Kernel of locally nilpotent

In this paper we study the kernel of a non-zero locally nilpotent -derivation of the polynomial ring over a noetherian integral domain containing a field of characteristic zero. We show that if is normal then the kernel has a graded -algebra structure isomorphic to the symbolic Rees algebra of an unmixed ideal of height one in , and, conversely, the symbolic Rees algebra of any unmixed height one ideal in can be embedded in as the kernel of a locally nilpotent -derivation of . We also give a necessary and sufficient criterion for the kernel to be a polynomial ring in general.

     

A note on residual variables of an affine fibration

In a recent paper [7], M.E. Kahoui has shown that if R   is a polynomial ring over C$\mathbb{C}$, A   an A³${\mathbb{A}}^3$-fibration over R, and W a residual variable of A then A   is stably polynomial over R[W]$R[W]$. In this article we show that the above result holds over any Noetherian domain R   provided the module of differentials _ΩR(A)${\Omega }_R(A)$ of the affine fibration A (which is necessarily a projective A-module by a theorem of Asanuma) is a stably free A-module.     

Phase diagram of carbon dioxide: update and challenges

We present the phase diagram of carbon dioxide with the most recent finding of coesite-like carbon dioxide, a missing analog to SiO₂, address several controversies on phase VII and phase IV in terms of the phase metastabilities and thermal path-dependent phase transitions, and discuss the implications to the generalized phase diagram of simple molecular solids.     

Theoretical spectroscopic studies of InI and InI+

Relativistic configuration interaction calculations are carried out to study the electronic structure and spectroscopic properties of InI and InI⁺. Potential energy curves of the ground and a number of low‐lying states are constructed. Spectroscopic parameters of the bound states of both species are computed and compared with the experimental and other theoretical data. Effects of spin‐orbit coupling on the spectroscopic properties are studied. Because of the presence of the heavy atoms the effect is large. The spin‐orbit splitting of the ground state (X²Π) of InI⁺ is more than 8350 cm^?1. As a result of the strong spin‐orbit interaction between X²Π and A²Σ⁺ of InI⁺, the potential energy curve of A²Σ becomes repulsive. Radiative lifetimes for the spin‐forbidden transitions such as A³Π?X¹Σ and B³Π₁ ?X¹Σ of InI and spin‐allowed transitions such as B²Σ⁺?A²Σ⁺, C²Π?A²Σ⁺, and B²Σ⁺?X²Π are calculated. Vertical and adiabatic ionization energies of InI and the electric dipole moments of both the neutral and ionic species are estimated. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Computational and experimental investigations on the effect of crystallinity and crystal size on Na-transport in nanoscaled Si: implications for Si-based anodes for Na-ion batteries

Journal of Solid State Electrochemistry - While Li transport in Si is well understood, little is known about Na transport, despite Si being considered a potential anode material for the upcoming...     

Electronic states and spectroscopic properties of SiTe and SiTe+

Ab initio based configuration interaction calculations have been carried out to study the low-lying electronic states and spectroscopic properties of the heaviest nonradioactive silicon chalcogenide molecule and its monopositive ion. Spectroscopic constants and potential energy curves of states of both SiTe and SiTe+ within 5 eV are reported. The calculated dissociation energies of SiTe and SiTe+ are 4.41 and 3.52 eV, respectively. Effects of the spin-orbit coupling on the electronic spectrum of both the species are studied in detail. The spin-orbit splitting between the two components of the ground state of SiTe+ is estimated to be 1880 cm(-1). Transitions such as 0+ (II)-X1Sigma(+)0+, 0+ (III)-X1Sigma(+)0+, E1Sigma(+)0+ -X1Sigma(+)0+, and A1Pi1-X1Sigma(+)0+ are predicted to be strong in SiTe. The radiative lifetime of the A1Pi state is less than a microsecond. The X(2)2Pi(1/2)-X(1)2Pi(3/2) transition in SiTe+ is allowed due to spin-orbit mixing. However, it is weak in intensity with a partial lifetime for the X2 state of about 108 ms. The electric dipole moments of both SiTe and SiTe+ in their low-lying states are calculated. The vertical ionization energies for the ionization of the ground-state SiTe to different ionic states are also reported.     

Singularly Perturbed Population Models with Reducible Migration Matrix: 2. Asymptotic Analysis and Numerical Simulations

The paper is concerned with asymptotic analysis of a singularly perturbed system of McKendrick equations of population with age and geographical structure. It is assumed that the migration between geographical patches occurs on a much faster time scale than the demographic processes and is described by a reducible Kolmogorov matrix. We apply a novel regularizing technique which makes the error estimates easier than that in previous papers and provide a numerical illustration of theoretical results.