Multiplicative order convergence in ff-algebras

A net $(x_\alpha)$ in an $f$-algebra $E$ is said to be multiplicative order convergent to $x\in E$ if \x_\alpha-x\u\oc 0 for all $u\in E_+$. In this paper, we introduce the notions $mo$-convergence, $mo$-Cauchy, $mo$-complete, $mo$-continuous and $mo$-KB-space. Moreover, we study the basic properties of these notions.Comment:

Patient-oriented and performance-based outcomes after knee autologous chondrocyte implantation: a timeline for the first year of recovery

It is well established that autologous chondrocyte implantation (ACI) can require extended recovery postoperatively; however, little information exists to provide clinicians and patients with a timeline for anticipated function during the first year after ACI. Objective: To document the recovery of functional performance of activities of daily living after ACI. Patients: ACI patients (n = 48, 29 male 35.1 ± 8.0 y). Intervention: All patients completed functional tests (weight-bearing squat, walk-across, sit-to-stand, step-up/over, and forward lunge) using the NeuroCom long force plate (Clackamas, OR) and completed patient-reported outcome measures (International Knee Documentation Committee Subjective Knee Evaluation Form, Lysholm, Western Ontario and McMaster Osteoarthritis Index WOMAC, and 36-Item Short-Form Health Survey) preoperatively and 3, 6, and 12 mo postoperatively. Main Outcome Measures: A covariance pattern model was used to compare performance and self-reported outcome across time and provide a timeline for functional recovery after ACI. Results: Participants demonstrated significant improvement in walk-across stride length from baseline (42.0% ± 8.9% height) at 6 (46.8% ± 8.1%) and 12 mo (46.6% ± 7.6%). Weight bearing on the involved limb during squatting at 30°, 60°, and 90° was significantly less at 3 mo than presurgery. Step-up/over time was significantly slower at 3 mo (1.67 ± 0.69 s) than at baseline (1.49 ± 0.33 s), 6 mo (1.51 ± 0.36 s), and 12 mo (1.40 ± 0.26 s). Step-up/over lift-up index was increased from baseline (41.0% ± 11.3% body weight BW) at 3 (45.0% ± 11.7% BW), 6 (47.0% ± 11.3% BW), and 12 mo (47.3% ± 11.6% BW). Forward-lunge time was decreased at 3 mo (1.51 ± 0.44 s) compared with baseline (1.39 ± 0.43 s), 6 mo (1.32 ± 0.05 s), and 12 mo (1.27 ± 0.06). Similarly, forward-lunge impact force was decreased at 3 mo (22.2% ± 1.4% BW) compared with baseline (25.4% ± 1.5% BW). The WOMAC demonstrated significant improvements at 3 mo. All patient-reported outcomes were improved from baseline at 6 and 12 mo postsurgery. Conclusions: Patients' perceptions of improvements may outpace physical changes in function. Decreased function for at least the first 3 mo after ACI should be anticipated, and improvement in performance of tasks requiring weight-bearing knee flexion, such as squatting, going down stairs, or lunging, may not occur for a year or more after surgery

Interaction Effects on the Magneto-optical Response of Magnetoplasmonic Dimers

The effect that dipole-dipole interactions have on the magneto-optical (MO) properties of magnetoplasmonic dimers is theoretically studied. The specific plasmonic versus magnetoplasmonic nature of the dimer's metallic components and their specific location within the dimer plays a crucial role on the determination of these properties. We find that it is possible to generate an induced MO activity in a purely plasmonic component, even larger than that of the MO one, therefore dominating the overall MO spectral dependence of the system. Adequate stacking of these components may allow obtaining, for specific spectral regions, larger MO activities in systems with reduced amount of MO metal and therefore with lower optical losses. Theoretical results are contrasted and confirmed with experiments for selected structures

Molybdenum (VI) imido complexes derived from chelating phenols : Synthesis, characterization and ɛ-Caprolactone ROP capability

Reaction of the bulky bi-phenols 2,2′-RCH[4,6-(t-Bu)₂C₆H₂OH]₂ (R = Me L¹ᵐᵉH₂, Ph L¹ᵖʰH₂) with the bis(imido) molybdenum(VI) tert-butoxides [Mo(NR¹)(NR²)(Ot-Bu)₂] (R¹ = R² = 2,6-C₆H₃-i-Pr₂; R¹ = t-Bu, R² = C₆F₅) afforded, following the successive removal of tert-butanol, the complexes [Mo(NC₆H₃ᵢ-Pr₂-2,6)₂L¹ᵐᵉ] (1), [Mo(NC₆H₃i-Pr₂-2,6)₂L¹ᵖʰ] (2) and [Mo(Nt-Bu)(μ-NC₆F₅)(L¹ᵐᵉ)]₂ (3). Similar use of the tri-phenol 2,6-bis(3,5-di-tert-butyl-2-hydroxybenzyl)-4-methylphenol (L²H₃) with [Mo(NC₆H₃ᵢ-Pr₂-2,6)₂(Ot-Bu)₂] afforded the oxo-bridged product [Mo(NC₆H₃i-Pr₂-2,6)(NCMe)(μ-O)L2H]₂ (4), whilst use of the tetra-phenols α,α,α′,α′-tetrakis(3,5-di-tert-butyl-2-hydroxyphenyl)-p- or -m-xylene L³ᵖH₄/L³ᵐH₄ led to {[Mo(NC₆H₃ᵢ-Pr₂-2,6)₂]₂(μ-L³ᵖ)} (5) or {[Mo(NC₆H₃ᵢ-Pr₂-2,6)₂]₂(μ-L³ᵐ)} (6), respectively. Similar use of [Mo(NC₆F₅)₂(Ot-Bu)₂] with L³ᵖH₄ afforded, after work-up, the complex {[Mo(NC₆F₅)(Ot-Bu)₂]₂(μ-L³ᵖ)}·6MeCN (7·6MeCN). Molecular structures of 1, 2·CH₂Cl₂, 3, 4·6MeCN, 6·2C₆H₁₄, and 7·6MeCN are reported and these complexes have been screened for their ability to ring open polymerize (ROP) ε-caprolactone; for comparative studies the precursor complex [Mo(NC₆H₃ᵢ-Pr₂-2,6)₂Cl₂(DME)] (DME = 1,2-dimethoxyethane) has also been screened. Results revealed that good activity is only achievable at temperatures of ≥100 °C over periods of 1 h or more. Polymer polydispersities were narrow, but observed molecular weights (Mn) were much lower than calculated values

Surface chemistry of heterobimetallic Ge-M (M = Mo, W) complexes in zeolite Y.

The intrazeolite chemistry of the two germylene complexes Cl2CTHF)GeM(CO)5 (M = Mo, W) was studied with x-ray absorption spectroscopy (Ge, Mo, W edge EXAFS) and in-situ FTIR/TPD-MS techniques. The slightly decarbonylated GeMo complex interacts with the framework of NaY zeolite at room temperature and retains the Ge-Mo bond up to about 100° C. In proton-loaded HY zeolite, framework interactions increase at elevated temperature, and the attached complex retains the Ge-Mo bond up to about 120° C. The Ge-Mo bond is cleaved at higher temperatures. MoClx and Mo-Mo species are formed in NaY and HY zeolite, respectively, while GeClx fragments are anchored to the zeolite framework. The complex Cl2(THF)GeW(CO)5 retains all five CO ligands up to about 100° C in both NaY and the proton form. Detectable anchoring occurs at room temperature in NaY and at about 80° C in the proton form. WC1X species are formed upon cleavage of the Ge-W bond at higher temperatures

Exogenous application of molybdenum affects the expression of CBF14 and the development of frost tolerance in wheat.

Wheat is able to cold acclimate in response to low temperatures and thereby increase its frost tolerance and the extent of this acclimation is greater in winter genotypes compared to spring genotypes. Such up-regulation of frost tolerance is controlled by Cbf transcription factors. Molybdenum (Mo) application has been shown to enhance frost tolerance of wheat and this study aimed to investigate the effect of Mo on the development of frost tolerance in winter and spring wheat. Results showed that Mo treatment increased the expression of Cbf14 in wheat under non-acclimating condition but did not alter frost tolerance. However, when Mo was applied in conjunction with exposure of plants to low temperature, Mo increased the expression of Cbf14 and enhanced frost tolerance in both spring and winter genotypes but the effect was more pronounced in the winter genotype. It was concluded that the application of Mo could be useful in situations where enhanced frost resistance is required. Further studies are proposed to elucidate the effect of exogenous of applications of Mo on frost resistance in spring and winter wheat at different growth stages