In 1962, Elizabeth Peal and Wallace Lambert of McGill University published a monograph entitled “The Relation of Bilingualism to Intelligence.”The research, conducted in Montreal with 10-year-old children, compared the performance of monolinguals t o that of bilingual, French/English-speaking subjects on a variety of standard tests of intelligence. In contrast to previous research on bilinguali...

In this paper we investigate the stability of the HIV-1 infection dynamical problem. An approach using the matrix Lambert W function for the analytical solution to system of delay differential equations is applied to this problem and compared with the result obtained using a bifurcation analysis. Mathematical Subject Classication (2010): 92B05, 92B99, 34D20, 34C23.

Problem statement: For ordinary dynamic systems (i.e., non-delayed), various methods such as linear least-squares, gradient-weighted least-squares, Kalman filtering and other robust techniques have been widely used in signal processing, robotics, civil engineering. On the other hand, time-delay estimation of systems with unknown time-delay is still a challenging problem due to difficulty in for...

A new chaotic circuit is practically realized, for the first time, using a Lambert W-function. The circuit consists of three main parts. The first part employs a well-known Wilson current mirror, whereas the second part is a simple resistor at the two connected emitters of the current mirror. Both parts form a new circuit for a Lambert W-function by enabling a term of an emitter current to be s...

We show how Rank-Crank type PDEs for higher order Appell functions due to Zwegers may be obtained from a generalized Lambert series identity due to the first author. Special cases are the Rank-Crank PDE due to Atkin and the third author and a PDE for a level 5 Appell function also found by the third author. These two special PDEs are related to generalized Lambert series identities due to Watso...

We address the problem of synthesizing a generalized Gaussian noise with exponent 1/2 by means of a nonlinear memoryless transformation applied to a uniform noise. We show that this transformation is expressable in terms of a special function known under the name of the Lambert W function. We review the main methods for numerical evaluation of the relevant branch of the (multivalued) Lambert W ...