Parity- and time-reversal-symmetry violating interaction constants required for the interpretation of a recent measurement (arXiv:1704.07928 [physics.atom-ph]) of corresponding symmetry violations in the $Ω=1$ (${^3Δ}_1$) science state of the HfF$^+$ molecular ion are reported. Using a relativistic four-component all-electron multi-reference configuration interaction model the nucleon-electron scalar-pseudoscalar interaction constant is determined as $W_S = 20.0$ [kHz]. An updated result for the electron electric-dipole-moment effective electric field of $|E_{\text{eff}}| = 22.7 \left[\frac{\rm GV}{\rm cm}\right]$ is obtained. Further results of relevance in the context of the search for leptonic charge-parity violation such as magnetic hyperfine interaction constants and electronic $G$-tensor for HfF$^+$ are presented.

The low energy scattering of heavy positively charged particles on hydrogen atoms (H) are investigated by solving the Faddeev equations in configuration space. A resonant value of the pH scattering length, $a=750\pm 5$ a.u., in the pp antisymmetric state was found. This large value indicates the existence of a first excited state with a binding energy B=1.14$\times10^{-9}$ a.u. below the H ground state. Several resonances for non zero angular momenta states are predicted.

Curious spectral properties of an ensemble of random unitary matrices appearing in the quantization of a map p -> p+alpha, q -> q+f(p+alpha) in [Giraud et al. nlin.CD/0403033] are investigated. When alpha=m/n with integer co-prime m,n and matrix dimension N -> infinity is such that mN = 1 or -1 mod n, local spectral statistics of this ensemble tends to the semi-Poisson distribution [Bogomolny et al. Eur. Phys. J. B 19, 121 (2001)] with arbitrary integer or half-integer level repulsion at small distances: R(s)-> s^{beta} when s -> 0 and beta=n-1 or n/2-1 depending on time-reversal symmetry of the map.

Acidic pH of the skin surface has been recognized as a regulating factor for the maintenance of the stratum corneum homeostasis and barrier permeability. The most important functions of acidic pH seem to be related to the keratinocyte differentiation process, the formation and function of epidermal lipids and the corneocyte lipid envelope, the maintenance of the skin microbiome and, consequently, skin disturbances and diseases. As acknowledged extrinsic factors that affect skin pH, topically applied products could contribute to skin health maintenance via skin pH value control. The obtained knowledge on skins’ pH could be used in the formulation of more effective topical products, which would add to the development of the so-called products ‘for skin health maintenance’. There is a high level of agreement that topical products should be acidified and possess pH in the range of 4 to 6. However, formulators, dermatologists and consumers would benefit from some more precise guidance concerning favorable products pH values and the selection of cosmetic ingredients which could be responsible for acidification, together with a more extensive understanding of the mechanisms underlaying the process of skin acidification by topical products.

In this comment on"Origin of correlated isolated flat bands in copper-substituted lead phosphate apatite"(arXiv:2307.16892 [cond-mat.supr-con]), we discuss the flat half-occupied two-band manifold that appears in $\mathrm{Pb}_9\mathrm{Cu}(\mathrm{PO}_4)_6(\mathrm{OH})_2$ when using a semilocal DFT functional. We argue that the flat band is an artifact of the functional's overestimation of the energy of the oxygen p states in the valence band. When using the HSE hybrid functional, the energy of the oxygen p states is reduced, and the copper-derived manifold splits into one fully occupied and one empty band. While these results do not rule out the possibility of superconductivity in doped LK-99, they do predict that stoichiometric $\mathrm{Pb}_9\mathrm{Cu}(\mathrm{PO}_4)_6(\mathrm{OH})_2$ is an insulator, not a superconductor. Furthermore, we have shown that future first-principles studies of these materials should employ hybrid functionals or other advanced methods to ensure that the oxygen-derived valence-band energies are correctly described.

This paper is withdrawn by the author. It is superseded by Makhlin's paper quant-ph/0002045.

This paper has been withdrawn by the authors

This chapter provides a concise survey on different dissipativity conditions that have appeared in the literature on economic model predictive control and discusses their decisive role in this context.

Newton's second law may be used to obtain a wave equation, which reduces to Schrodinger's equation in the nonrelativistic limit and for a conservative force.