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Yero I.G.,Rovira i Virgili University | Kuziak D.,Gdask University of Technology | Rodriguez-Velazquez J.A.,Rovira i Virgili University
Computers and Mathematics with Applications | Year: 2011

Given a set of vertices S=v1,v2,...,vk of a connected graph G, the metric representation of a vertex v of G with respect to S is the vector r(v|S)=(d(v,v1),d(v,v2),...,d(v, vk)), where d(v,vi), i∈1,...,k denotes the distance between v and vi. S is a resolving set for G if for every pair of distinct vertices u,v of G, r(u|S)≠r(v|S). The metric dimension of G, dim(G), is the minimum cardinality of any resolving set for G. Let G and H be two graphs of order n1 and n2, respectively. The corona product G⊙H is defined as the graph obtained from G and H by taking one copy of G and n1 copies of H and joining by an edge each vertex from the ith-copy of H with the ith-vertex of G. For any integer k<2, we define the graph G⊙kH recursively from G⊙H as G⊙ kH=(G⊙k-1H)⊙H. We give several results on the metric dimension of G⊙kH. For instance, we show that given two connected graphs G and H of order n1<2 and n2<2, respectively, if the diameter of H is at most two, then dim(G⊙ kH)=n1(n2+1)k-1dim(H). Moreover, if n2<7 and the diameter of H is greater than five or H is a cycle graph, then dim(G⊙kH)=n1(n2+1)k-1dim( K1⊙H). © 2011 Elsevier Ltd. All rights reserved. Source

Konopacka-Yskawa D.,Gdask University of Technology | Lackowski M.,Szewalski Institute of Fluid Flow Machinery
Journal of Crystal Growth | Year: 2011

Calcium carbonate precipitation was investigated in the gasslurry system in the reaction of calcium hydroxide and carbon dioxide. The precipitation process was occurred in the presence of ethylene glycol (EG). The used organic additive changed the viscosity of reactive mixture, the solubility of carbon dioxide and the solubility of calcium carbonate which influence CaCO3 precipitation conditions. The course of reaction was monitored by conductivity probe. The increase concentration of ethylene glycol in the reactive mixture caused higher CO2 usage to achieve the end point of reaction. Calcium carbonate was precipitated as calcite and produced CaCO3 particles formed agglomerates in all experiments. The size of obtained CaCO3 particles decreased when the EG concentration increased from 0% to 15% (by vol.). The further increase of EG concentration in solution up to 20% resulted in an increase of the size of CaCO3 particles. © 2011 Elsevier B.V. All rights reserved. Source

Dereniowski D.,Gdask University of Technology
Theoretical Computer Science | Year: 2012

The problems of (classical) searching and connected searching of weighted trees are known to be computationally hard. In this work we give a polynomial-time 3-approximation algorithm that finds a connected search strategy of a given weighted tree. This in particular yields constant factor approximation algorithms for the (non-connected) classical searching problems and for the weighted pathwidth problem for this class of graphs. © 2012 Elsevier B.V. All rights reserved. Source

Wasowicz T.J.,Gdask University of Technology | Kivimaki A.,CNR Institute of Materials | Coreno M.,Gas Phase Beamline Elettra | Coreno M.,CNR Institute of Inorganic Methodologies and Plasmas | Zubek M.,Gdask University of Technology
Journal of Physics B: Atomic, Molecular and Optical Physics | Year: 2012

The photofragmentation of isoxazole molecules producing excited atomic and molecular fragments has been investigated over the energy range 16-50eV, using photon-induced fluorescence spectroscopy. The following fragments have been identified by their fluorescence: the excited hydrogen atoms H(n), n = 3-7 and the diatomic CH(A 2Δ, B 2Σ -), CN(B 2Σ +) and C 2(d 3Π g) fragments. The diatomic fragments are vibrationally and highly rotationally excited. The fragmentation yield curves for the CH(A 2Δ), CN(B 2Σ +), C 2(d 3Π g) and the H(n), n = 3-7 deduced from their emission yields, were obtained in the photon energy ranges from their appearance energies up to 50eV. It is found that the fragmentation occurs via excitation into higher lying superexcited states of isoxazole. The vertical excitation energies of these states were determined and their possible fragmentation processes are discussed. © 2012 IOP Publishing Ltd. Source

Dzwonkowski M.,Gdask University of Technology | Dzwonkowski M.,Medical University of Gdask | Rykaczewski R.,Gdask University of Technology
Journal of Telecommunications and Information Technology | Year: 2015

In this paper Quaternion Feistel Cipher (QFC) with an infinite key space based on quaternion Julia sets is proposed. The basic structure of the algorithm is based on the scheme proposed in 2012 by Sastry and Kumar. The pro-posed algorithm uses special properties of quaternions to per-form rotations of data sequences in 3D space for each of the cipher rounds. It also uses Julia sets to form an infi-nite key space. The plaintext is divided into two square ma-trices of equal size and written using Lipschitz quaternions. A modular arithmetic was implemented for operations with quaternions. A computer-based analysis has been carried out and obtained results are shown at the end of this paper. Source

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