8 research outputs found
Symmetric Tensor Decomposition Description of Fermionic Many-Body Wavefunctions
The configuration interaction (CI) is a versatile wavefunction theory for
interacting fermions but it involves an extremely long CI series. Using a
symmetric tensor decomposition (STD) method, we convert the CI series into a
compact and numerically tractable form. The converted series encompasses the
Hartree-Fock state in the first term and rapidly converges to the full-CI
state, as numerically tested using small molecules. Provided that the length of
the STD-CI series grows only moderately with the increasing complexity of the
system, the new method will serve as one of the alternative variational methods
to achieve full-CI with enhanced practicability.Comment: 10 pages, 6 figure
Mass-independent area (or entropy) and thermodynamic volume products in conformal gravity
Varenius e o conhecimento matemático do século XVII Varenius and the mathematical knowledge in the seventeenth century
Neste artigo, discutimos o contexto do desenvolvimento da Geografia que, no século XVII, liberou-se do seu papel nas diferentes fés cristãs, bem como a importância da cisão dos Protestantes, em Luteranos e Calvinistas, para o processo de secularização, e o conseguinte estabelecimento da Geografia como ciência moderna. Analisamos a contribuição fundamental do luterano Bernhard Varen, cuja obra Geografia Geral apresenta o paradigma dessa nova ciência. Naquela época, a Geografia era considerada um ramo da matemática, e esta obra nos dá indÃcios sobre notações e conceitos matemáticos utilizados naquele século. Analisamos, particularmente, o uso da notação decimal de números não inteiros e algumas aplicações de conceitos trigonométricos, comparando a edição original com as principais reedições desta obra.<br>In this paper, we discuss the context for the development of geography from the seventeenth century when it became liberated from its function in the service of the different Christian faiths; we discuss the importance of the division of the Protestant confession into the Lutheran and the Reformed one for the process of secularization and for the establishment of geography as a modern science. We analyse the fundamental contribution by the Lutheran Bernhard Varen whose volume General Geography constitutes the paradigm for this new science. At that time, Geography was considered to be a branch of mathematics, and this book offers us insights into both, mathematical notations and mathematical procedures. We analyse, in particular, the use of the decimal number notation for nonintegral numbers and also some applications of trigonometry, comparing the original edition with the major re-editions of this seminal work