Critical vertices in k-connected digraphs Mader, W.
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg,
10/2017, Letnik:
87, Številka:
2
Journal Article
Recenzirano
Odprti dostop
It is proved that every non-complete, finite digraph of connectivity number
k
has a fragment
F
containing at most
k
critical vertices. The following result is a direct consequence: every
k
...-connected, finite digraph
D
of minimum out- and indegree at least
2
k
+
m
-
1
for positive integers
k
, m has a subdigraph
H
of minimum outdegree or minimum indegree at least
m
-
1
such that
D
-
x
is
k
-connected for all
x
∈
V
(
H
)
. For
m
=
1
, this implies immediately the existence of a vertex of indegree or outdegree less than 2
k
in a
k
-critical, finite digraph, which was proved in Mader (J Comb Theory (B) 53:260–272,
1991
).
Modeling of dynamical systems using ordinary differential equations is a popular approach in the field of systems biology. Two of the most critical steps in this approach are to construct dynamical ...models of biochemical reaction networks for large datasets and complex experimental conditions and to perform efficient and reliable parameter estimation for model fitting. We present a modeling environment for MATLAB that pioneers these challenges. The numerically expensive parts of the calculations such as the solving of the differential equations and of the associated sensitivity system are parallelized and automatically compiled into efficient C code. A variety of parameter estimation algorithms as well as frequentist and Bayesian methods for uncertainty analysis have been implemented and used on a range of applications that lead to publications.
The Data2Dynamics modeling environment is MATLAB based, open source and freely available at http://www.data2dynamics.org.
andreas.raue@fdm.uni-freiburg.de
Supplementary data are available at Bioinformatics online.
Energy-loss near-edge structure (ELNES) data of Mn-L2,3 and Fe-L2,3 ionization edges have been measured by means of quantitative electron energy-loss spectroscopy (EELS) for two series of Mn and Fe ...oxides with known formal cation oxidation states. In both series the absolute energy positions of Mn-L2,3 and Fe-L2,3 white-lines, as well as the white-line intensity ratio (L3/L2) vary with cation oxidation states. Additionally, spin–orbit spitting, i.e. the energy difference ΔE(L2−L3) between Mn-L2,3 white-lines decreases with increasing Mn oxidation state. With these data from known standards calibration curves on white-line intensity ratio Mn(L3/L2) vs. Mn oxidation state, and Fe(L3/L2) vs. Fe oxidation state were established.
EELS measurements on Mn and Fe doped ZnO thin films showed that the valence states of the dopants can unambiguously be determined by calibrating the Mn-L2,3 and Fe-L2,3 ELNES data against the measured standards. It is revealed that Mn in ZnO adopt a divalent state, thus Mn2+ ions substitute for Zn2+, whereas Fe dopants retain a trivalent oxidation state in the ZnO host lattice. Measurements on (Ba, Fe, Mn)-oxides revealed that both Fe and Mn cations are in a trivalent state. Thus, it is assumed that Mn3+ can partially be substituted for Fe3+ in barium hexaferrites.
Crystals of the quaternary compound In1-xGa1+xO3(ZnO)0.5 were grown by the optical floating-zone method using a mirror furnace with halogen lamps as heat source. X-ray diffraction (XRD) and electron ...diffraction yielded a hexagonal crystal system and the space group P63/mmc (No. 194). Structure refinement from single crystal XRD data at −90 °C (a = 3.3137(1) Å; c = 29.523(1) Å; wR2: 0.054) revealed a structure isotypic to YbFeO3(FeO)0.5 and consists of three different alternating layers: (i) layer of edge-sharing InO6 octahedra, (ii) a pair of two layers of corner-sharing (Ga/Zn)O4 tetrahedra corresponding to wurtzite structure type, and (iii) a layer of GaO5 trigonal-bipyramids (tbp). The polyhedra of layers (ii) and (iii) share corners with the InO6 octahedra, resulting in inverted orientations of the two (Ga/Zn)O4 layers in the wurtzite type region. Additionally, atomic resolution imaging in the electron microscope proves a perfect periodic stacking of the atomic layers. The analysis of individual crystals revealed an excess of Ga expressed by the composition range In1-xGa1+xO3(ZnO)0.5 with 0.20 ≤ x ≤ 0.82, determined by energy dispersive X-ray spectroscopy (EDXS). Consequently, the octahedral site is occupied with In and Ga in a ratio of In:Ga = 0.80:0.20 to 0.18:0.82, assuming that the tbp sites are only occupied by Ga. The transparent crystals as-received from floating-zone growth had a blueish color and became colorless after annealing at 1000 °C for 10 h in air. The as-prepared crystals are oxygen deficient and contain unpaired electrons (color centers) at vacant oxide sites proven by electron paramagnetic resonance with g-value of ca. 2.
InGaO3(ZnO)0.5 crystal imaged by high-resolution TEM with resolved cation positions and extracted EDX line-scan profiles for In, Ga and Zn as overlay. Section of crystal structure fits at cation positions. Display omitted
•First detailed X-ray structure analysis of InGaO3(ZnO)0.5 – IGZO with lowest Zn content.•Resolved cation layer distribution by high resolution (S)TEM studies.•First single crystals of InGaO3(ZnO)0.5 obtained by optical floating-zone method.•Color centers in oxygen deficient crystals proven by color change and electron paramagnetic resonance.
The X-ray crystal structure of the nucleosome core particle of chromatin shows in atomic detail how the histone protein octamer is assembled and how 146 base pairs of DNA are organized into a ...superhelix around it. Both histone/histone and histone/DNA interactions depend on the histone fold domains and additional, well ordered structure elements extending from this motif. Histone amino-terminal tails pass over and between the gyres of the DNA superhelix to contact neighbouring particles. The lack of uniformity between multiple histone/DNA-binding sites causes the DNA to deviate from ideal superhelix geometry.
Anode-supported Solid Oxide Fuel Cells (SOFCs) built with La0.58Sr0.4Fe0.8Co0.2O3 - delta (LSCF) as cathode material exhibit a high electrochemical performance at low temperatures. However, these ...LSCF perovskites are chemically incompatible with the YSZ electrolyte, reacting to SrZrO3 which acts as an inhibitor for ion conductivity. Therefore, an interlayer between electrolyte and cathode is needed to prevent Sr2+ migration towards the electrolyte. Among the materials we could imagine for this purpose, gadolinium doped ceria, e.g. Ce0.8Gd0.2O2 - delta (CGO) shows a good performance. The electrochemical performance of these cells depends on the microstructure of the CGO layer. The deposition method plays an important role for the microstructure of the layer. The deposition methods screen printing and physical vapor deposition were compared. Among the physical vapor deposition methods, the magnetron sputtering seems to be the more accurate technology to produce nearly dense layers with efficient Sr2+ retention. The correlation between the CGO layer microstructure and the performance of the cell and the Sr2+-retention was studied.
► Inversion domain boundaries in ZnO contain one full monolayer of dopants. ► EDS spectroscopic imaging by X-ray in Cs-corrected STEM provides rapid qualitative assessment of dopant distribution. ► ...EELS spectroscopic imaging is capable of providing qualitative and quantitative analysis of IDBs in ZnO. ► Atomic structure of basal IDBs in In–ZnO nanorods, including positions of oxygen columns, is elucidated by annular bright-field (ABF)-STEM imaging, even in thick samples.
ZnO with additions of Fe
2O
3 or In
2O
3 shows characteristic inversion domain structures. ZnO domains are separated by two types of inversion domain boundaries (IDBs): basal b-IDBs parallel to (0
0
0
1) planes, and complementary pairs of three possible variants of pyramidal p-IDBs parallel to
{
2
1
¯
1
¯
5
}
lattice planes. The structure and composition of IDBs were investigated in a sophisticated aberration-corrected scanning transmission electron microscope (probe-corrected TEM/STEM). It is shown that Fe and In additions are essentially located in monolayers within the IDBs, and EELS electron spectroscopic imaging (ESI) as well as EDS spectroscopic imaging by X-rays (SIX) are capable of rapidly mapping the element distribution. With solid solubility of trivalent dopant species well below 1
at.% within ZnO domains, the lateral spacings of b-IDBs are inversely proportional to the dopant concentration. Quantification of data acquired by ESI and SIX from well defined sample regions in STEM both confirm the assumption of one full monolayer of dopants per IDB. Atom columns of cations are well resolved in HAADF STEM imaging; experimental contrast intensities are approximately proportional to
Z
1.6. Furthermore, annular bright-field (ABF)-STEM imaging is capable of resolving oxygen columns even in thick sample regions, thus providing highly localized information on atom positions and lattice distortions, and enables the construction of more reliable structure models of IDBs in doped ZnO.
The time-dependent degradation of anode-supported Solid Oxide Fuel Cells (SOFCs) with La
0.58Sr
0.4Co
0.2Fe
0.8O
3−
δ
(LSCF) cathodes has been studied. Eight SOFCs have been tested over a period of ...1000 h under different operation conditions to investigate the influence of different operation parameters on the degradation of the electrochemical performance. The cells were tested at 700 or 800 °C, at 0.3 or 0.6 A/cm
2 and with 21% or 5% O
2 at the cathode side and showed performance losses of 2–4% per 1000 h. While an elevated temperature and an elevated oxygen partial pressure had a negative influence on long-term performance, the current density did not have a clear effect. Material analysis of the cells showed a formation of SrZrO
3 at the interface of the Ce
0.8Gd
0.2O
2−
δ
interlayer and the yttria stabilized zirconia (8YSZ) electrolyte during sintering of the cathode. There are indications of a further formation of this phase during the electrochemical characterization obtained from X-ray diffraction analysis on LSCF–YSZ powder mixtures that were exposed to 800 °C for 200 h.
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