The Opuntia ficus-indica (OFI) prickly pear peel, is a residue product and was used as a substrate in solid-state fermentation (SSF) to obtain bioactive compounds of interest due to its antimicrobial and antioxidant activity. A Box Hunter & Hunter design to evaluate the independent factors was used. These factors were temperature (°C), inoculum (spores/g), humidity (%), pH, NaNO3 (g/L), MgSO4 (g/L), KCl (g/L) and KH2PO4 (g/L). The response factors were hydrolyzable and condensed tannins amount. In addition, the fermentation extracts the antioxidant and antimicrobial activity were evaluated. The results showed that the humidity (%), inoculum (spores/g) and temperature (°C) affect the release of hydrolyzable and condensed tannins. The treatments 13 and 16 were the best to accumulate condensed (43 mg/g) and hydrolyzable tannins (3.8 mg/g) respectively. Besides, the fermented extracts showed a higher antioxidant activity compared than the unfermented peel extracts, as well as a high inhibition versus E. coli, Alternaria sp. and Botrytis spp. The use of the fermentation process is a good alternative for the recovery of waste and the accumulation of bioactive molecules with potential industrial application.

A method of solution to solve the compressible unsteady 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity equation in cylindrical coordinates is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow. A dimensionless parameter is introduced whereby in the large limit case a method of solution is sought for in the boundary layer of the tube. A reduction to a single partial differential equation is possible and integral calculus methods are applied for the case of a body force directed to the centre of the tube to obtain an integral form of the Hunter-Saxton equation. Also an extension for a more general body force is shown where in addition there is a rotational force applied.

This study investigates via Lie symmetry analysis the Hunter-Saxton equation, an equation relevant to the theoretical analysis of nematic liquid crystals. We employ the multiplier method to obtain conservation laws of the equation derived from first-order multipliers. Conservation laws of the Hunter-Saxton equation, in combination with the Lie point symmetries of the equation, enable us to perform symmetry reductions through employment of the double reduction method. The method exploits the relationship between Lie point symmetries and conservation laws to effectively reduce both the number of variables and the order of the equation. Five nontrivial conservation laws of the Hunter-Saxton equation are derived, four of which are found to have associated Lie point symmetries. Applying the double reduction method to the Hunter-Saxton equation results in a set of first-order ordinary differential equations, the solutions of which represent invariant solutions for the equation.

Enzyme replacement therapy (ERT) improves the somatic manifestations in mucopolysaccharidoses (MPS))．However, because intravenously administered enzymes cannot cross the blood brain barrier (BBB), ERT is ineffective against the progressive neurodegeneration and resultant severe central nervous system (CNS) symptoms observed in patients with neuronopathic MPS. Attempts to surmount this problem have been made with intrathecal and intracerebroventricular ERT intend to achieve CNS effects, but the burdens on patients are inimical to long-term multiple administrations. However, after pabinafusp alfa, a human iduronate-2-sulfatase fused with a BBB-crossing anti-transferrin receptor antibody, showed both central and peripheral efficacy in mice model, subsequent clinical trials in a total of 62 patients with MPS-II (Hunter syndrome) in Japan and Brazil substantiated this dual efficacy and provided an acceptable safety profile. To date, pabinafusp alfa is the only approved intravenous ERT effective against both the somatic and CNS symptoms of patients with MPS-II. This article summarizes the hitherto obtained preclinical and clinical evidence associated with this drug, and discusses the preclinical, translational and clinical challenges of evaluating, ameliorating and preventing the neurodegeneration in patients with MPS-II.