This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...

We give a proof of a generalization of Muirhead’s Inequality and informally explain its application in establishing an instantial relevance principle in Polyadic Inductive Logic. Mathematics subject classification (2000): 26D15.

A Euclidean (or hyperbolic) circle packing on a triangulated closed surface with prescribed inversive distance is locally determined by its cone angles. We prove this by establishing a variational principle.

The basic principle of entanglement processing says that entanglement cannot increase under local operations and classical communication. Based on this principle, we show that any entanglement measure E suitable for the regime of a high number of identically prepared entangled pairs satisfies ED < or = E < or = EF, where ED and EF are the entanglement of distillation and formation, respectively...

Severity (harm, invasiveness) scales focus the attention of both regulators and researchers on highly invasive experiments and thus help to promote the 3Rs, especially the refinement. A severity scale is critical to the quality of ethical review processes (ERPs) in limiting arbitrariness and situational opportunism of assessments, defining the acceptability ranges for some animal uses, especial...