in this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by jones [12] for length-biased data.the approach is based on the invariance principle for the empirical processes proved by horváth [10]. all simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by ...

We prove that a type-definable Lascar strong type has finite diameter. We answer also some other questions from [1] on Lascar strong types. We give some applications on subgroups of type-definable groups. In this paper T is a complete theory in language L and we work within a monster model C of T . For a0, a1 ∈ C let a0Θa1 iff 〈a0, a1〉 extends to an indiscernible sequence 〈an, n < ω〉. We define...

Authenticated Key Exchange protocols enable several parties to establish a shared cryptographically strong key over an insecure network using various authentication means, such as strong cryptographic keys or short (i.e., low-entropy) common secrets. The latter example is definitely the most interesting in practice, since no additional device is required, but just a human-memorable password, fo...

Let v be a product of at most three not necessarily distinct primes. We prove that there exists no strong external difference family with more than two subsets in an abelian group G order , except possibly when = C p 3 and is prime greater × 10 12 .