Tables are presented of good ternary and quaternary codes and they are used in the construction of dense sphere packings. Results include 1) tables of the best ternary and quaternary constacyclic codes (including cyclic codes) up to block length 50, 2 ) a class of optimal [ n , 21 codes over GF(q), 3) the ( U + U + w I2u + U I U ) construction, a new ternary code construction technique that can...

The integration of multiple materials with complementary absorptions into a single junction device is regarded as an efficient way to enhance the power conversion efficiency (PCE) of organic solar cells (OSCs). However, because of increased complexity with one more component, only limited high-performance ternary systems have been demonstrated previously. Here we report an efficient ternary ble...

We study pattern avoidance in the context of partial words. The problem of classifying the avoidable binary patterns has been solved, so we move on to ternary and more general patterns. Our results, which are based on morphisms (iterated or not), determine all the ternary patterns’ avoidability indices or at least give bounds for them.

We analyze the weighted height of random tries built from independent strings of i.i.d. symbols on the finite alphabet {1, . . . , d}. The edges receive random weights whose distribution depends upon the number of strings that visit that edge. Such a model covers the hybrid tries of de la Briandais (1959) and the TST of Bentley and Sedgewick (1997), where the search time for a string can be dec...

purpose of this study was to investigate the effect of the presence of the water soluble polymers viz hpmc, pvp and peg 6000 on aqueous solubility and complexation abilities of felodipine with or without presence of β-cyclodextrin (βcd) and hpβcd by phase solubility studies. the data revealed the initial increase in drug solubility followed by plateau in the presence of relatively low polymer c...

We study a construction of the Mathieu group M12 using a game reminiscent of Loyd’s “15-puzzle”. The elements of M12 are realized as permutations on 12 of the 13 points of the finite projective plane of order 3. There is a natural extension to a “pseudogroup” M13 acting on all 13 points, which exhibits a limited form of sextuple transitivity. Another corollary of the construction is a metric, a...

In this paper, the optimality of ternary arithmetic is investigated under strict mathematical formulation. The arithmetic systems are presented in generic form, as the means to encode numeric values, and the choice of radix is asserted as the main parameter to assess the efficiency of the representation, in terms of information compactness and estimated implementation cost in hardware. Using pr...

We consider the problem of classifying all positive-definite integer-valued quadratic forms that represent all positive odd integers. Kaplansky considered this problem for ternary forms, giving a list of 23 candidates, and proving that 19 of those represent all positive odds. (Jagy later dealt with a 20th candidate.) Assuming that the remaining three forms represent all positive odds, we prove ...

The analytical theory of one dimensional, dispersion free miscible displacement of oil by injection gas with nc component has shown that: the MMP is the lowest pressure at which any one of the initial oil, injection gas or crossover key tie lines becomes critical, which means that its length approaches to zero. In this paper, we propose a method for a solving multi component syst...