UV-Vis spectroscopic study preferential solvation and intermolecular interactions in methanol/1-propanol/acetonitrile by means of solvatochromic probes

Solvatochromic UV-Vis shifts of four indicators (4-nitroaniline, 4-nitroanisole, 4-nitrophenol and N,N-dimethy-1-4-nitro aniline) have been measured at 298.15 K in the ternary mixture methano1/1-propanol/acetonitrile (MeOH/1-PrOH/MeCN) in a total of 22 mole fractions, along with 18 additional mole fractions for each of the corresponding binary mixtures, MeOH/1-PrOH, 1-PrOH/MeCN and MeOH/MeCN. These values, combined with our previous experimental results for 2,6-dipheny1-4-(2,4,6-triphenylpyridinium-1-yl)phenolate (Reichardt's betaine dye) in the same mixtures, permitted the computation of the Kamlet-Taft solvent parameters, alpha, beta, and pi*. The rationalization of the spectroscopic behavior of each probe within each mixture's whole mole fraction range was achieved through the use of the Bosch and Roses preferential solvation model. The applied model allowed the identification of synergistic behaviors in MeCN/alcohol mixtures and thus to infer the existence of solvent complexes in solution. Also, the addition of small amounts of MeCN to the binary mixtures was seen to cause a significant variation in pi*, whereas the addition of alcohol to MeCN mixtures always lead to a sudden change in a and The behavior of these parameters in the ternary mixture was shown to be mainly determined by the contributions of the underlying binary mixtures. (C) 2014 Elsevier B.V. All rights reserved.

Characterization of molecular damage induced by UV photons and carbon ions on biomimetic heterostructures

The study of the effect of radiation on living tissues is a rather complex task to address mainly because they are made of a set of complex functional biological structures and interfaces. Particularly if one is looking for where damage is taking place in a first stage and what are the underlying reaction mechanisms. In this work a new approach is addressed to study the effect of radiation by making use of well identified molecular hetero-structures samples which mimic the biological environment. These were obtained by assembling onto a solid support deoxyribonucleic acid (DNA) and phospholipids together with a soft water-containing polyelectrolyte precursor in layered structures and by producing lipid layers at liquid/air interface with DNA as subphase. The effects of both ultraviolet (UV) radiation and carbon ions beams were systematically investigated in these heterostructures, namely damage on DNA by means vacuum ultraviolet (VUV), infrared (IR), X-Ray Photoelectron (XPS) and impedance spectroscopy. Experimental results revealed that UV affects furanose, PO2-, thymines, cytosines and adenines groups. The XPS spectrometry carried out on the samples allowed validate the VUV and IR results and to conclude that ionized phosphate groups, surrounded by the sodium counterions, congregate hydration water molecules which play a role of UV protection. The ac electrical conductivity measurements revealed that the DNA electrical conduction is arising from DNA chain electron hopping between base-pairs and phosphate groups, with the hopping distance equal to the distance between DNA base-pairs and is strongly dependent on UV radiation exposure, due loss of phosphate groups. Characterization of DNA samples exposed to a 4 keV C3+ ions beam revealed also carbon-oxygen bonds break, phosphate groups damage and formation of new species. Results from radiation induced damage carried out on biomimetic heterostructures having different compositions revealed that damage is dependent on sample composition, with respect to functional targeted groups and extent of damage. Conversely, LbL films of 1,2-dipalmitoyl-sn-Glycero-3-[Phospho-rac-(1-glycerol)] (Sodium Salt) (DPPG) liposomes, alternated with poly(allylamine hydrochloride) (PAH) revealed to be unaffected, even by prolonged UV irradiation exposure, in the absence of water molecules. However, DPPG molecules were damaged by the UV radiation in presence of water with cleavage of C-O, C=O and –PO2- bonds. Finally, the study of DNA interaction with the ionic lipids at liquid/air interfaces revealed that electrical charge of the lipid influences the interaction of phospholipid with DNA. In the presence of DNA in the subphase, the effects from UV irrladiation were seen to be smaller, which means that ionic products from biomolecules degradation stabilize the intact DPPG molecules. This mechanism may explain why UV irradiation does not cause immediate cell collapse, thus providing time for the cellular machinery to repair elements damaged by UV.

Espectroscopía de emisión de rayos x. Aplicación a la caracterización de materiales. X-ray emission spectroscopy. Application to materials characterization

La idea principal del proyecto abarca el estudio de parámetros y fenómenos físicos. Los avances logrados se aplicarán al desarrollo de software y metodologías para cuantificación de materiales mediante microanálisis con sonda de electrones y microscopía electrónica de barrido. El microanálisis no es una técnica absoluta, sino que requiere de estándares de referencia, para obviar el uso de ciertos parámetros geométricos y atómicos difíciles de conocer con una precisión adecuada. Para contar con un método sin estándares debe abordarse la determinación de parámetros atómicos e instrumentales, que es uno de los aspectos que se desea encarar en este proyecto. Por otro lado, también se pretende incluir los parámetros estudiados en un software de cuantificación desarrollado por integrantes del proyecto. Otro de los propósitos del plan de trabajo es estudiar la potencialidad de la resolución espacial de una microsonda de electrones con el fin de desarrollar una metodología para caracterizar interfases, bordes de granos e inclusiones, con resolución submicrométrica, ya que los métodos tradicionales de cuantificación se restringen al caso de muestras planas y homogéneas dentro del volumen de interacción, pero la caracterización de inhomogeneidades a nivel micrométrico no ha sido desarrollada todavía, salvo algunas excepciones. The main idea of this project involves the study of physical parameters and phenomena. The concretion of the different goals will permit the elaboration of softeare and methodologies for materials characterization by means of electron probe microanalysis and scanning microscopy. Electron probe microanalysis is not an absolute technique, but requires reference standards in order not to involve certain geometrical and atomic parameters for which high uncertainties cannot be avoided. In order to have standardless method, the determination of atomic and instrumental parameters must be accomplished, as will be faced through this project. Complementary, the parameters studied will be included in a quantification software developed in our research group of FaMAF. Another objective of this activity plan is to study the spatial resolution potentiality of a focalized electron beam, with the aim of characterizing interphases, grain boundaries and inclusions with submicron sensitivity, since the traditional quantification procedures are restricted to flat homogeneous samples, whereas the characterization of inhomogeneities has not been developed yet.

Electroquímica de sustancias de interés en los sistemas agroalimentario y de sanidad animal. Desarrollo de biosensores electroquímicos. Aplicaciones analíticas.Electrochemistry of substances of interest in agroalimentary and animal health systems. Development of electrochemical biosensors. Analytical applications.

Se estudiarán los mecanismos de reacción electroquímica de las micotoxinas (metabolitos tóxicos generados por hongos) citrinina (CIT), patulina (PAT) y moniliformina (MON), de los antioxidantes naturales alfa, beta, gama y delta tocoferoles, de los flavonoides fisetina (FIS), morina (MOR), luteolina (LUT), rutina (RUT), buteina (BUT), naringenina (NAR) y miricetina (MIR) y de las hormonas esteroides estradiol (EDIOL), estrona (EONA) y estriol (ETRIOL). Por otra parte, se implementarán técnicas electroanalíticas para la detección y cuantificación de estos sustratos en muestras de matrices naturales que los contengan. Se realizará el diseño y caracterización de biosensores enzimáticos a partir de peroxidasas y/o fosfatasa alcalina para la determinación de la micotoxina CIT y de los flavonoides y, por otro, de inmunosensores para las micotoxinas ocratoxina A (OTA) y PAT y hormonas. Para el anclaje de enzimas y/o anticuerpos, se estudiarán las propiedades de electrodos modificados por monocapas autoensambladas, nanotubos de carbono y partículas magnéticas. Se usarán las técnicas de voltamperometría cíclica, de onda cuadrada y de redisolución con acumulación adsortiva, espectroscopías de impedancia electroquímica, electrólisis a potencial controlado, uv-vis e IR, microbalanza de cristal de cuarzo y microscopías de alta resolución (SEM, TEM, AFM). La importancia de este proyecto apunta a la obtención de nuevos datos electroquímicos de los sustratos indicados y conocimientos relacionados con la aplicación de electrodos modificados en la preparación de biosensores y en el desarrollo de técnicas alternativas para la determinación de los analitos mencionados precedentemente. Electrochemical reaction mechanisms of mycotoxins (toxic metabolites generated by fungi) citrinin (CIT), Patulin (PAT) and moniliformin (MON), natural antioxidants alpha, beta, gamma and delta tocopherols, flavonoids fisetin (FIS), morin (MOR), luteolin (LUT), rutin (RUT), butein (BUT), naringenin (NAR), miricetin (MIR) and steroid hormones estradiol (EDIOL), estrone (EONA) and estriole (ETRIOL) will be explored. On the other hand, electroanalytical techniques for the detection and quantification of these substrates in samples of natural matrices will be implemented. The design and characterization of enzymatic biosensors from peroxidases and/or from alkaline phosphatase for the determination of CIT and flavonoids, and also of inmunosensors for ochratoxin A (OTA) and PAT and hormones will be performed. For the anchor of enzymes and/or antibody, properties of electrodes modified by self assembled monolayers, carbon nanotubes and magnetic particles will be explored. Cyclic, square wave and adsorptive stripping voltammetries, electrochemical impedance spectroscopy, controlled potential electrolysis, uv-vis and IR, quartz crystal microbalance and high-resolution microcopies (SEM, TEM, AFM) will be used. The importance of this project is aimed at obtaining new electrochemical data for the indicated substrates and knowledge on the application of modified electrodes in preparation of biosensors and in the development of alternative techniques for the determination of the above-mentioned analytes.

High-resolution spatial mapping of changes in the neurochemical profile after focal ischemia in mice.

After ischemic stroke, the ischemic damage to brain tissue evolves over time and with an uneven spatial distribution. Early irreversible changes occur in the ischemic core, whereas, in the penumbra, which receives more collateral blood flow, the damage is more mild and delayed. A better characterization of the penumbra, irreversibly damaged and healthy tissues is needed to understand the mechanisms involved in tissue death. MRSI is a powerful tool for this task if the scan time can be decreased whilst maintaining high sensitivity. Therefore, we made improvements to a (1) H MRSI protocol to study middle cerebral artery occlusion in mice. The spatial distribution of changes in the neurochemical profile was investigated, with an effective spatial resolution of 1.4 μL, applying the protocol on a 14.1-T magnet. The acquired maps included the difficult-to-separate glutamate and glutamine resonances and, to our knowledge, the first mapping of metabolites γ-aminobutyric acid and glutathione in vivo, within a metabolite measurement time of 45 min. The maps were in excellent agreement with findings from single-voxel spectroscopy and offer spatial information at a scan time acceptable for most animal models. The metabolites measured differed with respect to the temporal evolution of their concentrations and the localization of these changes. Specifically, lactate and N-acetylaspartate concentration changes largely overlapped with the T(2) -hyperintense region visualized with MRI, whereas changes in cholines and glutathione affected the entire middle cerebral artery territory. Glutamine maps showed elevated levels in the ischemic striatum until 8 h after reperfusion, and until 24 h in cortical tissue, indicating differences in excitotoxic effects and secondary energy failure in these tissue types. Copyright © 2011 John Wiley & Sons, Ltd.

Compartmentalized Cerebral Metabolism of [1,6-(13)C]Glucose Determined by in vivo (13)C NMR Spectroscopy at 14.1 T.

Cerebral metabolism is compartmentalized between neurons and glia. Although glial glycolysis is thought to largely sustain the energetic requirements of neurotransmission while oxidative metabolism takes place mainly in neurons, this hypothesis is matter of debate. The compartmentalization of cerebral metabolic fluxes can be determined by (13)C nuclear magnetic resonance (NMR) spectroscopy upon infusion of (13)C-enriched compounds, especially glucose. Rats under light α-chloralose anesthesia were infused with [1,6-(13)C]glucose and (13)C enrichment in the brain metabolites was measured by (13)C NMR spectroscopy with high sensitivity and spectral resolution at 14.1 T. This allowed determining (13)C enrichment curves of amino acid carbons with high reproducibility and to reliably estimate cerebral metabolic fluxes (mean error of 8%). We further found that TCA cycle intermediates are not required for flux determination in mathematical models of brain metabolism. Neuronal tricarboxylic acid cycle rate (V(TCA)) and neurotransmission rate (V(NT)) were 0.45 ± 0.01 and 0.11 ± 0.01 μmol/g/min, respectively. Glial V(TCA) was found to be 38 ± 3% of total cerebral oxidative metabolism, accounting for more than half of neuronal oxidative metabolism. Furthermore, glial anaplerotic pyruvate carboxylation rate (V(PC)) was 0.069 ± 0.004 μmol/g/min, i.e., 25 ± 1% of the glial TCA cycle rate. These results support a role of glial cells as active partners of neurons during synaptic transmission beyond glycolytic metabolism.

MR spectroscopy of the human brain with enhanced signal intensity at ultrashort echo times on a clinical platform at 3T and 7T.

Recently, the spin-echo full-intensity acquired localized (SPECIAL) spectroscopy technique was proposed to unite the advantages of short TEs on the order of milliseconds (ms) with full sensitivity and applied to in vivo rat brain. In the present study, SPECIAL was adapted and optimized for use on a clinical platform at 3T and 7T by combining interleaved water suppression (WS) and outer volume saturation (OVS), optimized sequence timing, and improved shimming using FASTMAP. High-quality single voxel spectra of human brain were acquired at TEs below or equal to 6 ms on a clinical 3T and 7T system for six volunteers. Narrow linewidths (6.6 +/- 0.6 Hz at 3T and 12.1 +/- 1.0 Hz at 7T for water) and the high signal-to-noise ratio (SNR) of the artifact-free spectra enabled the quantification of a neurochemical profile consisting of 18 metabolites with Cramér-Rao lower bounds (CRLBs) below 20% at both field strengths. The enhanced sensitivity and increased spectral resolution at 7T compared to 3T allowed a two-fold reduction in scan time, an increased precision of quantification for 12 metabolites, and the additional quantification of lactate with CRLB below 20%. Improved sensitivity at 7T was also demonstrated by a 1.7-fold increase in average SNR (= peak height/root mean square [RMS]-of-noise) per unit-time.

Heterogeneous 40Ar* distributions in naturally deformed muscovite: in situ UV-laser ablation evidence for micro structurally controlled intragrain diffusion

Micas are commonly used in Ar-40/Ar-39 thermochronological studies of variably deformed rocks yet the physical basis by which deformation may affect radiogenic argon retention in mica is poorly constrained. This study examines the relationship between deformation and deformation-induced microstructures on radiogenic argon retention in muscovite, A combination of furnace step-heating and high-spatial resolution in situ UV-laser ablation Ar-40/Ar-39 analyses are reported for deformed muscovites sampled from a granitic pegmatite vein within the Siviez-Mischabel Nappe, western Swiss Alps (Penninic domain, Brianconnais unit). The pegmatite forms part of the Variscan (similar to 350 Ma) Alpine basement and exhibits a prominent Alpine S-C fabric including numerous mica `fish' that developed under greenschist facies metamorphic conditions, during the dominant Tertiary Alpine tectonic phase of nappe emplacement. Furnace step-heating of milligram quantities of separated muscovite grains yields an Ar-40/Ar-39 age spectrum with two distinct staircase segments but without any statistical plateau, consistent with a previous study from the same area. A single (3 X 5 mm) muscovite porphyroclast (fish) was investigated by in situ UV-laser ablation. A histogram plot of 170 individual Ar-40/Ar-39 UV-laser ablation ages exhibit a range from 115 to 387 Ma with modes at approximately 340 and 260 Ma. A variogram statistical treatment of the (40)Ad/Ar-39 results reveals ages correlated with two directions; a highly correlated direction at 310 degrees and a lesser correlation at 0 degrees relative to the sense of shearing. Using the highly correlated direction a statistically generated (Kriging method) age contour map of the Ar-40/Ar-39 data reveals a series of elongated contours subparallel to the C-surfaces which where formed during Tertiary nappe emplacement. Similar data distributions and slightly younger apparent ages are recognized in a smaller mica fish. The observed intragrain age variations are interpreted to reflect the partial loss of radiogenic argon during Alpine (similar to 35 Ma) greenschist facies metamorphism. One-dirnensional diffusion modelling results are consistent with the idea that the zones of youngest apparent age represent incipient shear band development within the mica porphyroclasts, thus providing a network of fast diffusion pathways. During Alpine greenschist facies metamorphism the incipient shear bands enhanced the intragrain loss of radiogenic argon. The structurally controlled intragrain age variations observed in this investigation imply that deformation has a direct control on the effective length scale for argon diffusion, which is consistent with the heterogeneous nature of deformation. (C) 2001 Elsevier Science B.V. All rights reserved.

Chemical characterization and infrared spectroscopy of soil organic matter from two southern brazilian soils

Soil organic matter from the surface horizon of two Brazilian soils (a Latosol and a Chernosol), in bulk samples (in situ SOM) and in HF-treated samples (SOM), was characterized by elemental analyses, diffuse reflectance (DRIFT) and transmission Fourier transform infrared spectroscopy (T-FTIR). Humic acids (HA), fulvic acids (FA) and humin (HU) isolated from the SOM were characterized additionally by ultraviolet-visible spectroscopy (UV-VIS). After sample oxidation and alkaline treatment, the DRIFT technique proved to be more informative for the detection of "in situ SOM" and of residual organic matter than T-FTIR. The higher hydrophobicity index (HI) and H/C ratio obtained in the Chernosol samples indicate a stronger aliphatic character of the organic matter in this soil than the Latosol. In the latter, a pronounced HI decrease was observed after the removal of humic substances (HS). The weaker aliphatic character, the higher O/C ratio, and the T-FTIR spectrum obtained for the HU fraction in the Latosol suggest the occurrence of surface coordination of carboxylate ions. The Chernosol HU fraction was also oxygenated to a relatively high extent, but presented a stronger hydrophobic character in comparison with the Latosol HU. These differences in the chemical and functional group composition suggest a higher organic matter protection in the Latosol. After the HF treatment, decreases in the FA proportion and the A350/A550 ratio were observed. A possible loss of FA and condensation of organic molecules due to the highly acid medium should not be neglected.

Design of surface forces apparatus for tribology studies combined with nonlinear optical spectroscopy

We describe the design, calibration, and performance of surface forces apparatus with the capability of illumination of the contact interface for spectroscopic investigation using optical techniques. The apparatus can be placed in the path of a Nd-YAG laser for studies of the linear response or the second harmonic and sum-frequency generation from a material confined between the two surfaces. In addition to the standard fringes of equal chromatic order technique, which we have digitized for accurate and fast analysis, the distance of separation can be measured with a fiber-optic interferometer during spectroscopic measurements (2 Å resolution and 10 ms response time). The sample approach is accomplished through application of a motor drive, piezoelectric actuator, or electromagnetic lever deflection for variable degrees of range, sensitivity, and response time. To demonstrate the operation of the instrument, the stepwise expulsion of discrete layers of octamethylcyclotetrasiloxane from the contact is shown. Lateral forces may also be studied by using piezoelectric bimorphs to induce and direct the motion of one surface.

Modelling plant species distribution in alpine grasslands using airborne imaging spectroscopy.

Remote sensing using airborne imaging spectroscopy (AIS) is known to retrieve fundamental optical properties of ecosystems. However, the value of these properties for predicting plant species distribution remains unclear. Here, we assess whether such data can add value to topographic variables for predicting plant distributions in French and Swiss alpine grasslands. We fitted statistical models with high spectral and spatial resolution reflectance data and tested four optical indices sensitive to leaf chlorophyll content, leaf water content and leaf area index. We found moderate added-value of AIS data for predicting alpine plant species distribution. Contrary to expectations, differences between species distribution models (SDMs) were not linked to their local abundance or phylogenetic/functional similarity. Moreover, spectral signatures of species were found to be partly site-specific. We discuss current limits of AIS-based SDMs, highlighting issues of scale and informational content of AIS data.

Evidence for oxygen-island formation on Al(111): Cluster-model theory and x-ray photoelectron spectroscopy

The O 1s x-ray photoelectron spectroscopy spectrum for Al(111)/O at 300 K shows two components whose behavior as a function of time and variation of detection angle are consistent with either (a) a surface species represented by the higher binding-energy (BE) component and a subsurface species represented by the lower BE component, or (b) small close-packed oxygen islands with the interior atoms represented by the lower BE component and the perimeter atoms by the higher BE component. We have modeled both situations using ab initio Hartree-Fock wave functions for clusters of Al and O atoms. For an O atom in a threefold site, it was found that a below-surface position gave a higher O 1s BE than an above-surface position, incompatible with interpretation (a). This change in the O 1s BE could arise because the bond for O to Al may have a more covalent character when the O is below the surface than when it is above the surface. We present evidence consistent with this view. An O adatom island with all the O atoms in threefold sites gives calculated O 1s BE's which are significantly higher for the perimeter O atoms. Further, the results for an isolated O island without the Al substrate present also give higher BE¿s for the perimeter atoms. Both these results are consistent with interpretation (b). Published scanning-tunneling-microscopy data supports the suggestion that the chemisorbed state consists of small, close-packed islands, whereas the presence of two vibrational modes in high-resolution electron-energy-loss spectroscopy data has been interpreted as representing surface and subsurface oxygen atoms. In light of the present results, we suggest that a vibrational interpretation in terms of interior and perimeter adatoms should be considered.

Escherichia coli RuvBL268S: a mutant RuvB protein that exhibits wild-type activities in vitro but confers a UV-sensitive ruv phenotype in vivo.

The RuvABC proteins of Escherichia coli process recombination intermediates during genetic recombination and DNA repair. RuvA and RuvB promote branch migration of Holliday junctions, a process that extends heteroduplex DNA. Together with RuvC, they form a RuvABC complex capable of Holliday junction resolution. Branch migration by RuvAB is mediated by RuvB, a hexameric ring protein that acts as an ATP-driven molecular pump. To gain insight into the mechanism of branch migration, random mutations were introduced into the ruvB gene by PCR and a collection of mutant alleles were obtained. Mutation of leucine 268 to serine resulted in a severe UV-sensitive phenotype, characteristic of a ruv defect. Here, we report a biochemical analysis of the mutant protein RuvBL268S. Unexpectedly, the purified protein is fully active in vitro with regard to its ATPase, DNA binding and DNA unwinding activities. It also promotes efficient branch migration in combination with RuvA, and forms functional RuvABC-Holliday junction resolvase complexes. These results indicate that RuvB may perform some additional, and as yet undefined, function that is necessary for cell survival after UV-irradiation.

Selective resonance suppression 1H-[13C] NMR spectroscopy with asymmetric adiabatic RF pulses.

Despite obvious improvements in spectral resolution at high magnetic field, the detection of 13C labeling by 1H-[13C] NMR spectroscopy remains hampered by spectral overlap, such as in the spectral region of 1H resonances bound to C3 of glutamate (Glu) and glutamine (Gln), and C6 of N-acetylaspartate (NAA). The aim of this study was to develop, implement, and apply a novel 1H-[13C] NMR spectroscopic editing scheme, dubbed "selective Resonance suppression by Adiabatic Carbon Editing and Decoupling single-voxel STimulated Echo Acquisition Mode" (RACED-STEAM). The sequence is based on the application of two asymmetric narrow-transition-band adiabatic RF inversion pulses at the resonance frequency of the 13C coupled to the protons that need to be suppressed during the mixing time (TM) period, alternating the inversion band downfield and upfield from the 13C resonance on odd and even scans, respectively, thus suppressing the detection of 1H resonances bound to 13C within the transition band of the inversion pulse. The results demonstrate the efficient suppression of 1H resonances bound to C3 of Glu and Gln, and C4 of Glu, which allows the 1H resonances bound to C6 of NAA and C4 of Gln to be revealed. The measured time course of the resolved labeling into NAA C6 with the new scheme was consistent with the slow turnover of NAA.

Determination of the size of quantum dots by fluorescence spectroscopy.

There has been a lack of quick, simple and reliable methods for determination of nanoparticle size. An investigation of the size of hydrophobic (CdSe) and hydrophilic (CdSe/ZnS) quantum dots was performed by using the maximum position of the corresponding fluorescence spectrum. It has been found that fluorescence spectroscopy is a simple and reliable methodology to estimate the size of both quantum dot types. For a given solution, the homogeneity of the size of quantum dots is correlated to the relationship between the fluorescence maximum position (FMP) and the quantum dot size. This methodology can be extended to the other fluorescent nanoparticles. The employment of evolving factor analysis and multivariate curve resolution-alternating least squares for decomposition of the series of quantum dots fluorescence spectra recorded by a specific measuring procedure reveals the number of quantum dot fractions having different diameters. The size of the quantum dots in a particular group is defined by the FMP of the corresponding component in the decomposed spectrum. These results show that a combination of the fluorescence and appropriate statistical method for decomposition of the emission spectra of nanoparticles may be a quick and trusted method for the screening of the inhomogeneity of their solution.