Infrared Spectrum for the New Exobiological Nanomolecules Asi, Csi, Tsi and Gsi

The core of the work is based on the replacement of carbon atoms by silicon atoms, on the basis of four standard bases of DNA: A, C, G and T (adenine, cytosine, guanine, thymine). Determining with minimum computational methods via ab initio Hartree-Fock methods, infrared spectrum and their peak absorbance frequencies. The option for simple replacement of carbon by silicon is due to the peculiar characteristics between both. Atomic interactions under non-carbon conditions were studied, with only the Hydrogen, Silicon, Nitrogen and Oxygen atoms, in CNTP, for the four standard bases of DNA, A, C, G and T, thus obtaining by quantum chemistry four new compounds, named here as: ASi, CSi, GSi and TSi. Computational calculations admit the possibility of the formation of such molecules, their existence being possible via quantum chemistry. Calculations obtained in the ab initio Unrestricted and Restrict Hartree-Fock method, (UHF and RHF) in the set of basis used Effective core potential (ECP) minimal basis, UHF CEP-31G (ECP split valance) and UHF CEP-121G (ECP triple-split basis), CC-pVTZ (Correlation-consistent valence-only basis sets triple-zeta) and 6-311G**(3df, 3pd) (Gaussian functions quadruple-zeta basis sets).

Subalgebra analogue of Standard bases for ideals in $ K[[t_{1}, t_{2}, \ldots, t_{m}]][x_{1}, x_{2}, \ldots, x_{n}] $

<abstract><p>In this paper, we develop a theory for Standard bases of $ K $-subalgebras in $ K[[t_{1}, t_{2}, \ldots, t_{m}]] [x_{1}, x_{2}, ..., x_{n}] $ over a field $ K $ with respect to a monomial ordering which is local on $ t $ variables and we call them Subalgebra Standard bases. We give an algorithm to compute subalgebra homogeneous normal form and an algorithm to compute weak subalgebra normal form which we use to develop an algorithm to construct Subalgebra Standard bases. Throughout this paper, we assume that subalgebras are finitely generated.</p></abstract>

Convolutions on the complex torus

“Quasi-elliptic” functions can be given a ring structure in two different ways, using either ordinary multiplication, or convolution. The map between the corresponding standard bases is calculated. A related structure has appeared recently in the computation of Feynman integrals. The two approaches are related by a sequence of polynomials closely tied to the Eulerian polynomials.