Smeared heat-kernel coefficients on the ball and generalized cone

We consider smeared zeta functions and heat-kernel coefficients on the bounded, generalized cone in arbitrary dimensions. The specific case of a ball is analysed in detail and used to restrict the form of the heat-kernel coefficients $A_n$ on smooth manifolds with boundary. Supplemented by conformal transformation techniques, it is used to provide an effective scheme for the calculation of the $A_n$. As an application, the complete $A_{5/2}$ coefficient is given.Comment: 23 pages, JyTe

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

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

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

Schrödinger operators with δ and δ′-potentials supported on hypersurfaces

Self-adjoint Schrödinger operators with δ and δ′-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity results on the functions in their domains are obtained, and analogues of the Birman–Schwinger principle and a variant of Krein’s formula are shown. Furthermore, Schatten–von Neumann type estimates for the differences of the powers of the resolvents of the Schrödinger operators with δ and δ′-potentials, and the Schrödinger operator without a singular interaction are proved. An immediate consequence of these estimates is the existence and completeness of the wave operators of the corresponding scattering systems, as well as the unitary equivalence of the absolutely continuous parts of the singularly perturbed and unperturbed Schrödinger operators. In the proofs of our main theorems we make use of abstract methods from extension theory of symmetric operators, some algebraic considerations and results on elliptic regularity

Wage returns to university disciplines in Greece: are Greek Higher Education degrees Trojan Horses?

This paper examines the wage returns to qualifications and academic disciplines in the Greek labour market. Exploring wage responsiveness across various degree subjects in Greece is interesting, as it is characterised by high levels of graduate unemployment, which vary considerably by field of study, and relatively low levels of wage flexibility. Using micro-data from recently available waves (2002-2003) of the Greek Labour Force Survey (LFS), the returns to academic disciplines are estimated by gender and public/private sector. Quantile regressions and cohort interactions are also used to capture the heterogeneity in wage returns across the various disciplines. The results show considerable variation in wage premiums across the fields of study, with lower returns for those that have a marginal role to play in an economy with a rising services/shrinking public sector. Educational reforms that pay closer attention to the future prospects of university disciplines are advocated

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

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

New Kernels in Quantum Gravity

Recent work in the literature has proposed the use of non-local boundary conditions in Euclidean quantum gravity. The present paper studies first a more general form of such a scheme for bosonic gauge theories, by adding to the boundary operator for mixed boundary conditions of local nature a two-by-two matrix of pseudo-differential operators with pseudo-homogeneous kernels. The request of invariance of such boundary conditions under infinitesimal gauge transformations leads to non-local boundary conditions on ghost fields. In Euclidean quantum gravity, an alternative scheme is proposed, where non-local boundary conditions and the request of their complete gauge invariance are sufficient to lead to gauge-field and ghost operators of pseudo-differential nature. The resulting boundary conditions have a Dirichlet and a pseudo-differential sector, and are pure Dirichlet for the ghost. This approach is eventually extended to Euclidean Maxwell theory.Comment: 19 pages, plain Tex. In this revised version, section 5 is new, section 3 is longer, and the presentation has been improve