AC-operators were introduced by Berkson and Gillespie as a generalization in the context of well-boundedness of normal operators on Hilbert space. In this paper we explore some of the properties of these operators, such as the uniqueness of their splitting into real and imaginary parts, and their interpolation properties. We also examine the interpolation properties of the important subclass co...

Let E(·) : R → B(X) be the spectral decomposition of a trigonometrically well-bounded operator U acting on the arbitrary Banach space X, and suppose that the bounded function φ : T → C has the property that for each z ∈ T, the spectral integral R [0,2π] φ(e)dEz(t) exists, where Ez(·) denotes the spectral decomposition of the (necessarily) trigonometrically well-bounded operator (zU). We show th...

External fixation correction of angular deformities leads to secondary translation deformities when occurring around an axis located proximal or distal to the center of rotation of angulation (CORA); secondary length deformities result when correction occurs around an axis concave or convex to the CORA. With circular fixation, the hinge axis can be matched to the CORA. With monolateral fixation...

Motivated by problems in the spectral theory of linear operators the authors previously introduced a new concept of variation for functions defined on a nonempty compact subset of the plane. In this paper we examine the algebras of functions of bounded variation one obtains from these new definitions for the case where the underlying compact set is either a rectangle or the unit circle, and com...

We show that flag manifold $$\sigma $$ -models (including $$\mathbb{C}\mathbb{P}^{n-1}$$ , Grassmannian models as special cases) and their deformed versions may be cast in the form of gauged bosonic Thirring/Gross-Neveu-type systems. Quantum mechanically gauging is violated by chiral anomalies, which cancelled adding fermions. conjecture such are integrable check on some examples trigonometrica...

In this paper, we present a new two-step trigonometrically fitted symmetric Obrechkoff method. The method is based on the symmetric two-step Obrechkoff method, with eighth algebraic order, high phase-lag order and is constructed to solve IVPs with periodic solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. The numeri...

Langmuir waves propagate in fractal complex plasma with characteristics, which may cause some particles to be trapped or causes wave turbulences. This phenomenon appears the form of fractional order equations. Using an effective unified solver, new solitary profiles such as rational, trigonometrically and hyperbolical functions forms are discussed, using derivatives conformable sense. The modul...