Foundations for Relativistic Quantum Theory I: Feynman's Operator Calculus and the Dyson Conjectures

In this paper, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson's second conjecture for QED. In addition, we show that the expansion may be considered exact to any finite order by producing the remainder term. This implies that every nonperturbative solution has a perturbative expansion. Using a physical analysis of information from experiment versus that implied by our models, we reformulate our theory as a sum over paths. This allows us to relate our theory to Feynman's path integral, and to prove Dyson's first conjecture that the divergences are in part due to a violation of Heisenberg's uncertainly relations

A class of well-posed parabolic final value problems

This paper focuses on parabolic final value problems, and well-posedness is proved for a large class of these. The clarification is obtained from Hilbert spaces that characterise data that give existence, uniqueness and stability of the solutions. The data space is the graph normed domain of an unbounded operator that maps final states to the corresponding initial states. It induces a new compatibility condition, depending crucially on the fact that analytic semigroups always are invertible in the class of closed operators. Lax--Milgram operators in vector distribution spaces constitute the main framework. The final value heat conduction problem on a smooth open set is also proved to be well posed, and non-zero Dirichlet data are shown to require an extended compatibility condition obtained by adding an improper Bochner integral.Comment: 16 pages. To appear in "Applied and numerical harmonic analysis"; a reference update. Conference contribution, based on arXiv:1707.02136, with some further development

Matrix-assisted laser desorption ionization hydrogen/deuterium exchange studies to probe peptide conformational changes

AbstractHydrogen/deuterium (H/D) exchange chemistry monitored by matrix-assisted laser desorption ionization time-of-flight (MALDI-TOF) mass spectrometry is used to study solution phase conformational changes of bradykinin, α-melanocyte stimulating hormone, and melittin as water is added to methanol-d4, acetonitrile, and isopropanol-d8 solutions. The results are interpreted in terms of a preference for the peptides to acquire more compact conformations in organic solvents as compared to the random conformations. Our interpretation is supported by circular dichroism spectra of the peptides in the same solvent systems and by previously published structural data for the peptides. These results demonstrate the utility of MALDI-TOF as a method to monitor the H/D exchange chemistry of peptides and investigations of solution-phase conformations of biomolecules

Perturbations of Noise: The origins of Isothermal Flows

We make a detailed analysis of both phenomenological and analytic background for the "Brownian recoil principle" hypothesis (Phys. Rev. A 46, (1992), 4634). A corresponding theory of the isothermal Brownian motion of particle ensembles (Smoluchowski diffusion process approximation), gives account of the environmental recoil effects due to locally induced tiny heat flows. By means of local expectation values we elevate the individually negligible phenomena to a non-negligible (accumulated) recoil effect on the ensemble average. The main technical input is a consequent exploitation of the Hamilton-Jacobi equation as a natural substitute for the local momentum conservation law. Together with the continuity equation (alternatively, Fokker-Planck), it forms a closed system of partial differential equations which uniquely determines an associated Markovian diffusion process. The third Newton law in the mean is utilised to generate diffusion-type processes which are either anomalous (enhanced), or generically non-dispersive.Comment: Latex fil

Fourier transform ion cyclotron resonance mass spectrometric detection of small Ca2+-induced conformational changes in the regulatory domain of human cardiac troponin C

AbstractTroponin C (TnC), a calcium-binding protein of the thin filament of muscle, plays a regulatory role in skeletal and cardiac muscle contraction. NMR reveals a small conformational change in the cardiac regulatory N-terminal domain of TnC (cNTnC) on binding of Ca2+ such that the total exposed hydrophobic surface area increases very slightly from 3090 ± 86 Å2 for apo-cNTnC to 3108 ± 71 Å2 for Ca2+-cNTnC. Here, we show that measurement of solvent accessibility for backbone amide protons by means of solution-phase hydrogen/deuterium (H/D) exchange followed by pepsin digestion, high-performance liquid chromatography, and electrospray ionization high-field (9.4 T) Fourier transform Ion cyclotron resonance mass spectrometry is sufficiently sensitive to detect such small ligand binding-induced conformational changes of that protein. The extent of deuterium incorporation increases significantly on binding of Ca2+ for each of four proteolytic segments derived from pepsin digestion of the apo- and Ca2+-saturated forms of cNTnC. The present results demonstrate that H/D exchange monitored by mass spectrometry can be sufficiently sensitive to detect and identify even very small conformational changes in proteins, and should therefore be especially informative for proteins too large (or too insoluble or otherwise intractable) for NMR analysis

Архетип свобода у контексті французької політичної теорії та історії

Розглянуто сучасні підходи щодо аналізу політичної ментальності. У межах політологічного аналізу окреслено коло проблем, які потребують вирішення з використанням підходів психології. Зроблено висновок про те, що архетип “свобода” становить важливий елемент політичної ментальності французів.Modern approaches of analysis of political mentality are considered. Within the limits of political science analysis outlined circle of problems which need decision with the use of approaches of psychology. A conclusion is done that archetype freedom makes the important element of political mentality of French’s