We establish a linear variational principle extending Deville–Godefroy–Zizler’s one. use this to prove that if $X$ is Banach space having property $(\alpha )$ of Schachermayer and $Y$ any space, then the set all str

Practical approaches to constructing public key cryptosystems secure against chosen ciphertext attacks were rst initiated by Damgard and further extended by Zheng and Seberry. In this paper we rst point out that in some cryptosystems proposed by Zheng and Seberry the method for adding authentication capability may fail just under known plaintext attacks. Next, we present a new method for immuni...

We extend the recent result of G. Godefroy which concerns existence non-norm attaining Lipschitz maps in order to characterize norm attainment toward vectors for general setting underlying space. The main theorem present paper states that on a large class metric spaces is characterized by finite-dimensionality range As an extension his counterexample, some denseness results are also shown.

islamic architecture has a fundamental dignity and tries to preserve the spiritual and immortal elements. the most sensible characteristic of this type of art is the compatibility with the nature of islam; monotheism, which the mosque architecture provides the best bed for such purpose. the main model for constructing mosques, from both outward and internal spiritual truths point of view, is th...