An exact algorithm for the capacitated shortest spanning arborescence

We are given a complete and loop-free digraphG=(V, A), whereV={1,...,n} is the vertex set,A={(i, j) :i, j V} the arc set, andr V is a distinguishedroot vertex. For each arc (i, j) A, letc _ij be the associatedcost, and for each vertexi, letq _i 0 be the associateddemand (withq _r =0). Moreover, a nonnegativebranch capacity, Q, is defined.A Capacitated Shortest Spanning Arborescence rooted at r (CSSA _r ) is a minimum cost partial digraph such that: (i) each vertexj r has exactly one entering arc; (ii) for each vertexj r, a path fromr toj exists; (iii) for each branch leaving vertexr, the total demand of the vertices does not exceed the branch capacity,Q. A variant of theCSSA _r problem (calledD-CSSA _r ) arises when the out-degree of the root vertex is constrained to be equal to a given valueD. These problems are strongly NP-hard, and find practical applications in routing and network design. We describe a new Lagrangian lower bound forCSSA _r andD-CSSA _r problems, strengthened in a cutting plane fashion by iteratively adding violated constraints to the Lagrangian problem. We also present a new lower bound based on projection leading to the solution of min-cost flow problems. The two lower bounds are then combined so as to obtain an overall additive lower bounding procedure. The additive procedure is then imbedded in a branch-and-bound algorithm whose performance is enhanced by means of reduction procedures, dominance criteria, feasibility checks and upper bounding. Computational tests on asymmetric and symmetric instances from the literature, involving up to 200 vertices, are given, showing the effectiveness of the proposed approach.     

Fast atom bombardment mass spectrometric analysis of the partial ozonolysis products of poly(isoprene) and poly(chloroprene)

The low molecular weight compounds formed by partial ozonolysis of poly(isoprene) and poly(chloroprene) were analyzed by fast atom bombardment mass spectrometry (FABMS). In the poly(chloroprene) case, the ozonized mixtures were treated with piperidine before the MS analysis to transform in amide end groups the reactive acyl chlorides formed by the cleavage of double bonds along the main chain. Only one family of compounds having carboxyl and ketone or carboxyl and amide end groups were obtained from the ozonolysis of poly(isoprene) and poly(chloroprene), respectively. The assigned structures were confirmed by FAB-MS analysis of the GPC separation fractions [poly(chloroprene)] or by FAB-MS of the KOH-doped ozonolysis mixtures [poly(isoprene)]. It has been also ascertained, by GPC experiments, that poly(chloroprene) decomposes more rapidly than poly(isoprene) and poly(butadiene).     

Interpolation,compactness and JEP in soft model theory

Let be the following statement: “for any infinite regularκ, for any uniform ultrafilterD onκ,D isλ-descendingly incomplete for all infiniteλ”. is weaker than ?0^#. Assuming we prove the following: letL be a logic in which the class of sentences of typeτ is a set if so isτ; then: (I)L is compact iffL has JEP; (II)L satisfies Robinson Consistency Theorem iffL is compact and satisfies Craig Interpolation theorem; (III) if, in addition,L is single-sorted, thenL satisfies Robinson Consistency Theorem iffL has JEP^#. JEP (resp. JEP^#) are the natural generalizations for logicL of the familiar Joint Embedding Property of elementary (resp. complete) embeddings in first order logic. As a corollary, we characterize first order logic as the only logic having Löwenheim number equal toω together with JEP.     

Simultaneous determination of concentration,diffusion coefficient and number of electrons for electroactive species by combining suitable electroanalytical measurements

The electroanalytical method described for the simultaneous determination of concentration, the number of electrons involved in the redox process and diffusion coefficient is based on evaluation of the ratios between the currents recorded for the analyte and for an easily standardized reference species dissolved in the same medium. Three different electroanalytical techniques are used in which the currents exhibit, for two techniques at least, different dependences on both the diffusion coefficient and electron number. The approach is applicable to diffusion-controlled processes, regardless of the degree of reversibility involved. Reliability tests with electroactive organic compounds dissolved in dimethyl sulphoxide show that both accuracy and precision are within 10% depending on the chosen combination of techniques.     

Metabolic Profile of Agropyron repens (L.) P. Beauv. Rhizome Herbal Tea by HPLC-PDA-ESI-MS/MS Analysis

Agropyron repens (L.) P. Beauv. (couch grass) is a world-wide infesting rhizomatous plant with pharmacological applications. Chemical research is focused on its allelopathic and anti-inflammatory components, which are mainly present in the essential oil. Conversely, the aqueous extracts have been sparingly investigated, although the herbal tea is by far the most used formulation. To fill the gap, the metabolic profile of Agropyron repens rhizome herbal tea was investigated by electrospray ionization (ESI) tandem–mass spectrometry (MS/MS); the phenolic profile was investigated by HPLC-PDA-ESI-MS/MS. ESI-MS fingerprinting was provided, evidencing diagnostic ions for saccharides, organic acids and amino acids. The HPLC-PDA-ESI-MS/MS analysis evidenced at least 20 characteristic phenolic compounds, the most representative being caffeoyl and feruloyl quinic esters, followed by coumaric, caffeic and ferulic acids, and hesperidin among flavonoids. In addition, the essential amino acid tryptophan was identified for the first time. The results suggest new perspectives of applications for Agropyron repens rhizome.     

Approximate chemical analysis of volcanic glasses using Raman spectroscopy

The effect of chemical composition on the Raman spectra of a series of natural calcalkaline silicate glasses has been quantified by performing electron microprobe analyses and obtaining Raman spectra on glassy filaments (~450 µm) derived from a magma mingling experiment. The results provide a robust compositionally‐dependent database for the Raman spectra of natural silicate glasses along the calcalkaline series. An empirical model based on both the acquired Raman spectra and an ideal mixing equation between calcalkaline basaltic and rhyolitic end‐members is constructed enabling the estimation of the chemical composition and degree of polymerization of silicate glasses using Raman spectra. The model is relatively insensitive to acquisition conditions and has been validated using the MPI‐DING geochemical standard glasses 1 as well as further samples. The methods and model developed here offer several advantages compared with other analytical and spectroscopic methods such as infrared spectroscopy, X‐ray fluorescence spectroscopy, electron and ion microprobe analyses, inasmuch as Raman spectroscopy can be performed with a high spatial resolution (1 µm²) without the need for any sample preparation as a nondestructive technique. This study represents an advance in efforts to provide the first database of Raman spectra for natural silicate glasses and yields a new approach for the treatment of Raman spectra, which allows us to extract approximate information about the chemical composition of natural silicate glasses using Raman spectroscopy. We anticipate its application in handheld in situ terrestrial field studies of silicate glasses under extreme conditions (e.g. extraterrestrial and submarine environments). © 2015 The Authors Journal of Raman Spectroscopy Published by John Wiley & Sons Ltd     

Simulation of Atomic Force Microscopy for investigating BaTiO3 and LiMn2O4 nanostructures based on Phase Field Approach

Atomic Force Microscopy (AFM) probes the surface features of specimens using an extremely sharp tip scanning the sample surface while the force is applied. AFM is also widely used for investigating the electrically non-conductive materials by applying an electric potential on the tip. Piezoresponse Force Microscopy (PFM) and Electrochemical Strain Microscopy (ESM) are variants of AFM for different materials. Both PFM and ESM signals are obtained by observing the displacement of the tip when applying electric fields during the scanning process. The PFM technique is based on converse piezoelectric effect of ferroelectrics and the ESM technique is based on electrochemical coupling in solid ionic conductors. In this work, two continuum-mechanical formulations for simulation of PFM and ESM are discussed. In the first model, for PFM simulation, a phase field approach based on the Allen-Cahn equation for non-conserved order parameters is employed for ferroelectrics. Here, the polarization vector is chosen as order parameter. Since ferroelectrics have highly anisotropic properties, this model accounts for transversely isotropic symmetry using an invariant formulation. The polarization switching behavior under the electric field will be discussed with some numerical examples. In the simulation of ESM, we employ a constitutive model based on the work of Bohn et al. [8] for the modeling of lithium manganese dioxide LiMn₂O₄ (LMO). It simulates the deformation of the LMO particle according to an applied voltage and the evolution of lithium concentration after removing a DC pulse. The modeling results are compared to experimental data. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Critical Sets of Elliptic Equations

Given a solution u to a linear, homogeneous, second‐order elliptic equation with Lipschitz coefficients, we introduce techniques for giving improved estimates of the critical set ??(u)u {x :|δu|(x) = 0}, as well as the first estimates on the effective critical set ??_r(u), which roughly consists of points x such that the gradient of u is small somewhere on B_r(x) compared to the nonconstancy of u. The results are new even for harmonic functions on ?ⁿ. Given such a u, the standard first‐order stratification {l^k} of u separates points x based on the degrees of symmetry of the leading‐order polynomial of u‐u(x). In this paper we give a quantitative stratification of u, which separates points based on the number of almost symmetries of approximate leading‐order polynomials of u at various scales. We prove effective estimates on the volume of the tubular neighborhood of each , which lead directly to (n‐2 + ?)‐Minkowski type estimates for the critical set of u. With some additional regularity assumptions on the coefficients of the equation, we refine the estimate to give new proofs of the uniform (n‐2)‐Hausdorff measure estimate on the critical set and singular sets of u.© 2014 Wiley Periodicals, Inc.