I’ve proved existence of smooth solutions of Navier-Stokes equations. I sent this to a journal for peer review.
The proof is based on my general topology research that I did before and asked ChatGPT to use it to solve Navier-Stokes.
Particularly, my proof of existence of smooth solutions uses my theorem:
The lim (limit) functional can be linearly extended to the set of all functions. All continuous operations can be extended to the values of the extended limit, with all algebraic identities preseved.
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Equilibrado de piezas
El equilibrado es una etapa esencial en el mantenimiento de maquinaria agricola, asi como en la fabricacion de ejes, volantes, rotores y armaduras de motores electricos. El desequilibrio genera vibraciones que incrementan el desgaste de los rodamientos, generan sobrecalentamiento e incluso pueden causar la rotura de los componentes. Para evitar fallos mecanicos, es fundamental identificar y corregir el desequilibrio de forma temprana utilizando tecnicas modernas de diagnostico.
Metodos principales de equilibrado
Hay diferentes tecnicas para corregir el desequilibrio, dependiendo del tipo de componente y la intensidad de las vibraciones:
Equilibrado dinamico – Se utiliza en componentes rotativos (rotores y ejes) y se lleva a cabo mediante maquinas equilibradoras especializadas.
El equilibrado estatico – Se usa en volantes, ruedas y otras piezas donde es suficiente compensar el peso en un unico plano.
Correccion del desequilibrio – Se lleva a cabo mediante:
Perforado (retirada de material en la zona de mayor peso),
Colocacion de contrapesos (en ruedas y aros de volantes),
Ajuste de masas de balanceo (por ejemplo, en ciguenales).
Diagnostico del desequilibrio: equipos utilizados
Para identificar con precision las vibraciones y el desequilibrio, se utilizan:
Maquinas equilibradoras – Permiten medir el nivel de vibracion y determinan con exactitud los puntos de correccion.
Analizadores de vibraciones – Capturan el espectro de oscilaciones, detectando no solo el desequilibrio, sino tambien otros defectos (como el desgaste de rodamientos).
Sistemas de medicion laser – Se emplean para mediciones de alta precision en componentes criticos.
Las velocidades criticas de rotacion requieren especial atencion – regimenes en los que la vibracion aumenta drasticamente debido a la resonancia. Un equilibrado correcto previene danos en el equipo en estas condiciones de funcionamiento.
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