The paper examines the renewal function associated with a sequence of probability distributions, which is defined by concave recurrence relations or by an even more general procedure. The elementary renewal theorem is generalized to such sequences. The results can be used to establish renewal theorems for first death in branching processes, if only the possibly generation dependent probability generating functions converge to a limit.
AbstractPurposeThe aim was to determine effects of diluent monomer and monocalcium phosphate monohydrate (MCPM) on polymerization kinetics and volumetric stability, apatite precipitation, strontium release and fatigue of novel dual-paste composites for vertebroplasty.Materials and methodsPolypropylene (PPGDMA) or triethylene (TEGDMA) glycol dimethacrylates (25 wt%) diluents were combined with urethane dimethacrylate (70 wt%) and hydroxyethyl methacrylate (5 wt%). 70 wt% filler containing glass particles, glass fibers (20 wt%) and polylysine (5 wt%) was added. Benzoyl peroxide and MCPM (10 or 20 wt%) or N-tolyglycine glycidyl methacrylate and tristrontium phosphate (15 wt%) were included to give initiator or activator pastes. Commercial PMMA (Simplex) and bone composite (Cortoss) were used for comparison.ATR-FTIR was used to determine thermal activated polymerization kinetics of initiator pastes at 50-80 °C. Paste stability, following storage at 4-37 °C, was assessed visually or through mixed paste polymerization kinetics at 25 °C. Polymerization shrinkage and heat generation were calculated from final monomer conversions. Subsequent expansion and surface apatite precipitation in simulated body fluid (SBF) were assessed gravimetrically and via SEM. Strontium release into water was assessed using ICP-MS. Biaxial flexural strength (BFS) and fatigue properties were determined at 37 °C after 4 weeks in SBF.ResultsPolymerization profiles all exhibited an inhibition time before polymerization as predicted by free radical polymerization mechanisms. Initiator paste inhibition times and maximum reaction rates were described well by Arrhenius plots. Plot extrapolation, however, underestimated lower temperature paste stability. Replacement of TEGDMA by PPGDMA, enhanced paste stability, final monomer conversion, water-sorption induced expansion and strontium release but reduced polymerisation shrinkage and heat generation. Increasing MCPM level enhanced volume expansion, surface apatite precipitation and strontium release. Although the experimental composite flexural strengths were lower compared to those of commercially available Simplex, the extrapolated low load fatigue lives of all materials were comparable.ConclusionsIncreased inhibition times at high temperature give longer predicted shelf-life whilst stability of mixed paste inhibition times is important for consistent clinical application. Increased volumetric stability, strontium release and apatite formation should encourage bone integration. Replacing TEGDMA by PPGDMA and increasing MCPM could therefore increase suitability of the above novel bone
composites for vertebroplasty. Long fatigue lives of the composites may also ensure long-term durability of the materials.
The standard NMR and DOSY techniques allowed for the first time the on-line study of the polymerization kinetics together with the determination of number average molar mass Mn and mass average molar mass Mw.
The paper examines the renewal function associated with a sequence of probability distributions, which is defined by concave recurrence relations or by an even more general procedure. The elementary renewal theorem is generalized to such sequences. The results can be used to establish renewal theorems for first death in branching processes, if only the possibly generation dependent probability generating functions converge to a limit.
Temperature affects the polymerization behavior of dimethacrylate-based materials. This study describes the influence of pre-polymerization temperature and exposure duration on polymerization kinetics of a commercial dental photo-activated composite at the top and at 2-mm depth. We used the temperature-controlled stage of a diamond-attenuated-total-reflectance unit to pre-set composite temperature between 3° and 60°C. Composite was light-exposed by a conventional quartz-tungsten-halogen curing unit for 5, 10, 20, or 40 sec. Real-time conversion, maximum conversion rate ( Rpmax), time to achieve Rpmax, and conversion at Rpmax were calculated from infrared spectra. Composite pre-warming enhanced maximal polymerization rate and overall monomer conversion (top significantly greater than 2 mm). Time when Rpmax occurred did not change with temperature, but occurred sooner at the top than at 2-mm depth. Conversion at Rpmax increased with temperature, allowing more of the reaction to occur prior to vitrification than at room temperature.
The convergence of artificial intelligence and machine learning with material science holds significant promise to rapidly accelerate development timelines of new high-performance polymeric materials. Within this context, we report an inverse design strategy for polycarbonate and polyester discovery based on a recommendation system that proposes polymerization experiments that are likely to produce materials with targeted properties. Following recommendations of the system driven by the historical ring-opening polymerization results, we carried out experiments targeting specific ranges of monomer conversion and dispersity of the polymers obtained from cyclic lactones and carbonates. The results of the experiments were in close agreement with the recommendation targets with few false negatives or positives obtained for each class.<br>
Let $a_1,\ldots,a_n$ be distinct, positive integers with $(a_1,\ldots,a_n)=1$, and let k be an arbitrary field. Let $H(a_1,\ldots,a_n;z)$ denote the Hilbert series of the graded algebra k$[t^{a_1},t^{a_2},\ldots,t^{a_n}]$. We show that, when $n=3$, this rational function has a simple expression in terms of $a_1,a_2,a_3$; in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any $n\geq4$.
Polymerization Kinetics Stability, Volumetric Changes, Apatite Precipitation, Strontium Release and Fatigue of Novel Bone Composites for Vertebroplasty