The paper discusses the basic design of the critical facility, whose main purpose is the physics validation of AHWR. Apart from moderator level control, the facility will have shutdown systems based on shutoff rods and multiple ranges of neutron detection systems. In addition, it will have a flux mapping system based on 25 fission chambers, distributed in the core. We are planning to use this reactor for experiments with a suitable source to simulate an ADS system. Any desired sub-criticality can be achieved by adjusting the moderator level. Apart from perfecting our experimental techniques, in simple configurations, we intend to study the one-way coupled core in this facility. Preliminary calculations, employing a Monte Carlo code TRIPOLI, are presented.

In this paper, variable coefficient Benny equation (also called the KdV Burgers–Kuramoto equation) has been considered. By using the Painlevé analysis and Lie group analysis methods, the Painlevé properties and symmetries have been studied. Some solutions of the reduced ODEs are obtained.

The inclusive decays of 𝐵-mesons to charmonium have been studied in a data sample of 386 million $B\bar{B}$ events. The data sample has been collected by the Belle detector at the KEKB asymmetric energy 𝑒⁺𝑒⁻ collider operating at the $\Upsilon (4S)$ resonance. The branching fractions have been measured for the inclusive decays to $J/\psi + X$ and $\chi_{c1} +X$. The measured branching fraction for $J/\psi + X$ is $\mathcal{B}(B \rightarrow J/\psi (\rightarrow e^{+}e^{−}) + X) = (1.10 \pm 0.005 \pm 0.057)\%$ and $\mathcal{B}(B \rightarrow J/\psi (\rightarrow \mu^{+}\mu^{−})+X) = (1.08 \pm 0.004 \pm 0.056)\%$, while the inclusive $\chi_{c1} +X$ branching fraction is found to be $\mathcal{B}(B \rightarrow \chi_{c1} + X) = (0.44 \pm 0.01 \pm 0.06)\%$. The feed-down contribution from higher charmonium states is subtracted from the measured branching fractions and the direct branching fractions are obtained to be $\mathcal{B}(B \rightarrow J/\psi +X) = (0.77\pm 0.04 \pm 0.06)\%$ and $\mathcal{B}(B \rightarrow \chi_{c1} +X) =(0.41 \pm 0.01 \pm 0.06)\%$.