After the classification of the flag-transitive linear spaces, the attention has been turned to line-transitive linear spaces. In this article, we present a partial classification of the finite linear spaces $mathcal S$ on which an almost simple group $G$ with the socle $G_2(q)$ acts line-transitively.

We extend the discussion of projective group representations in quaternionic Hilbert space which was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary operators and then analyzed in terms of their generator structure. The multi–centrality and centrality assumptions are also analyzed in generator terms, and implica...

It is well known that the renormalization group equations depend on the scale where they are applied. This phenomenon is especially relevant for the massive fields in curved space, because the decoupling effects may be responsible for important cosmological applications like the graceful exit from the inflation and low-energy quantum dynamics of the cosmological constant. We investigate, using ...

BACKGROUND Functional near-infrared spectroscopy (fNIRS) is a method for monitoring hemoglobin responses using optical probes placed on the scalp. fNIRS spatial resolution is limited by the distance between channels defined as a pair of source and detector, and channel positions are often inconsistent across subjects. These challenges can lead to less accurate estimate of group level effects fr...

We reformulate Fourier-space crystallography in the language of cohomology of groups. Once the problem is understood as a classification of linear functions on the lattice, restricted by a particular group relation, and identified by gauge transformation, the cohomological description becomes natural. We review Fourier-space crystallography and group cohomology, quote the fact that cohomology i...

Based on the original idea of the density matrix renormalization group (DMRG) [1], i.e. to include the missing boundary conditions between adjacent blocks of the blocked quantum system, we present a rigorous and nonperturbative mathematical formulation for the realspace renormalization group (RG) idea invented by L.P. Kadanoff [2] and further developed by K.G. Wilson [3]. This is achieved by us...

We analyze the structure of the frequency space Q(F ) of a nonabelian free group F = F (a1, . . . , ak) consisting of all shift-invariant Borel probability measures on ∂F and construct a natural action of Out(F ) on Q(F ). In particular we prove that for any outer automorphism φ of F the conjugacy distortion spectrum of φ, consisting of all numbers ||φ(w)||/||w||, where w is a nontrivial conjug...

Two new rate-one full-diversity space-time block codes (STBC) are proposed. They are characterized by the lowest decoding complexity among the known rate-one STBC, arising due to the complete separability of the transmitted symbols into four groups for maximum likelihood detection. The first and the second codes are delay-optimal if the number of transmit antennas is a power of 2 and even, resp...