The mask of (2b + 4)-point n-ary subdivision scheme

In this paper, we present general formulae for the mask of (2b + 4)-point n-ary approximating as well as interpolating subdivision schemes for any integers ${b\,\geqslant\,0}$ and ${n\,\geqslant\,2}$ . These formulae corresponding to the mask not only generalize and unify several well-known schemes but also provide the mask of higher arity schemes. Moreover, the 4-point and 6-point a-ary schemes introduced by Lian [Appl Appl Math Int J 3(1):18–29, 2008] are special cases of our general formulae.     

Thermodynamic properties of sodium hexatitanate (Na2Ti6O13) at high temperature (298.15–1573 K)

Sodium hexatitanate (Na₂Ti₆O₁₃) was reported as an anode side material for Sodium ion batteries owing to low material cost, high energy efficiency, good thermal stability and long cycle life. Therefore, studies pertaining to the thermodynamic properties of Na₂Ti₆O₁₃ are indispensable for improving its service performance. However, a significant number of literature reviews concerning thermodynamic properties indicated that heat capacity of Na₂Ti₆O₁₃ at high temperatures should be confirmed. In this study, the 99.5% purity of Na₂Ti₆O₁₃ sample was successfully prepared via solid-state reaction using TiO₂ and Na₂CO₃ as initial materials. Heat capacity of the as-synthesized samples in the temperature range of 573–1523 K was measured using a multi-high temperature calorimeter 96 line. Heat capacity, Cp, from 298.15 to 1573 K was modeled as a polynomial formula with a prediction error of 3%: Cp = 474.08143 + 0.06286T-8.04068 × 10⁶ T⁻² (J⋅mol⁻¹⋅K⁻¹). In combination with the low-temperature data, heat capacity of Na₂Ti₆O₁₃ from 0 to 1573 K was given in present study. Values of changes in enthalpy, Gibbs free energy and entropy in the temperature range of 298.15–1573 K were calculated based on the temperature dependence of heat capacity.     

Thermodynamic properties of sodium pyrovanadate (Na4V2O7) at high temperature (298.15–873 K)

The sodium pyrovanadate (Na₄V₂O₇) powder was synthesized by solid-state reaction using sodium carbonate (Na₂CO₃) and vanadium pentoxide (V₂O₅) as raw materials. X-ray powder diffraction (XRD), scanning electron microscope (SEM), and differential scanning calorimeter (DSC) were used to accurately characterize the synthesized sample. The solid-state phase transformation from α-Na₄V₂O₇ to β-Na₄V₂O₇ occurs at the temperature 696 K and the enthalpy is equals to 1.03 ± 0.01 kJ/mol, the endothermic effect at 931 K and the enthalpy is equals to 31.35 ± 0.31 kJ/mol, which is related to the melting of Na₄V₂O₇. The high-temperature heat capacity of Na₄V₂O₇ was measured using a Multi-high temperature calorimeter 96 line and DSC. The obtained high-temperature heat capacity of Na₄V₂O₇, as a function of temperature, was modeled as: Cp=314.62+0.05T-5494390T^-2 J·mol^-1·K^-1 (298.15-873 K). The temperature dependence on heat capacity was then used for computing changes in the enthalpy, entropy, and Gibbs free energy at the specific temperature internal.     

Thermodynamic properties of magnesium orthovanadate Mg3(VO4)2 at high temperatures (298.15–1473 K)

Mg₃(VO₄)₂ powder was synthesized via a simple solid-state reaction under air atmosphere, and X-ray diffraction was employed to investigate the cell parameters of the as-prepared powder. The cell parameters indicated that the sample was crystallized in the form of Cmca orthorhombic system with lattice parameters, a = 6.053 Å, b = 11.442 Å, and c = 8.330 Å. The high-temperature enthalpy changes in Mg₃(VO₄)₂ were measured in the range of 573–1473 K by drop calorimetry for the first time. Furthermore, the temperature dependence of the heat capacity of Mg₃(VO₄)₂ was calculated by considering the enthalpy changes results. Thermodynamic properties (changes in enthalpy, entropy, and Gibbs free energy) were also calculated in the range of 298.15–1473 K.     

Variable Precision Algorithm for the Numerical Computation of the Fermi–Dirac Function ℱj(x) of Order j=−3/2

The purpose of this technical note is to present a piecewise Chebyshev expansion for the numerical computation of the Fermi–Dirac function _–3/2(x), –<x<. The variable precision algorithm we given automatically adjusts the degrees of the Chebyshev expansions so that _–3/2(x) can be efficiently computed to d significant decimal digits of accuracy, for a user specified value of d in the range 1d15.     

Analytical Expansion and Numerical Approximation of the Fermi–Dirac Integrals F j(x) of Order j=−1/2 and j=1/2

This paper uses properties of the Weyl semiintegral and semiderivative, along with Oldham's representation of the Randles–Sevcik function from electrochemistry, to derive infinite series expansions for the Fermi–Dirac integrals _j (x), –j=–1/2, 1/2. The practical use of these expansions for the numerical approximation of _–1/2(x) and _1/2(x) over finite intervals is investigated and an extension of these results to the higher order cases j=3/2, 5/2, 7/2 is outlined.     

Critical evaluation and thermodynamic assessment of the R2O–P2O5 (R = Li,Na and K) systems

The R₂O–P₂O₅ (R = Li, Na and K) systems are thermodynamically optimized based on the evaluated phase equilibria and thermodynamic data by the CALPHAD method. Liquid phase is described by the Modified Quasichemical Model, which takes short-range ordering in liquid solution into account. All intermediate phases RPO₃, R₅P₃O₁₀, R₄P₂O₇ and R₃PO₄ are treated as stoichiometric compounds and the corresponding polymorphic transitions are considered. A set of self-consistent model parameters for describing the Gibbs free energy of each phase are obtained. The experimental phase equilibria, enthalpy of formation, entropy, heat capacity and activity are reproduced well within experimental error limits. The calculated liquidus around compounds become flatter with the increase of P₂O₅ content, suggesting that the degree of stability of phosphate increases as its composition approaches R₃PO₄. The calculated enthalpies of formation for intermediate compounds become more negative and entropies become more positive with the increase of atomic numbers of alkali metals.     

The estimation of atmospheric corrections to one-channel (11 μ m) data from the AVHRR; simulation using AVHRR/ 2

It has been established that the sea-surface brightness temperatures Tb₄ in the 11 μ m channel and T_b4in the 12 μ m channel of the Advanced Very High Resolution Radiometer (AVHRR/ 2) are linearly related to a good degree of accuracy, i.e. T_b5= α+ β T_b4 Using AVHRR/ 2 data for various dates and from different parts of the world's oceans, the parameters a and 0 have been determined. The above relation may then be used for simulating T_b5 for those cases for which only Tb4 is available (e.g. for the AVHRR on TIROS-N, NOAA-6, NOAA-8, etc.). The brightness temperature TM and pseudo-brightness temperature T_b5 then enable one to use the split-window technique for estimating atmospherically-corrected sea-surface temperatures (SSTs) from the 11μ m channel data alone. Such an atmospheric correction technique should be a possibility because the 11μ m channel of the AVHRR on the various satellites in question are almost identical

This technique has been used with two split-window algorithms for correcting the data from the 11μ m channel of the AVHRR instrument on the TIROS-N satellite obtained off south-western Portugal. One of the algorithms gives ‘ skin’ temperatures and the other algorithm gives bulk temperatures. The resulting SSTs for twelve dates from 15 June 1979 to 14 June 1980 have been compared with sea-surface (skin) temperatures which were obtained with airborne radiometer data obtained on the same dates.     

Can human allergy drug fexofenadine,an antagonist of histamine (H1) receptor,be used to treat dog and cat? Homology modeling,docking and molecular dynamic Simulation of three H1 receptors in complex with fexofenadine

Fexofenadine, a potent antagonist to human histamine 1 (H₁) receptor, is a non-sedative third generation antihistamine that is widely used to treat various human allergic conditions such as allergic rhinitis, conjunctivitis and atopic dermatitis. Encouragingly, it’s been successfully used to treat canine atopic dermatitis, this supports the notion that it might have a great potential for treating other canine allergic conditions and other mammal pets such as dog. Regrettably, while there is a myriad of studies conducted on the interactions of antihistamines with human H₁ receptor, the similar studies on non-human pet H₁ are considerably scarce. The published studies using the first and second generation antihistamines drugs have shown that the antihistamine response is varied and unpredictable. Thus, to probe its efficacy on pet, the homology models of dog and cat H₁ receptors were built based on the crystal structure of human H₁ receptor bound to antagonist doxepin (PDB 3RZE) and fexofenadine was subsequently docked to human, dog and cat H₁ receptors. The docked complexes are then subjected to 1000 ns molecular dynamics (MD) simulations with explicit membrane. Our calculated MM/GBSA binding energies indicated that fexofenadine binds comparably to the three receptors; and our MD data also showed the binding poses, structural and dynamic features among three receptors are very similar. Therefore, our data supported the application of fexofenadine to the H₁ related allergic conditions of dog and cat. Nonetheless, subtle systemic differences among human, dog and cat H₁ receptors were also identified. Clearly, there is still a space to develop a more selective, potent and safe antihistamine alternatives such as Fexofenadine for dog or cat based on these differences. Our computation approach might provide a fast and economic way to predict if human antihistamine drugs can also be safely and efficaciously administered to animals.