PDF for Mathematics from the official Uttarakhand Board website. Access chapter-wise details for Mathematics with the link to ...

Since the election, the LTEs have unendingly predicted total disaster for our country, including the emergence of a dictator, ...

Learn about the APPSC Forest Beat Officer Syllabus 2025, including subject-wise topics, exam pattern, preparation tips & more on this page.

Taking inspiration from the Y2K bug, Quantropi talks about Y2Q, also called Q-day, meaning the day when quantum computers can break current encryption schemes. The 2021 Quantum Threat Timeline Report ...

In this paper the optimal discrete-time linear-quadratic regulator problem is carefully presented and the basic results are reviewed. Dynamic programming is used to determine the optimization ...

The present paper develops an optimal linear quadratic boundary controller for 2×2 linear hyperbolic partial differential equations (PDEs) with actuation on only one end of the domain. First-order ...

Systems of equation solved by the Cramer rule 95 Sec. 10. The rank of a matrix. The linear dependence of vectors and linear forms 105 Sec. 11. Systems of linear equations 115 Chapter III MATRICES AND ...

By extending the scope of a key insight behind Fermat’s Last Theorem, four mathematicians have made great strides toward ...

When she was just 17 years old, Hannah Cairo disproved the Mizohata-Takeuchi conjecture, breaking a four-decade-old mathematical assumption ...

Nature is marked not only by struggles for survival, but also by remarkable feats of cooperation. From microbes to insects to humans, organisms work together in a variety of ways to gather and share ...

The Langlands program has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new ...

This study proposes a comprehensive strategy to optimize the operation of real-world gas pipeline networks and support decision-making. The goal is to improve environmental sustainability by ...