Finite simple, unipotent Bol loops have recently been identified and constructed using group theory. However, the purely group-theoretical constructions of the actual loops are indirect, somewhat arbitrary in places, and rely on computer calculations to a certain extent. In the spirit of revisionism, this paper is intended to give a more explicit combinatorial specification of the smallest simp...

We present the i-ConeTM: a new projection-based panoramic display system for virtual environments. The i-ConeTM uses conical screen geometry, resulting in optimized projector placement to create an extended workspace for standing participants in a front projection curved screen display with a very large continuous field of view. Improved acoustical properties of the conical screen geometry enab...

We examine the open problem of finding the shortest string that contains each of the n! permutations of n symbols as contiguous substrings (i.e., the shortest superpermutation on n symbols). It has been conjectured that the shortest superpermutation has length ∑n k=1 k! and that this string is unique up to relabelling of the symbols. We provide a construction of short superpermutations that sho...

We describe how unintegrated parton distributions can be calculated from conventional integrated distributions. We extend and improve the ‘last-step’ evolution approach, and explain why doubly-unintegrated parton distributions are necessary. We generalise ktfactorisation to (z, kt)-factorisation. We apply the formalism to inclusive jet production in deep-inelastic scattering, mainly at leading ...

The characteristic functional (c.fl.) of a doubly stochastic Poisson process (DSPP) is studied and it provides us the finite dimensional distributions of the process and so its moments. It is also studied the case of a DSPP which intensity is a narrow-band process. The Karhunen–Loève expansion of its intensity is used to obtain the probability distribution function and a decomposition of this P...

To address different uncertainties associated with patient recruitment in multicentre clinical trials a mixed Poisson model is elaborated (patients arrive at different clinical centres according to delayed doubly stochastic Poisson processes with gamma distributed rates). Analytic approach to modeling and predicting the recruitment at the initial and ongoing stages is suggested. A Bayesian appr...

We consider a class of reflected backward doubly stochastic differential equations with time delayed generator (in short RBDSDE with time delayed generator), in this case generator at time t can depend on the values of a solution in the past. Under a Lipschitz condition, we ensure the existence and uniqueness of the solution.

In the context of effective Friedmann equation we classify the cosmologies in multiscalar models with an arbitrary scalar potential V according to their geometric properties. It is shown that all flat cosmologies are geodesics with respect to a conformally rescaled metric on the ‘augmented’ target space. Non-flat cosmologies with V = 0 are also investigated. It is shown that geodesics in a ‘dou...