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A typical problem in additive combinatorics is to find the structure of a set given an additive assumption about the set. Sárközy's conjecture is one such problem. The conjecture posits the nonexistence of a nontrivial 2-decomposition of the set Qp of quadratic residue modulo p. In this paper, we review the history and formulation of the conjecture. Then we survey the progress made towards this conjecture in which we first suppose that a 2-decomposition Qp = A+B exists, with │A│, │B│ ≥2. Next, we find bounds for the cardinalities of sets A and B while showcasing the techniques used in obtaining them. Finally, we suggest further problems by discussing the case for a 3-decomposition of Qp and other related problems. [ABSTRACT FROM AUTHOR]

Quadratic Residue Diffuser Skyline (SQRD) is an acoustic panel with the principle of working as a diffuser with a specific geometry (uneven), rigid and scatter sounds. SQRD is arranged with a multidimensional QRD pattern. The study aims to analyze the effect of shifting SQRD sequence positions on panels performance with SPL directivity parameters and diffusion coefficients. The SQRD used in this study has a size of N = 11. The shift variations used are symmetry configuration (V0), shift one (V1), to shift five (V5). The scattering frequency used for the analysis is 1600Hz, 2000Hz, 2500Hz, 3150Hz. The results showed that the shift in the position of SQRD sequences did not provide significant changes. This is shown by the pattern of SPL directivity that are almost uniform for all variations, and each variation of the panels used has good diffuser characteristics with a diffusion coefficient value above 0.83. [ABSTRACT FROM AUTHOR]

Magic square and stream cipher issues are both interesting and well-tried topics. In this paper, we are proposing a new scheme which streams cipher applications for random access files based on the magic square method. There are two thresholds required to secure our data, if using only decrypts by the stream cipher. It isn't to recovery original source. On other hand, we improve the model of cipher stream to strengthen and defend efficiently; it also was its own high speed and calculates to most parts of the key stream generator. [ABSTRACT FROM AUTHOR]