Accurate Q value for the Se double-electron-capture decay

The Q   value of the neutrinoless double-electron-capture (0νECEC$0\nu \text{ECEC}$) decay of ⁷⁴Se was measured by using the JYFLTRAP Penning trap. The determined value is 1209.169(49) keV, which practically excludes the possibility of a complete energy degeneracy with the second ²⁺$2^{+}$ state (1204.205(7) keV) of ⁷⁴Ge in a resonant 0νECEC$0\nu \text{ECEC}$ decay. We have also computed the associated nuclear matrix element by using a microscopic nuclear model with realistic two-nucleon interactions. The computed matrix element is found to be quite small. The failure of the resonant condition, combined with the small nuclear matrix element and needed p-wave capture, suppresses the decay rate strongly and thus excludes ⁷⁴Se as a possible candidate to search for resonant 0νECEC$0\nu \text{ECEC}$ processes.     

An exact solution of the moving boundary problem for the expansion of a plasma cylinder in a magnetic field

An exact analytic solution has been obtained for a uniformly expanding, neutral, infinitely conducting plasma cylinder in an external uniform and constant magnetic field. The electrodynamical aspects related to the emission and transformation of energy have been considered as well. The results obtained can be used in analysing the recent experimental and simulation data.     

EEG topography-specific BOLD changes: a continuous EEG-fMRI study in a patient with focal epilepsy

Blood oxygenation level dependent (BOLD) response related to interictal activity was evaluated in a patient with post-traumatic focal epilepsy at repeated continuous electroencephalogram (EEG)-functional magnetic resonance imaging examinations. Lateralized interictal EEG activity induced a main cluster of activation co-localized with the anatomical lesion. Spreading of EEG interictal activity to both frontal lobes evoked bilateral clusters of activation indicating that topography of BOLD response might depend on the spatial distribution of epileptiform activity.     

Radially polarized hyperbolic-cosine-Gaussian beam

Vector beams have attracted much interest recently. In this paper, focusing properties of the radially polarized hyperbolic-cosine-Gaussian beam are investigated. Simulation results show that the focal depth increases with increasing cosine parameter in the cosine term of the beam, while focal spot decreases simultaneously, namely, superresolution occurs. Focal depth increase velocity is quicker for larger cosine parameter, while the transverse focal spot shrinks more quickly for smaller cosine parameter. In addition, for two-portion concentric piecewise radially polarized hyperbolic-cosine-Gaussian beam with π phase shift in center circle portion, focal pattern evolves considerably with increasing cosine parameter, and the evolution principle differs for different radius of the center circle portion. Focal splitting and novel focal spots may appear. This kind of vector beam can be used in optical storage, optical manipulation, and lithography.     

Bifurcation of small limit cycles in cubic integrable systems using higher-order analysis

In this paper, we present a method of higher-order analysis on bifurcation of small limit cycles around an elementary center of integrable systems under perturbations. This method is equivalent to higher-order Melinikov function approach used for studying bifurcation of limit cycles around a center but simpler. Attention is focused on planar cubic polynomial systems and particularly it is shown that the system studied by ?o?a?dek (1995) [24] can indeed have eleven limit cycles under perturbations at least up to 7th order. Moreover, the pattern of numbers of limit cycles produced near the center is discussed up to 39th-order perturbations, and no more than eleven limit cycles are found.     

Lie symmetries of a system arising in plasma physics

Lie group classification for a diffusion‐type system that has applications in plasma physics is derived. The classification depends on the values of 5 parameters that appear in the system. Similarity reductions are presented. Certain initial value problems are reduced to problems with the governing equations being ordinary differential equations. Examples of potential symmetries are also presented.     

Fractional model and solution for the Black‐Scholes equation

This work presents a new model of the fractional Black‐Scholes equation by using the right fractional derivatives to model the terminal value problem. Through nondimensionalization and variable replacements, we convert the terminal value problem into an initial value problem for a fractional convection diffusion equation. Then the problem is solved by using the Fourier‐Laplace transform. The fundamental solutions of the derived initial value problem are given and simulated and display a slow anomalous diffusion in the fractional case.     

Reconstruction of kernel depending also on space variable

The paper deals with the reconstruction of the convolution kernel, together with the solution, in a mixed linear evolution system of hyperbolic type. This problem describes uniaxial deformations u of a cylindrical domain (0,π) × Ω, which is filled with a linear viscoelastic solid whose material properties are supposed to be uniform on Ω‐sections perpendicular to the x axis. Various types of boundary conditions in [0,T] × {0,π} × Ω are prescribed, whereas Dirichlet conditions are assumed in [0,T] × (0,π) × ∂Ω. To reconstruct both u and k, we suppose of knowing for any time tand any x ∈ (0,π) the flux of the viscoelastic stress vector through the boundary of the Ω‐section. The main novelty is that the unknown kernel k is allowed to depend, not only on the time variable t but also on the space variable x.     

A Fokas approach to the coupled modified nonlinear Schrödinger equation on the half‐line

In this work, we discuss the coupled modified nonlinear Schrödinger (CMNLS) equation, which describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. By use of the Fokas approach, the initial‐boundary value problem for the CMNLS equation related to a 3×3 matrix Lax pair on the half‐line is to be analyzed. Assuming that the solution {u(x,t),v(x,t)} of CMNLS equation exists, we will prove that it can be expressed in terms of the unique solution of a 3×3 matrix Riemann‐Hilbert problem formulated in the plane of the complex spectral parameter λ. Moreover, we also get that some spectral functions s(λ) and S(λ) are not independent of each other but meet a global relationship.