Some examples of exponentially harmonic maps

The aim of this paper is to study some examples of exponentially harmonic maps. We study such maps firstly on flat euclidean and Minkowski spaces and secondly on Friedmann-Lema\^ itre universes. We also consider some new models of exponentially harmonic maps which are coupled with gravity which happen to be based on a generalization of the lagrangian for bosonic strings coupled with dilatonic field.Comment: 16 pages, 5 figure

A Mass Bound for Spherically Symmetric Black Hole Spacetimes

Requiring that the matter fields are subject to the dominant energy condition, we establish the lower bound $(4\pi)^{-1} \kappa {\cal A}$ for the total mass $M$ of a static, spherically symmetric black hole spacetime. (${\cal A}$ and $\kappa$ denote the area and the surface gravity of the horizon, respectively.) Together with the fact that the Komar integral provides a simple relation between $M - (4\pi)^{-1} \kappa A$ and the strong energy condition, this enables us to prove that the Schwarzschild metric represents the only static, spherically symmetric black hole solution of a selfgravitating matter model satisfying the dominant, but violating the strong energy condition for the timelike Killing field $K$ at every point, that is, $R(K,K) \leq 0$. Applying this result to scalar fields, we recover the fact that the only black hole configuration of the spherically symmetric Einstein-Higgs model with arbitrary non-negative potential is the Schwarzschild spacetime with constant Higgs field. In the presence of electromagnetic fields, we also derive a stronger bound for the total mass, involving the electromagnetic potentials and charges. Again, this estimate provides a simple tool to prove a ``no-hair'' theorem for matter fields violating the strong energy condition.Comment: 16 pages, LATEX, no figure

Are there static texture?

We consider harmonic maps from Minkowski space into the three sphere. We are especially interested in solutions which are asymptotically constant, i.e. converge to the same value in all directions of spatial infinity. Physical 3-space can then be compactified and can be identified topologically (but not metrically!) with a three sphere. Therefore, at fixed time, the winding of the map is defined. We investigate whether static solutions with non-trivial winding number exist. The answer which we can proof here is only partial: We show that within a certain family of maps no static solutions with non-zero winding number exist. We discuss the existing static solutions in our family of maps. An extension to other maps or a proof that our family of maps is sufficiently general remains an open problem.Comment: 12 page Latex file, 1 postscript figure, submitted to PR

Calibrated Sub-Bundles in Non-Compact Manifolds of Special Holonomy

This paper is a continuation of math.DG/0408005. We first construct special Lagrangian submanifolds of the Ricci-flat Stenzel metric (of holonomy SU(n)) on the cotangent bundle of S^n by looking at the conormal bundle of appropriate submanifolds of S^n. We find that the condition for the conormal bundle to be special Lagrangian is the same as that discovered by Harvey-Lawson for submanifolds in R^n in their pioneering paper. We also construct calibrated submanifolds in complete metrics with special holonomy G_2 and Spin(7) discovered by Bryant and Salamon on the total spaces of appropriate bundles over self-dual Einstein four manifolds. The submanifolds are constructed as certain subbundles over immersed surfaces. We show that this construction requires the surface to be minimal in the associative and Cayley cases, and to be (properly oriented) real isotropic in the coassociative case. We also make some remarks about using these constructions as a possible local model for the intersection of compact calibrated submanifolds in a compact manifold with special holonomy.Comment: 20 pages; for Revised Version: Minor cosmetic changes, some paragraphs rewritten for improved clarit

Immunomodulator expression in trophoblasts from the feline immunodeficiency virus (FIV)-infected cat

<p>Abstract</p> <p>Background</p> <p>FIV infection frequently compromises pregnancy under experimental conditions and is accompanied by aberrant expression of some placental cytokines. Trophoblasts produce numerous immunomodulators that play a role in placental development and pregnancy maintenance. We hypothesized that FIV infection may cause dysregulation of trophoblast immunomodulator expression, and aberrant expression of these molecules may potentiate inflammation and compromise pregnancy. The purpose of this project was to evaluate the expression of representative pro-(TNF-α, IFN-γ, IL-1β, IL-2, IL-6, IL-12p35, IL-12p40, IL-18, and GM-CSF) and anti-inflammatory cytokines (IL-4, IL-5, and IL-10); CD134, a secondary co-stimulatory molecule expressed on activated T cells (FIV primary receptor); the chemokine receptor CXCR4 (FIV co-receptor); SDF-1α, the chemokine ligand to CXCR4; and FIV gag in trophoblasts from early-and late-term pregnancy.</p> <p>Methods</p> <p>We used an anti-cytokeratin antibody in immunohistochemistry to identify trophoblasts selectively, collected these cells using laser capture microdissection, and extracted total RNA from the captured cell populations. Real time, reverse transcription-PCR was used to quantify gene expression.</p> <p>Results</p> <p>We detected IL-4, IL-5, IL-6, IL-1β, IL-12p35, IL-12p40, and CXCR4 in trophoblasts from early-and late-term pregnancy. Expression of cytokines increased from early to late pregnancy in normal tissues. A clear, pro-inflammatory microenvironment was not evident in trophoblasts from FIV-infected queens at either stage of pregnancy. Reproductive failure was accompanied by down-regulation of both pro-and anti-inflammatory cytokines. CD134 was not detected in trophoblasts, and FIV gag was detected in only one of ten trophoblast specimens collected from FIV-infected queens.</p> <p>Conclusion</p> <p>Feline trophoblasts express an array of pro-and anti-inflammatory immunomodulators whose expression increases from early to late pregnancy in normal tissues. Non-viable pregnancies were associated with decreased expression of immunomodulators which regulate trophoblast invasion in other species. The detection of FIV RNA in trophoblasts was rare, suggesting that the high rate of reproductive failure in FIV-infected queens was not a direct result of viral replication in trophoblasts. The influence of placental immune cells on trophoblast function and pregnancy maintenance in the FIV-infected cat requires additional study.</p

Is diagnosis enough to guide interventions in mental health? Using case formulation in clinical practice

While diagnosis has traditionally been viewed as an essential concept in medicine, particularly when selecting treatments, we suggest that the use of diagnosis alone may be limited, particularly within mental health. The concept of clinical case formulation advocates for collaboratively working with patients to identify idiosyncratic aspects of their presentation and select interventions on this basis. Identifying individualized contributing factors, and how these could influence the person\u27s presentation, in addition to attending to personal strengths, may allow the clinician a deeper understanding of a patient, result in a more personalized treatment approach, and potentially provide a better clinical outcome.<br /

Examining the Evidence Base for Forensic Case Formulation: An Integrative Review of Recent Research

In the past decade, forensic case formulation (FCF) has become a key activity in many forensic services. However, the evidence base for FCF remains limited. This integrative review aimed to identify and evaluate all FCF research conducted since the lack of understanding within this field was highlighted by several academics in 2011. A rigorous literature search led to the identification of 14 studies fitting the inclusion criteria. Studies were critically evaluated and synthesised to create a summary of the recent research, to identify remaining gaps in our understanding, and to create an agenda for future research

QCD Strings as Constrained Grassmannian Sigma Model:

We present calculations for the effective action of string world sheet in R3 and R4 utilizing its correspondence with the constrained Grassmannian sigma model. Minimal surfaces describe the dynamics of open strings while harmonic surfaces describe that of closed strings. The one-loop effective action for these are calculated with instanton and anti-instanton background, reprsenting N-string interactions at the tree level. The effective action is found to be the partition function of a classical modified Coulomb gas in the confining phase, with a dynamically generated mass gap.Comment: 22 pages, Preprint: SFU HEP-116-9

Controllability on infinite-dimensional manifolds

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.Comment: 19 pages, 1 figur

Constant-angle surfaces in liquid crystals

We discuss some properties of surfaces in R3 whose unit normal has constant angle with an assigned direction field. The constant angle condition can be rewritten as an Hamilton-Jacobi equation correlating the surface and the direction field. We focus on examples motivated by the physics of interfaces in liquid crystals and of layered fluids, and discuss the properties of the constant-angle surfaces when the direction field is singular along a line (disclination) or at a point (hedgehog defect