for dealing with challenges...
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A comprehensive overview of software product management challenges
PublicationThe principal focus of software product management is to ensure the economic success of the product, which means to prolong the product life as much as possible with modest expenditures to maximizs profits. Software product managers play an important role in the software development organization while being responsible for the strategy, business case, product roadmap, high-level requirements, product deployment (release-management),...