We point out that in non-Hermitian systems, Jordan decomposition should replace eigendecomposition so all ``good approximate eigenstates'' of the system are identified. These states can be resonantly excited. As a concrete example, we study location and field distribution zero-energy corner quadrupole insulator (QI) split parameter space into three distinct regimes according to properties state...

A nonzero element x of a Lie algebra L over a field F is called extremal if [x, [x,L]] ⊆ Fx. Extremal elements are a well-studied class of elements in simple finite-dimensional Lie algebras of Chevalley type: they are the long root elements. In [CSUW01], Cohen, Steinbach, Ushirobira and Wales have studied Lie algebras generated by extremal elements, in particular those of Chevalley type. The au...

A new approach to formal solutions of (first order systems of) linear differential equations stressing as much as possible the similarity with systems of linear equations. This approach leads to a fine structure of formal solutions, comparable to [1] but from a different point of view. A quick introduction to characteristic classes (cf. [3]) will be given. 1 Linear algebra; recalling Jordan dec...

It is shown that there is an order isomorphism φ from the poset V of B ×B-orbits on the wonderful compactification of a semi-simple adjoint group G with Weyl group W to an interval in reverse Chevalley-Bruhat order on a non-canonically associated Coxeter group Ŵ (in general neither finite nor affine). Moreover, φ preserves the corresponding Kazhdan-Lusztig polynomials. Springer’s (partly conjec...

A nonzero element x of a Lie algebra L over a field F is called extremal if [x, [x,L]] ⊆ Fx. Extremal elements are a well-studied class of elements in simple finite-dimensional Lie algebras of Chevalley type: they are the long root elements. In [CSUW01], Cohen, Steinbach, Ushirobira and Wales have studied Lie algebras generated by extremal elements, in particular those of Chevalley type. The au...

This study aims to answer the question: What is nature of relationship between fiscal and monetary policy in Jordan? Are two policies complementary each other, alternatives, or go opposite directions?. applies vector autoregression VAR, Impulse Response Function test, Granger Causality the. Variance Decomposition Analysis. The results showed that there a bidirectional causal government expendit...

We characterize the space of restrictions real rational functions to certain algebraic Jordan curves in plane via Dirichlet-to-Neumann map associated domain complex bounded by curve and its Bergman kernel. The characterization leads a partial fractions-like decomposition for such new ways describe curves. multiply connected case is also explored.

We present explicit upper bounds for the number and size of conjugacy classes in finite Chevalley groups and their variations. These results have been used by many authors to study zeta functions associated to representations of finite simple groups, random walks on Chevalley groups, the final solution to the Ore conjecture about commutators in finite simple groups and other similar problems. I...