Epistemological and mathematical foundations of quantum mechanics

The concepts of measurement and measurable quantity are discussed. A probabilistic interpretation independent of the arrow of time is recommended and a definition of quantizable physical systems is given. The space of states of information about the physical system is Schwarz space rather than Hilbert space.     

Electrical conductivity as a method to study kinetics of solid-state reactions

A model for changes of electrical conductivity in the course of solid-state reaction has been demonstrated; it describes well the changes in the electrical conductivity of the reacting mixture ZnSe + Cr₂Se₃. The measurement method, the experimental data and the results calculated from the formulas derived in a previous publication have been presented. The experimental and theoretical curves of the temperature dependence of the electrical conductivity have similar shape. The theoretical values differ a little from the experimental ones. These differences allowed us to estimate the character of the changes of the concentration of defects in the product in the course of the reaction. Analysis of the assumptions and the application of the formulas previously presented was made.     

1H, 13C and 15N NMR spectra of ciprofloxacin

1H NMR assignment, including the values of delta(H) and J(H,H) for the cyclopropane moiety, and 13C NMR and 15N NMR spectral data for ciprofloxacin are presented.     

Some new kinds of pseudoprimes

We define some new kinds of pseudoprimes to several bases, which generalize strong pseudoprimes. We call them Sylow -pseudoprimes and elementary Abelian -pseudoprimes. It turns out that every which is a strong pseudoprime to bases 2, 3 and 5, is not a Sylow -pseudoprime to two of these bases for an appropriate prime

We also give examples of strong pseudoprimes to many bases which are not Sylow -pseudoprimes to two bases only, where or

     

Background Independence in Quantum Gravity and Forcing Constructions

A general duality connecting the level of a formal theory and of a metatheory is proposed. Because of the role of natural numbers in a metatheory the existence of a dual theory is conjectured, in which the natural numbers become formal in the theory but in formalizing non-formal natural numbers taken from the dual metatheory these numbers become nonstandard. For any formal theory there may be in principle a dual theory. The dual shape of the lattice of projections over separable Hilbert space is exhibited. The crucial ingredient of this dual theory is set-theoretical (Cohen) forcing. Then, some attempts have been made to exhibit the dual shape of the exotic smooth (small) structures on topological ⁴. There are striking similarities of both pictures. Nonstandard solutions of the equations of motion of 10-dimensional superstring of IIB type are described as a model theoretic extension of standard ones. Based on Brans conjecture one can predict the existence of sources of gravity in 4 dimensions. By their dual origins they carry quantum information as well. The generalized Maldacena conjecture appears naturally, which sheds light on a definition of background independent string theory.     

Weak barrelledness for C(X) spaces

Buchwalter and Schmets reconciled C_c(X) and C_p(X) spaces with most of the weak barrelledness conditions of 1973, but could not determine if -barrelled ⇔ ?^∞-barrelled for C_c(X). The areas grew apart. Full reconciliation with the fourteen conditions adopted by Saxon and Sánchez Ruiz needs their 1997 characterization of Ruess' property (L), which allows us to reduce the C_c(X) problem to its 1973 status and solve it by carefully translating the topology of Kunen (1980) and van Mill (1982) to find the example that eluded Buchwalter and Schmets. The more tractable C_p(X) readily partitions the conditions into just two equivalence classes, the same as for metrizable locally convex spaces, instead of the five required for C_c(X) spaces. Our paper elicits others, soon to appear, that analytically characterize when the Tychonov space X is pseudocompact, or Warner bounded, or when C_c(X) is a df-space (Jarchow's 1981 question).     

Cohen-Macaulay Properties of Thom-Boardman Strata II: The Defining Ideals of {Sigma}i, j

We consider the Zariski closure of Thom–Boardman strata^{i, j} in the jet space for map-germs (Cⁿ, 0) (C^p, 0). We applythe geometric technique of calculating syzygies to the desingularizationof ^{i, j} constructed by Ronga. We investigate when the normalizationof the coordinate ring of ^{i, j} is rational in the cases i =n – p + 1 or i = j = 1. We also consider when these coordinaterings are normal with rational singularities. 2000 MathematicsSubject Classification 13D02, 14B05, 14M05, 14M12, 58C25 (primary),58K20 (secondary).