The acquisition of new technology and its impact on a firm's competitive position

The strategic decision concerning the optimal and dynamic acquisition of new technology is examined. The model focuses on a profit maximizing firm that optimally derives its price, level of output, and its level and composition of productive capacity over time. The acquisition of new technology and reduction of existing capacity may occur simultaneously, so that the composition of the firm's productive resources may be upgraded over time. It is assumed that the acquisition of new technology causes a reduction in production costs and a direct increase in the firm's demand. The demand experienced by the firm may be directly increased as a result of acquiring new technology due to benefits such as expanded product-mix or volume capabilities, improved quality of output, or improved customer service (shorter production lead time). In addition, it is shown that demand is indirectly increased due to the reduced production costs that enable the firm to charge a lower price. Therefore, the strategic impact of acquiring new technology is captured, since its effect on future demand and the firm's ability to meet the demand are considered. The importance of capturing the increased demand potential offered by the new technology is demonstrated through the analysis of numerical examples. In addition, the effect on the optimal solution caused by a variety of environmental conditions is examined. For example, the impact of technological innovation is observed by defining (i) the cost of acquiring technology as a decreasing function of time, and (ii) the effectiveness of new technology on reducing operating costs as an increasing function of time.     

Non-Cayley Vertex-Transitive Graphs of Order Twice the Product of Two Odd Primes

For a positive integer n, does there exist a vertex-transitive graph Γ on n vertices which is not a Cayley graph, or, equivalently, a graph Γ on n vertices such that Aut Γ is transitive on vertices but none of its subgroups are regular on vertices? Previous work (by Alspach and Parsons, Frucht, Graver and Watkins, Marusic and Scapellato, and McKay and the second author) has produced answers to this question if n is prime, or divisible by the square of some prime, or if n is the product of two distinct primes. In this paper we consider the simplest unresolved case for even integers, namely for integers of the form n = 2pq, where 2 < q < p, and p and q are primes. We give a new construction of an infinite family of vertex-transitive graphs on 2pq vertices which are not Cayley graphs in the case where p ≡ 1 (mod q). Further, if p ? 1 (mod q), p ≡ q ≡ 3(mod 4), and if every vertex-transitive graph of order pq is a Cayley graph, then it is shown that, either 2pq = 66, or every vertex-transitive graph of order 2pq admitting a transitive imprimitive group of automorphisms is a Cayley graph.     

QSAR modeling of in vitro inhibition of cytochrome P450 3A4

We report the QSAR modeling of cytochrome P450 3A4 (CYP3A4) enzyme inhibition using four large data sets of in vitro data. These data sets consist of marketed drugs and drug-like compounds all tested in four assays measuring the inhibition of the metabolism of four different substrates by the CYP3A4 enzyme. The four probe substrates are benzyloxycoumarin, testosterone, benzyloxyresorufin, and midazolam. We first show that using state-of-the-art QSAR modeling approaches applied to only one of these four data sets does not lead to predictive models that would be useful for in silico filtering of chemical libraries. We then present the development and the testing of a multiple pharmacophore hypothesis (MPH) that is formulated as a conceptual extension of the traditional QSAR approach to modeling the promiscuous binding of a large variety of drugs to CYP3A4. In the simplest form, the MPH approach takes advantage of the multiple substrate data sets and identifies the binding of test compounds as either proximal or distal relative to that of a given substrate. Application of the approach to the in silico filtering of test compounds for potential inhibitors of CYP3A4 is also presented. In addition to an improvement in the QSAR modeling for the inhibition of CYP3A4, the results from this modeling approach provide structural insights into the drug-enzyme interactions. The existence of multiple inhibition data sets in the BioPrint database motivates the original development of the concept of a multiple pharmacophore hypothesis and provides a unique opportunity for formulating alternative strategies of QSAR modeling of the inhibition of the in vitro metabolism of CYP3A4.     

Cationic phosphorus-carbon-pnictogen cages isolobal to [C5R5]+

The cationic cages nido-[C2Bu(t)2P2E]+ (E = As, Sb), which are isolobal to the cyclopentadienyl cation, adopt square based pyramidal structures with the heavy pnictogen atom at the apex; NMR and computational methods have been used to probe the dynamic behaviour of the complexes.     

Calorimetrically measurable enthalpic isotope effect

Calorimetric techniques have revealed that the enthalpy of reaction with water is more exothermic by about 2.2 kcal/mol, for the perdeuteriated naphthalene anion radical (K+C10D8*-(s) + H2O(liq) --> 1/2C10D8H2(s) + 1/2C10D8(s) + KOH(aq)) than it is for the perprotiated system. These results, when coupled with the known enthalpy of electron transfer between naphthalene and its perdeuteriated analogue imply that the heat of hydrogenation of naphthalene decreases by about 1.8 kcal/mol upon perdeuteriation of the naphthalene.     

Group factorisations,uniform automorphisms,and permutation groups of simple diagonal type

We present a new proof, which is independent of the finite simple group classification and applies also to infinite groups, that quasiprimitive permutation groups of simple diagonal type cannot be embedded into wreath products in product action. The proof uses several deep results that concern factorisations of direct products involving subdirect subgroups. We find that such factorisations are controlled by the existence of uniform automorphisms.     

Imprimitive symmetric graphs with cyclic blocks

Let Γ be a graph admitting an arc-transitive subgroup G of automorphisms that leaves invariant a vertex partition with parts of size v≥3. In this paper we study such graphs where: for connected by some edge of Γ, exactly two vertices of B lie on no edge with a vertex of C; and as C runs over all parts of connected to B these vertex pairs (ignoring multiplicities) form a cycle. We prove that this occurs if and only if v=3 or 4, and moreover we give three geometric or group theoretic constructions of infinite families of such graphs.     

Symmetric diameter two graphs with affine-type vertex-quasiprimitive automorphism group

We study the class of G-symmetric graphs Γ with diameter 2, where G is an affine-type quasiprimitive group on the vertex set of Γ. These graphs arise from normal quotient analysis as basic graphs in the class of symmetric diameter 2 graphs. It is known that ${G \cong V \rtimes G_0}$ , where V is a finite-dimensional vector space over a finite field and G ₀ is an irreducible subgroup of GL (V), and Γ is a Cayley graph on V. In particular, we consider the case where ${V = \mathbb {F}_p^d}$ for some prime p and G ₀ is maximal in GL (d, p), with G ₀ belonging to the Aschbacher classes ${\mathcal {C}_2, \mathcal {C}_4, \mathcal {C}_6, \mathcal {C}_7}$ , and ${\mathcal {C}_8}$ . For ${G_0 \in \mathcal {C}_i, i = 2,4,8}$ , we determine all diameter 2 graphs which arise. For ${G_0 \in \mathcal {C}_6, \mathcal {C}_7}$ we obtain necessary conditions for diameter 2, which restrict the number of unresolved cases to be investigated, and in some special cases determine all diameter 2 graphs.