We integrate an expressive class of description logics (DLs) and answer set programming by extending the latter to support inverted predicates and infinite domains, features that are present in most DLs. The extended language, conceptual logic programming (CLP) proves to be a viable alternative for intuitively representing and reasoning nonmonotonically, in a decidable way, with possibly infini...

A black hole is considered a gravitational one-dimensional point of singularity containing an infinite mass within an infinitely small space, and spacetime curves infinitely. Within this singularity all the laws of physics are no longer valid. The physical domains of the large macroscopic scale are described by general relativity and on the small microscopic scale by quantum effects. It is prop...

The classical Schwarz-Christoffel formula gives conformal mappings of the upper half-plane onto domains whose boundaries consist of a finite number of line segments. In this paper, we explore extensions to boundary curves which in one sense or another are made up of infinitely many line segments, with specific attention to the “infinite staircase” and to the Koch snowflake, for both of which we...

A construction of prismatic Hardy space infinite elements to discretize wave equations on unbounded domains Ω in H loc(Ω), Hloc(curl; Ω) and Hloc(div; Ω) is presented. As our motivation is to solve Maxwell’s equations we take care that these infinite elements fit into the discrete de Rham diagram, i.e. they span discrete spaces, which together with the exterior derivative form an exact sequence...

A novel upper power domain construction is deened by means of strongly compact sets. Its power domains contain less elements than the classical ones in terms of compact sets, but still admit all necessary operations, i.e. they contain less junk. The notion of strong compactness allows a proof of stronger properties than compactness would, e.g. an intrinsic universal property of the upper power ...

In this work we study Dirac operators on two-dimensional domains coupled to a magnetic field perpendicular the plane. We focus infinite-mass boundary condition (also called MIT bag condition). case of bounded domains, establish asymptotic behavior low-lying (positive and negative) energies in limit strong field. Moreover, for constant $B$, problem half-plane find that operator has continuous sp...

Conventional wisdom holds that the von Neumann entropy corresponds to thermodynamic entropy, but Meir Hemmo and Orly Shenker have recently argued against this view by attacking Neumann’s argument. I argue Shenker’s arguments fail because of several misunderstandings about statistical-mechanical domains applicability, nature mixed states, role approximations in physics. As a result, their all ca...

In this paper, meant as a companion to arXiv:2006.04458, we consider class of non-integrable $2D$ Ising models in cylindrical domains, and discuss two key aspects the multiscale construction their scaling limit. particular, provide detailed derivation Grassmann representation model, including self-contained presentation exact solution nearest neighbor model cylinder. Moreover, prove precise asy...

The initial lower and upper power domain constructions P _ and P ^ commute under composition for all cpos. The common result P _ (P ^ X) and P ^ (P _ X) is the free frame over the cpo X.

Stably compact spaces Xs can be described as being derived from compact ordered spaces X by weakening their topology to the open upper sets. In this paper the probabilistic powerdomain of a stably compact space Xs is investigated using the compact ordered space X and classical tools from measure theory and functional analysis. This allows to derive in a unified and elegant way known and new res...