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Let D be a strong digraph. The strong distance between two vertices u and v in D, denoted by sdD(u,v), is the minimum size (the number of arcs) of a strong subdigraph of D containing u and v. For a vertex v of D, the strong eccent...
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Let D be a strong digraph. The strong distance between two vertices u and v in D, denoted by sdD(u,v), is the minimum size (the number of arcs) of a strong subdigraph of D containing u and v. For a vertex v of D, the strong eccentricity se(v) is the strong distance between v and a vertex farthest from v. The minimum strong eccentricity among all vertices of D is the strong radius, denoted by srad(D), and the maximum strong eccentricity is the strong diameter, denoted by sdiam(D). The optimal strong radius (resp. strong diameter) srad(G) (resp. sdiam(G)) of a graph G is the minimum strong radius (resp. strong diameter) over all strong orientations of G. Juan et al. (2008) [Justie Su-Tzu Juan, Chun-Ming Huang, I-Fan Sun, The strong distance problem on the Cartesian product of graphs, Inform. Process. Lett. 107 (2008) 4551] provided an upper and a lower bound for the optimal strong radius (resp. strong diameter) of the Cartesian products of any two connected graphs. In this work, we determine the exact value of the optimal strong radius of the Cartesian products of two connected graphs and a new upper bound for the optimal strong diameter. Furthermore, these results are also generalized to the Cartesian products of any n (n>2) connected graphs.
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In this paper, we synthesized ~105 ± 15 nm cubic phase KMnF_3:Yb~(3+),Er~(3+) NPs, ~195 ± 10 nm hexagonal phase NaYF_4:Yb~(3+),Tm~(3+) NPs, and ~200 ± 10 nm hexagonal phase NaYF_4:Yb~(3+),Er~(3+) NPs. Under the excitation of 98...
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In this paper, we synthesized ~105 ± 15 nm cubic phase KMnF_3:Yb~(3+),Er~(3+) NPs, ~195 ± 10 nm hexagonal phase NaYF_4:Yb~(3+),Tm~(3+) NPs, and ~200 ± 10 nm hexagonal phase NaYF_4:Yb~(3+),Er~(3+) NPs. Under the excitation of 980 nm, the strong red upconversion luminescence (~4F_(9/2)→~4I_(15/2), the peak is located at ~653 nm) of Er~(3+) ions of KMnF_3:Yb~(3+),Er~(3+) NPs can be seen, the strong blue upconversion luminescence (~1D_2→~3F_4, ~1G_4→~3H_6; the peaks are located at ~451nm and ~477 nm, respectively) of Tm~(3+) ions of NaYF_4:Yb~(3+),Tm~(3+) NPs can be observed, and the strong green upconversion luminescence (~4I_(11/2)→~4I_(15/2), 4S3/2→~4I_(15/2); the peaks are located at ~524nm and ~541 nm, respectively) of Er~(3+) ions of NaYF_4:Yb~(3+),Er~(3+) NPs can be found. The mixed white upconversion luminescent materials can be obtained by adjusting the doping ratio of the above NPs. Cyclohexane solution of red, blue, green, and the mixed white NPs can be used as ink, and "JLNU" is written on paper with a pen. Without 980nm radiation, nothing could be seen. Under 980 nm irradiation, the colored letters "JLNU" can be seen. Red, blue, green, and the mixed white upconversion NPs can be used in security anticounterfeiting.
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Abstract For a graph G, L(G)2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemarg...
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Abstract For a graph G, L(G)2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L(G)^2$$\end{document} is the square of the line graph of G – that is, vertices of L(G)2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L(G)^2$$\end{document} are edges of G and two edges e,f∈E(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e,f\in E(G)$$\end{document} are adjacent in L(G)2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L(G)^2$$\end{document} if at least one vertex of e is adjacent to a vertex of f and e≠f\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e\ne f$$\end{document}. The strong chromatic index of G, denoted by s′(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s'(G)$$\end{document}, is the chromatic number of L(G)2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L(G)^2$$\end{document}. A strong clique in G is a clique in L(G)2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L(G)^2$$\end{document}. Finding a bound for the maximum size of a strong clique in a graph with given maximum degree is a problem connected to a famous conjecture of Erd?s and Ne?et?il concerning strong chromatic index of graphs. In this note we prove that a size of a strong clique in a claw-free graph with maximum degree Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta $$\end{document} is at most Δ2+12Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta ^2 + \frac{1}{2}\varDelta $$\end{document}. This result improves the only known result 1.125Δ2+Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.125\varDelta ^2+\varDelta $$\end{document}, which is a bound for the strong chromatic index of claw-free graphs.
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We introduce adequate concepts of expansion of a digraph to obtain a sequential construction of minimal strong digraphs. We characterize the necessary and sufficient condition for an external expansion of a minimal strong digraph ...
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We introduce adequate concepts of expansion of a digraph to obtain a sequential construction of minimal strong digraphs. We characterize the necessary and sufficient condition for an external expansion of a minimal strong digraph to be a minimal strong digraph. We prove that every minimal strong digraph of order n≥2 is the expansion of a minimal strong digraph of order n-1 and we give sequentially generative procedures for the constructive characterization of the classes of minimal strong digraphs. Finally we describe algorithms to compute unlabeled minimal strong digraphs and their isospectral classes.
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There are several theorems describing the intricate relationship between flatness and associated primes over commutative Noetherian rings. However, associated primes are known to act badly over non-Noetherian rings, so one needs a...
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There are several theorems describing the intricate relationship between flatness and associated primes over commutative Noetherian rings. However, associated primes are known to act badly over non-Noetherian rings, so one needs a suitable replacement. In this paper, we show that the behavior of strong Krull primes most closely resembles that of associated primes over a Noetherian ring. We prove an analogue of a theorem of Epstein and Yao characterizing flat modules in terms of associated primes by replacing them with strong Krull primes. Also, we partly generalize a classical equational theorem regarding flat base change and associated primes in Noetherian rings. That is, when associated primes are replaced by strong Krull primes, we show containment in general and equality in many special cases. One application is of interest over any Noetherian ring of prime characteristic. We also give numerous examples to show that our results fail if other popular generalizations of associated primes are used in place of strong Krull primes.
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Strong field control scenarios are investigated in the CH_3I predissociation dynamics at the origin of the second absorption B-band, in which state-selective electronic predissociation occurs through the crossing with a valence di...
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Strong field control scenarios are investigated in the CH_3I predissociation dynamics at the origin of the second absorption B-band, in which state-selective electronic predissociation occurs through the crossing with a valence dissociative state. Dynamic Stark control (DSC) and pump–dump strategies are shown capable of altering both the predissociation lifetime and the product branching ratio.
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Patient’s perceptions are gaining popularity to evaluate the quality of healthcare facilities delivered. A study was conducted to understand the visual comfort condition of hospital ward patients with reference to the physical as...
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Patient’s perceptions are gaining popularity to evaluate the quality of healthcare facilities delivered. A study was conducted to understand the visual comfort condition of hospital ward patients with reference to the physical aspects of natural, artificial and ambient light. We undertook an observational study in which 136 consecutive inpatients of both the genders were evaluated. POE (Post occupancy evaluation) questionnaire method for visual comfort in 3 multi-specialty hospitals was used for assessment. Post occupancy evaluation allows direct comparison of the physical parameters with the inputs of the occupant’s perception. The gathered data was analyzed using SPSS statistical package to determine the co-relation in patient’s visual comfort and light levels. The qualitative findings noted a positive contribution of patient satisfaction and daylight (72%) as well as ambient daylight levels (77%). Thus, there is preference for natural day lighting as against artificial lighting and natural lighting reduces lighting energy demand. Also, there is a positive preference to certain illumination quality and levels in patients for visual comfort.? This study hence provides data for visual comfort which is the main and yet understudied determinant of lighting requirements in a ward setup and also suggests economical recommendations to modify architectural design and maximize use of natural light in wards.
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Given a directed graph G, an edge is a strong bridge if its removal increases the number of strongly connected components of G. Similarly, we say that a vertex is a strong articulation point if its removal increases the number of ...
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Given a directed graph G, an edge is a strong bridge if its removal increases the number of strongly connected components of G. Similarly, we say that a vertex is a strong articulation point if its removal increases the number of strongly connected components of G. In this paper, we present linear-time algorithms for computing all the strong bridges and all the strong articulation points of directed graphs, solving an open problem posed in Beldiceanu et al. (2005) [2].
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The strong resolving graph G(SR) of a connected graph G was introduced by Oellermann and Peters-Fransen (2007) as a tool to study the strong metric dimension of G. Recently, Kuziak et al. (2018) studied the realization and charact...
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The strong resolving graph G(SR) of a connected graph G was introduced by Oellermann and Peters-Fransen (2007) as a tool to study the strong metric dimension of G. Recently, Kuziak et al. (2018) studied the realization and characterization problems of strong resolving graphs and they pose a conjecture: The graph equation G(SR) congruent to K-r,K-s has no solution for any r, s >= 2. In this paper we give a positive answer to this conjecture. (C) 2019 Elsevier B.V. All rights reserved.
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