DECAY OF POSITIVE WAVES OF HYPERBOLIC BALANCE LAWS Dedicated to Professor Constantine M. Dafermos on the occasion of his 70th birthday

Historically,decay rates have been used to provide quantitative and qualitative information on the solutions to hyperbolic conservation laws.Quantitative results include the establishment of convergence rates for approximating procedures and numerical schemes.Qualitative results include the establishment of results on uniqueness and regularity as well as the ability to visualize the waves and their evolution in time.This work presents two decay estimates on the positive waves for systems of hyperbolic and genuinely nonlinear balance laws satisfying a dissipative mechanism.The result is obtained by employing the continuity of Glimm-type functionals and the method of generalized characteristics [7,17,24].     

Structure elucidation and chromatographic identification of anthraquinone components of cochineal (Dactylopius coccus) detected in historical objects

Cochineal is one of the most well known organic red dyes. Dactylopius coccus Costa (Dactylopiidae) is a scale insect that is used as the source of the dye known as Mexican cochineal. Although cochineal is today a natural food colorant (E120) and although it has been used in art objects (textiles and paintings) for centuries, its exact chemical consistency is not well clarified except for carminic acid which is the major component and kermesic and flavokermesic acids. Several minor components (typically less than 5% of the colouring material) remained unknown or partially studied, although their presence has been reported in numerous analytical works related to art objects. Chemical investigation of the methanol extract of the dried insects, after subsequent HPLC chromatographic separations, led to the isolation and structure elucidation of six new anthraquinones, along with the known compounds carminic acid, kermesic acid and flavokermesic acid. The new compounds formerly described as DCII and DCIII, were found to be the 2-C-glucoside of flavokermesic acid and 4-aminocarminic acid, respectively, while DCIV and DCVII were found to be the α/β C-glucofuranosides of kermesic acid, and were studied as a mixture due to equilibrium. In addition, 3-O-glucoside of flavokermesic acid (DCOFK), and 3,4-dideoxycarminic acid (DDCA) were identified. The structures of the new compounds were elucidated on the basis of their NMR and MS data. Finally, the new compounds were detected in silk dyed with cochineal, lake pigment and, furthermore, in historical objects of the cultural heritage (icon and textile) using LC–DAD and LC–MS.     

Oxidative Stress Response of Blakeslea trispora Induced by Iron Ions During Carotene Production in Shake Flask Culture

The adaptive response of the fungus Blakeslea trispora to the oxidative stress induced by iron ions during carotene production in shake flask culture was investigated. The culture response to oxidative stress was studied by measuring the specific activities of catalase (CAT) and superoxide dismutase (SOD). The addition of 1.0 mM of FeCl₃ to the medium was associated with a mild oxidative stress as evidenced by remarkable increase of the specific activities of SOD and CAT. On the other hand, the addition 5.0 mM of FeCl₃ caused a strong oxidative stress resulting in a drastic decrease in carotene concentration. The oxidative stress in B. trispora changed the composition of the carotenes and caused a significant increase of γ-carotene ratio. The highest concentration of carotenes (115.0?±?3.5 mg/g dry biomass) was obtained in the basal medium without the addition of FeCl₃ after 8 days of fermentation. In this case, the carotenes consisted of β-carotene (46.3 %), γ-carotene (40.1 %), and lycopene (13.6 %). The addition of 1.0 mM of FeCl₃ into the medium did not change the concentration of carotenes. But, the composition of carotenes was changed with a drastic increase of γ-carotene ratio (61.6 %) and a decrease in β-carotene and lycopene ratio (31.2 and 7.2 %, respectively).     

Disequilibrium of dissolved <Superscript>234</Superscript>U/<Superscript>238</Superscript>U and <Superscript>210</Superscript>Po/<Superscript>210</Superscript>Pb in Greek rivers

For the first time, a radiological study for the dissolved ²³⁸U, ²³⁴U, ²¹⁰Pb and ²¹⁰Po was held in major Greek rivers across the country. ²³⁴U/²³⁸U activity ratios are above one in all samples and ²¹⁰Po/²¹⁰Pb activity ratios are respectively below the unit indicating the disequilibrium in the samples. Quite satisfactory correlations were observed among ²³⁴U and ²³⁸U as well as among ²¹⁰Po and ²¹⁰Pb values. Uranium isotopes were separated by ion exchange and electroplated on stainless steel plates. ²¹⁰Po was spontaneously deposited on nickel plates, while ²¹⁰Pb was indirectly determined through the ingrowth of ²¹⁰Po. The sources were measured by a-spectrometry.     

Pattern-recognition system,designed on GPU,for discriminating between injured normal and pathological knee cartilage

The aim was to design a pattern-recognition (PR) system for discriminating between normal and pathological knee articular cartilage of the medial femoral (MFC) and tibial condyles (MTC). The data set comprised segmented regions of interest (ROIs) from coronal and sagittal 3-T magnetic resonance images of the MFC and MTC cartilage of young patients, 28 with abnormality-free knee and 16 with pathological findings. The PR system was designed employing the probabilistic neural network classifier, textural features from the segmented ROIs and the leave-one-out evaluation method, while the PR system's precision to “unseen” data was assessed by employing the external cross-validation method. Optimal system design was accomplished on a consumer graphics processing unit (GPU) using Compute Unified Device Architecture parallel programming. PR system design on the GPU required about 3.5 min against 15 h on a CPU-based system. Highest classification accuracies for the MFC and MTC cartilages were 93.2% and 95.5%, and accuracies to “unseen” data were 89% and 86%, respectively. The proposed PR system is housed in a PC, equipped with a consumer GPU, and it may be easily retrained when new verified data are incorporated in its repository and may be of value as a second-opinion tool in a clinical environment.     

A Multifunctional Bichromophoric Nanoaggregate for Fluorescence Imaging and Simultaneous Photogeneration of RNOS and ROS

We report the design, preparation, and properties of a nanoaggregate formed in phosphate buffer solution by a porphyrin–β‐cyclodextrin (β‐CD) conjugate and a nitric oxide photodonor tailored to fit the β‐CD cavity. The small nanoassembly with a diameter of about 13 nm exhibits the typical red fluorescence of the porphyrin chromophore. The empty cavity of the β‐CD unit in the nanoaggregate is able to accommodate the NO photodonor, thereby forming a supramolecular bichromophoric aggregate with diameter of about 16 nm. This nanoconstruct preserves the fluorescence of the porphyrin core and is able to generate nitric oxide and singlet oxygen under illumination with visible light. The nanoassembly internalizes in melanoma cells, can be mapped therein by fluorescence microscopy, and induces a significant level of cell mortality, probably due to the combined action of reactive nitrogen oxide species (RNOS) and reactive oxygen species (ROS).     

On a Nonlinear Model for Tumor Growth: Global in Time Weak Solutions

We investigate the dynamics of a class of tumor growth models known as mixed models. The key characteristic of these type of tumor growth models is that the different populations of cells are continuously present everywhere in the tumor at all times. In this work we focus on the evolution of tumor growth in the presence of proliferating, quiescent and dead cells as well as a nutrient. The system is given by a multi-phase flow model and the tumor is described as a growing continuum Ω with boundary ?Ω both of which evolve in time. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behavior, diffusion and viscosity in the weak formulation.     

Sharp decay estimates for hyperbolic balance laws

We consider strictly hyperbolic and genuinely nonlinear systems of hyperbolic balance laws in one-space dimension. Sharp decay estimates are derived for the positive waves in an entropy weak solution. The result is obtained by introducing a partial ordering within the family of positive Radon measures, using symmetric rearrangements and a comparison with a solution of Burgers's equation with impulsive sources as well as lower semicontinuity properties of continuous Glimm-type functionals.     

On a Nonlinear Model for Tumor Growth in a Cellular Medium

We investigate the dynamics of a nonlinear model for tumor growth within a cellular medium. In this setting the “tumor” is viewed as a multiphase flow consisting of cancerous cells in either proliferating phase or quiescent phase and a collection of cells accounting for the “waste” and/or dead cells in the presence of a nutrient. Here, the tumor is thought of as a growing continuum \(\Omega \) with boundary \(\partial \Omega \) both of which evolve in time. In particular, the evolution of the boundary \(\partial \Omega \) is prescibed by a given velocity \({{{\varvec{V}}}.}\) The key characteristic of the present model is that the total density of cancerous cells is allowed to vary, which is often the case within cellular media. We refer the reader to the articles (Enault in Mathematical study of models of tumor growth, 2010; Li and Lowengrub in J Theor Biol, 343:79–91, 2014) where compressible type tumor growth models are investigated. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behavior, diffusion, viscosity and pressure in the weak formulation, as well as convergence and compactness arguments in the spirit of Lions (Mathematical topics in fluid dynamics. Compressible models, 1998) [see also Donatelli and Trivisa (J Math Fluid Mech 16: 787–803, 2004), Feireisl (Dynamics of viscous compressible fluids, 2014)].