On the chromatic number of random graphs

In this paper we consider the classical Erdős–Rényi model of random graphs G_n,p. We show that for p=p(n)n^−3/4−δ, for any fixed δ>0, the chromatic number χ(G_n,p) is a.a.s. ℓ, ℓ+1, or ℓ+2, where ℓ is the maximum integer satisfying 2(ℓ−1)log(ℓ−1)p(n−1).     

Multifunctional lanthanum tetraphosphonates: flexible, ultramicroporous and proton-conducting hybrid frameworks

A new flexible ultramicroporous solid, La(H(5)DTMP)·7H(2)O (1), has been crystallized at room temperature using the tetraphosphonic acid H(8)DTMP, hexamethylenediamine-N,N,N',N'-tetrakis(methylenephosphonic acid). Its crystal structure, solved by synchrotron powder X-ray diffraction, is characterised by a 3D pillared open-framework containing 1D channels filled with water. Upon dehydration, a new related crystalline phase, La(H(5)DTMP) (2) is formed. Partial rehydration of 2 led to La(H(5)DTMP)·2H(2)O (3). These new phases contain highly corrugated layers showing different degrees of conformational flexibility of the long organic chain. The combination of the structural study and the gas adsorption characterization (N(2) and CO(2)) suggests an ultramicroporous flexible framework. NO isotherms are indicative of a strong irreversible adsorption of NO within the pores. Impedance data indicates that 1 is a proton-conductor with a conductivity of 8 × 10(-3) S cm(-1) at 297 K and 98% of relative humidity, and an activation energy of 0.25 eV.     

Investigation of viscosity and crystallization in supercooled-liquid region of Zr-based glassy alloys

Using viscosity measurement method and in-situ heating synchrotron radiation, the viscosity of the (Zr_0.55Al_0.1Ni_0.05Cu_0.3)_100 ? xY_x (x = 0, 0.5, 1, 2) bulk metallic glasses (BMGs) in their supercooled liquid regions (SLRs) and the in-situ heating nucleation were investigated, respectively. In the SLR, the (Zr_0.55Al_0.1Ni_0.05Cu_0.3)₉₉Y₁ metallic glass which shows distinct plastic strain in compression exhibits higher viscosity than the other three BMGs, however their Poisson's ratios are almost the same. The synchrotron diffraction results show that crystallization happened in the SLR of the (Zr_0.55Al_0.1Ni_0.05Cu_0.3)₉₉Y₁ glassy alloy, which could be the reason for the higher viscosity and larger plastic strain in compression compared to the other three alloys. The fracture surfaces of the glassy alloys were observed and analyzed.     

A Simple Road for the Transformation of Few-Layer Graphene into MWNTs

We report the direct formation of multiwalled carbon nanotubes (MWNT) by ultrasonication of graphite in dimethylformamide (DMF) upon addition of ferrocene aldehyde (Fc-CHO). The tubular structures appear exclusively at the edges of graphene layers and contain Fe clusters. Fc in conjunction with benzyl aldehyde, or other Fc derivatives, does not induce formation of NT. Higher amounts of Fc-CHO added to the dispersion do not increase significantly MWNT formation. Increasing the temperature reduces the amount of formation of MWNTs and shows the key role of ultrasound-induced cavitation energy. It is concluded that Fc-CHO first reduces the concentration of radical reactive species that slice graphene into small moieties, localizes itself at the edges of graphene, templates the rolling up of a sheet to form a nanoscroll, where it remains trapped, and finally accepts and donates unpaired electron to the graphene edges and converts the less stable scroll into a MWNT. This new methodology matches the long held notion that CNTs are rolled up graphene layers. The proposed mechanism is general and will lead to control the production of carbon nanostructures by simple ultrasonication treatments.     

Sample sonication after trichloroacetic acid precipitation increases protein recovery from cultured hippocampal neurons, and improves resolution and reproducibility in two-dimensional gel electrophoresis

Protein precipitation with TCA followed by acetone washing is frequently used to clean samples before 2-DE. However, the difficulty in solubilizing TCA-precipitated proteins causes some variability in 2-D gels and makes it difficult to detect some proteins. In this work we show that sonication of the samples, after TCA precipitation followed by elution in sample buffer, increases total protein recovery, and improves reproducibility and matching ratios between gels when analyzed by specialized software.     

Ab initio calculations of the O1s XPS spectra of ZnO and Zn oxo compounds

O1s core level binding energies of oxygen atoms in bulk ZnO, at different ZnO surfaces, and in some Zn oxo compounds were calculated by means of wave function based quantum chemical ab initio methods. Initial and final state effects were obtained by Koopmans' theorem and at the DeltaSCF level, respectively. After correction for scalar relativistic effects and electron correlation, the calculated XPS peak positions are in excellent agreement with the available experimental data for all systems included in the present study. The O1s core level shifts between an isolated H2O molecule and the Zn oxo compounds or ZnO, as well as between oxygen atoms in bulk ZnO and at various ZnO surfaces, can be understood by means of Madelung potentials and electronic relaxation or screening. XPS spectra were calculated for various cluster models which are designed to describe different possibilities of stabilizing the polar O-terminated ZnO(0001) surface by the adsorption of H atoms. The experimental spectra are only compatible with the theoretical results for the fully hydroxylated H-ZnO(0001) surface exhibiting a (1x1) surface structure.     

Ab initio calculations for the Zn 2s and 2p core level binding energies in Zn oxo compounds and ZnO

The Zn 2s and 2p core level binding energies of ZnO and a few Zn oxo compounds containing Zn in its oxidation state +2 were calculated by means of wave function based quantum chemical ab initio methods. The computations were performed at two levels of approximation. First, Hartree-Fock calculations were carried out for the ground state of the neutral systems yielding the "initial state" effects, i.e. the shifts of the core level binding energies due to the changes in the chemical environment of the Zn atom under consideration (Koopmans' theorem level, KT). In the second step, Hartree-Fock calculations were performed for the core ionized states in order to account for the relaxation effects after ionization, i.e. for the "final state" effects (DeltaSCF level). Scalar relativistic corrections and spin-orbit coupling were included in a "spin-orbit-coupling configuration interaction" (SOC-CI) treatment both at the KT and DeltaSCF levels. In all Zn oxo compounds (Zn(4)O(formate)(6), Zn(4)O(acetate)(6) and several ZnO cubanes) small negative initial state shifts between -1.0 and 0.0 eV (relative to the free Zn atom) were found which are caused by the negative charges at the surrounding O atoms. The relaxation effects vary between -1.0 and -0.5 eV, such that the calculated total shifts are moderately negative (-1.5 to -0.5 eV). Embedded ZnO clusters of increasing size, ranging from Zn(13)O(4) to Zn(69)O(38), were used as models for bulk ZnO, the Zn 2s and 2p core level shifts calculated for these clusters being extrapolated to infinite cluster size. The calculations show that bulk ZnO has a rather large negative initial state shift of -2.1 +/- 0.1 eV, due to the Madelung potential at the Zn atom, and a comparatively small relaxation contribution of -1.0 +/- 0.1 eV. This yields a total shift of -3.1 +/- 0.2 eV (both for 2s and 2p, relative to atomic Zn), which is in very good agreement with experiment, -2.9 +/- 0.2 eV. The surprising experimental observation that the Zn 2s and 2p XPS peak positions are nearly identical in Zn metal and ZnO is explained by the fact that the sum of initial and final state effects is accidentally the same for the two systems though the individual contributions differ quite significantly: the initial and final state shifts amount to +2.4 and -5.1 eV for Zn metal vs.-2.1 and -1.0 eV for ZnO.     

Synthesis of oxadiazoloquinoxaline,oxathiadiazoloquinoxaline and oxadiazolobenzothiazine derivatives

Bis‐amidoxime 1 reacts with phosgene, thiophosgene and thionylchloride to give the corresponding bisfused oxadiazolo‐ and oxathiadiazoloquinoxalines 2, 4, 5 along with the unexpected furazano‐derivative 3 , while monoamidoximes 9, 13 by treatment with ethyl chloroformate affords the oxadiazoloquinoxaline and the oxadiazolobenzothiazine derivatives 14, 15 along with the dicarboxylated product 16 .     

On the representability of totally unimodular matrices on bidirected graphs

We present a polynomial time algorithm to construct a bidirected graph for any totally unimodular matrix B by finding node-edge incidence matrices Q and S such that QB=S. Seymour’s famous decomposition theorem for regular matroids states that any totally unimodular (TU) matrix can be constructed through a series of composition operations called k-sums starting from network matrices and their transposes and two compact representation matrices B₁,B₂ of a certain ten element matroid. Given that B₁,B₂ are binet matrices we examine the k-sums of network and binet matrices. It is shown that thek-sum of a network and a binet matrix is a binet matrix, but binet matrices are not closed under this operation for k=2,3. A new class of matrices is introduced, the so-called tour matrices, which generalise network, binet and totally unimodular matrices. For any such matrix there exists a bidirected graph such that the columns represent a collection of closed tours in the graph. It is shown that tour matrices are closed under k-sums, as well as under pivoting and other elementary operations on their rows and columns. Given the constructive proofs of the above results regarding the k-sum operation and existing recognition algorithms for network and binet matrices, an algorithm is presented which constructs a bidirected graph for any TU matrix.     

Safe density ratio modeling

An important problem in logistic regression modeling is the existence of the maximum likelihood estimators. In particular, when the sample size is small, the maximum likelihood estimator of the regression parameters does not exist if the data are completely, or quasicompletely separated. Recognizing that this phenomenon has a serious impact on the fitting of the density ratio model–which is a semiparametric model whose profile empirical log-likelihood has the logistic form because of the equivalence between prospective and retrospective sampling–we suggest a linear programming methodology for examining whether the maximum likelihood estimators of the finite dimensional parameter vector of the model exist. It is shown that the methodology can be effectively utilized in the analysis of case–control gene expression data by identifying cases where the density ratio model cannot be applied. It is demonstrated that naive application of the density ratio model yields erroneous conclusions.