In this paper, we construct the Hall-Janko graph within the split Cayley hexagon H(4). Using this graph we then construct the near-octagon of order (2, 4) as a subgeometry of the dual of H(4), with J2 : 2 as its automorphism group. These constructions are based on a lemma determining the possibilities for the structure of the intersection of two subhexagons of order 2 in H(4).

We construct a one-dimensional contact interaction (ε potential) which induces the discontinuity of the wave function while keeping its derivative continuous. By combining the ε potential and the Dirac’s δ function, we construct most general one-dimensional contact interactions allowable under the time reversal symmetry. We present some elementary results for the scattering problem which sugges...

Since the extension principles of constructing wavelet frames were presented, a lot of symmetric and compactly supported wavelet frames with high vanishing moments have been constructed. However the problem of constructing periodic wavelet frames with the help of extension principles is open. In this paper, we will construct tight periodic wavelet frames using the unitary extension principle an...

In order to construct quantum [[n, 0, d]] codes for (n, d) = (56, 15), (57, 15), (58, 16), (63, 16), (67, 17), (70, 18), (71, 18), (79, 19), (83, 20), (87, 20), (89, 21), (95, 20), we construct self-dual additive F4-codes of length n and minimum weight d from circulant graphs. The quantum codes with these parameters are constructed for the first time.

We consider regular Calabi-Yau hypersurfaces in N -dimensional smooth toric varieties. On such a hypersurface in the neighborhood of the large complex structure limit point we construct a fibration over a sphere S whose generic fibers are tori T. Also for certain one-parameter families of such hypersurfaces we show that the monodromy transformation is induced by a translation of the T fibration...

We propose a consistent setup for a holographic dual of Bjorken flow of strongly coupled large-Nc N=4 SYM-theory plasma. We employ Eddington-Finkelstein type coordinates for the dual geometry, and we propose a late-time expansion there. We construct the dual geometry order by order, and we show that the transport coefficients are determined by the regularity of the geometry. We also show that t...

We present an ansatz which enables us to construct heterotic/M-theory dual pairs in four dimensions. It is checked that this ansatz reproduces previous results and that the massless spectra of the proposed new dual pairs agree. The new dual pairs consist of M-theory compactifications on Joyce manifolds of G 2 holonomy and Calabi-Yau compactifications of heterotic strings. These results are furt...

We propose a class of AdS/CFT dual pairs which have small internal dimensions on the gravity side. Starting from known Freund-Rubin AdS/CFT dual pairs, we use 7-branes to nearly cancel the curvature energy of the internal dimensions while maintaining their stabilization. This leads to a new corner of the landscape – a class of AdS solutions with a hierarchically large AdS radius – with a dual f...

It is shown that for every finite set of disjoint convex polygonal obstacles in the plane, with a total of n vertices, the free space around the obstacles can be partitioned into open convex cells whose dual graph (defined below) is 2-edge connected. Intuitively, every edge of the dual graph corresponds to a pair of adjacent cells that are both incident to the same vertex. Aichholzer et al. rec...

Given a frame for a subspace W of a Hilbert space H, we consider a class of oblique dual frame sequences. These dual frame sequences are not constrained to lie in W . Our main focus is on shift-invariant frame sequences of the form {φ(· − k)}k∈Z in subspaces of L2(R); for such frame sequences we are able to characterize the set of shift-invariant oblique dual Bessel sequences. Given frame seque...