Rosenbloom and Tsfasman introduced a new metric (RT metric) which is a generalization of the Hamming metric. In this paper we study the distance graphs of spaces Zn q and Sn with Rosenbloom -Tsfasman metric. We also describe the degrees of vertices, components and the chromatic number of these graphs. Distance graphs of general direct product spaces also described.

A vector space over a field K (R or C) is a set X with operations vector addition and scalar multiplication satisfy properties in section 3.1. [1] An inner product space is a vector space X with inner product 〈·, ·〉 : X ×X → K satisfying • 〈x + y, z〉 = 〈x, z〉+〈y, z〉, • 〈αx, y〉 =α〈x, y〉, • 〈x, y〉 = 〈y, x〉, • 〈x, x〉 ≥ 0 with 〈x, x〉 = 0 ⇐⇒ x = 0. [2] An inner product induces a norm on X via ‖x‖ =p...

We present a complete basis of multi-trace multi-matrix operators that has a diagonal two point function for the free matrix field theory at finite N . This generalises to multiple matrices the single matrix diagonalisation by Schur polynomials. Crucially, it involves intertwining the gauge group U(N) and the global symmetry group U(M) with Clebsch-Gordan coefficients of symmetric groups Sn. Wh...

We prove the existence of a deformation quantization for integrable Poisson structures on R 3 and give a generalization for a special class of three dimensional manifolds. The program of deformation quantization of the function algebra on a sym-plectic manifold extends naturally to manifolds with nonregular Poisson structures. In contrast to symplectic manifolds the existence of star products o...

In this paper we study the possibility of real zeros near s = 1 for the RankinSelberg L-functions L(s, f × g) and L(s, sym(g) × sym(g)), where f, g are newforms, holomorphic or otherwise, on the upper half plane H, and sym(g) denotes the automorphic form on GL(3)/Q associated to g by Gelbart and Jacquet ([GJ79]). We prove that the set of such zeros of these L-functions is the union of the corre...

The methylglutamate analog (2S,4R)-4-methylglutamate (SYM 2081) has been shown to potently displace high affinity [3H]kainate binding to cortical tissue and to recombinant kainate receptors, and to evoke rapidly desensitizing responses in electrophysiological recordings. We have used two electrode voltage clamp recordings to compare the potency and efficacy of SYM 2081 with other alpha-amino-3-...

Euclidean supersymmetric theories are obtained from Minkowskian theories by performing a reduction in the time direction. This procedure elucidates certain mysterious features of Zumino’s N=2 model in four dimensions, provides manifestly hermitian Euclidean counterparts of all non-mimimal SYM theories, and is also applicable to supergravity theories. We reanalyse the twists of the 4d N=2 and N=...

The Energy-Delay product or ED product was proposed as a metric to gauge design effectiveness. This metric is widely used in the area of low-power architecture research, however it is also often improperly used when reporting a new architecture design that addresses energy-performance effectiveness. In this paper, we discuss two common fallacies from the literature: (1) the way the ED product i...

for (1), see [1], transfer the standard bracket [ , ] in sym E to the Lie algebra structures on their domain. We prove that the three new brackets are compatible. The Noether operator A0 is invertible on an open dense subset of E . This yields two recursion operators Ri = Âi ◦ A −1 0 : sym E → sym E . The images of Ri are again closed w.r.t. the commutation, and this property is retained by the...

The highly debated three-body dissociation of sym-triazine to three HCN products has been investigated by translational spectroscopy and high-level ab initio calculations. Dissociation was induced by charge exchange between the sym-triazine radical cation and cesium. Calculated state energies and electronic couplings suggest that sym-triazine is produced in the 3s Rydberg and pi* <-- n manifold...