Coulomb screening in graphene with topological defects

We analyze the screening of an external Coulomb charge in gapless graphene cone, which is taken as a prototype of a topological defect. In the subcritical regime, the induced charge is calculated using both the Green’s function and the Friedel sum rule. The dependence of the polarization charge on the Coulomb strength obtained from the Green’s function clearly shows the effect of the conical defect and indicates that the critical charge itself depends on the sample topology. Similar analysis using the Friedel sum rule indicates that the two results agree for low values of the Coulomb charge but differ for the higher strengths, especially in the presence of the conical defect. For a given subcritical charge, the transport cross-section has a higher value in the presence of the conical defect. In the supercritical regime we show that the coefficient of the power law tail of polarization charge density can be expressed as a summation of functions which vary log periodically with the distance from the Coulomb impurity. The period of variation depends on the conical defect. In the presence of the conical defect, the Fano resonances begin to appear in the transport cross-section for a lower value of the Coulomb charge. For both sub and supercritical regime we derive the dependence of LDOS on the conical defect. The effects of generalized boundary condition on the physical observables are also discussed.     

一个关于肿瘤治疗的自由边界问题的数学分析

§1Introduction Avarietyofpartialdifferentialequationmodelsfortumorgrowthortherapyhave beendevelopedinthelastthreedecades[see2,3,16-18,21-26].Mostofthosemodelsare informoffreeboundaryproblems,andareverydiversified.Rigorousmathematical analysisofsuchfreeboundaryproblemshasdrawngreatinterest,andmanyinteresting resultshavebeenestablished[4-15].Inthispaperwedealwithamathematicalmodeldescribingtumorchemotherapy.In thismodelthetumorisviewedasdenselypacked,radially-symmetricsphereofradiusR(t)contain…     

Energy Storage by Poly(<Emphasis Type="Italic">o</Emphasis>-anisidine) Matrix During Oxidative Hydrolysis

The chromaticity of poly(o-anisidine) (POAN) doped with different acids (HA), HA-doped POAN, has been studied by the spectrophotometric technique and the results were substantiated by molecular mechanics (MM+) calculations. The observed absorbance decrease (λ around 720 nm, dark green coloration) with increasing concentration of the inorganic oxidizing agent (KMnO₄) can be attributed to the oxidative hydrolysis mechanism. The oxidative hydrolysis constant (K _h) is highly dependent on the strength of the acid used. The HClO₄-doped POAN matrix has the ability to store about 128.878 kJ⋅g⁻¹ chromogenic energy (CE) at the wavelength 720 nm in a condensed lightweight form. MM+ calculations suggest that the potential energy (PE) in kJ⋅mol⁻¹ of the optimum molecular geometric (OMG) structure of the HClO₄-doped POAN matrix is at least two (2.052) times more stable than the OMG of the base form (POAN-EB) of the POAN matrix. Kinetic parameters of the oxidative hydrolysis reaction of the HA-doped POAN matrix were deduced from absorbance variations with time. The results of computer-oriented kinetic analysis indicate that the rate-controlling step for HA-doped POAN oxidative hydrolysis is governed by the Ginstling-Bronshein equation that represents three-dimensional diffusion (D4). Activation parameters for the oxidative hydrolysis of the HClO₄-doped POAN matrix were computed and discussed.     

Guanidine-based task-specific ionic liquids as catalysts for aza-Michael addition under solvent-free conditions

An efficient and facile protocol for aza-Michael addition of aliphatic and aromatic amines to electron-deficit alkenes using [TMG][Lac] as catalyst under solvent-free conditions was established.     

Freeze-drying for the stabilisation of shellfish toxins in mussel tissue (<Emphasis Type="Italic">Mytilus edulis</Emphasis>) reference materials

Two samples of mussels (Mytilus edulis) were collected from the southwest of Ireland. One sample contained domoic acid, the other sample contained okadaic acid, dinophysistoxin-2 and azaspiracid-1, -2 and -3. Wet and freeze-dried reference materials were prepared from each of the two samples to test for differences in homogeneity, stability and extractability of the analytes in either condition. Wet materials were homogenised, aliquoted and hermetically sealed under argon and subsequently frozen at −80 °C. Dry materials were similarly homogenised but frozen in flat cakes prior to freeze-drying. After grinding, sieving and further homogenisation, the resulting powder was aliquoted and hermetically sealed. Domoic acid materials were characterised using HPLC–UV, while LC–MS was used for the determination of lipophilic toxins. The extractabilities of all phycotoxins studied were comparable for wet and freeze-dried materials once a sonication step had been carried out for reconstitution of the freeze-dried materials prior to extraction. Homogeneity was assessed through replicate analysis of the phycotoxins (n = 10), and was found to be similar for wet and freeze-dried materials, for both hydrophilic and lipophilic toxins. Water contents were determined for both wet and freeze-dried materials, and particle size was determined for the freeze-dried materials. Stability was evaluated isochronously over eight months at four temperatures (−20, +4, +20 and +40 °C). The freeze-dried material containing domoic acid was stable over the whole duration at all temperatures, while in the wet material domoic acid degraded to some extent at all temperatures except −20 °C. In freeze-dried and wet materials containing lipophilic toxins, okadaic acid, dinophysistoxin-2, azaspiracid-1 and azaspiracid-2 were stable over the whole duration at all conditions, while concentrations of azaspiracid-3 changed significantly in both materials at some storage temperatures. Figure Aliquots of freeze-dried and wet mussel tissue reference materials containing the various shellfish toxins examined in the study     

Monitoring of PAHs in air by collection on XAD-2 adsorbent then microwave-assisted thermal desorption coupled with headspace solid-phase microextraction and gas chromatography with mass spectrometric detection

Microwave-assisted thermal desorption (MAD) coupled to headspace solid-phase microextraction (HS-SPME) has been studied for in-situ, one-step, sample preparation for PAHs collected on XAD-2 adsorbent, before gas chromatography with mass spectrometric detection. The PAHs on XAD-2 were desorbed into the extraction solution, evaporated into the headspace by use of microwave irradiation, and absorbed directly on a solid-phase microextraction fiber in the headspace. After desorption from the SPME fiber in the hot GC injection port, PAHs were analyzed by GC–MS. Conditions affecting extraction efficiency, for example extraction solution, addition of salt, stirring speed, SPME fiber coating, sampling temperature, microwave power and irradiation time, and desorption conditions were investigated. Experimental results indicated that extraction of 275 mg XAD-2, containing 10–200 ng PAHs, with 10-mL ethylene glycol–1 mol L⁻¹ NaCl solution, 7:3, by irradiation with 120 W for 40 min (the same as the extraction time), and collection with a PDMS–DVB fiber at 35 °C, resulted in the best extraction efficiency. Recovery was more than 80% and RSD was less than 14%. Optimum desorption was achieved by heating at 290 °C for 5 min. Detection limits varied from 0.02 to 1.0 ng for different PAHs. A real sample was obtained by using XAD-2 to collect smoke from indoor burning of joss sticks. The amounts of PAHs measured varied from 0.795 to 2.53 ng. The method is a simple and rapid procedure for determination of PAHs on XAD-2 absorbent, and is free from toxic organic solvents.     

Optimization of the Production of Thermostable endo-β-1,4 Mannanases from a Newly Isolated <Emphasis Type="Italic">Aspergillus niger gr</Emphasis> and <Emphasis Type="Italic">Aspergillus flavus gr</Emphasis>

The aim of this work was to establish optimal conditions for the maximum production of endo-β-1,4 mannanases using cheaper sources. Eight thermotolerant fungal strains were isolated from garden soil and compost samples collected in and around the Gulbarga University campus, India. Two strains were selected based on their ability to produce considerable endo-β-1,4 mannanases activity while growing in liquid medium at 37 °C with locust bean gum (LBG) as the only carbon source. They were identified as Aspergillus niger gr and Aspergillus flavus gr. The experiment to evaluate the effect of different carbon sources, nitrogen sources, temperatures and initial pH of the medium on maximal enzyme production was studied. Enzyme productivity was influenced by the type of polysaccharide used as the carbon source. Copra meal defatted with n-hexane showed to be a better substrate than LBG and guar gum for endo-β-1,4 mannanases production by A. niger gr (40.011 U/ml), but for A. flavus gr (33.532 U/ml), the difference was not significant. Endo-β-1,4 mannanases produced from A. niger gr and A. flavus gr have high optimum temperature (65 and 60 °C) and good thermostability in the absence of any stabilizers (maintaining 50% of residual activity for 8 and 6 h, respectively, at 60 °C) and are stable over in a wide pH range. These new strains offer an attractive alternative source of enzymes for the food and feed processing industries.