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

So, the equation seems to equal: Be smart, have an open heart, and God will show himself to you. Or strive to understand, ...

This technical note addresses the stability analysis of linear systems governed by continuous-time difference equations with multiple delays. We propose new sufficient conditions for L 2 -exponential ...

As AI tools become more embedded, they also expose institutions to a new class of risk - one that blends technology, ethics, ...

Closed-form equations that give the value of an arbitrary complex impedance transformed through a length of dissipationless, nonuniform transmission line with exponential cosine-squared, and parabolic ...

The stochastic 3D Navier–Stokes equation with damping driven by a multiplicative noise is considered in this paper. The stability of weak solutions to the stochastic 3D Navier–Stokes equations with ...

Quantum computers have the potential to speed up computation, help design new medicines, break codes, and discover exotic new ...

I’ve seen it time and again in my decades of coaching entrepreneurs and athletes – consistency is the hidden multiplier that separates the extraordinary from the average. When I talk about building ...

A phonon-based theoretical framework for liquids marks a major step toward a universal equation of state with broad implications across physics, chemistry and engineering ...

This study introduces a valuable spring-bead model for epithelial cell layers, designed to improve previous cell-resolved approaches and to understand the connection between the biophysics of ...

Organizations responsible for data security cannot afford to wait for quantum to arrive before building their defenses.