Limit computable integer parts

Let R be a real closed field. An integer part I for R is a discretely ordered subring such that for every ${r \in R}$ , there exists an ${i \in I}$ so that i ?? r < i?+?1. Mourgues and Ressayre (J Symb Logic 58:641?C647, 1993) showed that every real closed field has an integer part. The procedure of Mourgues and Ressayre appears to be quite complicated. We would like to know whether there is a simple procedure, yielding an integer part that is ${\Delta^0_2(R)}$ ??limit computable relative to R. We show that there is a maximal Z-ring ${I \subseteq R}$ which is ${\Delta^0_2(R)}$ . However, this I may not be an integer part for R. By a result of Wilkie (Logic Colloquium ??77), any Z-ring can be extended to an integer part for some real closed field. Using Wilkie??s ideas, we produce a real closed field R with a Z-ring ${I \subseteq R}$ such that I does not extend to an integer part for R. For a computable real closed field, we do not know whether there must be an integer part in the class ${\Delta^0_2}$ . We know that certain subclasses of ${\Delta^0_2}$ are not sufficient. We show that for each ${n \in \omega}$ , there is a computable real closed field with no n-c.e. integer part. In fact, there is a computable real closed field with no n-c.e. integer part for any n.     

Some Applications of the Hodge-de Rham Decomposition to Ricci Solitons

The aim of this paper is to present a link between the Perelman potential for a compact Ricci soliton M ⁿ and the Hodge-de Rham decomposition theorem, we shall use this result to present an integral formula which enables us to establish conditions under which the Ricci soliton is trivial. Moreover, given a Ricci soliton such that its associated vector field X is a conformal vector field we show that in the compact case X is a Killing vector field, while for the non-compact case, either the soliton is Gaussian or X is a Killing vector field.     

Biodiesel Residual Glycerol Metabolism by Klebsiella pneumoniae: Pool of Metabolites Under Anaerobiosis and Oxygen Limitation as a Function of Feeding Rates

The metabolism of residual glycerol from biodiesel synthesis by Klebsiella pneumoniae BLh-1 was investigated in this study. Batch and fed-batch cultivations were performed in bioreactors under anaerobic and oxygen limitation conditions. Results of batch cultivations showed that the main product was 1,3-propanediol (1,3-PD) in both conditions, although the higher yields and productivities (0.46 mol mol^?1 glycerol and 1.22 g?L^?1?h^?1, respectively) were obtained under anaerobic condition. Large amounts of ethanol were also produced under batch anaerobic condition, peaking at 12.30 g?L^?1. Batch cultivations under oxygen limitation were characterized by faster growth kinetics, with higher biomass production but lower conversions of glycerol into 1,3-PD, with yields and productivities of 0.33 mol mol^?1 glycerol and 0.99 g?L^?1?h^?1, respectively. The fed-batch cultivations were carried out in order to investigate the effects of feeding of raw glycerol on cells. Fed-batch under anaerobiosis showed that 1,3-PD and ethanol concentrations increased with the feeding rate, with maximal productions of 26.12 and 19.2 g?L^?1, respectively. The oxygen limitation conditions diverted the bacterium metabolism to an elevated lactic acid formation, reaching 59 g?L^?1 in higher feeding rates of glycerol, but lowering the production of ethanol.     

A new inclusion complex of amlodipine besylate and soluble β-cyclodextrin polymer: preparation, characterization and dissolution profile

Amlodipine besylate (AML) has become the most popular blood pressure medication for hypertensive pets. It belongs to the class I (high solubility and high permeability) according to BCS and is marketed in Europe only as white tablets equivalent to 2.5, 5.0 and 10.0 mg of amlodipine for oral administration. Unfortunately, oral AML dosage for cats and dogs is in the range 0.1–0.2 and 0.625–0.125 mg/kg/die respectively. Moreover, AML shows a slight solubility in water according to Ph. Eur. 7°. According to these considerations, the aim of this work was the complexation between soluble β-cyclodextrin polymer (CD) and AML using the solubilization/freeze-dried method to obtain powders easily dosable and soluble in water for the treatment of hypertension in pets. The complex in solution was evaluated by phase solubility studies that indicated the optimal 2:1 drug/CD ratio to form a stable complex. UV–Vis absorption and circular dichroism showed the formation of a complex with a weak bond such as confirmed by differential scanning calorimetry, infrared spectroscopy and fluorescence microscopy. In vitro dissolution/release tests were performed in water to investigate the influence of formulative parameters on drug dissolution/release properties. The inclusion of AML in CD increased its wettability, dissolution rate and solubility in water. This method could be a suitable approach for the administration of an extemporaneous solution of the antihypertensive drug to guarantee a correct dose to pets increasing the compliance.     

Enantioselective synthesis of iridal, the parent molecule of the iridal triterpenoid class

The monocyclic triterpene iridal 1 (parent molecule) is synthesized by an approach that allows access for several representatives of the iridal family as well as diversely substituted analogues. The success of the proposed synthetic plan depends upon the effortless stereoselective establishment of the trans C10/C11 dimethyl relationship in B-ring moiety 7 using a domino-based methodology and the higly efficient Miyaura-Suzuki type sp3-sp2 segment coupling 7 and 8, respectively.     

Nitroprusside-PEO enthalpic interaction as a driving force for partitioning of the [Fe(CN)(5)NO](2-) anion in aqueous two-phase systems formed by poly(ethylene oxide) and sulfate salts

Ions are known to concentrate in the salt-enriched phase of aqueous two-phase systems, with the only known exception being the pertechnetate anion, TcO(4)(-). We have discovered a second ion, nitroprusside anion (NP), which is markedly transferred from the salt phase to the polymer phase. The partitioning behavior of [Fe(CN)(5)NO](2-) anion was investigated in ATPS formed by poly(ethylene oxide) of molar mass 3350 and 35000 g mol(-1), and different sulfate salts (Na(2)SO(4), Li(2)SO(4), and MgSO(4)). On the basis of a model, the nitroprusside high affinity for the macromolecular phase was attributed to an enthalpic specific interaction between the anion and ethylene oxide unit. Partition coefficients increased exponentially with tie-line length increase, reaching values as high as 1000 and showing a relationship very dependent on the salt nature, but independent of the polymer molar mass.     

Coordination polymer adsorbent for matrix solid-phase dispersion extraction of pesticides during analysis of dehydrated Hyptis pectinata medicinal plant by GC/MS

The coordination polymer [Zn(BDC)(H₂O)₂]_n was tested for extraction of pyrimethanil, ametryn, dichlofluanid, tetraconazole, flumetralin, kresoxim-methyl and tebuconazole from the medicinal plant Hyptis pectinata, with analysis using gas chromatography-mass spectrometry in selected ion monitoring mode (GC/MS, SIM). Experiments carried out at different fortification levels (0.1, 0.5 and 1.0 μg g⁻¹) resulted in recoveries in the range 73-97%, and RSD values were between 5 and 12% for the [Zn(BDC)(H₂O)₂]_n sorbent. Detection and quantification limits ranged from 0.02 to 0.07 μg g⁻¹ and from 0.05 to 0.1 μg g⁻¹, respectively, for the different pesticides studied. The method developed was linear over the range tested (0.04-14.0 μg g⁻¹), with correlation coefficients ranging from 0.9987 to 0.9998. Comparison between [Zn(BDC)(H₂O)₂]_n and the commercial phase C₁₈-bonded silica showed good performance of the [Zn(BDC)(H₂O)₂]_n polymeric sorbent for the pesticides tested.     

Temperature effect on electrochemical properties of lithium manganese phosphate with carbon coating and decorating with MWCNT for lithium-ion battery

Journal of Solid State Electrochemistry - The increasing demands for higher energy density and higher power capacity of Li-ion secondary batteries have led to a search for electrode materials whose...