Asymptotic enumeration of dense 0-1 matrices with specified line sums

Let s=(s₁,s₂,…,sm) and t=(t₁,t₂,…,tn) be vectors of non-negative integers with . Let B(s,t) be the number of m×n matrices over {0,1} with jth row sum equal to sj for 1?j?m and kth column sum equal to tk for 1?k?n. Equivalently, B(s,t) is the number of bipartite graphs with m vertices in one part with degrees given by s, and n vertices in the other part with degrees given by t. Most research on the asymptotics of B(s,t) has focused on the sparse case, where the best result is that of Greenhill, McKay and Wang (2006). In the case of dense matrices, the only precise result is for the case of equal row sums and equal column sums (Canfield and McKay, 2005). This paper extends the analytic methods used by the latter paper to the case where the row and column sums can vary within certain limits. Interestingly, the result can be expressed by the same formula which holds in the sparse case.     

On planarity of compact, locally connected, metric spaces

Independently, Claytor [Ann. Math. 35 (1934), 809–835] and Thomassen [Combinatorica 24 (2004), 699–718] proved that a 2-connected, compact, locally connected metric space is homeomorphic to a subset of the sphere if and only if it does not contain K ₅ or K _3;3. The “thumbtack space” consisting of a disc plus an arc attaching just at the centre of the disc shows the assumption of 2-connectedness cannot be dropped. In this work, we introduce “generalized thumbtacks” and show that a compact, locally connected metric space is homeomorphic to a subset of the sphere if and only if it does not contain K ₅, K _3;3, or any generalized thumbtack, or the disjoint union of a sphere and a point.     

The asymptotic numbers of regular tournaments,Eulerian digraphs and Eulerian oriented graphs

LetRT(n), ED(n) andEOG(n) be the number of labelled regular tournaments, labelled loop-free simple Eulerian digraphs, and labelled Eulerian oriented simple graphs, respectively, onn vertices. Then, asn,, for any>0. The last two families of graphs are also enumerated by their numbers of edges. The proofs use the saddle point method applied to appropriaten-dimensional integrals.     

Demonstration of a 100 Hz repetition rate gain-saturated diode-pumped table-top soft x-ray laser

We demonstrate the operation of a gain-saturated table-top soft x-ray laser at 100?Hz repetition rate. The laser generates an average power of 0.15?mW at λ=18.9 nm, the highest laser power reported to date from a sub-20-nm wavelength compact source. Picosecond laser pulses of 1.5?μJ energy were produced at λ=18.9 nm by amplification in a Mo plasma created by tailoring the temporal intensity profile of single pump pulses with 1?J energy produced by a diode-pumped chirped pulse amplification Yb:YAG laser. Lasing was also obtained in the 13.9?nm line of Ni-like Ag. These results increase by an order of magnitude the repetition rate of plasma-based soft x-ray lasers opening the path to milliwatt average power table-top lasers at sub-20?nm wavelengths.     

Simultaneous high speed PIV and CH PLIF using R-branch excitation in the C2Σ+-X2Π (0,0) band

Simultaneous particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) utilizing R-branch transitions in the C-X (0,0) band were performed at a 10-kHz repetition-rate in a turbulent premixed flame. The CH lines at 310.690?nm (from the R-branch of the C-X band) used here have greater efficiency than A-X and B-X transitions, which allows for high-framerate imaging with low laser pulse energy. Most importantly, the simultaneous imaging of both CH PLIF and PIV is enabled by the use of a custom edge filter, which blocks scattering at the laser wavelength (below ～311?nm) while efficiently transmitting fluorescence at longer wavelengths. The Hi-Pilot Bunsen burner operated with a turbulent Reynolds number of 7900 was used to demonstrate simultaneous PIV and CH PLIF utilizing this filtered detection scheme. Instances where pockets of products were observed well upstream of the mean flame brush are found to be the result of out-of-plane motion of the flame sheet. Such instances can lead to ambiguous results when interpreting the thickness of reaction layers. However, the temporally resolved nature of the present diagnostics facilitate the identification and proper treatment of such situations. The strategy demonstrated here can yield important information in the study of turbulent flames by providing temporally resolved flame dynamics in terms of flame sheet visualization and velocity fields.     

An unconventional method for measuring the Tc L3‐edge of technetium compounds

Tc L₃‐edge XANES spectra have been collected on powder samples of SrTcO₃ (octahedral Tc⁴⁺) and NH₄TcO₄ (tetrahedral Tc⁷⁺) immobilized in an epoxy resin. Features in the Tc L₃‐edge XANES spectra are compared with the pre‐edge feature of the Tc K‐edge as well as other 4d transition metal L₃‐edges. Evidence of crystal field splitting is obvious in the Tc L₃‐edge, which is sensitive to the coordination number and oxidation state of the Tc cation. The Tc L₃ absorption edge energy difference between SrTcO₃ (Tc⁴⁺) and NH₄TcO₄ (Tc⁷⁺) shows that the energy shift at the Tc L₃‐edge is an effective tool for studying changes in the oxidation states of technetium compounds. The Tc L₃‐edge spectra are compared with those obtained from Mo and Ru oxide standards with various oxidation states and coordination environments. Most importantly, fitting the Tc L₃‐edge to component peaks can provide direct evidence of crystal field splitting that cannot be obtained from the Tc K‐edge.     

Highly symmetric networks derived from cubane-related octametallic complexes of a new oxyanion of carbon, C4O7(4-), each molecule attached to eight neighbors by 24 equivalent hydrogen bonds

Aqueous reaction mixtures containing dihydroxyfumaric acid, M2+ (M = Zn, Co, Fe, and Mg) and acetate ion at room temperature give crystals, suitable for single-crystal X-ray diffraction studies, of composition [(MII)8(C4O7)4(H2O)12].24H2O, in which the C4O74- component is the alkoxide-tricarboxylate tetra-anionic species -OC(CO2-)3, a new oxyanion of carbon. All four compounds crystallize in the body-centered space group I3m with cell dimensions a approximately 15.0 A. Discrete electrically neutral [(MII)8(C4O7)4(H2O)12] molecules are present, with a cubane-like core consisting of four trigonal prismatic metal centers and four mu3-alkoxo bridges from separate -OC(CO2-)3 ligands. The octametallic molecule is highly symmetrical, with four fac tri-aqua octahedral metal centers tetrahedrally appended to the central cubane-based [(MII)8(C4O7)4 ]8- unit. The molecules assemble in the crystal in a body-centered cubic fashion, each being attached to its eight neighbors by 24 equivalent hydrogen bonds-an extreme example of self-complementarity.     

Comparative tests to improve the gas chromatographic analysis of chlorobornanes in fish samples

A comparison was made between electron capture negative ionization quadrupole mass spectrometry (ECNI-MS) and electron capture detection (ECD) with regard to repeatability and reproducibility for the gas chromatographic (GC) analysis of toxaphene congeners [chlorobornanes (CHBs)]. The tests, including standard solutions and several cleaned fish extracts, showed larger relative standard deviations (RSDs) for the repeatability of ECNI-MS but no differences in the reproducibility of the 2 techniques. The sensitivity of the GC-ECNI-MS was considerably better than that of GC/ECD. Four stepwise-designed comparative tests were also conducted on GC analysis, cleanup, and the complete method. The results showed that, according to the current state-of-the-art, coefficients of variation for the between-laboratory performance were not < 20% and were usually between 20 and 30%. In spite of separation problems, e.g., for CHB 26, which cannot be separated into a single-component peak, a 95% methyl 5% phenyl polysiloxane (CP Sil 8) column was preferred to more polar columns for the analysis of CHBs 26, 40, 41, 44, 50, and 62. CHB 62 was more difficult to determine than CHB 26 and 50. Addition of the CHBs 40, 41, and 44 to the standard set of 3 chlorobornanes (26, 50, and 62) resulted in more separation problems. A 3-step cleanup method was recommended.