The connection between the exact quasirelativistic approach developed in the title reference [W. Kutzelnigg and W. Liu, J. Chem. Phys. 123, 241102 (2005)] and the method of elimination of the small component in matrix form developed previously by Dyall is explicitly worked out. An equation that links Hermitian and non-Hermitian formulations of the exact quasirelativistic theory is derived. Besi...

Rognes andWeibel used Voevodsky’s work on the Milnor conjecture to deduce the strong Dwyer-Friedlander form of the Lichtenbaum-Quillen conjecture at the prime 2. In consequence (the 2-completion of) the classifying space for algebraic K-theory of the integers Z[1/2] can be expressed as a fiber product of wellunderstood spaces BO and BGL(F3) over BU . Similar results are now obtained for Hermiti...

Difference equations of the form X ( t ) = F * ( t ) X ( t 1 ) F ( t ) F * ( t ) X ( t 1)G(t)[ l + G * ( t ) X ( t 1)G(t)]t G * ( t ) X ( t 1)F(t)+ Q(t ) and their associated Hermitian matrices H ( t ) = (0 v F* _C,C.)(t) are studied. Solution of different Riccati equations can be compared if the difference of their corresponding Hermitian matrices is semidefinite for all t. An application to t...

The Ising limit of a conventional Hermitian parity-symmetric scalar quantum field theory is a correlated limit in which two bare Lagrangian parameters, the coupling constant g and the negative mass squared −m2, both approach infinity with the ratio −m2/g = α > 0 held fixed. In this limit the renormalized mass of the asymptotic theory is finite. Moreover, the limiting theory exhibits universal p...

We propose a Preconditioned Locally Harmonic Residual (PLHR) method for computing several interior eigenpairs of a generalized Hermitian eigenvalue problem, without traditional spectral transformations, matrix factorizations, or inversions. PLHR is based on a short-term recurrence, easily extended to a block form, computing eigenpairs simultaneously. PLHR can take advantage of Hermitian positiv...

Non-Hermitian skin effect exhibits the collapse of extended bulk modes into extensive number localized boundary states in open conditions. Here we demonstrate disorder-driven phase transition trivial non-Hermitian system to higher-order phase. In contrast clean systems, disorder-induced form an arc complex energy plane, which is manifestation dynamical transition. At transition, corner and char...

In this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring R such that, every regular matrix admits a diagonal power-reduction.

This paper gives double angle theorems that bound the change in an invariant subspace of an indefinite Hermitian matrix in the graded form H = D∗AD subject to a perturbation H → H̃ = D∗(A+ A)D. These theorems extend recent results on a definite Hermitian matrix in the graded form (Linear Algebra Appl. 311 (2000) 45) but the bounds here are more complicated in that they depend on not only relativ...