On the structure of some non-periodic groups whose subgroups of infinite special rank are transitively normal

A group G has a finite special rank r, if every finitely generated subgroup of G can be generated by at most r elements, and there exists a finitely generated subgroup H which has exactly r generators. This paper is devoted to genera lized radical non-Abelian groups of infinite special rank whose subgroups of infinite special rank are transitively normal.

Machine learning prediction of the electronic property of binary transition metal alloys

Machine learning methods have garnered much attention and use in computational catalysis. Previous studies have demonstrated rapid and accurate prediction of a variety of catalytic properties as well as the underlying potential energy landscapes. In particular, d-band center, defined as the first moment of the d-projected density of states, has been widely used as the key descriptor of activity trends for reactions catalyzed by metal surfaces. In this work, we construct a gradient boosting regression (GBR) model for prediction of the d-band center of bulk binary transition metal alloys. An accurate model is obtained using a dataset of over 1200 alloys from the Materials Project database spanning the entire d-block of the periodic table. The d-band centers, periodic groups, and relative compositions of the constituent metals are determined to have the highest feature importance scores, consistent with the underlying physics of the alloy. The regression model presented here offer a promising strategy of rapid property prediction with physical interpretability to aid the optimization and discovery of efficient heterogeneous catalysts.

On the structure of some non-periodic groups whose subgroups of infinite special rank are transitively normal

A group $G$ has a finite special rank $r$ if every finitely generated subgroup of $G$ is generated by at most $r$ elements and there is a finitely generated subgroup of $G$ which has exactly $r$ generators. If there is not such $r$, then we say that $G$ has infinite special rank. In this paper, we study generalized radical non-abelian groups of infinite special rank whose subgroups of infinite special rank are transitively normal.

On infinite groups in which all abelian subgroups are locally cyclic

The structure of locally soluble periodic groups in which every abelian subgroup is locally cyclic was described over 20 years ago. We complete the aforementioned characterization by dealing with the non-periodic case. We also describe the structure of locally finite groups in which all abelian subgroups are locally cyclic.

Spatial Form of a Hamiltonian Dysthe Equation for Deep-Water Gravity Waves

An overview of a Hamiltonian framework for the description of nonlinear modulation of surface water waves is presented. The main result is the derivation of a Hamiltonian version of Dysthe’s equation for two-dimensional gravity waves on deep water. The reduced problem is obtained via a Birkhoff normal form transformation which not only helps eliminate all non-resonant cubic terms but also yields a non-perturbative procedure for surface reconstruction. The free surface is reconstructed from the wave envelope by solving an inviscid Burgers’ equation with an initial condition given by the modulational Ansatz. Particular attention is paid to the spatial form of this model, which is simulated numerically and tested against laboratory experiments on periodic groups and short-wave packets. Satisfactory agreement is found in all these cases.

Electron Transfer through a Natural Oxide Layer on Real Metal Surfaces Occurring during Sliding with Polytetrafluoroethylene: Dependence on Heat of Formation of Metal Oxides

Electron emission (EE) from real metal surfaces occurring during sliding contact with a polytetrafluoroethylene (PTFE) rider has been investigated using the thermodynamic data of metal oxides and the X-ray photoelectron spectroscopy (XPS) intensity ratio of oxygen/metal on the surfaces. EE was termed triboelectron emission (TriboEE). Rolled metal sheets of 18 types were used. The metal‒oxygen bond energy calculated from the heat of the formation of metal oxide, (D(M–O)), was shown to be a key factor in dividing the EE into two routes, the so-called Schottky effect and the tunnel effect, due to the surface oxide layer. The metals in periodic groups 4 (Ti and Zr), 5 (V, Nb, and Ta), and 6 (Mo and W) maintained higher values of D(M–O), while, moving down the groups, the TriboEE intensity increased, being ascribed to the former route. In groups 10 (Ni, Pd, and Pt) and 11 (Cu, Ag, and Au), the D(M–O) values decreased moving down the groups, but the TriboEE intensity increased significantly, which can be attributed to the latter route. Furthermore, with the increase in the electrical conductivity of metals, the TriboEE intensity became remarkably high, while the D(M–O) value fell rapidly and became almost constant. The XPS results showed that the dependence of the D(M–O) and XPS metal core intensity on the O1s intensity and the XPS intensity ratio of the O1s/metal core was different between groups 10 and 11 and groups 4, 5, and 6. It was concluded that, under the electric field caused on the real metal surface by the friction with PTFE, the electron from metals with small D(M–O) values predominantly tunnels the surface oxide layer as a surface barrier, while with large D(M–O) values, the electron passes over the top of the barrier.

On non-periodic groups with non-Dedekind norm of Abelian noncyclic subgroups

Non-periodic groups without free Abelian subgroups of rank 2 with non-Dedekind norm of Abelian noncyclic subgroups are studied.