To discuss the possibility that the superconductivities in NaxCoO2·yH2O are induced by electron correlation, we investigate the possible pairing symmetry based on the single-band Hubbard model whose dispersion of the bare energy band is obtained using the band structure calculation of NaxCoO2·yH2O. The superconducting transition temperature is estimated by solving the Éliashberg equation. In th...

This paper introduces GSSS (Genetic State-Space Search). The integration of two general search paradigms — genetic search and state-space-search provides a general framework which can be applied to a large variety of search problems. Here, we show how GSSS solves constrained optimization problems (COPs). Basically, it searches for "promising search states" from which good solutions can be easil...

The expectation values of a Hermitian operator  in (2s + 1)2 specific coherent states of a spin are known to determine the operator unambiguously. As shown here, (almost) any other set of (2s + 1)2 coherent state projectors also provide a basis for self-adjoint operators. This is proved by considering the determinant of the Gram matrix associated with the coherent state projectors as a Hamilto...

We present a complete axiomatisation of the operator of projection onto state in the Duration Calculus (DC ) relative to validity in DC without extending constructs. Projection onto state was introduced and studied extensively in our earlier works. We first establish the completeness of a system of axioms and proof rules for the operator relative to validity in the extension of DC by neighbourh...

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

For a time-independent Schrödinger equation with Hamiltonian operator H = −∆ + V on L(R ) we call Gz = RzV , the Green function operator, where Rz is the resolvent of −∆. We consider an iteration scheme that is based on the operator Gz. Under standard conditions on the potential V , which include the Coulomb interaction, we prove the convergence of the iteration to the ground state energy and e...

This paper seeks to construct a representation of the algebra of angular momentum (SU(2) algebra) in terms of the operator relations corresponding to Gentile statistics in which one quantum state can be occupied by n particles. First, we present an operator realization of Gentile statistics. Then, we propose a representation of angular momenta. The result shows that there exist certain underlyi...

The consensus operator is used for cumulative belief fusion in subjective logic, and takes beliefs on binary frames of discernment as input. Coarsening to a binary state space is therefore needed in case the original frame is larger than binary. Coarsening causes information loss in general, and can lead to inconsistent results when applying the consensus operator. We presents a method for norm...

We derive a mathematical mechanism of infrared catastrophe from the idea for the proof in [22, 23] and generalize it so that we can apply it to several models in quantum field theory. We define the Carleman operator from the operator-theoretical pull-through formula on ground states. Characterizing infrared catastrophe by the Carleman operator, we study the mechanism of infrared catastrophe. An...