Natural emergence

Emergence is analyzed by the principle of least action. The supreme law of nature describes diverse systems as actions that evolve from one state to another by consuming free energy in least time. As the system will either gain or lose quanta at the step of evolution, the systemic characteristics after the change of state cannot be reduced to those before the change. The change will invariably entail also a change in inter‐actions, which are flows of energy on paths that integrate ingredient systems to a synergistic system. New qualities will emerge along with opening interactions just as old ones will disappear along with ceasing interactions. The analysis of emergence as a natural process reveals that its irreducible and unpredictable nature does not result from complexity as such but because the natural process itself is molding the surroundings where it is evolving. © 2012 Wiley Periodicals, Inc. Complexity, 2012     

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     

Anisotropic Fourier multipliers and singular integrals for vector-valued functions

We show that an anisotropic Mihlin-type condition on the symbol guarantees the boundedness of the associated Fourier multiplier operator on L ^p (R ⁿ ,X) for 1 < p < ∞ and an arbitrary UMD space X. In many cases, this result can be used as a substitute for the Marcinkiewicz–Lizorkin multiplier theorem, which is invalid in general UMD spaces. An application to anisotropic singular integrals is given. Mathematics Subject Classification (2000) 42B15, 42B20, 46E40