In this article, we develop an algorithm that computes the -pure threshold of a binomial hypersurface over a field of characteristic 0$">. This algorithm is related to earlier work of Shibuta and Takagi (e.g., both depend on properties of certain associated rational polytopes), but differs in that it works in all characteristics.

This research presents an experimental study on a scaled prototype of a bladeless wind turbine that operates based on the principle of vortex-induced vibrations (VIV-BWT) with the implementation of bio-inspired design of a columnar-cactus type mast. The aerodynamic performance of columnar-cactus type masts with different numbers of ribs was investigated and compared with that of a conventional cylindrical mast. The objective of this novel proposal is to maximize wind energy conversion efficiency through vortex-induced vibrations, thereby enhancing energy generation. The present study focuses on the geometry of the columnar-cactus type mast as a vortex generator, which significantly influences the performance of this type of VIV wind energy harvester. The findings reveal that the geometric configuration of the cactus-inspired mast and the mast angle promote vortex formation, leading to higher lift coefficients and forces. Consequently, this results in greater vortex-induced vibration magnitudes. For instance, at a wind speed of 6.0 m/s and a mast angle of 0°, the 6-rib cactus-type mast exhibits 12 times greater VIV amplitude compared to the conventional cylindrical mast, while the 5-rib and 7-rib cactus-type masts show 2.4- and 2.2-times greater amplitudes, respectively. However, for wind speeds below 5 m/s, the cylindrical mast demonstrates superior VIV performance.

In a classic small tokamak, the magnetic confinement is achieved by toroidal coils that fit into a donut-shape mechanical structure. To facilitate their handling and maintenance as well as the access to various auxiliaries components, their design has evolved toward a modular configuration. For such demountable design, it is important to guarantee the electrical continuity of the winding of the coil across the modular parts through electrical contacts. The resulting joints rely on pressure and specific materials to transfer high current densities at a good mechanical stability and manageable losses. In the present work, a prototype of a circular demountable toroidal field coil (CDTFC) was designed and built to test some technical choices to be used in the final coils of a table-top tokamak referred to as TPM-1U. For this small tokamak, the magnet wires to wind the toroidal coils should be able to handle large pulsed currents in the tens of thousands of Amperes whereas the coil joints should handle a peak current density of at least 75 kA/cm2. The case study here is the TPM-U1 table-top tokamak. Its conceptual design is recalled and mechanical and magnetic details of the demountable coil prototype are provided. For the experimental test, the contacts were slightly pressed using a custom-made contact assembly and current pulses between 4 kA and 8 kA were fedto the coil prototype. The degradation of the joint was visually estimated by assessing the amount of micro-melting, plastic deformation and oxidation appearing at the interface between the materials in contact. It is shown that the selected AWG-04 magnet wire is appropriate for carrying kiloAmpere range pulsed currents and that the CuBe contacts are able to withstand current densities larger than the specification, up to 263 kA/cm2, under low contact pressures of a few mega-Pascal simplifying their handling. Some technical choices have been probed on a prototype coil yielding a generic sequence of tasks to build and test mechanically and electromagnetically demountable coils and their joints. En un peque˜no tokamak cl´asico, el confinamiento magn´etico se logra con bobinas toroidales que se colocan en una estructura mec´anica en forma de rosquilla. Para facilitar su manejo y mantenimiento, as´ı como el acceso a varios componentes auxiliares, su dise˜no ha evolucionado hacia una configuraci´on modular. Para tal dise˜no desmontable es importante garantizar la continuidad el´ectrica del embobinado de la bobina a trav´es de las partes modulares de los contactos el´ectricos. La operaci´onconfiable de las uniones resultantes est´a basada en la presi´on, los materiales espec´ıficos para transferir altas densidades de corriente a una buena estabilidad mec´anica y p´erdidas manejables. En el presente trabajo, un prototipo de bobina circular desmontable para campo toroidal se dise˜nó y construyó con el fin de probar algunas opciones t´ecnicas implementadas en las bobinas finales de un tokamak de mesa designado como TPM-1U. Para este peque˜no tokamak, el alambre magneto usado para el embobinado de las bobinas deber´ıa de ser capaz de manejar corrientes pulsadas de alta magnitud en el orden de algunos miles de Amperes, mientras que las uniones deber´ıan manejar densidades de corriente de al menos 75 kA/cm2. El caso de estudio aqui es el tokamak de mesa TPM-1U. Se hace ´enfasis en su dise˜no conceptual y se aportan detalles mec´anicos y magnéticos del prototipo de bobina desmontable. Para la prueba experimental, los contactos fueron presionados ligeramente usando un ensamblaje t´ıpico de contacto y se hicieron pasar pulsos de corriente de 4 kA a 8 kA a la bobina prototipo. La degradaci´on de la uni´on se estim´o visualmente evaluando la cantidad de microfusi´on, deformaci´on pl´astica y oxidaci´on que aparece en las interfaces de los materiales en contacto. Se demuestra que el alambre magneto seleccionado AWG-04 es apropido para el transporte de corrientes pulsadas en el rango de kilo-Ampere y que los contactos de CuBe son capacesde soportar densidades m´as grandes que las especificadas, hasta 263 kA/cm2, con presiones bajas de contacto de algunos mega-Pascales simplificando su manejo. Algunas elecciones t´ecnicas han sido probadas sobre una bobina prototipo dando una secuencia gen´erica de tareas para construir y probar mecanicamente y electromagneticamente bobinas desmontables en sus zonas desmontables.