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1.
A strong edge-coloring of a graph is a proper edge-coloring such that edges at distance at most 2 receive different colors. It is known that every planar graph has a strong edge-coloring by using at most 4Δ+4 colors, where Δ denotes the maximum degree of the graph. In this paper, we will show that 19 colors are enough to color a planar graph with maximum degree 4.  相似文献   
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We report the synthesis of a new class of thermally stable and strongly luminescent cyclometalated iridium(III) complexes 1 – 6 , which contain the 2‐acetylbenzo[b]thiophene‐3‐olate (bt) ligand, and their application in organic light‐emitting diodes (OLEDs). These heteroleptic iridium(III) complexes with bt as the ancillary ligand have a decomposition temperature that is 10–20 % higher and lower emission self‐quenching constants than those of their corresponding complexes with acetylacetonate (acac). The luminescent color of these iridium(III) complexes could be fine‐tuned from orange (e.g., 2‐phenyl‐6‐(trifluoromethyl)benzo[d]thiazole (cf3bta) for 4 ) to pure red (e.g., lpt (Hlpt=4‐methyl‐2‐(thiophen‐2‐yl)quinolone) for 6 ) by varying the cyclometalating ligands (C‐deprotonated C^N). In particular, highly efficient OLEDs based on 6 as dopant (emitter) and 1,3‐bis(carbazol‐9‐yl)benzene (mCP) as host that exhibit stable red emission over a wide range of brightness with CIE chromaticity coordinates of (0.67, 0.33) well matched to the National Television System Committee (NTSC) standard have been fabricated along with an external quantum efficiency (EQE) and current efficiency of 9 % and 10 cd A?1, respectively. A further 50 % increase in EQE (>13 %) by replacing mCP with bis[4‐(6H‐indolo[2,3‐b]quinoxalin‐6‐yl)phenyl]diphenylsilane (BIQS) as host for 6 in the red OLED is demonstrated. The performance of OLEDs fabricated with 6 (i.e., [(lpt)2Ir(bt)]) was comparable to that of the analogous iridium(III) complex that bore acac (i.e., [(lpt)2Ir(acac)]; 6 a in this work) [Adv. Mater.­ 2011 , 23, 2981] fabricated under similar conditions. By using ntt (Hnnt=3‐hydroxynaphtho[2,3‐b]thiophen‐2‐yl)(thiophen‐2‐yl)methanone) ligand, a substituted derivative of bt, the [(cf3bta)2Ir(ntt)] was prepared and found to display deep red emission at around 700 nm with a quantum yield of 12 % in mCP thin film.  相似文献   
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We adopt an orthogonal wavelet packet decomposition (OWPD) filtering approach to cancel harmonic interference noises arising from an AC power source in time domain and remove the resulting rf voltage interference noise from the mass spectra acquired by using a charge detection frequency-scan quadrupole ion trap mass spectrometer. With the use of a phase lock resampling technique, the transform coefficients of the rf interference in signals become a constant, exhibiting a shift of the baseline in different rf phases. The rf interference is therefore removable by shifting the baselines back to zero in OWPD coefficients. The approach successfully reduces the time-domain background noise from 1367 electrons (rms) to 408 electrons (rms) (an improvement of 70?%) and removes the high frequency noise components in the charge detection ion trap mass spectrometry. Unlike other smoothing or averaging methods commonly used in the mass-to-charge (m/Ze) domain, our approach does not cause any distortion of original signals.  相似文献   
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The Laplacian, signless Laplacian and normalized Laplacian characteristic polynomials of a graph are the characteristic polynomials of its Laplacian matrix, signless Laplacian matrix and normalized Laplacian matrix, respectively. In this paper, we mainly derive six reduction procedures on the Laplacian, signless Laplacian and normalized Laplacian characteristic polynomials of a graph which can be used to construct larger Laplacian, signless Laplacian and normalized Laplacian cospectral graphs, respectively.  相似文献   
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The second largest Laplacian eigenvalue of a graph is the second largest eigenvalue of the associated Laplacian matrix. In this paper, we study extremal graphs for the extremal values of the second largest Laplacian eigenvalue and the Laplacian separator of a connected graph, respectively. All simple connected graphs with second largest Laplacian eigenvalue at most 3 are characterized. It is also shown that graphs with second largest Laplacian eigenvalue at most 3 are determined by their Laplacian spectrum. Moreover, the graphs with maximum and the second maximum Laplacian separators among all connected graphs are determined.  相似文献   
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Chemical reaction systems are dynamical systems that arise in chemical engineering and systems biology. In this work, we consider the question of whether the minimal (in a precise sense) multistationary chemical reaction networks, which we propose to call ‘atoms of multistationarity,’ characterize the entire set of multistationary networks. Our main result states that the answer to this question is ‘yes’ in the context of fully open continuous-flow stirred-tank reactors (CFSTRs), which are networks in which all chemical species take part in the inflow and outflow. In order to prove this result, we show that if a subnetwork admits multiple steady states, then these steady states can be lifted to a larger network, provided that the two networks share the same stoichiometric subspace. We also prove an analogous result when a smaller network is obtained from a larger network by ‘removing species.’ Our results provide the mathematical foundation for a technique used by Siegal- Gaskins et al. of establishing bistability by way of ‘network ancestry.’ Additionally, our work provides sufficient conditions for establishing multistationarity by way of atoms and moreover reduces the problem of classifying multistationary CFSTRs to that of cataloging atoms of multistationarity. As an application, we enumerate and classify all 386 bimolecular and reversible two-reaction networks. Of these, exactly 35 admit multiple positive steady states. Moreover, each admits a unique minimal multistationary subnetwork, and these subnetworks form a poset (with respect to the relation of ‘removing species’) which has 11 minimal elements (the atoms of multistationarity).  相似文献   
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L(j,k)-number of Direct Product of Path and Cycle   总被引:1,自引:0,他引:1  
For positive numbers j and k, an L(j,k)-labeling f of G is an assignment of numbers to vertices of G such that |f(u)-f(v)|≥j if uv∈E(G), and |f(u)-f(v)|≥k if d(u,v)=2. Then the span of f is the difference between the maximum and the minimum numbers assigned by f. The L(j,k)-number of G, denoted by λj,k(G), is the minimum span over all L(j,k)-labelings of G. In this paper, we give some results about the L(j,k)-number of the direct product of a path and a cycle for j≤k.  相似文献   
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