The partition bound introduced in [4] is a way to prove lower bounds in classical communication and query complexity. While the partition bound provides a strong and general way to prove lower bounds, it remains open how tight the bounds obtained from this method are. In this work we give quadratically tight lower bounds via a strengthened version of the partition bound, which we call the publi...

In this note, we define the concepts of admissible relation and admissible partition for an arbitrary BL-general fuzzy automaton.In particular, a connection between the admissible partition and the quotient BL-general fuzzy automaton is presented.It is shown that if we use the maximal admissible partition, then we obtain a quotient BL-general fuzzy automaton and this quotient is minimal. Finall...

the distribution behavior of ofloxacin enantiomers was examined in the aqueous and organic solvent of a two-phase system containing chiral selector l-tartarate. the effect of extraction equilibrium time, buffer ph, organic solvents and length of alkyl chain of l-tartarate on the partition coefficients and enantioselectivity of racemic ofloxacin were investigated, respectively. the l-tartarate f...

We prove that for any partition (λ1, . . . , λd2) of size dm there exists k ≥ 1 such that the tensor square of the irreducible representation of the symmetric group Skdm with respect to the rectangular partition (km, . . . , km) contains the irreducible representation corresponding to the stretched partition (kλ1, . . . , kλd2). We also prove a related approximate version of this statement in w...

We propose an information-theoretic clustering approach that incorporates a pre-known partition of the data, aiming to identify common clusters that cut across the given partition. In the standard clustering setting the formation of clusters is guided by a single source of feature information. The newly utilized pre-partition factor introduces an additional bias that counterbalances the impact ...

A cocoloring of a graph G is a partition of the vertex set of G such that each set of the partition is either a clique or an independent set in G. Some special cases of the minimum cocoloring problem are of particular interest. We provide polynomial-time algorithms to approximate a minimum cocoloring on graphs, partially ordered sets and sequences. In particular, we obtain an efficient algorith...

SMARANDACHE TERMS AND FACTOR PARTITIONS (Amarnath Murthy ,S.E. (E & T), Well'Logging Services,Oil And Natural Gas Corporation Ltd. ,Sabarmati, Ahmedbad, India380005.) ABSTRACT: In [1] we define SMARANDACHE FACTOR PARTITION FUNCTION (SFP) , as follows: Let U1, U2 , U3 , ... Ur be a set of r natural numbers and P1, P2, P3 , ... Pr be arbitrarily chosen distinct primes then F(u1 , U2 , U3 , ... u ...