Some features and predictions of a recently proposed model based on diquark-antidiquark bound states are illustrated. Its ability in accomodating newly discovered charmed resonances around 4 GeV is discussed.

In this paper we consider the existence of nontrivial perfect codes in the Johnson graph J(n, w). We present combinatorial and number theory techniques to provide necessary conditions for existence of such codes and reduce the range of parameters in which 1-perfect and 2-perfect codes may exist.

We will construct an MDS(= the most distance separable) code C which admits a decomposition C = ⊕iCi such that every factor is still MDS. An effective way of decoding will be also discussed.

The Chernoff-Hoeffding bounds are fundamental probabilistic tools. An elementary approach is presented to obtain a Chernoff-type upper-tail bound for the number of prime factors of a random integer in {1, 2, . . . , n}. The method illustrates tail bounds in negatively-correlated settings.

We discuss five ways of proving Chernoff’s bound and show how they lead to different extensions of the basic bound.

Alpha-Hydroxy ketones with an aromatic and aliphatic substituent were prepared with condensation of aromatic and aliphatic aldehydes in the presence of polymer-bound thiazolium salt.

We construct a lot of new [n, 4, d]9 codes whose lengths are close to the Griesmer bound and prove the nonexistence of some linear codes attaining the Griesmer bound using some geometric techniques through projective geometries to determine the exact value of n9(4, d) or to improve the known bound on n9(4, d) for given values of d, where nq(k, d) is the minimum length n for which an [n, k, d]q ...