Polyhedral Cones of Magic Cubes and Squares

Using computational algebraic geometry techniques and Hilbert bases of polyhedral cones we derive explicit formulas and generating functions for the number of magic squares and magic cubes.Comment: 14 page

Comparison of methods for logic-query implementation

AbstractA logic query Q is a triple < G, LP, D, where G is the query goal, LP is a logic program without function symbols, and D is a set of facts, possibly stored as tuples of a relational database. The answers of Q are all facts that can be inferred from LP ∪ D and unify with G. A logic query is bound if some argument of the query goal is a constant; it is canonical strongly linear (a CSL query) if LP contains exactly one recursive rule and this rule is linear, i.e., only one recursive predicate occurs in its body. In this paper, the problem of finding the answers of a bound CSL query is studied with the aim of comparing for efficiency some well-known methods for implementing logic queries: the eager method, the counting method, and the magic-set method. It is shown that the above methods can be expressed as algorithms for finding particular paths in a directed graph associated to the query. Within this graphical formalism, a worst-case complexity analysis of the three methods is performed. It turns out that the counting method has the best upper bound for noncyclic queries. On the other hand, since the counting method is not safe if queries are cyclic, the method is extended to safely implement this kind of queries as well

MAGIC sensitivity to millisecond-duration optical pulses

The MAGIC telescopes are a system of two Imaging Atmospheric Cherenkov Telescopes (IACTs) designed to observe very high energy (VHE) gamma rays above ~50 GeV. However, as IACTs are sensitive to Cherenkov light in the UV/blue and use photo-detectors with a time response well below the ms scale, MAGIC is also able to perform simultaneous optical observations. Through an alternative system installed in the central PMT of MAGIC II camera, the so-called central pixel, MAGIC is sensitive to short (1ms - 1s) optical pulses. Periodic signals from the Crab pulsar are regularly monitored. Here we report for the first time the experimental determination of the sensitivity of the central pixel to isolated 1-10 ms long optical pulses. The result of this study is relevant for searches of fast transients such as Fast Radio Bursts (FRBs).Comment: Proceedings of the 35th International Cosmic Ray Conference (ICRC 2017), Bexco, Busan, Korea (arXiv:1708.05153

Squaring the magic squares of order 4

In this paper, we present the problem of counting magic squares and we focus on the case of multiplicative magic squares of order 4. We give the exact number of normal multiplicative magic squares of order 4 with an original and complete proof, pointing out the role of the action of the symmetric group. Moreover, we provide a new representation for magic squares of order 4. Such representation allows the construction of magic squares in a very simple way, using essentially only five particular 4X4 matrices

ADVANCE OF SMARANDACHE APPROACH TO SOLVING SYSTEMS OF DIOPHANTlNE EQUATIONS

By developing F. Smarandache (algebraic) approach to solving systems of Diophantine equations we elaborate a set of new computative algorithms and analytical formulae, which may be used for fmding numerical solutions of some combinatorial and number-theoretic problems