abstract

The mass and decay of the \(s\bar {s}\) member of the \(1^{3}F_{4}\) meson nonet are investigated in the framework of the Regge phenomenology and the \(^{3}P_{0}\) model. We propose, based on the results, that the assignment of the \(s\bar {s}\) member of the \(1^{3}F_{4}\) meson nonet will require additional testing in the future. Our results also provide information for future studies of the \(1^{3}F_{4}\) meson nonet.

abstract

The aim of our article is to introduce and investigate the effect of memory on the consumer model under the influence of advertisements. This model describes the movement from potential buyers to buyers under the influence of advertisements. For the non-delayed model, the local stability of equilibria is investigated by using its characteristic equation. The theory of fractional differential equations (FDEs) is applied to determine the fractional-order values \(q\) at which the model undergoes Hopf bifurcation. For the delayed model, we introduced the fractional-order consumer model under the time-delay effect. The time-delay parameter makes the model dynamics richer, which explains the model’s behavior more realistically. By considering the time-delay value as a bifurcation parameter beside the fractional-order \(q\), the Hopf bifurcation is analyzed. We calculated the formula of the time-delay value that leads to Hopf bifurcation. Furthermore, for supporting the theoretical outcomes, we give some examples, which illustrate the influence of both the fractional order and the time delay on the behavior of the model. We also introduced the distributed order consumer model which is a generalization of the integer and fractional orders ones. We considered two different expressions for the weight function to illustrate the stability and to get the periodic solution. A good agreement between both theoretical analysis and simulation results is found.

abstract

We have recently discovered a smooth vacuum-wormhole solution of the first-order equations of general relativity. Here, we obtain the corresponding multiple-vacuum-wormhole solution. Assuming that our world is essentially Minkowski spacetime with a large number of these vacuum-defect wormholes inserted, there is then another flat spacetime with opposite spatial orientation, which may be called a “mirror” world. We briefly discuss some phenomenological aspects and point out that there will be no significant vacuum-Cherenkov radiation in our world, so that ultrahigh-energy cosmic rays do not constrain the typical size and separation of the wormhole mouths (different from the constraints obtained for a single Minkowski spacetime with similar defects). Other signatures from a “gas” of vacuum-defect wormholes are mentioned, including a possible time machine.

abstract

Generalized transverse momentum distributions (GTMDs), the Wigner and the Husimi distributions of quarks in the pion are evaluated in a chiral quark model at the one-loop level. Analytic expressions are obtained for GTMDs, allowing for a qualitative discussion of their features, whereas the Wigner and the Husimi distributions are obtained with numerical integration of simple formulas. We explain the features of the Wigner distributions, in particular their non-positivity. In our model, the Husimi distributions, which are interpreted as coarse-grained Wigner distributions, are not mathematically positive-definite, but the magnitude of their negative values is tiny and occurs at large transverse momenta and impact parameters. Hence, as expected, coarse graining leads to better-behaved functions from the point of view of the probabilistic interpretation.