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

Thermodynamical Consistent Modeling and Analysis of Nematic Liquid Crystal Flows

The general Ericksen-Leslie system for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal model is then investigated analytically. A fairly complete dynamic theory is developed by analyzing these systems as quasilinear parabolic evolution equations in an $L^p-L^q$-setting. First, the existence of a unique, local strong solution is proved. It is then shown that this solution extends to a global strong solution provided the initial data are close to an equilibrium or the solution is eventually bounded in the natural norm of the underlying state space. In these cases, the solution converges exponentially to an equilibrium in the natural state manifold

Spectral asymmetry for bag boundary conditions

We give an expression, in terms of boundary spectral functions, for the spectral asymmetry of the Euclidean Dirac operator in two dimensions, when its domain is determined by local boundary conditions, and the manifold is of product type. As an application, we explicitly evaluate the asymmetry in the case of a finite-length cylinder, and check that the outcome is consistent with our general result. Finally, we study the asymmetry in a disk, which is a non-product case, and propose an interpretation.Comment: Some minor changes. To appear in Journal of Physics A: Mathematical and Genera

Emission projections 2008-2012 versus National Allocation Plans II

We compare the national allocation plans (NAPs), proposed and submitted by EU Member States as of October 2006, with our estimations for CO2 emissions by the installations covered by these NAPs. The collective allocations proposed under phase II NAPs exceed the historic trend of emissions extrapolated forward. Using our projections we find, depending on uncertainty in fuel prices, economic growth rates, performance of the non-power sector and CDM/JI availability, a 15% chance of a ‘dead market’ with emissions below cap even at zero prices. With an expected inflow of committed CDM/JI credits of 100 MtCO2/year, allowance supply will exceed demand in 50% of cases without any carbon price, and in 80% of our €20/tCO2 scenarios. Banking of allowances towards post-2012 conditions could create additional demand, but this is difficult to anticipate and conditional on policy evolution. The proposed phase II NAPs would result in low prices and only small volumes of CDM/JI would enter the EU ETS. CDM/JI would almost exclusively be public-sector funded, placing the cost of Kyoto compliance entirely upon governments

Electrophysiological effects of nicotinic and electrical stimulation of intrinsic cardiac ganglia in the absence of extrinsic autonomic nerves in the rabbit heart

BackgroundThe intrinsic cardiac nervous system is a rich network of cardiac nerves that converge to form distinct ganglia and extend across the heart and is capable of influencing cardiac function.ObjectiveThe goals of this study were to provide a complete picture of the neurotransmitter/neuromodulator profile of the rabbit intrinsic cardiac nervous system and to determine the influence of spatially divergent ganglia on cardiac electrophysiology.MethodsNicotinic or electrical stimulation was applied at discrete sites of the intrinsic cardiac nerve plexus in the Langendorff-perfused rabbit heart. Functional effects on sinus rate and atrioventricular conduction were measured. Immunohistochemistry for choline acetyltransferase (ChAT), tyrosine hydroxylase, and/or neuronal nitric oxide synthase (nNOS) was performed using whole mount preparations.ResultsStimulation within all ganglia produced either bradycardia, tachycardia, or a biphasic brady-tachycardia. Electrical stimulation of the right atrial and right neuronal cluster regions produced the largest chronotropic responses. Significant prolongation of atrioventricular conduction was predominant at the pulmonary vein-caudal vein region. Neurons immunoreactive (IR) only for ChAT, tyrosine hydroxylase, or nNOS were consistently located within the limits of the hilum and at the roots of the right cranial and right pulmonary veins. ChAT-IR neurons were most abundant (1946 ± 668 neurons). Neurons IR only for nNOS were distributed within ganglia.ConclusionStimulation of intrinsic ganglia, shown to be of phenotypic complexity but predominantly of cholinergic nature, indicates that clusters of neurons are capable of independent selective effects on cardiac electrophysiology, therefore providing a potential therapeutic target for the prevention and treatment of cardiac disease

A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

An approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions

In this paper, we provide an approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions and discuss the application of this approach in some physical problems. Concretely, we construct the equations for these three quantities; this allows us to achieve them by directly solving equations. In order to construct the equations, we introduce shifted local one-loop effective actions, shifted local vacuum energies, and local spectral counting functions. We solve the equations of one-loop effective actions, vacuum energies, and spectral counting functions for free massive scalar fields in $\mathbb{R}^{n}$, scalar fields in three-dimensional hyperbolic space $H_{3}$ (the Euclidean Anti-de Sitter space $AdS_{3}$), in $H_{3}/Z$ (the geometry of the Euclidean BTZ black hole), and in $S^{1}$, and the Higgs model in a $(1+1)$-dimensional finite interval. Moreover, in the above cases, we also calculate the spectra from the counting functions. Besides exact solutions, we give a general discussion on approximate solutions and construct the general series expansion for one-loop effective actions, vacuum energies, and spectral counting functions. In doing this, we encounter divergences. In order to remove the divergences, renormalization procedures are used. In this approach, these three physical quantities are regarded as spectral functions in the spectral problem.Comment: 37 pages, no figure. This is an enlarged and improved version of the paper published in JHE

System design and integration analysis for the Integrated Booking System (IBS)

In accordance with tasking for the Military Traffic Management Command (MTMC), the Oak Ridge National Laboratory (ORNL) investigated design and integration issues and identified specific options for MTMC`s Integrated Booking System (IBS). Three system designs are described: the single-server, stand-alone IBS; the area-based IBS; and the fully-integrated IBS. Because of the functional and technical requirements of IBS and because of the MTMC strategy of sharing resources, ORNL recommends the fully-integrated design. This option uses the excess computing resources provided through the architectural components of the Integrated Cargo Database (ICDB) and provides visibility over the cargo record from initial request through final delivery

Wodzicki Residue for Operators on Manifolds with Cylindrical Ends

We define the Wodzicki Residue TR(A) for A in a space of operators with double order (m_1,m_2). Such operators are globally defined initially on R^n and then, more generally, on a class of non-compact manifolds, namely, the manifolds with cylindrical ends. The definition is based on the analysis of the associate zeta function. Using this approach, under suitable ellipticity assumptions, we also compute a two terms leading part of the Weyl formula for a positive selfadjoint operator belonging the mentioned class in the case m_1=m_2.Comment: 24 pages, picture changed, added references, corrected typo

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