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...

5 We give an optimal degree condition for a tripartite graph to have 6 a spanning subgraph consisting of complete graphs of order 3. This 7 result is used to give an upper bound of 2∆ for the strong chromatic 8 number of n vertex graphs with ∆ ≥ n/6. 9

The paper addresses the cheating prevention in secret sharing. We consider secret sharing with binary shares. The secret also is binary. This model allows us to use results and constructions from the well developed theory of cryptographically strong boolean functions. In particular, we prove that for given secret sharing, the average cheating probability over all cheating vectors and all origin...