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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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Biology Direct
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Transplantation Direct
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Plant Direct
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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),...
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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...
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New Product Creativity Dimensions and Performance
PublicationA new product’s meaningfulness and novelty are recognized as two distinct and important dimensions. Thus, researchers started to investigate their impact on new product performance. However, researchers’ reports on the impact of novelty on performance are still mixed, and several issues need to be solved. One of these problems is comparing how strongly each of these dimensions affects the new product performance. The other is to...
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A note on total reinforcement in graphs
PublicationIn this note we prove a conjecture and inprove some results presendet in a recent paper of N. Sridharan, M.D. Elias, V.S.A. Subramanian, Total reinforcement number of a graph, AKCE Int. J. Graphs Comb. 4 (2) (2007) 197-202.
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More than just a beer – Brewers' spent grain, spent hops, and spent yeast as potential functional fillers for polymer composites
PublicationBeer is among the most popular beverages in the world, with the production distributed uniformly between the biggest continents, so the utilization of brewing by-products is essential on a global scale. Among their potential recipients, the plastics industry offers extensive range of potential products. Herein, the presented study investigated the application of currently underutilized solid brewing by-products (brewers' spent...
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Edge and Pair Queries-Random Graphs and Complexity
PublicationWe investigate two types of query games played on a graph, pair queries and edge queries. We concentrate on investigating the two associated graph parameters for binomial random graphs, and showing that determining any of the two parameters is NP-hard for bounded degree graphs.
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The new concept of product. Cooling band
PublicationThe chapter below presents the innovative solution consist in applying the cooling band to help holding the hot object. The solution was found through substitute inputs analysis and brain storm method. The new product was submitted in Polish Patent Office under the No. W.120905.
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Different sources of market information and product innovativeness
PublicationThe purpose of this study is to identify whether the gathering of market information from different sources – i.e. from customers, competitors and other entities – is related to product innovativeness. The relationships proposed so far have not been empirically investigated but they can have important theoretical and practical implications for product innovation. To achieve the purpose of the paper data concerning 287 new products...
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Computational aspects of greedy partitioning of graphs
PublicationIn this paper we consider a variant of graph partitioning consisting in partitioning the vertex set of a graph into the minimum number of sets such that each of them induces a graph in hereditary class of graphs P (the problem is also known as P-coloring). We focus on the computational complexity of several problems related to greedy partitioning. In particular, we show that given a graph G and an integer k deciding if the greedy...
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Non-isolating bondage in graphs
PublicationA dominating set of a graph $G = (V,E)$ is a set $D$ of vertices of $G$ such that every vertex of $V(G) \setminus D$ has a neighbor in $D$. The domination number of a graph $G$, denoted by $\gamma(G)$, is the minimum cardinality of a dominating set of $G$. The non-isolating bondage number of $G$, denoted by $b'(G)$, is the minimum cardinality among all sets of edges $E' \subseteq E$ such that $\delta(G-E') \ge 1$ and $\gamma(G-E')...
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2-outer-independent domination in graphs
PublicationWe initiate the study of 2-outer-independent domination in graphs. A 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 at least two neighbors in D, and the set V(G)\D is independent. The 2-outer-independent domination number of a graph G is the minimum cardinality of a 2-outer-independent dominating set of G. We show that if a graph has minimum degree at least two,...
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Theory and Applications of Graphs
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Edge coloring of graphs of signed class 1 and 2
PublicationRecently, Behr (2020) introduced a notion of the chromatic index of signed graphs and proved that for every signed graph (G, σ) it holds that ∆(G) ≤ χ′(G,σ) ≤ ∆(G) + 1, where ∆(G) is the maximum degree of G and χ′ denotes its chromatic index. In general, the chromatic index of (G, σ) depends on both the underlying graph G and the signature σ. In the paper we study graphs G for which χ′(G, σ) does not depend on σ. To this aim we...
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The hat problem on a union of disjoint graphs
PublicationThe topic is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of winning. In this version every player...
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Experience-Based Product Inspection Planning for Industry 4.0
PublicationIn this paper we describe how our Smart Virtual Product Development (SVPD) system can be used to enhance product inspection planning. The SVPD system is comprised of three main modules, these being the design knowledge management (DKM) module, the manufacturing capability and process planning (MCAPP) module, and the product inspection planning (PIP) module. Experiential knowledge relating to formal decisional events is collected,...
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Marek Czachor prof. dr hab.
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Tensor-product versus geometric-product coding
PublicationKodowanie przy pomocy iloczynów tensorowych, a kodowanie przy pomocy iloczynów geometrycznych. Formalizm jest zilustrowany przy pomocy paru przykładów.
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Smart Innovation Management in Product Life Cycle
PublicationThe present paper proposes a framework for smart innovation management of the product using a Smart Knowledge Management System comprising Set of Experience Knowledge Structure (SOEKS) and Decisional DNA. This proposed system will allow the entrepreneurs and organizations to perform the innovation process technically and quickly as this framework will store knowledge as well as experiences of the past innovations done in various...
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Common Independence in Graphs
PublicationAbstract: The cardinality of a largest independent set of G, denoted by α(G), is called the independence number of G. The independent domination number i(G) of a graph G is the cardinality of a smallest independent dominating set of G. We introduce the concept of the common independence number of a graph G, denoted by αc(G), as the greatest integer r such that every vertex of G belongs to some independent subset X of VG with |X|...
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Deterministic Rendezvous in Restricted Graphs
PublicationIn this paper we consider the problem of synchronous rendezvous in which two anonymous mobile entities (robots) A and B are expected to meet at the same time and point in a graph G = (V;E). Most of the work devoted to rendezvous in graphs assumes that robots have access to the same sets of nodes and edges, where the topology of connections may be initially known or unknown. In our work we assume the movement of robots is restricted...
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The role of robotisation in improving bakery product quality
PublicationThe article aims to present the role of robotisation in increasing bakery product quality, as it is closely linked to machine reliability, as well as hygienic and sanitary conditions. All machines employed in the production process ought to be maintained at full production potential and reliability, which also has a fundamental influence on the final product’s quality. While participating in the 2014-2020 Smart Growth Operational...
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Three-fast-searchable graphs
PublicationIn the edge searching problem, searchers move from vertex to vertex in a graph to capture an invisible, fast intruder that may occupy either vertices or edges. Fast searching is a monotonic internal model in which, at every move, a new edge of the graph G must be guaranteed to be free of the intruder. That is, once all searchers are placed the graph G is cleared in exactly |E(G)| moves. Such a restriction obviously necessitates...
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The Role of a Software Product Manager in Various Business Environments
PublicationThe aim of the paper is to identify the role of the software product manager depending on the size of the company and the characteristics of the product they are working on. This has been achieved in cooperation with 15 experts from the IT industry. The companies were divided into 4 levels of size: micro-enterprises, small businesses, medium businesses and large enterprises. The characteristics of the products were divided into...
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On bipartization of cubic graphs by removal of an independent set
PublicationWe study a new problem for cubic graphs: bipartization of a cubic graph Q by deleting sufficiently large independent set.
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Reactions of solute species at an electrode modified with titanocene functionalized polypyrrole film: ferrocene and titanocene dichloride
PublicationPo raz pierwszy zbadano możliwość intermediacji ładunku poprzez centra tytanocenowe polimeru modyfikowanego chemicznie związanymi grupami dichloro tytanocenowymido polipirolu. Badano reakcje elektrodowe ferrocenu i dichlorotytanocenu. Wykazano aktywność elektrodową w zakresie potencjałów redoks pary Ti(IV/TiIII)w stosunku do reakcji redoks ferrocenu i reakcji dichlorotytanocenu. Wykazano, że centra TcCl2 polimeru są zadowalająco...
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Chromatic cost coloring of weighted bipartite graphs
PublicationGiven 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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NEW PRODUCT DEVELOPMENT FROM THE PERSPECTIVE OF CREATING A COMPETITIVE ADVANTAGE
PublicationIt is acknowledged that achieving product-based competitive advantage is a key task for a company. However, there is still a research gap in determining those specific actions in the process of developing new products that arise from companies' efforts to achieve product-based competitive advantage. Therefore, the aim of this study is to determine the specific actions in the new product development (NPD) process that result from...
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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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Evaluation of Selected UX Techniques by Product Managers - A Preliminary Survey
PublicationIn this paper we present the results of an opinion survey among 28 IT product managers who evaluated the subjective usefulness of 24 selected UX techniques to 6 IT product management tasks derived from ProdBOK®. We selected the UX techniques based on the literature review and 6 interviews with experienced IT product managers. Based on the survey results, we propose our recommendation of useful techniques for 5 of the 6 studied...
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On Computational Aspects of Greedy Partitioning of Graphs
PublicationIn this paper we consider a problem of graph P-coloring consisting in partitioning the vertex set of a graph such that each of the resulting sets induces a graph in a given additive, hereditary class of graphs P. We focus on partitions generated by the greedy algorithm. In particular, we show that given a graph G and an integer k deciding if the greedy algorithm outputs a P-coloring with a least k colors is NP-complete for an infinite...
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The Backbone Coloring Problem for Small Graphs
PublicationIn this paper we investigate the values of the backbone chromatic number, derived from a mathematical model for the problem of minimization of bandwidth in radio networks, for small connected graphs and connected backbones (up to 7 vertices). We study the relationship of this parameter with the structure of the graph and compare the results with the solutions obtained using the classical graph coloring algorithms (LF, IS), modified...
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Block graphs with large paired domination multisubdivision number
PublicationThe 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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Graphs hard-to-process for greedy algorithm MIN
PublicationWe compare results of selected algorithms that approximate the independence number in terms of the quality of constructed solutions. Furthermore, we establish smallest hard- to-process graphs for the greedy algorithm MIN.
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Birch sap concentrate as a potential modern food product
PublicationThis paper presents birch sap concentrate obtained by the reverse osmosis method. It is characterized by sweet taste, high content of minerals and no risk to consumers in terms of content of heavy metals standardized in the European Union food legislation. This beverage has all the features of a modern food product, i.e. it has an attractive taste, is obtained using new technology, meets the clean label requirements and can be...
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Framework for Product Innovation Using SOEKS and Decisional DNA
PublicationProduct innovation always requires a foundation based on both knowledge and experience. The production and innovation process of products is very similar to the evolution process of humans. The genetic information of humans is stored in genes, chromosomes and DNA. Similarly, the information about the products can be stored in a system having virtual genes, chromosomes and decisional DNA. The present paper proposes a framework for...