Non-Hermitian skin effects and exceptional points are topological phenomena characterized by integer winding numbers. In this study, we give methods to theoretically detect generalizing inversion symmetry. The generalization of symmetry is unique non-Hermitian systems. We show that parities the numbers can be determined from energy eigenvalues on inversion-invariant momenta when generalized pre...

A topology on a lattice L or more generally on a partially ordered set P is called an intrinsic topology if it is de ned directly from the order Early ex amples of such topologies were the interval topology of O Frink Fr and the order topology introduced by G Birkho Bi The early intrinsic topolo gies were typically symmetric i e the topology de ned on L agreed with the topology de ned on L the ...

This paper addresses two closely related aspects of subjective information. First, no two agents necessarily see the same thing when they observe the same object. Second, no two agents have the same concepts in mind when they use the same term in a shared language. I present a framework to give rigorous meaning to these ideas, in particular by modeling them in appropriate topologies. From there...

We revise and extend the foundation of computable topology in the framework of Type-2 theory of effectivity, TTE, where continuity and computability on finite and infinite sequences of symbols are defined canonically and transferred to abstract sets by means of notations and representations. We start from a computable topological space, which is a T0-space with a notation of a base such that in...

In order to obtain better coverage of the population of interest and cost less, a number of surveys employ dual frame structure, in which independent samples are taken from two overlapping sampling frames. This research considers chi-squared tests in dual frame surveys when categorical data is encountered. We extend generalized Wald’s (1943) test, Rao-Scott first-order and second-order correcte...

Working constructively, we study continuous directed complete posets (dcpos) and the Scott topology. Our two primary novelties are a notion of intrinsic apartness sharp elements. Being apart is positive formulation being unequal, similar to how inhabitedness nonemptiness. To exemplify sharpness, note that lower real if only it located. first main result for large class dcpos, Bridges-Vita topol...

Many existing token-based, distributed mutual exclusion algorithms can be generalized by a single algorithm. The number of messages required to provide mutual exclusion is dependent upon the logical topology imposed on the nodes and the policy used to forward requests. This paper extends the generalized algorithm to support prioritized requests and presents models that can be used to analyze th...

Multilevel inverters have been developed due to limitations of the conventional two-level voltage source inverters (VSIs). Most of the topologies of multilevel inverters that have been presented in the literature are based on the sharing of the rated voltage between the switches so that the switches with lower voltage ratings can be used. In these topologies, the current rating of all of the sw...

In this paper, we extend the method of Scott and Barreto and present an explicit and simple algorithm to generate families of generalized MNT elliptic curves. Our algorithm allows us to obtain all families of generalized MNT curves with any given cofactor. Then, we analyze the complex multiplication equations of these families of curves and transform them into generalized Pell equation. As an e...