In this paper, we present an efficient numerical method for multiphase image segmentation using a multiphase-field model. The method combines the vector-valued Allen– Cahn phase-field equation with initial data fitting terms containing prescribed interface width and fidelity constants. An efficient numerical solution is achieved using the recently developed hybrid operator splitting method for ...

The notion of operator-valued frames (OVFs) by Kaftal et al. (Trans Am Math Soc 361(12):6349–6385, 2009) and G-frames Sun (J Anal Appl 322(1):437–452, 2006) do not include all generalizations notions for Hilbert spaces. For this purpose, we introduce the weak (weak OVFs) which covers known Theory weak-OVFs is more demanding than theory OVFs due to following: One, frame operator may factor anoth...

In this article we define some aggregation operators for bipolar-valued hesitant fuzzy sets. These operations include bipolar-valued hesitant fuzzy ordered weighted averaging (BPVHFOWA) operator, bipolar-valued hesitant fuzzy ordered weighted geometric (BPVHFOWG) operator and their generalized forms. We also define hybrid aggregation operators and their generalized forms and solved a decision-m...

Frames on Hilbert C*-modules have been defined for unital C*algebras by Frank and Larson [5] and operator-valued frames on a Hilbert space have been studied in [8]. The goal of this paper is to introduce operatorvalued frames on a Hilbert C*-module for a σ-unital C*-algebra. Theorem 1.4 reformulates the definition given in [5] in terms of a series of rank-one operators converging in the strict ...

We extend the de Branges-Beurling theorem characterizing shift-invariant spaces boundedly contained in Hardy space of square-summable power series to full Fock over Cd. Here, is identified as Non-commutative (NC) Space Taylor several non-commuting variables. then proceed study lattice operations on NC kernels and operator-valued multipliers between vector-valued spaces. In particular, we demons...

Fourier multiplier theorems provides one of the most important tools in the study of partial differential equations and embedding theorems. They are very often used to establish maximal regularity of elliptic and parabolic differential operator equations. Operator–valued multiplier theorems in Banach–valued function spaces have been discussed extensively in [1, 2, 3, 5, 7, 8, 9, 10, 11, 12 ]. B...

This article discusses the basic properties of finite-dimensional Boolean vector spaces and their linear transformations. We first introduce a natural Boolean-valued inner product and discuss orthonormal bases. We show that all bases are orthonormal and have the same cardinality. It is shown that the set of subspaces form an atomistic orthomodular poset. We then demonstrate that an operator tha...