On making two Steiner triple systems disjoint

We prove that if (S₁, β₁) and (S₂, β₂) are two Steiner triple systems of order v and if S is a set of v points, then there exist two disjoint Steiner triple systems (S, β₁′) and (S, β₂′) with (S₁, β₁) ? (S, β₁′) and (S₂, β₂) ? (S, β₂′).     

On the maximum number of disjoint Steiner triple systems

Let D(v) be the maximum number of pairwise disjoint Steiner triple systems of order v. We prove that D(3v)≥2v+D(v) for every v ≡ 1 or 3 (mod 6), v≥3. As a corollary, we have D(3ⁿ)=3ⁿ-2 for every n≥1.     

A simplification of the proof of the existence of reverse steiner triple systems of order congruent to 1 modulo 24

A Steiner triple system is called reverse if it admits an involutory automorphism with exactly one fixed point. We give a new short construction of reverse Steiner triple systems of order congruent to 1 modulo 24.     

Addendum to: Existence and Uniqueness Theorem for Slant Immersions and its Applications

There are some obscurity and mistake in [2]. In this note we clarify the obscurity by providing a detailed proof and make a correction on the mistake.     

Simulating Perpetuities

A perpetuity is a random variable that can be represented as , where the W _i's are i.i.d. random variables. We study exact random variate generation for perpetuities and discuss the expected complexity. For the Vervaat family, in which 0,U$$ " align="middle" border="0"> uniform [0, 1], all the details of a novel rejection method are worked out. There exists an implementation of our algorithm that only uses uniform random numbers, additions, multiplications and comparisons.     

Fast chromatographic determination of polycyclic aromatic hydrocarbons in aerosol samples from sugar cane burning

The influence of the pH on the complexation equilibria between (S)- or (R)-alprenolol and the cellulase Cel7A was investigated by isothermal titration calorimetry. The results obtained agree with those of previous, similar studies of the same equilibria in which the protein was immobilized on silica particles, packed in a chromatographic column. The association constant and the complexation enthalpy and entropy of the (S)-enantiomer increase with increasing pH. For (R)-alprenolol, the binding is endothermic at all pH values. Thus, for both enantiomers in the pH range 5.5-6.8, the binding is an entropically driven process.