We define pseudo-reality and pseudo-adjointness of a Hamiltonian, H, as ρHρ−1 = H∗ and μHμ−1 = H ′, respectively. We prove that the former yields the necessary condition for spectrum to be real whereas the latter helps in fixing a definition for inner-product of the eigenstates. Here we separate out adjointness of an operator from its Hermitian-adjointness. It turns out that a Hamiltonian posse...

In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...

In this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. Weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

Benign lesions may simulate bronchogenic carcinoma by virtue of radiologic appearance or false-positive cytologic studies. A lung opacity initially suspected to be malignant was, on review, considered to be a loculated effusion. Needle biopsy yielded cells which appeared malignant. The resected lesion was a benign infarct.

As an example of the categorical apparatus of pseudo algebras over 2-theories, we show that pseudo algebras over the 2theory of categories can be viewed as pseudo double categories with folding or as appropriate 2-functors into bicategories. Foldings are equivalent to connection pairs, and also to thin structures if the vertical and horizontal morphisms coincide. In a sense, the squares of a do...