Recent content by reterty

There is the following linear Volterra equation of the second kind $$ y(x)+\int_{0}^{x} K(x-s) y(s)\,{\rm d}s = 1 $$ with kernel $$ K(x-s) = 1 - 4 \sum_{n=1}^{\infty} \dfrac{1}{\lambda_n^2} e^{-\beta \lambda_n^2 (x-s)} $$ where $y(0)=1$, $\beta>0$ and $\lambda_n$ is the $n$-th positive root...

Recently, I have received a referee report on my paper in which reviewer states the following: "... in all known direct band gap semiconductors the electron effective mass is isotropic or has a negligible anisotropy in a comparison with the hole effective mass which can have much more...

The problem of bound states of an electron trapped in a dipole field is being studied by Alhaidari and company. (See, for example, https://arxiv.org/ftp/arxiv/papers/0707/0707.3510.pdf). It is not clear to me why the point dipole approximation is used everywhere in such calculations. Can't an...

Ok, it is necessary using the stationary-action principle show that the vectors of the instantaneous velocity and force over time should approach each other in direction

No, my question concerns the nature of the aligning effect (see above)

I mean force fields: classical gravitational or electric field

I would like to discuss the nature of the following effect. At whatever angle and with whatever initial speed the particle fly into a uniform potential field, over time the directions of the instantaneous velocity and field strength converge. The kinematics and dynamics here are trivial, but I...

For example: https://www.researchgate.net/publication/305345527_A_New_Relativistic_Extension_of_the_Harmonic_Oscillator_Satisfying_an_Isochronicity_Principle

Let us consider relativistic particle (electron) which moves with relativistic speed ##v## in the Coulomb field (in the field of a fixed heavy nucleus). The main question is what is the potential energy of a particle in such a static field? Landau and Lifshitz in their book "Field Theory"...

As is well known, almost periodic functions can be represented as a Fourier series with incommensurable (non-multiple) frequencies https://en.wikipedia.org/wiki/Almost_periodic_function. It seems to me that I came up with an integral criterion for the degree of non-periodicity. The integral of a...

No, we consider the case of capacitors in series connected with battery. The first plate of the first capacitor has charge q, whereas the second plate of the last capacitor has charge -q. Intermediate plates are charged through influence and it is necessary to prove that their absolute values...

As you know, "in the classics" the charges of the capacitor plates are equal in absolute value and opposite in sign. However, let us consider a series connection of capacitors. In this case, a charge of the opposite sign is induced on every second plate of each capacitor due to electrostatic...

I think, I found this type of transitions. They are realized by increasing the pressure at a fixed temperature for substances with an anomalous dependence of the melting point on pressure (decreasing it with increasing pressure). Such substances include bismuth, antimony, ice, cast iron and...

the minimum of a potential moving the right, whereas in the standart first-order transition within Landau theory it moves left.

I am looking for possible examples and a variant of Landau's theory of phase transitions for an exotic order-disorder phase transition, in which a thermodynamic system jumps into a disordered (or less orderly) state by reaching the maximum critical value of the order parameter. That is, in one...