A Runge-Kutta/WENO method for solving equations for small-amplitude wave propagation in a saturated elastic porous medium

A high-accuracy Runge-Kutta/WENO method of up to fourth order with respect to time and fifth order with respect to space is developed for the numerical modeling of small-amplitude wave propagation in a steady fluid-saturated elastic porous medium. A system of governing equations is derived from a general thermodynamically consistent model of a compressible fluid flow through a saturated elastic porous medium, which is described by a hyperbolic system of conservation laws with allowance for finite deformations of the medium. The results of numerical solution of one- and two-dimensional wave fields demonstrate the efficiency of the method.     

Growth of SrTiO3 on Si(001) by hybrid molecular beam epitaxy

We report the heteroepitaxial growth of SrTiO₃ thin films on Si(001) by hybrid molecular beam epitaxy (hMBE). Here, elemental strontium and the metal‐organic precursor titanium tetraisopropoxide (TTIP) were co‐supplied in the absence of additional oxygen. The carbonization of pristine Si surfaces during native oxide removal was avoided by freshly evaporating Sr into the hMBE reactor prior to loading samples. Nucleation, growth and crystallization behavior as well a structural properties and film surfaces were characterized for a series of 46‐nm‐thick SrTiO₃ films grown with varying Sr to TTIP fluxes to study the effect of non‐stoichiometric growth conditions on film lattice parameter and surface morphology. High quality SrTiO₃ thin films with epitaxial relationship (001)SrTiO₃ || (001)Si and [110]SrTiO₃ || [100]Si were demonstrated with an amorphous layer of around 4 nm thickness formed at the SrTiO₃/Si interface. The successful growth of high quality SrTiO₃ thin films with atomically smooth surfaces using a thin film technique with scalable growth rates provides a promising route towards heterogeneous integration of functional oxides on Si. (© 2014 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Robust ordinal regression for value functions handling interacting criteria

We present a new method called UTA^GMS–INT for ranking a finite set of alternatives evaluated on multiple criteria. It belongs to the family of Robust Ordinal Regression (ROR) methods which build a set of preference models compatible with preference information elicited by the Decision Maker (DM). The preference model used by UTA^GMS–INT is a general additive value function augmented by two types of components corresponding to “bonus” or “penalty” values for positively or negatively interacting pairs of criteria, respectively. When calculating value of a particular alternative, a bonus is added to the additive component of the value function if a given pair of criteria is in a positive synergy for performances of this alternative on the two criteria. Similarly, a penalty is subtracted from the additive component of the value function if a given pair of criteria is in a negative synergy for performances of the considered alternative on the two criteria. The preference information elicited by the DM is composed of pairwise comparisons of some reference alternatives, as well as of comparisons of some pairs of reference alternatives with respect to intensity of preference, either comprehensively or on a particular criterion. In UTA^GMS–INT, ROR starts with identification of pairs of interacting criteria for given preference information by solving a mixed-integer linear program. Once the interacting pairs are validated by the DM, ROR continues calculations with the whole set of compatible value functions handling the interacting criteria, to get necessary and possible preference relations in the considered set of alternatives. A single representative value function can be calculated to attribute specific scores to alternatives. It also gives values to bonuses and penalties. UTA^GMS–INT handles quite general interactions among criteria and provides an interesting alternative to the Choquet integral.     

Convex equipartitions: the spicy chicken theorem

We show that, for any prime power $n$ and any convex body $K$ (i.e., a compact convex set with interior) in $\mathbb{R }^d$ , there exists a partition of $K$ into $n$ convex sets with equal volumes and equal surface areas. Similar results regarding equipartitions with respect to continuous functionals and absolutely continuous measures on convex bodies are also proven. These include a generalization of the ham-sandwich theorem to arbitrary number of convex pieces confirming a conjecture of Kaneko and Kano, a similar generalization of perfect partitions of a cake and its icing, and a generalization of the Gromov–Borsuk–Ulam theorem for convex sets in the model spaces of constant curvature.     

On D-posets of fuzzy sets

D-posets of fuzzy sets constitute a natural simple mathematical structure in which relevant notions of generalized probability theory can be formalized. We present a classification of D-posets leading to a hierarchy of distinguished subcategories of D-posets related to probability and study their relationships. This contributes to a better understanding of the transition from classical probability theory to fuzzy probability theory. In particular, we describe the transition from the Boolean cogenerator {0, 1} to the fuzzy cogenerator [0, 1] and prove that the generated ?ukasiewicz tribes form an epireflective subcategory of the bold algebras.     

Fixed points of a mapping and Hyers–Ulam stability

We show that many general results on Hyers–Ulam stability of some functional equations in a single variable follow immediately from a simple fixed point theorem. The theorem is formulated for self-maps of some subsets of the space of functions from a nonempty set into the set of reals. We also give some applications of that theorem, e.g., in investigations of solutions of some difference equations and functional inequalities.     

Estimates for the Derivatives of the Poisson Kernel on Nilpotent Meta-Abelian Groups

Let S be a semi direct product \(S=N\rtimes A\) where N is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and A is isomorphic with ? ^k , k?>?1. We consider a class of second order left-invariant differential operators on S of the form \(\mathcal{L}_\alpha=L^a+\Delta_\alpha,\) where α?∈?? ^k , and for each a?∈?? ^k , L ^a is left-invariant second order differential operator on N and \(\Delta_\alpha=\Delta-\langle\alpha,\nabla\rangle,\) where Δ is the usual Laplacian on ? ^k . Using some probabilistic techniques (skew-product formulas for diffusions on S and N respectively, the concept of the derivative of a measure, etc.) we obtain an upper bound for the derivatives of the Poisson kernel for \(\mathcal{L}_\alpha.\) During the course of the proof we also get an upper estimate for the derivatives of the transition probabilities of the evolution on N generated by L ^σ(t), where σ is a continuous function from [0,?∞?) to ? ^k .     

Optimization of immunoaffinity enrichment and detection: toward a comprehensive characterization of the phosphotyrosine proteome of K562 cells by liquid chromatography-mass spectrometry

Phosphorylation of protein tyrosine residues regulates many cell functions and has also been proved to be involved in oncogenesis. Thus, the identification of the phosphotyrosine (pTyr) proteome of cells is a very important task. Since tyrosine phosphorylation represents only around 1% of the total human phosphoproteome, the study of pTyr proteins is rather challenging. Here we report the optimization study of the phosphotyrosine proteome using K562 cells as a model system. A substantial segment of the phosphotyrosine proteome of K562 cells was characterized by immunoaffinity enrichment with 4G10 and PYKD1 antibodies followed by LC-MS/MS analysis. 480 non-redundant pTyr peptides corresponding to 342 pTyr proteins were found. 141 pTyr peptides were not described elsewhere. The mass spectrometry approach involving high-resolving FTMS analysis of precursor ions and subsequent detection of CID fragments in a linear ion trap was considered as optimal. For detection of low abundant pTyr peptides pooling of individual immunoaffinity enrichments for one LC-MS/MS analysis was crucial. The enrichment properties of the monoclonal PYKD1 antibody were presented for the first time, also in comparison to the 4G10 antibody. PYKD1 was found to be more effective for protein enrichment (1.2 and 5% efficiency at peptide and protein level correspondingly), while 4G10 showed better results when peptide enrichment was performed (15% efficiency versus 3.6% at protein level). Substantially different subsets of the phosphoproteome were enriched by these antibodies. This finding together with previous studies demonstrates that comprehensive pTyr proteome characterization by immunoprecipitation requires multiple antibodies to be used for the affinity enrichment.     

Variable selection in near-infrared spectroscopy: benchmarking of feature selection methods on biodiesel data

In the present work, microwave heating initiated precipitation polymerization was developed to prepare podophyllotoxin (PPT) molecularly imprinted polymers (MIPs), resulting in much shorter polymerization time and better particle morphology. Prior to the polymerization, ultraviolet and FTIR spectroscopy were used to study the interactions between PPT and the functional monomers. The synthesized parameters were respectively optimized and the optimal conditions for the efficient adsorption property were template: PPT, 1 mmol; functional monomer: acrylamide, 6 mmol; bi-crosslinker: ethylene glycol dimethacrylate, 20 mmol and divinylbenzene, 20 mmol; porogen: acetonitrile, 40 mL; initiator: azobisisobutyronitrile, 0.01mol L?1; polymerization temperature: 60°C. FTIR spectroscopy, SEM and thermal analysis were used to characterize the MIPs. The results of the equilibrium rebinding experiments and the competitive adsorption experiments showed that these imprinted polymers exhibited good adsorption ability for the PPT. Scatchard analysis illustrated that two and one types of binding sites were generated in the MIPs and non-imprinted polymers (NIPs), respectively. Using the prepared MIPs as the solid phase extraction (SPE) sorbent, PPT was extracted selectively and efficiently from Dysosma versipellis, Sinopodophyllum hexandrum and Diphylleia sinensis. The regression equation was y=5.873×10?x+17075.659 with the correlation coefficient of 0.9994 in the concentration range of 0.005-0.4 mg mL?1. After washing and eluting the SPE column with methanol and MeOH/acetic acid solution (v/v, 9:1), the limits of detection were 0.12-0.18 μg mL?1 and their recoveries were in the range of 89.5-91.1% with all RSDs lower than 3.7.     

The S1/S2 exciton interaction in 2-pyridone·6-methyl-2-pyridone: Davydov splitting, vibronic coupling, and vibronic quenching

The excitonic splitting between the S(1) and S(2) electronic states of the doubly hydrogen-bonded dimer 2-pyridone[middle dot]6-methyl-2-pyridone (2PY·6M2PY) is studied in a supersonic jet, applying two-color resonant two-photon ionization (2C-R2PI), UV-UV depletion, and dispersed fluorescence spectroscopies. In contrast to the C(2h) symmetric (2-pyridone)(2) homodimer, in which the S(1) ← S(0) transition is symmetry-forbidden but the S(2) ← S(0) transition is allowed, the symmetry-breaking by the additional methyl group in 2PY·6M2PY leads to the appearance of both the S(1) and S(2) origins, which are separated by Δ(exp) = 154 cm(-1). When combined with the separation of the S(1) ← S(0) excitations of 6M2PY and 2PY, which is δ = 102 cm(-1), one obtains an S(1)/S(2) exciton coupling matrix element of V(AB, el) = 57 cm(-1) in a Frenkel-Davydov exciton model. The vibronic couplings in the S(1)/S(2) ← S(0) spectrum of 2PY·6M2PY are treated by the Fulton-Gouterman single-mode model. We consider independent couplings to the intramolecular 6a(') vibration and to the intermolecular σ(') stretch, and obtain a semi-quantitative fit to the observed spectrum. The dimensionless excitonic couplings are C(6a(')) = 0.15 and C(σ(')) = 0.05, which places this dimer in the weak-coupling limit. However, the S(1)/S(2) state exciton splittings Δ(calc) calculated by the configuration interaction singles method (CIS), time-dependent Hartree-Fock (TD-HF), and approximate second-order coupled-cluster method (CC2) are between 1100 and 1450 cm(-1), or seven to nine times larger than observed. These huge errors result from the neglect of the coupling to the optically active intra- and intermolecular vibrations of the dimer, which lead to vibronic quenching of the purely electronic excitonic splitting. For 2PY·6M2PY the electronic splitting is quenched by a factor of ~30 (i.e., the vibronic quenching factor is Γ(exp) = 0.035), which brings the calculated splittings into close agreement with the experimentally observed value. The 2C-R2PI and fluorescence spectra of the tautomeric species 2-hydroxypyridine·6-methyl-2-pyridone (2HP·6M2PY) are also observed and assigned.