| In order to improve the eeciency of the Secure Electronic Transaction (SET) protocol, Hanaoka et al. proposed a light weight version of the SET protocol, called \LITESET"at ACISP '98. They claimed that LITESET has about 50% reduction in computational time and about 80% reduction in communication overhead by using a signcryp-tion scheme. We propose another way to construct an eecient SET proto...

In this paper we present some properties of set-norm exhaustive set multifunctions and also of atoms and pseudo-atoms of set multifunctions taking values in the family of non-empty subsets of a commutative semigroup with unity.

Prove that any strictly monotone sequence (Uα)α<γ of open subsets of X has countable length, i.e. γ is countable. Hint: Use the same idea as in the proof of (a). (c) Show that every monotone sequence (Uα)α<ω1 open subsets of X eventually stabilizes, i.e. there is γ < ω1 such that for all α < ω1 with α ≥ γ, we have Uα = Uγ. Hint: Use the regularity of ω1. (d) Conclude that parts (a), (b) and (c)...

Let A be a subset of a ring with cardinality |A| = N . The sum set and the product set are 2A = A+A = {a1 +a2 | ai ∈ A} and A = AA = {a1a2 | ai ∈ A}. The study of sum-product sets is to estimate the sizes of 2A and A asymptotically when N is very large. Since Erdős and Szemerédi conjectured that if A ⊂ Z, at least one of |2A| and |A2| should be bigger than cN for any constant c, a lot of work h...

In this paper a new class of sets called  regular generalized  $delta$-closed set (briefly rg$delta$-closed set)is introduced and its properties are studied. Several examples are provided to illustrate the behaviour of these new class of sets.

Lacosamide is an anticonvulsant hypothesized to enhance slow inactivation of neuronal Na(+) channels for its therapeutic action. Cardiac Na(+) channels display less and incomplete slow inactivation, but their sensitivity toward lacosamide remains unknown. We therefore investigated the action of lacosamide in human cardiac Nav1.5 and Nav1.5-CW inactivation-deficient Na(+) channels. Lacosamide sh...