Owing to advances in the overall performance and anti-interception capability of radars, designs radar waveforms with good correlation properties have been a concern for researchers. In this paper, we propose novel method based on convolutional neural networks (CNNs) designing single or multiple unimodular sequences auto- cross-correlation weighted properties. The framework sequence optimizatio...

The point of this note is to prove that the secrecy function attains its maximum at y = 1 on all known extremal even unimodular lattices. This is a special case of a conjecture by Belfiore and Solé. Further, we will give a very simple method to verify or disprove the conjecture on any given unimodular lattice.

The conformal invariance of unimodular gravity survives quantum corrections, even in the presence of conformal matter. Unimodular gravity can actually be understood as a certain truncation of the full Einstein-Hilbert theory, where in the Einstein frame the metric tensor has unit determinant. Our result is compatible with the idea that the corresponding restriction in the functional integral is...

In the article we settle down the problem of permanence of property RD under group extensions. We show that if 1 → N → G → Q → 1 is a short exact sequence of compactly generated groups such that Q has property RD, and N has property RD with respect to the restriction of a word-length on G, then G has property RD. We also generalize the result of Ji and Schweitzer stating that locally compact gr...

A tournament is unimodular if the determinant of its skew-adjacency matrix $1$. In this paper, we give some properties and constructions tournaments. $T$ with $S$ invertible $S^{-1}$ a tournament. spectral characterization tournaments given. Lastly, show that every $n$-tournament can be embedded in by adding at most $n - \lfloor\log_2(n)\rfloor$ vertices.

Finite projective (lattice) geometries defined over rings instead of fields have recently been recognized to be of great importance for quantum information theory. We believe that there is much more potential hidden in these geometries to be unleashed for physics. There exist specific rings over which the projective spaces feature two principally distinct kinds of basic constituents (points and...