Tribute to Pasquale Montagna, 1950-2010

In 1653, the French philosopher and scientist Blaise Pascal published "Treatise on the Equilibrium of Liquids," which discussed the principles of static fluids. A static fluid is a fluid that is not in motion. When a fluid is not flowing, we say that the fluid is in static equilibrium. If the fluid is water, we say it is in hydrostatic equilibrium. For a fluid in static equilibrium, the net force on any part of the fluid must be zero; otherwise, the fluid will start to flow. Pascal observed...

Grieving is a complex psychological and emotional process that varies significantly among individuals. George Bonanno's research on bereavement identified four distinct patterns of grieving, offering a nuanced understanding of how people cope with significant loss, such as the death of a spouse, over extended periods. These patterns — resilience, recovery, chronic dysfunction, and delayed grief — highlight the diversity in emotional responses and adaptive mechanisms.
Resilience
The resilience...

A single mitochondrion is a bean-shaped organelle enclosed by a double-membrane system. The outer membrane of mitochondria is smooth and contains many porins - the integral membrane transporters. Porins enable free diffusion of ions and small uncharged molecules through the outer mitochondrial membrane but limit the transport of molecules larger than 5000 Daltons. Further, the outer mitochondrial membrane forms a unique structure called membrane contact sites with other subcellular organelles,...

Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.

Parseval's theorem is a fundamental concept in signal processing and harmonic analysis. It asserts that for a periodic function, the average power of the signal over one period equals the sum of the squared magnitudes of all its complex Fourier coefficients. This theorem, named after Marc-Antoine Parseval, provides a powerful tool for analyzing the energy distribution in signals.
Interestingly, Parseval's theorem also holds for the trigonometric form of the Fourier series, which expresses a...

The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.