In this paper, two different ways of introducing alternation for lattice-valued (referred to as {L}valued)  regular tree grammars and {L}valued top-down tree automata are compared. One is the way which defines the alternating regular tree grammar, i.e., alternation is governed by the non-terminals of the grammar and the other is the way which combines state with alternation. The first way is ta...

In the present paper, we study frames for finite-dimensional vector spaces over an arbitrary field. We develop a theory of dual in order to obtain and different representations elements space provided by frame. relate introduced with classical one Hilbert apply it three types spaces: conjugate closed subfields complex numbers (in particular, cyclotomic fields), metric spaces, ultrametric normed...

Polygon, subdivision, and NURBS are three mainstream modeling techniques widely applied in commercial software packages. They require heavy manual operations, involve a lot of design variables leading to big data, high storage costs slow network transmissions. In this paper, we integrate the strengths boundary-based surface creation partial differential equation (PDE)-based geometric obtain fir...

EXTENDED ABSTRACT. In recent years, networked multi-agent systems have attracted much research attention from various disciplines of engineering and science due to their interdisciplinary nature and broad potential applications. Collective behaviors arise from simple local interaction rules in complex networked systems. Graph Laplacian plays a very important role in analysis of networked multi-...

We provide a probabilistic and infinitesimal view of how the principal component analysis procedure (PCA) can be generalized to analysis of nonlinear manifold valued data. Starting with the probabilistic PCA interpretation of the Euclidean PCA procedure, we show how PCA can be generalized to manifolds in an intrinsic way that does not resort to linearization of the data space. The underlying pr...

In this paper, we study the stability of phase retrieval problems via a family locally stable frame measurements in Banach spaces, which call “locally and conditionally connected” (LSCC) measurement schemes. For any signal f space, associate it with weighted graph Gf, defined by LSCC scheme, show that retrievability is determined connectivity Gf. We quantify two common measures connectivity: Th...

The purpose of this note is to compare the rings of continuous functions, integer-valued or real-valued, in pointfree topology with those in classical topology. To this end, it first characterizes the Boolean frames (= complete Boolean algebras) whose function rings are isomorphic to a classical one and then employs this to exhibit a large class of frames for which the functions rings are not o...

In this paper, we introduce a new sort of interval valued $left(in ,in vee q_{widetilde{k}}^{widetilde{delta }}right) $-fuzzy bi-ideal in ordered semigroups which is the generalization of interval valued $left( in ,in vee q_{%widetilde{k}}right) $-fuzzy bi-ideal and interval valued $left( in ,in vee qright) $-fuzzy bi-ideal of ordered semigroups. We give examples in which we show that these str...

The system of N scalar particles with Grassmann-valued color charges plus the color SU(3) Yang-Mills field is reformulated on spacelike hypersurfaces. The Dirac observables are found and the physical invariant mass of the system in the Wigner-covariant rest-frame instant form of dynamics (covariant Coulomb gauge) is given. From the reduced Hamilton equations we extract the second order equation...

A new equational foundation is presented for the Fluent Calculus , an established predicate calculus formalism for reasoning about actions. We discuss limitations of the existing axiomatizations of both equality of states and what it means for a uent to hold in a state. Our new and conceptually even simpler theory is shown to overcome the restrictions of the existing approach. We prove that the...