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

Ellipticity Conditions for the Lax Operator of the KP Equations

The Lax pseudo-differential operator plays a key role in studying the general set of KP equations, although it is normally treated in a formal way, without worrying about a complete characterization of its mathematical properties. The aim of the present paper is therefore to investigate the ellipticity condition. For this purpose, after a careful evaluation of the kernel with the associated symbol, the majorization ensuring ellipticity is studied in detail. This leads to non-trivial restrictions on the admissible set of potentials in the Lax operator. When their time evolution is also considered, the ellipticity conditions turn out to involve derivatives of the logarithm of the tau-function.Comment: 21 pages, plain Te

Isobutylmethylxanthine fails to stimulate chloride secretion in cystic fibrosis airway epithelia.

It has been proposed that a combination of an activated adenylyl cyclase and a high concentration of a phosphodiesterase inhibitor (isobutylmethylxanthine [IBMX], 5 mM) stimulates Cl- secretion mediated by the heterologously expressed cystic fibrosis transmembrane regulator protein carrying the most common cystic fibrosis (CF) mutation (delta F508). We tested whether Cl- secretion could be stimulated by this protocol in vitro and in vivo in CF airway epithelia expressing endogenous delta F508 CFTR protein. In cultured airway preparations, forskolin (a direct adenylyl cyclase activator) stimulated Cl- secretion in amiloride-pretreated normal (delta Isc = 7.1 +/- 1.7 microA.cm-2) but not CF tissues (delta Isc = -02 +/- 0.1 microA.cm-2). Unexpectedly, IBMX partially inhibited the forskolin-induced Cl- secretion in normal tissues; IBMX addition had no effect on CF tissues. Direct measurements of cell cAMP concentrations revealed that 0.1 mM IBMX and forskolin produced the maximum levels of cell cAMP levels attainable with this drug combination, and 5 mM IBMX was without further effect. The combination of forskolin (10(-5) M) and isoproterenol, an adenylyl cyclase activator (10(-5) M), produced approximately 3 times higher levels of cAMP than forskolin/IBMX but also did not induce Cl- secretion in CF tissues

Strong ellipticity and spectral properties of chiral bag boundary conditions

We prove strong ellipticity of chiral bag boundary conditions on even dimensional manifolds. From a knowledge of the heat kernel in an infinite cylinder, some basic properties of the zeta function are analyzed on cylindrical product manifolds of arbitrary even dimension.Comment: 16 pages, LaTeX, References adde

Klein-Gordon Solutions on Non-Globally Hyperbolic Standard Static Spacetimes

We construct a class of solutions to the Cauchy problem of the Klein-Gordon equation on any standard static spacetime. Specifically, we have constructed solutions to the Cauchy problem based on any self-adjoint extension (satisfying a technical condition: "acceptability") of (some variant of) the Laplace-Beltrami operator defined on test functions in an $L^2$-space of the static hypersurface. The proof of the existence of this construction completes and extends work originally done by Wald. Further results include the uniqueness of these solutions, their support properties, the construction of the space of solutions and the energy and symplectic form on this space, an analysis of certain symmetries on the space of solutions and of various examples of this method, including the construction of a non-bounded below acceptable self-adjoint extension generating the dynamics

Unravelling the mechanisms of vibrational relaxation in solution

We present a systematic study of the mode-specific vibrational relaxation of NO(2) in six weakly-interacting solvents (perfluorohexane, perfluoromethylcyclohexane, perfluorodecalin, carbon tetrachloride, chloroform, and d-chloroform), chosen to elucidate the dominant energy transfer mechanisms in the solution phase. Broadband transient vibrational absorption spectroscopy has allowed us to extract quantum state-resolved relaxation dynamics of the two distinct NO(2) fragments produced from the 340 nm photolysis of N(2)O(4) → NO(2)(X) + NO(2)(A) and their separate paths to thermal equilibrium. Distinct relaxation pathways are observed for the NO(2) bending and stretching modes, even at energies as high as 7000 cm(–1) above the potential minimum. Vibrational energy transfer is governed by different interaction mechanisms in the various solvent environments, and proceeds with timescales ranging from 20–1100 ps. NO(2) relaxation rates in the perfluorocarbon solvents are identical despite differences in acceptor mode state densities, infrared absorption cross sections, and local solvent structure. Vibrational energy is shown to be transferred to non-vibrational solvent degrees of freedom (V-T) through impulsive collisions with the perfluorocarbon molecules. Conversely, NO(2) relaxation in chlorinated solvents is reliant on vibrational resonances (V-V) while V-T energy transfer is inefficient and thermal excitation of the surrounding solvent molecules inhibits faster vibrational relaxation through direct complexation. Intramolecular vibrational redistribution allows the symmetric stretch of NO(2) to act as a gateway for antisymmetric stretch energy to exit the molecule. This study establishes an unprecedented level of detail for the cooling dynamics of a solvated small molecule, and provides a benchmark system for future theoretical studies of vibrational relaxation processes in solution

The hybrid spectral problem and Robin boundary conditions

The hybrid spectral problem where the field satisfies Dirichlet conditions (D) on part of the boundary of the relevant domain and Neumann (N) on the remainder is discussed in simple terms. A conjecture for the C_1 coefficient is presented and the conformal determinant on a 2-disc, where the D and N regions are semi-circles, is derived. Comments on higher coefficients are made. A hemisphere hybrid problem is introduced that involves Robin boundary conditions and leads to logarithmic terms in the heat--kernel expansion which are evaluated explicitly.Comment: 24 pages. Typos and a few factors corrected. Minor comments added. Substantial Robin additions. Substantial revisio

Forehead reflectance photoplethysmography to monitor heart rate: preliminary results from neonatal patients

Around 5%–10% of newborn babies require some form of resuscitation at birth and heart rate (HR) is the best guide of efficacy. We report the development and first trial of a device that continuously monitors neonatal HR, with a view to deployment in the delivery room to guide newborn resuscitation. The device uses forehead reflectance photoplethysmography (PPG) with modulated light and lock-in detection. Forehead fixation has numerous advantages including ease of sensor placement, whilst perfusion at the forehead is better maintained in comparison to the extremities. Green light (525 nm) was used, in preference to the more usual red or infrared wavelengths, to optimize the amplitude of the pulsatile signal. Experimental results are presented showing simultaneous PPG and electrocardiogram (ECG) HRs from babies (n = 77), gestational age 26–42 weeks, on a neonatal intensive care unit. In babies ≥32 weeks gestation, the median reliability was 97.7% at ±10 bpm and the limits of agreement (LOA) between PPG and ECG were +8.39 bpm and −8.39 bpm. In babies <32 weeks gestation, the median reliability was 94.8% at ±10 bpm and the LOA were +11.53 bpm and −12.01 bpm. Clinical evaluation during newborn deliveries is now underway