Levin’s MLS projection operator allows defining a surface from a set of points and represents a versatile procedure to generate points on this surface. Practical problems of MLS surfaces are a complicated non-linear optimization to compute a tangent frame and the (commonly overlooked) fact that the normal to this tangent frame is not the surface normal. An alternative definition of Point Set Su...

In the present paper an approach to nonmonotonic reasoning is discussed which is inspired by the paradigm of abstract model theory. The aim is to analyse non-monotonic reasoning within the framework of inference operations based on model operators. This is done by using the concept of a deductive frame and its semantical counterpart, a semantical frame. These are considered as a basis for nonmo...

We review the notion of perfect recall in the literature on interpreted systems, game theory, and epistemic logic. In the context of Epistemic Temporal Logic (ETL), we give a (to our knowledge) novel frame condition for perfect recall, which is local and can straightforwardly be translated to a defining formula in a language that only has next-step temporal operators. This frame condition also ...

This paper introduces a new, fully recursive algorithm for computing moving frames and differential invariants of Lie pseudo-group actions. The recursive method avoids unwieldy symbolic expressions that complicate the treatment of large scale applications of the equivariant moving frame method. The development leads to novel results on partial moving frames, structure equations, and new differe...

We develop a natural generalization of vector-valued frame theory, we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case and extends to higher multiplicity their dilation approach. We prove several results for operator-valued frames concerning duality, disjointeness, complementar...

The concepts of basis and frame are studied in the classical literature of functional analysis, Fourier analysis, and wavelet theory in a wide range. In this paper, we consider an operator-theoretic approach to discrete frame theory on a separable Hilbert space. For this purpose, we define a special type of frames and bases, called wavelet-type frames and wavelet-type bases, obtained by acting ...

We find the time evolution of the system of two non-interacting unstable particles, distinguishable as well as identical ones, in arbitrary reference frame having only the Kraus operators governing the evolution of its components in the rest frame. We than calculate in the rigorous way Einstein–Podolsky–Rosen quantum correlation functions for K0K̄0 system in the singlet state taking into account...

We develop a natural generalization of vector-valued frame theory, which we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case and extends to higher multiplicity their dilation approach. We prove several results for operator-valued frames concerning duality, disjointedness, compl...

We introduce a new order-topological semantics for the positive modal mu-calculus over modal compact Hausdorff spaces, which are generalizations of descriptive frames. We define Sahlqvist sequents in this language, prove Esakia’s lemma and Sahlqvist preservation theorem for this semantics. We show that every Sahlqvist sequent has a frame correspondent in first-order logic with fixed-point opera...

We study the structure of operators from the Schwartz space S (R) into the tempered distributions S (R) that commute with a discrete subgroup of translations. The formalism leads to simple derivations of recent results about the frame operator of shift-invariant systems, Gabor and wavelet frames.