This deep learning is not Google's deep learning, AI but how we grasp deep learning. Such as Path G's interpretation of gauge invariance is intuitive; Quantum Sense's approach to the Schrödinger equation focuses on problem-solving; and at a high level, I observed that ARRB suggests that physics and mathematics serve primarily to translate collected or … Continue reading “Deep Learning”

Given that Deepseek has opened its model, it enables business owners to deploy it locally, thereby harnessing the advantages of AI while also safeguarding the most sensitive and critical privacy of their data and client information. To effectively deploy a project locally, one must acquire a comprehensive understanding of essential skills and knowledge. to be … Continue reading Open-sourced DeepSeek Models’ Huge Commercial Potential

Ehrenfest’s theorem shows that quantum expectation values follow classical mechanics on average, but quantum fluctuations can cause deviations.

First is the axiom of extensionality, if two sets contain exactly the same elements, then they are the same set. The second one is axiom of empty set. Third, axiom of pairing, if you have two sets, you can put them together into a new set. axiom of unition meaning to merge sets together, axiom … Continue reading The Nine Axioms of Set Theory

For centuries, mathematics education has been anchored in Euclidean geometry and Cartesian coordinates. From the rigid constructs of points, lines, and planes to the static nature of axes and fixed coordinate systems, students have been taught an outdated framework that does not reflect the deep, dynamic structures that govern modern physics and engineering. It is … Continue reading Rethinking Math Education: From Euclidean Geometry to Differential Geometry

First of all, Geometry, bundles, differential manifolds, topological manifolds, topology, set theory and underneath the logic to build the mathematic edifice to understand truly law of nature: special relativity, classical physics, quantum physics, general relativity, chemistry and electromagnetism etc. The paper's content is as follows: the first filed theory on James Clerk Maxwell, Herman Weyl, … Continue reading Fiber bundles, Yang and the geometry of spacetime: paper by Federico Pasinato 01

Core Architecture OpenManus is built on an agent-based architecture with a hierarchical inheritance pattern: BaseAgent (app/agent/base.py): The foundation class that provides: Memory management State transitions Execution loop control Stuck state detection ReActAgent (app/agent/react.py): Extends BaseAgent with: Think-Act cycle pattern Abstract methods for thinking and acting ToolCallAgent (app/agent/toolcall.py): Extends ReActAgent with: Tool/function calling capabilities Tool execution handling Response processing … Continue reading OpenManus Project Structure

The Proca Lagrangian is a fundamental concept in Quantum Field Theory (QFT) that describes the dynamics of a massive vector field (a field associated with a particle of spin-1 that has mass). It is named after the Romanian physicist Alexandru Proca, who first formulated it. The Proca Lagrangian is particularly important in the study of massive gauge bosons, such as … Continue reading Proca Lagrangian 

When undertaking the transition to advanced studies of curved space, in contrast to Euclidean space, it is essential to comprehend the notion of covariant derivatives, while also further exploring our established understanding of directional derivatives to effectively distinguish between the two. Key Differences Curvature Effects The directional derivative does not consider curvature—it is simply the … Continue reading Compare Directional Derivative and Covariant Derivative

A comprehensive understanding of the ordinary derivative in flat space is well established; nevertheless, the requirement for the covariant derivative emerges from the characteristics of curved space. In our universe, specifically within the framework of space-time, spaces are intrinsically curved as opposed to flat. Accordingly, the derivative must incorporate the consideration that the basis vectors … Continue reading What is Covariant Derivative in Flat and Curved Space