An asymmetric Fuglede-Putnam’s Theorem for w−hyponormal operators and class Y operators is proved, as a consequence of this result, we obtain that the range of the generalized derivation induced by the above classes of operators is orthogonal to its kernel.

A mechanical equilibrium equation of a vesicle membrane under a generalized elastic bending energy is obtained in this paper. Moreover, the derivation of this equilibrium equation bases on some shape optimization tools. This approach is new and more concise than the tensorial tools previously used for this problem.

Working at the level of Poisson brackets, we describe the extension of the generalized Wakimoto realization of a simple Lie algebra valued current, J, to a corresponding realization of a group valued chiral primary field, b, that has diagonal monodromy and satisfies Kb ′ = Jb. The chiral WZNW field b is subject to a monodromy dependent exchange algebra, whose derivation is reviewed, too.

For arbitrary values of a parameter λ ∈ R, finite-time blowup of solutions to the generalized, inviscid Proudman-Johnson equation is studied via a direct approach which involves the derivation of representation formulae for solutions to the problem. Mathematics Subject Classification (2010). 35B44, 35B10, 35B65, 35Q35.

We introduce Lie-Nijenhuis bialgebroids as Lie endowed with an additional derivation-like object. They give a complete infinitesimal description of Poisson-Nijenhuis groupoids, and key examples include manifolds, holomorphic flat bialgebra bundles. To achieve our goal we develop theory "generalized derivations" their duality, extending the well-established derivations on vector

This paper presents a unified mathematical derivation of the asymptotic behaviour of the three main forms of partial directed coherence (PDC). Numerical examples are used to contrast PDC, gPDC (generalized PDC) and iPDC (information PDC) as to meaning and applicability and, more importantly, to show their essential statistical equivalence insofar as connectivity inference is concerned.

As part of a more general program of developing multiple-scale models of turbulence, Schiestel suggested a derivation of the homogeneous part of the dissipation rate transport equation. Schiestel's approach is generalized to rotating turbulence. The resulting model reproduces the main features observed in decaying rotating turbulence.

The m-clover is the plane curve defined by the polar equation rm/2 = cos (m2 θ). In this article we extend a well-known derivation of the Wallis product to derive a generalized Wallis product for arc lengths of m-clovers.

This paper presents a generalized formula of spatial correlation (SC) approximation with closed-form solution for three-dimensional (3D) incoming waves in multipath fading environment. The derivation of the formula is based on a novel model of angular power spectrum (APS) and the validity is verified by simulation results.

We use the Itô stochastic calculus to give a simple derivation of the Lindblad form for the generator of a completely positive density matrix evolution, by specialization from the corresponding global form for a completely positive map. As a by-product, we obtain a generalized generator for a completely positive stochastic density matrix evolution.