Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems

We study the hybridizable discontinuous Galerkin (HDG) method for the spatial discretization of time fractional diffusion models with Caputo derivative of order 0 < α < 1. For each time t ∈ [0, T], when the HDG approximations are taken to be piecewise polynomials of degree k ≥ 0 on the spatial domain Ω, the approximations to the exact solution u in the L _∞(0, T; L ₂(Ω))-norm and to ?u in the \(L_{\infty }(0, \textit {T}; \mathbf {L}_{2}({\Omega }))\)-norm are proven to converge with the rate h ^k+1 provided that u is sufficiently regular, where h is the maximum diameter of the elements of the mesh. Moreover, for k ≥ 1, we obtain a superconvergence result which allows us to compute, in an elementwise manner, a new approximation for u converging with a rate h ^k+2 (ignoring the logarithmic factor), for quasi-uniform spatial meshes. Numerical experiments validating the theoretical results are displayed.     

Numerical solution for a sub-diffusion equation with a smooth kernel

In this paper we study the numerical solution of an initial value problem of a sub-diffusion type. For the time discretization we apply the discontinuous Galerkin method and we use continuous piecewise finite elements for the space discretization. Optimal order convergence rates of our numerical solution have been shown. We compare our theoretical error bounds with the results of numerical computations. We also present some numerical results showing the super-convergence rates of the proposed method.     

Characterization of the mupirocin biosynthesis gene cluster from Pseudomonas fluorescens NCIMB 10586

The polyketide antibiotic mupirocin (pseudomonic acid) produced by Pseudomonas fluorescens NCIMB 10586 competitively inhibits bacterial isoleucyl-tRNA synthase and is useful in controlling Staphylococcus aureus, particularly methicillin-resistant Staphylococcus aureus. The 74 kb mupirocin biosynthesis cluster has been sequenced, and putative enzymatic functions of many of the open reading frames (ORFs) have been identified. The mupirocin cluster is a combination of six larger ORFs (mmpA-F), containing several domains resembling the multifunctional proteins of polyketide synthase and fatty acid synthase type I systems, and individual genes (mupA-X and macpA-E), some of which show similarity to type II systems (mupB, mupD, mupG, and mupS). Gene knockout experiments demonstrated the importance of regions in mupirocin production, and complementation of the disrupted gene confirmed that the phenotypes were not due to polar effects. A model for mupirocin biosynthesis is presented based on the sequence and biochemical evidence.     

Palladium-catalysed direct arylation of a tris-cyclometallated Ir(III) complex bearing 2,2'-thienylpyridine ligands: a powerful tool for the tuning of luminescence properties

Palladium-catalysed direct 5-arylation of metallated thiophenes of fac-Ir(N^C(3')-thpy)(3) with aryl bromides via C-H bond functionalisation allows the synthesis of a variety of new Ir complexes in only one step (thpyH = 2,2'-thienylpyridine). The method offers simple modification of the nature of the ligand and hence of the photophysical properties of such complexes.     

Crystal lattice dynamics and phase transitions mechanism in potassium hydro (deutrium) sulphate crystals

The phase transition in KHSO₄ crystals of varying deutrium content and different Cu²⁺ concentration is studied. The specific heat at constant pressure,C _p, and DTA measurements are investigated. The measurements are carried out in the vicinity of phase transitionT _c =468 K. Multiple peaks are observed in the temperature dependence ofC _p and a noticeable change due to Cu²⁺ dopant. This behaviour can be attributed to the fact of order disappearance in partial melting of proton in sublattice.

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Zusammenfassung Es wurde die Phasenumwandlung in KHSO₄ Kristallen mit unterschiedlichem Deuteriumgehalt und unterschiedlicher Cu²⁺-Konzentration studiert. Die isobare spezifische WÄrmeC _p und DTA-Messungen wurden untersucht. Die Messungen wurden in der NÄhe des PhasenumwandlungspunktesT _c =468 K durchgeführt. In TemperaturabhÄngigkeit vonC _p wurden Mehrfachpeaks sowie eine bemerkbare Änderung in AbhÄngigkeit vom Cu²⁺-Gehalt beobachtet. Dieses Verhalten wurde erklÄrt.

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On leave Alexandria University, Faculty of Science, Physics Department, Alexandria EGYPT     

Thermal anomaly in LiKSO4 crystals in the temperature range 300–800 K

Thermal analysis, DTA, TG, TMA and DSC were performed on LiKSO₄ in the temperature range 300 to 800 K, using a Heraeus TA 500 thermal analyser. The thermal expansion coefficients measured along the three fundamental crystallogrpahic axes, together with the specific heatC _p, show anomalous behaviour around the phase transition temperature of these crystals atT _c=705 K. Anisotropy in the thermal expansion coefficient as well as endothermic peaks aroundT _c were also observed, while no loss of weight was detected. The temperature-dependence of the thermal conductivity of LiKSO₄ crystals has been estimated, using the temperature-variation of the thermal diffusivity.     

Specific heat and phase transition of (Li1−xKx)2SO4 single crystals

A specific heat study of (Li_1–xK_x)₂SO₄ — LKS — mixed crystals has been made in a wide concentration rangex covering the temperature range 300–800 K. The phase diagram was determined. It is shown that a variation of the Li⁺:K⁺ concentration changes the critical behaviour of the specific heat. The results are discussed in terms of scattering mechanisms of energy carriers.

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Zusammenfassung Bei Temperaturen zwischen 300 und 800 K wurde für einen breiten Konzentrationsbereich für x die spezifische Wärme von (Li_1–xK_x)₂SO₄-Mischkristallen untersucht und das entsprechende Phasendiagramm erstellt. Es wurde gezeigt, daß eine Änderung des Verhältnisses Li⁺:K⁺ auch das kritische Verhalten der spezifischen Wärme verändert. Die Ergebnisse werden hinsichtlich von Sreuungsmechanismen der Energieträger diskutiert.

     

Studies on transition metal murexide complexes

Iron, cobalt, nickel, copper, zinc, cadmium and mercury murexide complexes have been prepared and characterized. The thermal properties of these complexes are studied deeply by DTA technique where their thermal peaks are explained. The multi-stages thermal decomposition mechanism is proposed. The thermodynamic parameters of the decomposition steps are calculated. The entropy change values for all complexes are of the same magnitude and all transition states of the thermal reactions are more ordered than the reactants. The thermal reactions proceed in complicated mechanisms. The fractions appeared in the calculated orders of the thermal reactions confirmed that these reactions proceeded via complex mechanisms.     

The Influence ofγ-irradiation on the thermophysical properties of potassium ammonium sulphate crystals

The effect ofγ-irradiation on the thermal properties of KNH₄SO₄ single crystals in the temperature range 300–600 K is investigated. The variation ofC _P as a function of radiation dose is determined. Analysis of the results indicates that changes induced in the thermal behaviour of KNH₄SO₄ crystal byγ-irradiation might be due to direct collision with lattice atom and multiple atom displacement.     

Spectroscopic studies on a ‘turn-on’ fluorescent sensor for transition metals with selective ‘turn-off’ for mercury(II) ions

Spectroscopic studies on a dansyl-based fluorescent sensor N-(4-aminophenyl)-5-(dimethylamino)naphthalene-1-sulphonamide (1) and its interactions with transition metals are reported. The sensor's absorption and emission spectra exhibited different profiles at different polarities and pH values. Enhanced fluorescence was observed in the presence of chromium(III) ions in methanol, while the emission was quenched significantly in the presence of mercury(II) ions both in methanol and aqueous solution. The binding constants of 1 to chromium(III) in methanol and to mercury(II) ions in methanol and aqueous solution were calculated.