Riesz-Jacobi transforms as principal value integrals

We establish an integral representation for the Riesz transforms naturally associated with classical Jacobi expansions. We prove that the Riesz-Jacobi transforms of odd orders express as principal value integrals against kernels having non-integrable singularities on the diagonal. On the other hand, we show that the Riesz-Jacobi transforms of even orders are not singular operators. In fact they are given as usual integrals against integrable kernels plus or minus, depending on the order, the identity operator. Our analysis indicates that similar results, existing in the literature and corresponding to several other settings related to classical discrete and continuous orthogonal expansions, should be reinvestigated so as to be refined and in some cases also corrected.Comment: 30 page

Topological enslavement in evolutionary games on correlated multiplex networks

Governments and enterprises strongly rely on incentives to generate favorable outcomes from social and strategic interactions between individuals. The incentives are usually modeled by payoffs in evolutionary games, such as the prisoner's dilemma or the harmony game, with imitation dynamics. Adjusting the incentives by changing the payoff parameters can favor cooperation, as found in the harmony game, over defection, which prevails in the prisoner's dilemma. Here, we show that this is not always the case if individuals engage in strategic interactions in multiple domains. In particular, we investigate evolutionary games on multiplex networks where individuals obtain an aggregate payoff. We explicitly control the strength of degree correlations between nodes in the different layers of the multiplex. We find that if the multiplex is composed of many layers and degree correlations are strong, the topology of the system enslaves the dynamics and the final outcome, cooperation or defection, becomes independent of the payoff parameters. The fate of the system is then determined by the initial conditions

Radiative decays of the (0+,1+)(0^+,1^+) strange-bottom mesons

In this article, we assume that the $(0^+,1^+)$ strange-bottom mesons are the conventional $b\bar{s}$ mesons, and calculate the electromagnetic coupling constants $d$, $g_1$, $g_2$ and $g_3$ using the light-cone QCD sum rules. Then we study the radiative decays $B_{s0}\to B_s^* \gamma$, $B_{s1}\to B_s \gamma$, $B_{s1}\to B_s^* \gamma$ and $B_{s1}\to B_{s0} \gamma$, and observe that the widths are rather narrow. We can search for the $(0^+,1^+)$ strange-bottom mesons in the invariant $B_s \pi^0$ and $B^*_s \pi^0$ mass distributions in the strong decays or in the invariant $B_s^*\gamma$ and $B_s\gamma$ mass distributions in the radiative decays.Comment: 16 pages, 4 figures, revised versio

Signal from noise retrieval from one and two-point Green's function - comparison

We compare two methods of eigen-inference from large sets of data, based on the analysis of one-point and two-point Green's functions, respectively. Our analysis points at the superiority of eigen-inference based on one-point Green's function. First, the applied by us method based on Pad?e approximants is orders of magnitude faster comparing to the eigen-inference based on uctuations (two-point Green's functions). Second, we have identified the source of potential instability of the two-point Green's function method, as arising from the spurious zero and negative modes of the estimator for a variance operator of the certain multidimensional Gaussian distribution, inherent for the two-point Green's function eigen-inference method. Third, we have presented the cases of eigen-inference based on negative spectral moments, for strictly positive spectra. Finally, we have compared the cases of eigen-inference of real-valued and complex-valued correlated Wishart distributions, reinforcing our conclusions on an advantage of the one-point Green's function method.Comment: 14 pages, 8 figures, 3 table