The energy conservation of lossless network reflects a series of novel symmetry in S parameter. This paper presents the generalized modulus symmetry, spurious reciprocity, constant characteristic phase and determinant of the lossless block network. The perfect matching condition of block load network [Γl] and the invariable lossless property of S parameter of generalized block network are devel...

If in the classical S-category P, 1) continuous mappings are replaced by compact-open strong shape (= coss) morphisms (cf. §1 or [1], §2), and 2) ∧-products are properly reinterpreted, then an S-duality theorem for arbitrary subsets X ⊂ S (rather than for compact polyhedra) holds (Theorem 2.1). 0. Introduction. In a previous paper [1] we introduced the concept of coss-shape (compact-open strong...

In his middle-period dialogues, Plato worked out at least the rough outlines of a distinctive theory of knowledge. According to the chronology that seems most plausible, he first sketched the outlines of this theory in Meno; then he revised and developed the theory further in Phaedo and the Republic; and finally, in Theaetetus, he probed the theory in depth, by subjecting it to a series of sear...

Structured arguments are commonly used to communicate to stakeholders that safety, security or other attributes of a system are achieved. Due to the growing complexity of systems, more uncertainties appear and the confidence in arguments tends to be less justifiable by reviewing. In this paper, we propose a quantitative method to assess the confidence in structured arguments, like safety cases....

The lifetime of Charles Sanders Peirce spanned a period of tremendous change and development in human knowledge, in the sciences in general. He was a young man of twenty in the year that Origin of Species was published; he approached the end of his life just before Albert Einstein presented us with General Relativity. His lifetime saw the emergence of psychology as a discipline separate from ph...

The ABC conjecture is a central open problem in modern number theory, connecting results, techniques and questions ranging from elementary number theory and algebra to the arithmetic of elliptic curves to algebraic geometry and even to entire functions of a complex variable. The conjecture asserts that, in a precise sense that we specify later, if A,B,C are relatively prime integers such that A...

Here we survey questions and results on the Hodge theory of hyperkähler quotients, motivated by certain S-duality considerations in string theory. The problems include L2 harmonic forms, Betti numbers and mixed Hodge structures on the moduli spaces of Yang-Mills instantons on ALE gravitational instantons, magnetic monopoles on R3 and Higgs bundles on a Riemann surface. Several of these spaces a...

Intense-field many-body S-matrix theory (IMST) provides a systematic ab initio approach to investigate the dynamics of atoms and molecules interacting with intense laser radiation. We review the derivation of IMST as well as its diagrammatic representation and point out its advantage over the conventional ‘prior’ and ‘post’ expansions which are shown to be special cases of IMST. The practicalit...

Hume developed an original and revolutionary theoretical paradigm for explaining the spontaneous emergence of the classic conventions of justice—stable possession, transference of property by consent, and the obligation to fulfill promises. In a scenario of scarce external resources, Hume’s central idea is that the development of the rules of justice responds to a sense of common interest that ...

Data envelopment analysis (DEA) is an effective tool for supporting decision-makers to assess bankruptcy, uncertainty concepts including intervals, and game theory. The bankruptcy problem with the qualitative parameters is an economic problem under uncertainty. Accordingly, we combine the concepts of the DEA game theory and uncertain models as interval linear programming (ILP), which can be app...