MediMath Science

1. Vectors Vectors  are mathematical entities characterized by both magnitude and direction. They are essential for describing physical quantities such as blood flow velocity, forces acting on joints, and features in image analysis for deep learning. A vector in three-dimensional space is written as: \[ \mathbf{v} = v_x \hat{i} + v_y \hat{j} + v_z \hat{k}, \] where \(\hat{i} = (1,0,0)\), \(\hat{j} = (0,1,0)\), and \(\hat{k} = (0,0,1)\) are the unit vectors along the \(x\)-, \(y\)-, and \(z\)-axes, respectively. The components \(v_x\), \(v_y\), and \(v_z\) represent the magnitude of the vector in the \(x\)-, \(y\)-, and \(z\)-directions.  Vectors can describe the speed and direction of  blood flow  in vessels, facilitating the analysis of hemodynamics. They are also used to model  forces  acting on prosthetic joints or tissues, aiding in the study of biomechanics and prosthetic design. A vector in \(n\)-dimensional space is written as: \[ \mathbf{x} = (x_1, ...

In today’s financial markets, a troubling asymmetry has emerged between those who sell technological dreams and those who buy them. Founders, CEOs, and early investors often understand how distant true commercialization remains, while many young retail investors—driven by optimism and headlines—see only the promise, not the timeline. This imbalance creates a structural divide: the informed side monetizes expectations, while the uninformed side absorbs the losses. Quantum computing offers a striking example. The 2025 Nobel Prize in Physics was awarded to John Clarke, Michel H. Devoret, and John M. Martinis “for the discovery of macroscopic quantum mechanical tunnelling and energy quantisation in an electric circuit.” Their work revealed that quantum effects—once confined to the microscopic world—can emerge in circuits large enough to see, laying the foundation for today’s superconducting qubits. Quantum systems promise radically new ways of computation through superposition, entangleme...