A Jarn\'ik type theorem for planar curves: everything about the parabola

The well known theorems of Khintchine and Jarn\'ik in metric Diophantine approximation provide comprehensive description of the measure theoretic properties of real numbers approximable by rational numbers with a given error. Various generalisations of these fundamental results have been obtained for other settings, in particular, for curves and more generally manifolds. In this paper we develop the theory for planar curves by completing the theory in the case of parabola. This represents the first comprehensive study of its kind in the theory of Diophantine approximation on manifolds.Comment: 13 pages. Revised versio

Frustrated Metastable Behavior of Magnetic and Transport Properties in Charge Ordered La1-xCaxMnO3+d Manganites

We have studied the effect of metastable, irreversibility induced by repeated thermal cycles on the electric transport and magnetization of polycrystalline samples of La1-xCaxMnO3 (0.48\leq x \leq 0.55) close to charge ordering. With time and thermal cycling (T<300 K) there is an irreversible transformation of the low-temperature phase from a partially ferromagnetic and metallic to one that is less ferromagnetic and highly resistive for the composition close to charge ordering (x=050 and 0.52). Irrespective of the actual ground state of the compound, the effect of thermal cycling is towards an increase of the amount of the insulating phase. We have observed the magnetic relaxation in the metastable state and also the revival of the metastable state (in a relaxed sample) due to high temperature thermal treatment. We observed changes in the resistivity and magnetization as the revived metastable state is cycled. The time changes in the magnetization are logarithmic in general and activation energies are consistent with those expected for electron transfer between Mn ions. Changes induced by thermal cycling can be inhibited by applying magnetic field. These results suggest that oxygen non-stoichiometry results in mechanical strains in this two-phase system, leading to the development of frustrated metastable states which relax towards the more stable charge-ordered and antiferromagnetic microdomains. Our results also suggest that the growth and coexistence of phases gives rise to microstructural tracks and strain accommodation, producing the observed irreversibility.Comment: 13 Pages, 10 Figure

The Macroeconomic Management of Increased Aid: Policy Lessons from Recent Experience

This paper investigates the macroeconomic challenges created by a surge in aid inflows. It develops an analytical framework for examining possible policy responses to increased aid, in terms of absorption and spending of aid?where the central bank controls absorption through monetary policy and the sale of foreign exchange and the fiscal authority controls spending. Different combinations of absorption and spending lead to different macroeconomic consequences. Evidence from five countries that recently experienced an aid surge (Ethiopia, Ghana, Tanzania, Mozambique and Uganda) shows no support for aid-related real exchange rate appreciation in these countries, but indicates that the fear of Dutch disease played an important part in the policy reaction to aid surges. Fiscal and monetary authorities should coordinate their responses to an aid surge, because an uncoordinated response?typically when fiscal authority wants to spend aid while the central bank wants to avoid exchange rate appreciation?can have serious negative macroeconomic consequences.aid, exchange rate, aid absorption, policy

SELF-ASSEMBLED CHITOSAN NANOPARTICLES FOR PERCUTANEOUS DELIVERY OF CAFFEINE: PREPARATION, CHARACTERIZATION AND IN VITRO RELEASE STUDIES

Objective: Chitosan (CS)–tripolyphosphate (TPP)–nanoparticles (NPs) have been extensively studied during the past few decades due to their well-recognized applicability in various fields. The present study attempts to optimise the development of these nanoparticles to enhance the percutaneous delivery of caffeine.Methods: CS-TPP-NPs were prepared via ionic cross-linking of CS and TPP and were characterized. The influence of several formulation conditions (CS: TPP mass ratio and concentration of caffeine) and process parameters (stirring speed, stirring time and ultra-sonication time) on the colloidal characteristics of CS-TPP-NPs were investigated and the resulting nanoparticles were characterized using scanning electron microscopy (SEM), transmission electron microscopy (TEM), Fourier transform infrared (FTIR) and x-ray diffraction (XRD) analyses. Physicochemical properties, including particle size, zeta potential and polydispersity index (PDI) were examined, and in vitro release studies were conducted to ascertain the release profile of caffeine from the nanoparticles. In addition, the colloidal stability of the prepared NPs was also assessed on storage.Results: Process parameters appeared to exert a significant effect on the physicochemical characteristics of the CS-TPP-NPs. The CS-TPP-NPs prepared under optimum conditions (CS concentration of 0.2 mg/ml, CS: TPP volume ratio of 25:12 ml, stirred at 700 rpm for 60 min, with 0.97 mg/ml caffeine concentration and treatment with low ultra-sonication for 30 min) had shown a mean particle size of ~143.43±1.69 nm, zeta potential of+43.13±1.10 mV, PDI of ~0.30±0.01. A drug loading capacity and encapsulation efficiency of 48.89% and 60.69%, respectively, were obtained. Cumulative release study for drug-loaded CS-NPs was significantly (p&lt;0.001, paired t-test) higher (58.7% caffeine released) compared to control formulation (41.5% caffeine released) after 72 h. Stability studies conducted for 28 d showed that caffeine-loaded CS-NPs degraded much quicker when stored at 25 â°C than 4 â°C. It was also noted that caffeine-loaded CS-NPs in the freeze-dried form were unstable as the surface charge of nanoparticles dropped from positive zeta potential to-3.55 mV within 2 d at 4 â°C and at 25 â°C, surface charge dropped to-3.16 mV within 14 d of the experiment.Conclusion: Chitosan (CS)–tripolyphosphate (TPP)–nanoparticles (NPs) appear to be a promising strategy to achieve sustained percutaneous delivery of caffeine