An ideal point method adopting grey relational entropy to estimate life cycle cost with effectiveness of torpedo

To making the decision of the developing blue prints,ideal point method was selected to estimate the life cycle cost with effectiveness of torpedo.At the same time,the concept of grey relational entropy of the grey system theory was adopted to compute the distance between each blue print and the ideal point(or negative ideal point).The blue print,nearest to the ideal point and farthest to the negative ideal point,is the best one.As an example,four blue prints of torpedo were estimated.The result indicates the practical value of this method.

Determination of the Range of Magnetic Interactions from the Relations between Magnon Eigenvalues at High-Symmetry k Points

Magnetic exchange interactions(MEIs) define networks of coupled magnetic moments and lead to a surprisingly rich variety of their magnetic properties. Typically MEIs can be estimated by fitting experimental results.Unfortunately, how many MEIs need to be included in the fitting process for a material is unclear a priori,which limits the results obtained by these conventional methods. Based on linear spin-wave theory but without performing matrix diagonalization, we show that for a general quadratic spin Hamiltonian, there is a simple relation between the Fourier transform of MEIs and the sum of square of magnon energies(SSME). We further show that according to the real-space distance range within which MEIs are considered relevant, one can obtain the corresponding relationships between SSME in momentum space. By directly utilizing these characteristics and the experimental magnon energies at only a few high-symmetry k points in the Brillouin zone, one can obtain strong constraints about the range of exchange path beyond which MEIs can be safely neglected. Our methodology is also generally applicable for other Hamiltonian with quadratic Fermi or Boson operators.

ETA INVARIANTS, DIFFERENTIAL CHARACTERS AND FLAT VECTOR BUNDLES

The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundles by proper submersions is proved,with Chern classes with coefficients in C/Q. These results are much related to prior work of Gillet-Soule, Bismut-Lott and Lott.

Existence of Solutions of Generalized Quasi-Variational Relation Problems by the Inductive Relations and Some Applications

By the inductive relations,this paper first obtains some existence theorems of solutions for generalized quasi-variational relation problems,which are different from other papers.As applications,some existence theorems of solutions for generalized quasi-equilibrium problems and NS-equilibria for noncooperative games under uncertainty are obtained.