The aim of this paper is to continue analyzing the interactions in the three-body system made up of the Sun, the Moon, and the Earth. First, we review new details about Moon-Earth connections, with a special focus on mechanical forces. Following, we expand the study to consider the pair Sun-Earth, with calculations for electromagnetic forces. The objective in both cases is to know how mechanical and electromagnetic forces affect seismological events on Earth. Our calculations found that Solar Cycles have no direct interaction with earthquake variations. Instead, we established that there is an internal discrepancy for quakes below 35 km detected in some of the regions analyzed. The results indicate that geomagnetic variations must be studied next to understand their connections to earthquakes.

Abstract:
The aim of this paper is to evaluate the worldwide variation of deep and ultra-deep earthquakes
(DQ and UDQ) during the period 1996-2017. This project found only three locations
around the globe presenting this kind of seismicity. Although there are other global settings
showing deep seismicity, they are not periodical and cannot be considered by a statistical
view. The three areas with intense activity for DQ and UDQ events are located mostly in
subduction areas. The largest variations of DQ and UDQ border the Pacific Ocean and include
the North Pacific, South Pacific, and South America. The major difference in this set
is that the first two sites are subduction zones and the South American occurrences happened
in the interior of the continent. Another anomaly is an internal layer between 300 -
500 km in South America that shows no tremors in the period studied. However, below 500
km activity reappears, even at extreme depths of up to 650 km. We suggested that the reason
for those occurrences would be due to an anomaly in the asthenosphere in this region. This
anomaly would probably be presenting a breakable material that was pushed by the Nazca
platform against the South America plate. Other depths below 100 km in all the regions are
discussed as well. We suggested that the reason for those occurrences was an anomaly
created in the asthenosphere as part of the process of the South America collision with the
Nazca plate. Part of the Nazca plate has subducted below South America, creating a slab as
deep as 500 km. The convergent slab is still moving against South America and sinking due
to the gravity and rotation of the Earth. The discrepancies in the occurrences we tracked at
different locations indicated that this slab had different thicknesses around South America.
We found similar results for Vanuatu and Fiji; in these regions UDQ events occur at the
subduction zones under the ocean with depths greater than 700 km. Here, a possible explanation
is that part of the lithosphere is subducted at these depths and is causing tremors.

Abstract:
The classical Weyl-von Neumann theorem states that for any self-adjoint operator $A$ in a separable Hilbert space $\mathfrak H$ there exists a (non-unique) Hilbert-Schmidt operator $C = C^*$ such that the perturbed operator $A+C$ has purely point spectrum. We are interesting whether this result remains valid for non-additive perturbations by considering self-adjoint extensions of a given densely defined symmetric operator $A$ in $\mathfrak H$ and fixing an extension $A_0 = A_0^*$. We show that for a wide class of symmetric operators the absolutely continuous parts of extensions $\widetilde A = {\widetilde A}^*$ and $A_0$ are unitarily equivalent provided that their resolvent difference is a compact operator. Namely, we show that this is true whenever the Weyl function $M(\cdot)$ of a pair $\{A,A_0\}$ admits bounded limits $M(t) := \wlim_{y\to+0}M(t+iy)$ for a.e. $t \in \mathbb{R}$. This result is applied to direct sums of symmetric operators and Sturm-Liouville operators with operator potentials.

Abstract:
We use the boundary triplet approach to extend the classical concept of perturbation determinants to a more general setup. In particular, we examine the concept of perturbation determinants to pairs of proper extensions of closed symmetric operators. For an ordered pair of extensions we express the perturbation determinant in terms of the abstract Weyl function and the corresponding boundary operators. A crucial role in our approach plays so-called almost solvable extensions. We obtain trace formulas for pairs of self-adjoint, dissipative and other pairs of extensions and express the spectral shift function in terms of the abstract Weyl function and the characteristic function of almost solvable extensions. We emphasize that for pairs of dissipative extensions our results are new even for the case of additive perturbations. In this case we improve and complete some classical results of M.G. Krein for pairs of self-adjoint and dissipative operators. We apply the main results to ordinary differential operators and to elliptic operators as well.

Abstract:
In this paper we carried out an investigation about the possible causes for the enhancement of earthquakes in USA the last seven years. Our statistical and physical models indicated that the increased evolution of events in the country depends from the human actions. For further analysis we divided the country into three main seismological regions: western, central and, eastern. We roughly classified the areas by their thickness of Earth’s crust in a variation 25-45-25 km. The thickest area is in the mid-continent and most of this region are part of the Great Plains. In our study we are going to investigate the reason for the Mississippi Lime in Oklahoma a very thick area, started an unusual earthquake activity since 2010, most at Oklahoma/Kansas border. In this region also there are many anthropogenic activities concerning with the waste water wells and more than 4000 of them are active in the state. Wastewater disposal wells typically operate for longer duration and inject much more fluid than hydraulic fracturing, making them more likely to induce earthquakes. Enhanced oil recovery injects fluid into rock layers where oil and gas have already been extracted, while wastewater injection often occurs in never-before-touched rocks. Therefore, wastewater injection can raise pressure levels more than enhanced oil recovery, and thus increases the likelihood of induced earthquakes. Most injection wells do not trigger felt earthquakes. A combination of many factors is necessary for injection to induce felt earthquakes. These include the injection rate and total volume injected; the presence of faults or unknown fractures that are large enough to produce felt earthquakes; stresses that are large enough to produce earthquakes; and the presence of pathways for the fluid pressure to travel from the injection point to faults. Finally other causes of human action triggering earthquakes fluid injection, hydraulic fracturing, enhanced oil recovery, mining, nuclear explosions, some of them will be mentioned and investigated in this paper. We also intend to explain why not all the waste wells are triggering earthquakes and how it would be strongly attached to the unevenness of the Earth’s crust.

Abstract:
In this paper the scattering matrix of a scattering system consisting of two selfadjoint operators with finite dimensional resolvent difference is expressed in terms of a matrix Nevanlinna function. The problem is embedded into an extension theoretic framework and the theory of boundary triplets and associated Weyl functions for (in general nondensely defined) symmetric operators is applied. The representation results are extended to dissipative scattering systems and an explicit solution of an inverse scattering problem for the Lax-Phillips scattering matrix is presented.

Abstract:
Pulsed neutron diffraction investigations have been performed in the ferroelectric PZT system, Pb(Zr1-xTix)O3, doped with 1%wt. of Nb2O5, as a function of both temperature and composition. The study has been made in a wide range of temperatures encompassing the three known phases in Zr-rich PZT: ferroelectric low temperature (R3c), ferroelectric high temperature (R3m) and paraelectric (Pm3m). The combination of the temperature and the composition dependence of the structural parameters allowed the determination of the special relationship, recently pointed out by Corker et al., between the octahedral strain (z) and the tilt angle (w) in the ferroelectric low temperature phase (FL) of PZT. The strain-tilt coupling coefficient has been found to decrease linearly with Ti content and the composition at which z and w de-couple to be of x=0.30.

Abstract:
For scattering systems consisting of a (family of) maximal dissipative extension(s) and a selfadjoint extension of a symmetric operator with finite deficiency indices, the spectral shift function is expressed in terms of an abstract Titchmarsh-Weyl function and a variant of the Birman-Krein formula is proved.

Abstract:
In this paper we show the existence of a large class of spherically symmetric data $d$ (on a spacelike hypersurface $S$), from which a perfect fluid spacetime (surrounded by vacuum) develops. This spacetime contains an event horizon (with trapped surfaces behind it). The data $d$ are regular and {\it innociuous}, i.e. the data--surface $S$ does not contain any point of the horizon or of the trapped surface area. We give auxiliary data on an auxiliary hypersurface $H$ and also on the star boundary; then we solve Einstein's equations for perfect fluid in the future and past of $H$. Our solution induces the above mentioned data $d$ on some chosen spacelike hypersurface $S$ in the past of $H$. By construction $H$ turns out to be the matter part of the horizon, once we attach a vacuum to our matter spacetime. Obviously, from these data $d$ on $S$ it develops (into the future) the event horizon $H$. We solve the constraint equations for the auxiliary data posed on the null--surface $H$. This reduces the choice of these data to the choice of the density $\rho$ and $R:=[\text{curvature}]^{-1/2}$. Our data fulfil positivity of $\rho$, $2m/R=1$ (at the star boundary) and other properties. This is archieved by an algorithm, which for given $\rho $ yields $R$ (from an input parameter function $h \in C^1( \left[0,1\right],\left]0,-\infty \right[)$).

Abstract:
A recent paper by Herbut in J. Phys. A: Math. Gen. {\bf 29}, 1 (1996) is shown to contain an internal inconsistency which invalidates the principal conclusion of the paper that the magnetic penetration depth diverges with an XY-exponent rather than a mean-field exponent, as predicted some time ago by Kiometzis, Kleinert, and Schakel (KKS).