This paper is devoted for a rigorous investigation of Hahn’s difference operator and the associated calculus. Hahn’s difference operator generalizes both the difference operator and Jackson’s q-difference operator. Unlike these two operators, the calculus associated with Hahn’s difference operator receives no attention. In particular, its right inverse has not been constructed before. We aim to...

PURPOSE We developed an inverse technique for tissue morcellation by modifying the conventional upward technique and then examined its safety and efficiency. MATERIALS AND METHODS From July 2008 to December 2010, a total of 389 consecutive patients treated with holmium laser enucleation of the prostate (HoLEP) were enrolled in this study. For tissue morcellation, we used an upward technique f...

In this paper the conjugate gradient (CG) method is employed for identifying the parameters of crack in a functionally graded beam from natural frequency measurement. The crack is modeled as a massless rotational spring with sectional flexibility. By using the Euler-Bernoulli beam theory on two separate beams respectively and applying the compatibility requirements of the crack, the characteris...

A Hermitian matrix X is called a g-inverse of a Hermitian matrix A, denoted by A, if it satisfies AXA = A. In this paper, a group of explicit formulas are established for calculating the global maximum and minimum ranks and inertias of the difference A − PNP , where both A and N are Hermitian g-inverses of two Hermitian matrices A and N , respectively. As a consequence, necessary and sufficient...

A Hermitian matrix X is called a g-inverse of a Hermitian matrix A, denoted by A, if it satisfies AXA = A. In this paper, a group of explicit formulas are established for calculating the global maximum and minimum ranks and inertias of the difference A − PNP , where both A and N are Hermitian g-inverses of two Hermitian matrices A and N , respectively. As a consequence, necessary and sufficient...