Electrochemical treatment of tumours: a simplified mathematical model

Electrochemical treatment of tumours implies that tumour tissue is treated with a direct current. During electrolysis, electrical energy is converted to chemical energy through electrochemical reactions at the electrodes. The anode is preferably placed in the tumour and the cathode in a blood vessel or in fresh surrounding tissue. The main electrochemical reactions are chlorine and oxygen evolution, at the anode, if platinum is used. Hydrogen evolution takes place at the cathode. The aim of this paper is to show how mathematical modelling can be used as a tool for defining and optimising the operating conditions of electrochemical treatment (ET) of tumours. A simplified mathematical model is presented for direct current treatment of tumours, focusing on tissue surrounding a spherical platinum anode. The tissue is treated as an aqueous solution of sodium chloride and only the major electrochemical reactions are considered. The model is based on transport equations of ionic species in dilute solutions. Kinetic expressions for the electrochemical reactions, at the anode surface, are introduced. Inputs to the model are the applied current density, and sizes of the anode and electrolyte domain. Concentration profiles of the ionic species and potential distribution, as a function of time, are calculated. In addition, current yields of the anode reactions are obtained from the model.     

Two-dimensional scaling limits via marked nonsimple loops

We postulate the existence of a natural Poissonian marking of the double (touching) points of SLE₆ and hence of the related continuum nonsimple loop process that describes macroscopic cluster boundaries in 2D critical percolation. We explain how these marked loops should yield continuum versions of near-critical percolation, dynamical percolation, minimal spanning trees and related plane filling curves, and invasion percolation. We showthat this yields for some of the continuum objects a conformal covariance property that generalizes the conformal invariance of critical systems. It is an open problem to rigorously construct the continuum objects and to prove that they are indeed the scaling limits of the corresponding lattice objects.     

A Branch-and-Bound Algorithm for Concave Network Flow Problems

In this paper a Branch-and-Bound (BB) algorithm is developed to obtain an optimal solution to the single source uncapacitated minimum cost Network Flow Problem (NFP) with general concave costs. Concave NFPs are NP-Hard, even for the simplest version therefore, there is a scarcity of exact methods to address them in their full generality. The BB algorithm presented here can be used to solve optimally single source uncapacitated minimum cost NFPs with any kind of concave arc costs. The bounding is based on the computation of lower bounds derived from state space relaxations of a dynamic programming formulation. The relaxations, which are the subject of the paper (Fontes et al., 2005b) and also briefly discussed here, involve the use of non-injective mapping functions, which guarantee a reduction on the cardinality of the state space. Branching is performed by either fixing an arc as part of the final solution or by removing it from the final solution. Computational results are reported and compared to available alternative methods for addressing the same type of problems. It could be concluded that our BB algorithm has better performance and the results have also shown evidence that it has a sub-exponential time growth.     

Synthesis of optically active α-benzyl paraconic acids and their esters and assignment of their absolute configuration

The cis- and trans-4-benzylparaconic acids and their ethyl esters were synthesized with high enantiomeric excess by hydrolysis of the corresponding diastereomeric lactonic esters using α-chymotrypsin. Thus, at low conversion values, cis- and trans-4-benzyl-5-oxo-3-tetrahydrofurancarboxylic acids were separately isolated with 99% ee and 92% ee, respectively. Both ethyl ester diastereomers were also obtained in enantiopure form. The absolute configuration of the trans-lactonic acid was assigned by ¹H NMR analysis of its ester derivatives with both enantiomers of 1-(9-anthryl)-2,2,2-trifluoroethanol, while that of the cis-lactonic acid was assigned by means of X-ray analysis of a crystalline derivative. The circular dichroism curves of the products obtained are also reported.     

Synthesis and characterization of micro/nanoscopic Pb(Zr<Subscript>0.52</Subscript>Ti<Subscript>0.48</Subscript>)O<Subscript>3</Subscript> fibers by electrospinning

Micro/nanoscopic Pb(Zr_0.52Ti_0.48)O₃ fibers were synthesized from commercially available zirconium n-pro-poxide, titanium isopropoxide, and lead 2-ethylhexanoate. Using xylene as a solvent, they were mixed to form a precursor solution with a suitable viscosity for electrospinning. The solution was analyzed using thermo-gravimetric and differential thermal methods. Ultra-fine fibers and mats were electrostatically drawn from the precursor solution. The as-deposited materials were sintered for 2 h at 400, 500, 600, 700 and 800 °C, respectively. Sintered mats or fibers were characterized using X-ray diffraction (XRD), scanning electron microscopy (SEM), Auger electron spectroscopy (AES), Raman micro-spectrometry and scanning-probe microscopy (SPM). The SEM results revealed that the fibers had diameters varying from hundreds of nanometers to 10 m. Using AES, the elements Pb, Zr, Ti and O, as well as residual C, were detected on the surface of the fibers. Raman and XRD spectra indicated that the precursors began to transform into the intermediate pyrochlore phase at 400 °C, followed by the perovskite Pb(Zr_0.52Ti_0.48)O₃ phase above 600 °C. Scanning-probe microscopy (SPM), operated in the piezo-response imaging mode, revealed spontaneous polarization domains in the fibers, with diameters ranging from 100 to 500 nm. PACS 61.46.+w; 77.90.+k; 81.07.-b; 81.16.-c     

Synthesis of phosphorus‐carbide thin films by magnetron sputtering

Phosphorus‐carbide, CP_x (0.025 ≤ x ≤ 0.1), thin films have been synthesized by magnetron sputtering from pressed graphite–phosphorus targets. The films were characterized by X‐ray photoelectron spectroscopy, transmission electron microscopy and diffraction, and nanoindentation. CP_0.1 ex‐hibits C–P bonding in an amorphous structure with elements of curved graphene planes, yielding a material with unique short range order. These features are consistent with what has been predicted by our results of theoretically modeled synthetic growth of CP_x . The films are mechanically resilient with hardness up to 24 GPa and elastic recovery up to 72%. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Similarities and differences between cobalamins and cobaloximes. Accurate structural determination of methylcobalamin and of LiCl- and KCl-containing cyanocobalamins by synchrotron radiation

The accurate crystal structure determinations of MeCbl (1), CNCbl.2LiCl (2), and CNCbl.KCl (3), based on synchrotron diffraction data collected at 100 K and using high-quality single crystals, are reported. Refinements gave R1 indices of 0.0834 (1), 0.0434 (2), and 0.0773 (3). The influence of the water of crystallization and ion content on the crystal packing of these and other cobalamins (XCbl) is discussed, and a relationship between the crystal packing and the corrin side chain conformations is presented. An analysis of the bond lengths within the corrin moiety, based on 13 accurate structures with several X groups, shows that the trend of the C-C and C-N distances can be interpreted in terms of electronic and steric factors. The variation in structural, NMR and IR spectroscopic, and electrochemical properties are compared with those of cobaloximes, the B12 model, when X is varied. This comparison indicates that the pi-back-donation from metal to the CN axial ligand and the transmission of the trans influence of the X ligand are more effective in cobalamins than in cobaloximes. These findings are consistent with a significantly greater availability of electron charge on Co in cobalamins, and, hence, a semiquantitative evaluation of the electronic difference between the cobalt centers in the two systems is allowed.     

A new classical solution of the Yang-Mills field equations

The MIT bag theory is used to calculate the quarl anti-quark annihilation amplitude for the ??γ transition and produces m_?²/∫_? = 0.13 compared to the experimental result of 0.11.     

Orientational effect of the phenylsulfonyl group in the thermal spiroketalization of dihydroxyketone equivalents

The thermal cyclization of a dihydroxyketone equivalent 4b leads to the predominant formation of crystalline 4-(benzenesulfonyl)-1,6-dioxaspiro[4.5]decane ( 8 ). Under similar reaction conditions the tetrahydrofuranylidene derivative 6 is obtained from ketone 4c . It does appear that the phenylsulfonyl group is a factor which influences the course of the reaction leading to the preferential formation of one of the possible stereoisomers.     

Simultaneous selection,amplification and isolation of a pseudo-peptide receptor by an immobilised N-methyl ammonium ion template

Immobilised N-methyl ammonium ions have been used to simultaneously select, amplify and isolate a pseudo-peptide receptor from a dynamic library of hydrazones.