Iterative approximation of fixed points of Prešić operators on partial metric spaces

We study the convergence of the Pre?i? type k‐step iterative method for a class of operators satisfying Pre?i? type contractive conditions on the setting of partial metric spaces. Some examples are presented to illustrate our obtained results. As applications of the presented convergence theorems, we derive global attractivity results for a class of matrix difference equations. Numerical experiments are also presented to illustrate the theoretical findings.     

On $$\gamma $$ γ - and local $$\gamma $$ γ -vectors of the interval subdivision

Journal of Algebraic Combinatorics - We show that the $$\gamma $$ -vector of the interval subdivision of a simplicial complex with a nonnegative and symmetric h-vector is nonnegative. In...     

Axiomatisability problems for <Emphasis Type="Italic">S</Emphasis>-posets

Let \(\mathcal{C}\) be a class of ordered algebras of a given fixed type τ. Associated with the type is a first order language L _τ , which must also contain a binary predicate to be interpreted by the ordering in members of \(\mathcal{C}\). One can then ask the question, when is the class \(\mathcal{C}\) axiomatisable by sentences of L _τ ? In this paper we will be considering axiomatisability problems for classes of left S-posets over a pomonoid S (that is, a monoid S equipped with a partial order compatible with the binary operation). We aim to determine the pomonoids S such that certain categorically defined classes are axiomatisable. The classes we consider are the free S-posets, the projective S-posets and classes arising from flatness properties. Some of these cases have been studied in a recent article by Pervukhin and Stepanova. We present some general strategies to determine axiomatisability, from which their results for the classes of weakly po-flat and po-flat S-posets will follow. We also consider a number of classes not previously examined.     

Metachronal propulsion of non-Newtonian viscoelastic mucus in an axisymmetric tube with ciliated walls

Cilia-induced flow of viscoelastic mucus through an idealized two-dimensional model of the human trachea is presented.The cilia motion is simulated by a metachronal wave pattern which enables the mobilization of highly viscous mucus even at nonzero Reynolds numbers.The viscoelastic mucus is analyzed with the upper convected Maxwell viscoelastic formulation which features a relaxation time and accurately captures normal stress generation in shear flows.The governing equations are transformed from fixed to wave(laboratory)frame with appropriate variables and resulting differential equations are perturbed about wave number.The trachea is treated as an axisymmetric ciliated tube.Radial and axial distributions in axial velocity are calculated via the regular perturbation method and pressure rise is computed with numerical integration using symbolic software MATHEMATICA^‘TM’.The influence of selected parameters which is cilia length,and Maxwell viscoelastic material parameter i.e.relaxation time for prescribed values of wave number are visualized graphically.Pressure rise is observed to increase considerably with elevation in both cilia length and relaxation time whereas the axial velocity is markedly decelerated.The simulations provide some insight into viscous-dominated cilia propulsion of rheological mucus and also serve as a benchmark for more advanced modeling.     

Co-thickness and oxidation states effect on magnetic anisotropy in Co/MgO heterostructure

Interfacial magnetism and magnetic anisotropy constant ($K_i$) in Co/MgO heterostructure have been studied using ab-initio density functional calculations. It is found that interfacial Co spin magnetic moment shows a strong interdependence on Co-O bond lengths and a reasonable spin-polarization of ～80% is established as a function of Co layers. Our results revealed a saturated positive (out-of-plane) $K_i$ of +2.80 mJ/m² at ≥12 Co layers (～1.6 nm Co thickness), which is associated with orbital magnetic moment difference in [100] and [001] direction along with a strong hybridization between $d_{xy}$ and $d_{x^2?y^2}$ orbitals through orbital angular momentum operator $\stackrel{?}{L_z}$. Furthermore, it is shown that the $K_i$ magnitude almost remains constant and weakens in the case of under- and over-oxidations in the interfacial MgO and Co layers, respectively. Interestingly, $K_i$ improved for oxygen migrated interface due to enhanced $d_{xy}$ and $d_{x^2?y^2}$ orbitals coupling. The disordered interfaces stability is checked by analyzing the formation energy. Hence, the present findings disclose that the higher Co thickness in ordered Co/MgO structure supports to out-of-plane [001] (positive) $K_i$, which could be useful for its technological implementation in high-density magnetic data storage devices with high thermal stability.     

用纳米压痕法分析溶剂对聚醚醚酮(PEEK)力学性能的影响

Poly (ether ether ketone)(PEEK) is a high-performance semi-crystalline thermoplastic polymer.Exposure of the polymeric surface to solvents can have a strong effect like softening/swelling of polymeric network or dissolution.In this study,nano-indentation analysis was performed to study the effect of acetone on the surface mechanical properties of PEEK using different exposure time.The experiments were performed with a constant loading rate (10 nm/s) to a maximum indentation displacement (1000 nm).A 30-second hold segment was included at the maximum load to account for any creep effects followed by an unloading segment to 80% unloading.The indentation hardness and the elastic modulus were computed as a continuous function of the penetration displacement in the continuous stiffness mode (CSM) indentation.The experimental data showed that the peak load decreased from ~5.2 mN to ~1.7 mN as exposure time in solvent environment increased from 0 to 18 days.The elastic modulus and the hardness of PEEK samples also displayed a decreasing trend as a function of exposure time in the solvent environment.Two empirical models were used to fit the experimental data of hardness as a function of exposure time which showed a good agreement with the experimental values.     

Paenibacillus polymyxa PKB1 produces variants of polymyxin B-type antibiotics

Polymyxins are cationic lipopeptide antibiotics active against many species of Gram-negative bacteria. We sequenced the gene cluster for polymyxin biosynthesis from Paenibacillus polymyxa PKB1. The 40.8 kb gene cluster comprises three nonribosomal peptide synthetase-encoding genes and two ABC transporter-like genes. Disruption of a peptide synthetase gene abolished all antibiotic production, whereas deletion of one or both transporter genes only reduced antibiotic production. Computational analysis of the peptide synthetase modules suggested that the enzyme system produces variant forms of polymyxin B (1 and 2), with D-2,4-diaminobutyrate instead of L-2,4-diaminobutyrate in amino acid position 3. Two antibacterial metabolites were resolved by HPLC and identified by high-resolution mass spectrometry and MS/MS sequencing as the expected variants 3 and 4 of polymyxin B₁ (1) and B₂ (2). Stereochemical analysis confirmed the presence of both D-2,4-diaminobutyrate and L-2,4-diaminobutyrate residues.     

Structure activity relationship of bergenin,p-hydroxybenzoyl bergenin, 11-O-galloylbergenin as potent antioxidant and urease inhibitor isolated from Bergenia ligulata

Ethanol extract of the aerial parts of Bergenia ligulata was subjected to solvent–solvent separation followed by various chromatographic techniques that lead to isolation of bergenine (1), p-hydroxybenzoyl bergenin (2), 11-O-galloylbergenin (3) and methyl gallate (4) as major constituents. Ethyl acetate fraction showed a dose-dependent urease inhibitory pattern with IC₅₀ value of 54μg/mL. Structures of compounds 1 and 3 were established by XRD and 2, 4 by NMR. All these compounds were subjected to DPPH scavenging activity, reducing power assay and urease inhibitory activity. The EC₅₀ 7.45 ± 0.2 μg/mL and 5.39 ± 0.28 μg/mL values in terms of antioxidant and reducing power, respectively, were less for 3. Compounds 1–3 showed moderate to significant urease inhibitory potential with IC₅₀ 57.1 ± 0.7, IC₅₀ 48.4 ± 0.3 and 38.6 ± 1.5. Antioxidant activities and urease inhibitory potential were investigated and compound 3 was found to be the most active.     

Thermal Decomposition Kinetics of Some Di‐ and Triorganotin(IV) Carboxylates Derived from para‐Nitrophenylethanoic Acid

Thermogravimetric (TG) investigations of organotin(IV) carboxylates with the general formula R_mSnL_4−m (where R=CH₃, C₂H₅, n‐C₄H₉, C₆H₅, cyclo‐C₆H₁₁, n‐C₈H₁₇, m=2, 3, and L=para‐nitrophenylethanoate anion) have been performed. Derivative thermogravimetry (DTG) and differential thermal analysis (DTA) techniques, Horowitz‐Metzger method and the fundamental thermodynamic relations are used to evaluate the thermokinetic parameters of each thermal degradation pattern. Results reveal that the thermal stability is functional to Sn C and Sn O bonds. In the case of R₂SnL₂, activation energy, reaction order and pre‐exponential factor associated with the bulk degradation processes increase as the alkane chain length increases. Hence, Oct₂SnL₂ is thermally more stable than Bu₂SnL₂, which in turn is more resistant to thermal dissociation than Et₂SnL₂. The same phenomenon is not observed for R₃SnL compounds because their degradation is highly irregular. Furthermore, R₂SnL₂ has larger values of kinetic parameters than those of corresponding triorganotin(IV) para‐nitrophenylethanotes. Thermodynamic parameters of these compounds also reinforce the above facts.