The q-analogue of the Higgs algebra

In this paper, the q-generalization of the Higgs algebra is considered. The realization of this algebra is shown in an explicit form using a nonlinear transformation of the creation-annihilation operators of the q-harmonic oscillator. This transformation is the performance of two operations, namely, a “correction” using a function of the original Hamiltonian, and raising to the fourth power the creation and annihilation operators of a q-harmonic oscillator. The choice of the “correcting” function is justified by the standard form of commutation relations for the operators of the metaplectic realization Uq(SU(1,1)). Further possible directions of research are briefly discussed to summarize the results obtained. The first direction is quite obvious. It is the consideration of the problem when the dimension of the operator space increases or for any value N. The second direction can be associated with the analysis of the relationship between q-generalizations of the Higgs and Hahn algebras.

Explicit Stable Finite Difference Methods for Diffusion-Reaction Type Equations

By the iteration of the theta-formula and treating the neighbors explicitly such as the unconditionally positive finite difference (UPFD) methods, we construct a new 2-stage explicit algorithm to solve partial differential equations containing a diffusion term and two reaction terms. One of the reaction terms is linear, which may describe heat convection, the other one is proportional to the fourth power of the variable, which can represent radiation. We analytically prove, for the linear case, that the order of accuracy of the method is two, and that it is unconditionally stable. We verify the method by reproducing an analytical solution with high accuracy. Then large systems with random parameters and discontinuous initial conditions are used to demonstrate that the new method is competitive against several other solvers, even if the nonlinear term is extremely large. Finally, we show that the new method can be adapted to the advection–diffusion-reaction term as well.

The Fourth Government

Annotation: As the influence of journalism as a "fourth power" expands, it becomes more and more criticized by various social forces. If the objections are really well-founded - the journalist's (publication, program) confession, the right attitude - is to accept, acknowledge, correct the criticism. It is one thing for a journalist (publication, program) to object to a course of action. Keywords: Journalism, principle, debate, authority, protest, criticism, publication, fact, position, objective, pure information audience, approach, etc.

Plasmon resonance at the interface dielectric - nanocomposite material with superconducting inclusions

This article theoretically considers surface plasmon resonance in composite structures. The features of the surface plasmon resonance arising at the interface with media containing nanoparticles from a high-temperature superconductor are investigated. The dielectric constant of spherical superconducting inclusions is considered taking into account Gorter-Casimir two-fluid model. The temperature dependence of the electrodynamic parameters of the superconductor is taken into account. The two-fluid model, the dependence of the concentration of non-superconducting electrons in a superconductor is often used as the fourth power of temperature nn~T4. In this work, a phenomenological model is used, according to which the electron concentration of non-superconducting electrons in a superconductor is determined by the formula nn~Tγ with γ=1.3÷2. This model is in good agreement with experimental data for high-temperature ceramic superconductors. The dispersion characteristics of surface plasmons arising in a planar structure with a thin nanocomposite superconductor layer are investigated. It is shown that the dispersion characteristics depend significantly on temperature.

Using ephaptic coupling to estimate the synaptic cleft resistivity of the calyx of Held synapse

At synapses, the pre- and postsynaptic cells get so close that currents entering the cleft do not flow exclusively along its conductance, gcl. A prominent example is found in the calyx of Held synapse in the medial nucleus of the trapezoid body (MNTB), where the presynaptic action potential can be recorded in the postsynaptic cell in the form of a prespike. Here, we developed a theoretical framework for ephaptic coupling via the synaptic cleft, and we tested its predictions using the MNTB prespike recorded in voltage-clamp. The shape of the prespike is predicted to resemble either the first or the second derivative of the inverted presynaptic action potential if cleft currents dissipate either mostly capacitively or resistively, respectively. We found that the resistive dissipation scenario provided a better description of the prespike shape. Its size is predicted to scale with the fourth power of the radius of the synapse, explaining why intracellularly recorded prespikes are uncommon in the central nervous system. We show that presynaptic calcium currents also contribute to the prespike shape. This calcium prespike resembled the first derivative of the inverted calcium current, again as predicted by the resistive dissipation scenario. Using this calcium prespike, we obtained an estimate for gcl of ~1 μS. We demonstrate that, for a circular synapse geometry, such as in conventional boutons or the immature calyx of Held, gcl is scale-invariant and only defined by extracellular resistivity, which was ~75 Ωcm, and by cleft height. During development the calyx of Held develops fenestrations. We show that these fenestrations effectively minimize the cleft potentials generated by the adult action potential, which might otherwise interfere with calcium channel opening. We thus provide a quantitative account of the dissipation of currents by the synaptic cleft, which can be readily extrapolated to conventional, bouton-like synapses.

Geometrical Classification of Self-Similar Motion of Two-Dimensional Three Point Vortex System by Deviation Curvature on Jacobi Field

In this study, we geometrically analyze the relation between a point vortex system and deviation curvatures on the Jacobi field. First, eigenvalues of deviation curvatures are calculated from relative distances of point vortices in a three point vortex system. Afterward, based on the assumption of self-similarity, time evolutions of eigenvalues of deviation curvatures are shown. The self-similar motions of three point vortices are classified into two types, expansion and collapse, when the relative distances vary monotonously. Then, we find that the eigenvalues of self-similarity are proportional to the inverse fourth power of relative distances. The eigenvalues of the deviation curvatures monotonically convergent to zero for expansion, whereas they monotonically diverge for collapse, which indicates that the strengths of interactions between point vortices related to the time evolution of spatial geometric structure in terms of the deviation curvatures. In particular, for collapse, the collision point becomes a geometric singularity because the eigenvalues of the deviation curvature diverge. These results show that the self-similar motions of point vortices are classified by eigenvalues of the deviation curvature. Further, nonself-similar expansion is numerically analyzed. In this case, the eigenvalues of the deviation curvature are nonmonotonous but converge to zero, suggesting that the motion of the nonself-similar three point vortex system is also classified by eigenvalues of the deviation curvature.

Mpemba Effect- the Effect of Time

By analyzing the relation between time and speed, the relation between time and gravitational field, the gravitational redshift of photon and the black-body radiation theorem, the conclusion that time on an object is proportional to the fourth power of the absolute temperature of the object is obtained. Applying the above conclusion about the nature of time, the author analyzes the Mpemba effect and the inverse Mpemba effect, and reaches the following conclusion: the Mpemba effect is the time effect produced when heat flows from objects into space, and the "inverse" Mpemba effect is the time effect produced when heat flows from space into objects.

Experimental verification of the field theory of specific heat with the scaling in crystalline matter

The field (geometrical) theory of specific heat is based on the universal thermal sum, a new mathematical tool derived from the evolution equation in the Euclidean four-dimensional spacetime, with the closed time coordinate. This theory made it possible to explain the phenomena of scaling in the heat capacity of condensed matter. The scaling of specific heat of the carbon group elements with a diamond lattice is revisited. The predictions of the scaling characteristics for natural diamond and grey tin are verified with published experimental data. The fourth power in temperature in the quasi-low temperature behaviour of the specific heat of both materials is confirmed. The phenomenon of scaling in the specific heat, previously known only in glassy matter, is demonstrated for some zincblend lattice compounds and diamond lattice elements, with their characteristic temperatures. The nearly identical elastic properties of grey tin and indium antimonide is the cause for similarity of their thermal properties, which makes it possible to make conjectures about thermal properties of grey tin.