Compatibility of Drotaverine Hydrochloride with Ibuprofen and Ketoprofen Nonsteroidal Anti-Inflammatory Drugs Mixtures

Formulations with two or more active pharmaceutical ingredients (APIs) are a researched trend due to their convenient use compared with multiple medications. Moreover, drug-drug combinations may have a synergistic effect. Drotaverine hydrochloride (D-HCl) is commonly used for its antispasmodic action. The combination of a spasmolytic and an analgesic drug such as ibuprofen (Ibu) or ketoprofen (Ket) could become the answer for the treatment of localized pain. D-HCl:Ibu and D-HCl:Ket drug-drug interactions leading to the formation of eutectic compositions with increased bioavailability, obtained by mechanosynthesis, a green, solvent-free method was explored for the first time. The compatibility of Ibuprofen, Ketoprofen, and Drotaverine Hydrochloride was investigated using differential scanning calorimetry (DSC), X-ray diffraction (XRD), and Fourier-Transform Infrared spectroscopy (FTIR). Solid-liquid equilibrium (SLE) phase diagrams for the binary systems of active pharmaceutical ingredients were developed and the Tammann diagrams were designed to determine the eutectic compositions. The excess thermodynamic functions G^E for the pre-, post-, and eutectic compositions were obtained using the computed activity coefficients data. Results show that drotaverine-based pharmaceutical forms for pain treatment may be obtained at 0.9 respectively 0.8 molar fractions of ibuprofen and ketoprofen which is advantageous because the maximum allowed daily dose of Ibu is about 6 times higher than those of D-HCl and Ket. The obtained eutectics may be a viable option for the treatment of pain associated with cancer therapy.     

Post's program and incomplete recursively enumerable sets

A set A of nonnegative integers is recursively enumerable (r.e.) if A can be computably listed. It is shown that there is a first-order property, Q(X), definable in E, the lattice of r.e. sets under inclusion, such that (i) if A is any r.e. set satisfying Q(A) then A is nonrecursive and Turing incomplete and (ii) there exists an r.e. set A satisfying Q(A). This resolves a long open question stemming from Post's program of 1944, and it sheds light on the fundamental problem of the relationship between the algebraic structure of an r.e. set A and the (Turing) degree of information that A encodes.