Abstract For each $$n\ge 0$$ n ≥ 0 , let $$\mu _n$$ μ be a tight probability measure on the Borel $$\sigma $$ σ -field of metric space S . Let $$(T,{\mathcal {C}})$$ ( T</...

The paper presents a theorem for representation a given cone as a Bishop–Phelps cone in normed spaces and studies interior and separation properties for Bishop–Phelps cones. The representation theorem is formulated in the form of a necessary and sufficient condition and provides relationship between the parameters determining the BishopPhelps cone. The necessity is given in reflexive Banach spa...

Following [9] some properties of Q-probability and Q-states are studied. Representation theorem of Q-probabilities and Q-states, the existence of the joint observable and The central limit theorem are proved. Keywords—Q-probability, Q-state, representation theorem, intuitionistic fuzzy events, joint Q-observable, Central limit theorem.

An alleged theorem of Neven, Smart and Warinschi (NSW) about the security of Schnorr signatures seems to have a flaw described in this report. Schnorr signatures require representation of an element in a discrete logarithm group as a hashable bit string. This report describes a defective bit string representation of elliptic curve points. Schnorr signatures are insecure when used with this defe...

In this paper we study the W -weighted Drazin inverse of the bounded linear operators between Banach spaces and its representation theorem. Based on this representation, utilizing the spectral theory of Banach space operators, we derive an approximating expression of the W -weighted Drazin inverse and an error bound. Also, a perturbation theorem for the W -weighted Drazin inverse is uniformly o...