Kinetic (cellular) models of cell progression and competition with the immune system

This paper deals with the modelling of the immune response to the evolution of progressing (corrupted) endothelial cells, i.e. cancer cells. A mathematical model is proposed, on the basis of mathematical methods of the kinetic theory for a large system of interacting cells. Then a qualitative analysis is carried out to prove the existence of the solutions of the Cauchy problem related to the model and to show some results on the asymptotic behavior. Some computational simulations complete the analysis on the asymptotic behavior of the solutions, which depending on parameters and initial conditions shows either the prevalence of progressing cells or their depletion due to the action of the immune system.     

Rational points of bounded height on Del Pezzo surfaces of degree six

LetK be a number field. Denote byV ₃ a split Del Pezzo surface of degree six overK and by ω its canonical divisor. Denote byW ₃ the open complement of the exceptional lines inV ₃. LetN _{W s}(−ω, X) be the number ofK-rational points onW ₃ whose anticanonical heightH _−ω is bounded byX. Manin has conjectured that asymptoticallyN _{W 3}(−ω, X) tends tocX(logX)³, wherec is a constant depending only on the number field and on the normalization of the height. Our goal is to prove the following theorem: For each number fieldK there exists a constantc _K such thatN _{W 3}(−ω, X)≤c_KX(logX)^3+2r , wherer is the rank of the group of units ofO _K. The constantc _K is far from being optimal. However, ifK is a purely imaginary quadratic field, this proves an upper bound with a correct power of logX. The proof of Manin's conjecture for arbitrary number fields and a precise treatment of the constants would require a more sophisticated setting, like the one used by [Peyre] to prove Manin's conjecture and to compute the correct asymptotic constant (in some normalization) in the caseK=ℚ. Up to now the best result for arbitraryK goes back, as far as we know, to [Manin-Tschinkel], who gives an upper boundN _{W 3}(−ω,X)≤cX^l+ε. The author would like to express his gratitude to Daniel Coray and Per Salberger for their generous and indispensable support.     

Nonlinear response of SDOF systems under combined deterministic and random excitations

Dynamical systems subjected to random excitations exhibit non-linear behavior for sufficiently large motion. The multiple time scale method has been extensively utilized in the framework of non-linear deterministic analysis to obtain two averaged first-order differential equations describing the slow time scale modulation of amplitude and phase response. In this paper the multiple time scale method, opportunely modified to take properly into account the correlation structure of the stochastic input process, is adopted to derive a stochastic frequency-response relationship involving the response amplitude statistics and the input power spectral density. A low-intensity noise is assumed to separate the strong mean motion from its weak fluctuations. The moment differential equations of phase and amplitude are derived and a linearization technique applied to evaluate the second order statistics. The theory is validated through digital simulations on a nonlinear single degree of freedom model for the transversal oscillation of a cantilever beam with tip force and to a Duffing-Rayleigh oscillator, to analyze non-linear damping effects.     

Linear wave modes for dissipative fluids with rate type constitutive equations

Summary In this paper we study in detail one-dimensional linear plane harmonic waves in dissipative fluids within the framework of extended linear irreversible thermodynamics. The results for the acoustic mode are compared with the available experimental data on the dispersion and absorption of sound in monatomic gases.

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Sommario Vengono studiate dettagliatamente le onde armoniche piane unidimensionali per i fluidi dissipativi nell'ambito della termodinamica estesa irreversibile lineare. I risultati ottenuti per il modo acustico di propagazione sono raffrontati con i risultati sperimentali sulla dispersione e l'assorbimento del suono nei gas monoatomici.

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Research supported by C.N.R., G.N.F.M.     

The contact problem for a class of orthotropic elastic solids

The contact problem between two orthotropic solids is examined. The problem is solved by using Lodge's method, which permits the transformation of the boundary-value problem of an anisotropic solid to a form identical with the corresponding problem of an isotropic medium. The proposed solution is then compared with known results of certain cases and it is observed that it producesHertz's solution when used for an isotropic case,Lodge's solution when applied to contact between an orthotropic solid and a rigid plane and, finally,Love's solution if the solid is transversely isotropic with the axis of material symmetry perpendicular to the rigid plane of contact.     

[RhIII(dmbpy)2Cl2]+ as a Highly Efficient Catalyst for Visible‐Light‐Driven Hydrogen Production in Pure Water: Comparison with Other Rhodium Catalysts

We report a very efficient homogeneous system for the visible‐light‐driven hydrogen production in pure aqueous solution at room temperature. This comprises [Rh^III(dmbpy)₂Cl₂]Cl ( 1 ) as catalyst, [Ru(bpy)₃]Cl₂ ( PS1 ) as photosensitizer, and ascorbate as sacrificial electron donor. Comparative studies in aqueous solutions also performed with other known rhodium catalysts, or with an iridium photosensitizer, show that 1) the PS1 / 1 /ascorbate/ascorbic acid system is by far the most active rhodium‐based homogeneous photocatalytic system for hydrogen production in a purely aqueous medium when compared to the previously reported rhodium catalysts, Na₃[Rh^I(dpm)₃Cl] and [Rh^III(bpy)Cp*(H₂O)]SO₄ and 2) the system is less efficient when [Ir^III(ppy)₂(bpy)]Cl ( PS2 ) is used as photosensitizer. Because catalyst 1 is the most efficient rhodium‐based H₂‐evolving catalyst in water, the performance limits of this complex were further investigated by varying the PS1 / 1 ratio at pH 4.0. Under optimal conditions, the system gives up to 1010 turnovers versus the catalyst with an initial turnover frequency as high as 857 TON h^?1. Nanosecond transient absorption spectroscopy measurements show that the initial step of the photocatalytic H₂‐evolution mechanism is a reductive quenching of the PS1 excited state by ascorbate, leading to the reduced form of PS1 , which is then able to reduce [Rh^III(dmbpy)₂Cl₂]⁺ to [Rh^I(dmbpy)₂]⁺. This reduced species can react with protons to yield the hydride [Rh^III(H)(dmbpy)₂(H₂O)]²⁺, which is the key intermediate for the H₂ production.     

A reliable and simple method for the assay of neuroendocrine tumor markers in human urine by solid-phase microextraction–gas chromatography-triple quadrupole mass spectrometry

Homovanillic acid (HVA), vanylmandelic acid (VMA), and 5-hydroxyindoleacetic acid (5-HIAA) are the metabolites of some catecholamines such as epinephrine, nor-epinephrine, dopamine and serotonin and their quantification is used in the diagnosis and management of patients with neurocrine tumors. A novel approach in the assay of these biomarkers in human urine samples by solid phase microextraction (SPME) combined with gas chromatography-triple quadrupole mass spectrometry (GC–QqQ-MS) is presented. A preliminary derivatization with ethyl chloroformate/ethanol was used and the corresponding derivatives were then extracted by SPME in immersion mode. The performance of five SPME fibers and three chloroformates were evaluated in univariate mode and the best results were obtained using the polyacrylate fiber and ethyl chloroformate. The variables affecting the efficiency of SPME analysis were optimized by the multivariate approach of “Experimental design” and, in particular, a central composite design (CCD) was applied. The optimum working conditions in terms of response values were achieved by performing analysis at room temperature with addition of NaCl (9.5%) and with an extraction time of 25.8 min. Identification and quantification of analytes were carried out by using a gas chromatography-triple quadrupole mass spectrometry (GC–QqQ MS) system in multiple reaction monitoring (MRM) acquisition. An evaluation of all analytical parameters shows that the proposed method provides satisfactory results. Very good linearities were, in fact, achieved in the tested calibration ranges with correlation coefficient values >0.99 for all the analytes and accuracies and RSDs calculated for between-run and tested at concentrations of 1, 10, and 80 mg L⁻¹ were ranging from 91.3% to 106.6%, and from 0.5 to 8.9%, respectively. Moreover, the LOD values obtained can be considered very satisfactory (1.3, 0.046 and 24.3 μg L⁻¹ for HVA, VMA and 5-HIAA, respectively). The developed protocol represents, therefore, a simple, rapid and selective tool for assaying these acidic biomarkers in urine samples for neuroendocrine cancer diagnosis.