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

Realizations of Differential Operators on Conic Manifolds with Boundary

We study the closed extensions (realizations) of differential operators subject to homogeneous boundary conditions on weighted L_p-Sobolev spaces over a manifold with boundary and conical singularities. Under natural ellipticity conditions we determine the domains of the minimal and the maximal extension. We show that both are Fredholm operators and give a formula for the relative index.Comment: 41 pages, 1 figur

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

Local regularity for fractional heat equations

We prove the maximal local regularity of weak solutions to the parabolic problem associated with the fractional Laplacian with homogeneous Dirichlet boundary conditions on an arbitrary bounded open set $\Omega\subset\mathbb{R}^N$. Proofs combine classical abstract regularity results for parabolic equations with some new local regularity results for the associated elliptic problems.Comment: arXiv admin note: substantial text overlap with arXiv:1704.0756

Improved estimation of glomerular filtration rate (GFR) by comparison of eGFRcystatin C and eGFRcreatinine

Objective. GFR-prediction equations based upon cystatin C and creatinine have better diagnostic performance in estimating GFR than equations based upon only one of the two markers. The present work concerns in what way a comparison between separate estimations of GFR based upon cystatin C (eGFR(cystatin C)) or creatinine (eGFR(creatinine)) can be used to evaluate the diagnostic performance of a combined cystatin C-and creatinine-based estimation of GFR. Methods. The difference between eGFR(cystatin C) and eGFR(creatinine) was compared with measured GFR (iohexol clearance) and a combined cystatin C- and creatinine-based estimation of GFR in a Swedish-Caucasian cohort of 857 adult patients. Results. A difference between eGFR(cystatin C) and eGFR(creatinine) of >= 40% indicated a markedly reduced diagnostic performance of the combined cystatin C- and creatinine-based estimation of GFR. Conclusion. Comparison of the agreement between eGFR(cystatin C) and eGFR(creatinine) can be used to evaluate the diagnostic performance of combined cystatin C-and creatinine-based estimations of GFR. If 'threshold values' for discordance are exceeded, it must be considered whether the clinical context requires the use of an invasive gold standard method to measure GFR. In some clinical contexts either creatinine or cystatin C are known to be invalidated as markers of GFR and in these situations the use of only the cystatin C-or the creatinine-based GFR estimate should be considered when the 'threshold values' are exceeded

Lack of Assortative Mating for Tail, Body Size, or Condition in the Elaborate Monomorphic Turquoise-Browed Motmot (\u3cem\u3eEumomota superciliosa\u3c/em\u3e)

Elaborate male and female plumage can be maintained by mutual sexual selection and function as a mate-choice or status signal in both sexes. Both male and female Turquoise-browed Motmot (Eumomota superciliosa) have long tails that terminate in widened blue-and-black rackets that appear to hang, unattached, below the body of the bird. I tested whether mutual sexual selection maintains the Turquoise-browed Motmot’s elaborate tail plumage by testing the prediction that mating occurs in an assortative manner for tail plumage. I also tested whether assortative mating occurs for body size, a potential measure of dominance, and for phenotypic condition, a measure of individual quality. Assortative mating was measured (1) within all pairs in the study population, (2) within newly formed pairs, and (3) within experimentally induced pairs that formed after removal of females from stable pairs. Assortative mating was not found for tail plumage, body size, or phenotypic condition in any of these samples. Therefore, there was no support for the “mutual sexual selection” hypothesis. I discuss the hypothesis that the tail is sexually selected in males only, and that natural selection accounts for the evolutionary maintenance of the elaborate female tail. La existencia de plumaje elaborado en los machos y las hembras puede ser mantenida por selecci´on sexual mutua, y funcionar como una se˜nal para la selecci´on de parejas o del estatus de los individuos en ambos sexos. Tanto los machos como las hembras de la especie Eumomota superciliosa tienen colas largas que terminan en unas raquetas ensanchadas de color azul y negro, que parecen colgar debajo del cuerpo de las aves. En este estudio prob´e si el plumaje elaborado de la cola de esta especie es mantenido mediante selecci´on sexual mutua, evaluando la predicci´on de que el apareamiento es asociativo con respecto al plumaje de la cola. Tambi´en prob´e si existe apareamiento asociativo con respecto al tama˜no (una medida potencial de la dominancia) y con respecto a la condici´on fenot´ıpica (una medida de la calidad de los individuos). El apareamiento asociativo fue medido para todas las parejas de la poblaci´on de estudio, para parejas formadas recientemente y para parejas cuya formaci´on fue inducida experimentalmente mediante la remoci´on de las hembras de parejas estables. No se encontr´o apareamiento asociativo con respecto al plumaje de la cola, al tama˜no corporal, ni a la condici´on fenot´ıpica en ninguna de estas muestras. Por lo tanto, no existi´o respaldo para la hip´otesis de selecci´on sexual mutua. Discuto la hip´otesis que plantea que la cola es objeto de selecci´on sexual s´olo en los machos, y que la selecci´on natural permite explicar el mantenimiento evolutivo de la cola elaborada en las hembras

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

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