Vanishing of derived limits of non-standard inverse systems

It is proved that for certain non-standard versions of inverse systems G of R-modules, we have for n>0.The result is applied to define a reasonably canonical non-standard resolution for an arbitrary inverse system G of R-modules, such that the application of the inverse limit functor yields a complex whose cohomology groups are isomorphic to the derived limits, limn. Furthermore, the non-standard resolution gives also the maps limng, and the connecting homomorphisms to a reasonable degree.We also prove that for miscellaneous types of inverse systems H of modules, the system H is a direct summand of .     

Hydrolytic reactions of diribonucleoside 3',5'-(3'-N-phosphoramidates): kinetics and mechanisms for the P-O and P-N bond cleavage of 3'-amino-3'-deoxyuridylyl-3',5'-uridine

Hydrolytic reactions of 3'-amino-3'-deoxyuridylyl-3',5'-uridine (2a), an analogue of uridylyl-3',5'-uridine having the 3'-bridging oxygen replaced with nitrogen, have been followed by RP HPLC over a wide pH range. The only reaction taking place under alkaline conditions (pH > 9) is hydroxide ion-catalyzed hydrolysis (first-order in [OH(-)]) to a mixture of 3'-amino-3'-deoxyuridine 3'-phosphoramidate (7) and uridine (4). The reaction proceeds without detectable accumulation of any intermediates. At pH 6-8, a pH-independent formation of 3'-amino-3'-deoxyuridine 2'-phosphate (3) competes with the base-catalyzed cleavage. Both 3 and in particular 7 are, however, rather rapidly dephosphorylated under these conditions to 3'-amino-3'-deoxyuridine (5). In all likelihood, both 3 and 7 are formed by an intramolecular nucleophilic attack of the 2'-hydroxy function on the phosphorus atom, giving a phosphorane-like intermediate or transition state. Under moderately acidic conditions (pH 2-6), the predominant reaction is acid-catalyzed cleavage of the P-N3' bond (first-order in [H(+)]) that yields an equimolar mixture of 5 and uridine 5'-phosphate (6). The reaction is proposed to proceed without intramolecular participation of the neighboring 2'-hydroxyl group. Under more acidic conditions (pH < 2), hydrolysis to 3 and 4 starts to compete with the cleavage of the P-N bond, and this reaction is even the fastest one at pH < 1. Formation of 2'-O,3'-N-cyclic phosphoramidate as an intermediate appears probable, although its appearance cannot be experimentally verified. The rate constants for various partial reactions have been determined. The reaction mechanisms and the effect that replacing the 3'-oxygen with nitrogen has on the behavior of the phosphorane intermediate are discussed.     

A New Definition of A Priori Knowledge: In Search of a Modal Basis

In this paper I will offer a novel understanding of a priori knowledge. My claim is that the sharp distinction that is usually made between a priori and a posteriori knowledge is groundless. It will be argued that a plausible understanding of a priori and a posteriori knowledge has to acknowledge that they are in a constant bootstrapping relationship. It is also crucial that we distinguish between a priori propositions that hold in the actual world and merely possible, non-actual a priori propositions, as we will see when considering cases like Euclidean geometry. Furthermore, contrary to what Kripke seems to suggest, a priori knowledge is intimately connected with metaphysical modality, indeed, grounded in it. The task of a priori reasoning, according to this account, is to delimit the space of metaphysically possible worlds in order for us to be able to determine what is actual.     

Conical square function estimates in UMD Banach spaces and applications to H ∞-functional calculi

We study conical square function estimates for Banach-valued functions and introduce a vector-valued analogue of the Coifman-Meyer-Stein tent spaces. Following recent work of Auscher-M^cIntosh-Russ, the tent spaces in turn are used to construct a scale of vector-valued Hardy spaces associated with a given bisectorial operator A with certain off-diagonal bounds such that A always has a bounded H ^∞-functional calculus on these spaces. This provides a new way of proving functional calculus of A on the Bochner spaces L ^p (ℝ ⁿ ; X) by checking appropriate conical square function estimates and also a conical analogue ofBourgain’s extension of the Littlewood-Paley theory to the UMD-valued context. Even when X = ℂ, our approach gives refined p-dependent versions of known results.     

Diagonalization and representation results for nonpositive sesquilinear form measures

We study decompositions of operator measures and more general sesquilinear form measures E into linear combinations of positive parts, and their diagonal vector expansions. The underlying philosophy is to represent E as a trace class valued measure of bounded variation on a new Hilbert space related to E. The choice of the auxiliary Hilbert space fixes a unique decomposition with certain properties, but this choice itself is not canonical. We present relations to Naimark type dilations and direct integrals.     

Parametrization of reflection groups acting in a disk

We study parametrizations of conjugacy classes of reflection groups acting in a disk or a half-plane. The most natural parametrization can be expressed in terms of multipliers of the transformations belonging to the group in question. We call such a parametrization geometric, and we study the problem of finding a minimal geometric parametrization. Our methods are completely elementary and the results are general in that the groups under consideration need not be discontinuous.Subject classification: primary 30F35, secondary 32G13, 30F10     

Information-theoretic approaches to branching in search

Deciding what question to branch on at each node is a key element of search algorithms. In this paper, we describe a collection of techniques for branching decisions that are motivated from an information-theoretic perspective. The idea is to drive the search to reduce the uncertainty (entropy) in the current subproblem. We present four families of methods for branch question selection in mixed integer programming that use this idea. In the first, a variable to branch on is selected based on lookahead. This method performs comparably to strong branching on MIPLIB, and better than strong branching on hard real-world procurement optimization instances on which CPLEX’s default strong branching outperforms CPLEX’s default branching strategy. The second family combines this idea with strong branching. The third family does not use lookahead, but instead exploits the tie between indicator variables and the variables they govern. This significantly outperforms the state-of-the-art branching strategies on both combinatorial procurement problems and facility location problems. The fourth family concerns branching using carefully constructed linear inequality constraints over sets of variables.     

Still Elusive – Pd(II)-Mediated Base Pairing by an Acetophenone Oxime Palladacycle within 15N-Labelled Double-Helical Oligonucleotides

Both α and β anomers of an acetophenone C-nucleoside were synthesized and incorporated in the middle of short oligodeoxynucleotides. The ketone oligonucleotides were converted to ¹⁵N-labelled oxime oligonucleotides by treatment with ¹⁵N-hydroxylamine and, finally, cyclopalladated by treatment with lithium tetrachloropalladate. Comparison of the UV melting profiles of duplexes bearing the β anomer of either the palladacyclic or the metal-free oxime C-nucleoside suggested formation of a stable Pd(II)-mediated base pair, especially with adenine or thymine as the base pairing partner. Melting profiles of the corresponding duplexes bearing the α anomer were much more convoluted, precluding meaningful comparison. ¹⁵N NMR spectra were obtained for the β anomeric oxime oligonucleotide as well as its palladacyclic derivative but the signals unfortunately diminished below detection limit when the latter was hybridized with a complementary strand placing a ¹⁵N3-labelled thymine opposite to the palladacyclic residue.