On computation of the first Baues--Wirsching cohomology of a freely-generated small category

The Baues--Wirsching cohomology is one of the cohomologies of a small category. Our aim is to describe the first Baues--Wirsching cohomology of the small category generated by a finite quiver freely. We consider the case where the coefficient is a natural system obtained by the composition of a functor and the target functor. We give an algorithm to obtain generators of the vector space of inner derivations. It is known that there exists a surjection from the vector space of derivations of the small category to the first Baues--Wirsching cohomology whose kernel is the vector space of inner derivations.Comment: 11 page

A guide to performing skin-prick testing in practice: tips and tricks of the trade

Atopy can manifest in childhood as infantile eczema (atopic dermatitis), allergic rhinitis and asthma. In practice, it is critical to identify the offending allergen in atopic individuals. This will not only influence therapeutic interventions, but may also have a significant impact on the individual’s quality of life. The most common clinical test for allergy detection is the introduction of an allergen directly into the skin in the form of a skin-prick test. Skin-prick testing is recommended in the diagnostic workup for allergies because it is reliable, safe, convenient, inexpensive, minimally invasive, and has the advantage of multiple allergen testing in one, 15- to 20-minute, test. Skin-prick testing can be performed from birth onwards. Although there is a small risk of developing anaphylaxis, the test remains safe to perform in a consultation room or at the patient’s bedside. Worldwide, a skin-prick test remains the test of choice for allergy because of its convenience and cost-effectiveness. A globally accepted guideline for skin-prick testing is still lacking and would be beneficial to both patient and physician.Keywords: allergy, indications, contraindications, cut-off points, measurement

Aspects of Diffeomorphism and Conformal invariance in classical Liouville theory

The interplay between the diffeomorphism and conformal symmetries (a feature common in quantum field theories) is shown to be exhibited for the case of black holes in two dimensional classical Liouville theory. We show that although the theory is conformally invariant in the near horizon limit, there is a breaking of the diffeomorphism symmetry at the classical level. On the other hand, in the region away from the horizon, the conformal symmetry of the theory gets broken with the diffeomorphism symmetry remaining intact.Comment: Accepted in Euro. Phys. Letters., Title changed, abstract modified, major modifications made in the pape

The value of pimecrolimus in improving quality of life of children with severe eczema – an open non-randomised study

Background: Atopic eczema is a common skin condition. It has the potential to severely impair quality of life in affected children. Pimecrolimus is currently registered for mild-moderate eczema but in clinical practice children with more severe disease are often treated with this therapy in an attempt to find a safe addition to long-term topical corticosteroid usage. The aim of this study was to test the value of pimecrolimus in improving quality of life in children with severe atopic eczema.Methods: This a single site, phase 4, non-randomised, open label trial of pimecrolimus use in children aged 4 months to 12 years living withmoderate to very severe atopic eczema. The study was conducted at Steve Biko Academic Hospital. Patients with unsatisfactorily controlled disease despite conventional topical therapy, adequate use of emollients, allergen avoidance and non-pharmacological skin hygiene were enrolled. A ParentIndex Quality of Life Questionnaire was completed by parents before and three months after using pimecrolimus.Results: A total of 24 patients were recruited, 20 of whom completed the study. Ninety per cent of patients had co-morbid asthma and allergicrhinitis. The Parent Index Quality of Life demonstrated a mean 33% score improvement after the use of pimecrolimus. There was an attendant reduction in cost of therapy to these patients.Conclusions: Pimecrolimus usage should be extended to patients with more severe atopic eczema as the improvement in quality of life is important and demonstrable.Keywords: severe eczema; topical steroids; calcineurin inhibitors; pimecrolimus; quality of lif

Supersymmetric Quantum Mechanics for String-Bits

We develop possible versions of supersymmetric single particle quantum mechanics, with application to superstring-bit models in view. We focus principally on space dimensions $d=1,2,4,8$, the transverse dimensionalities of superstring in $3,4,6,10$ space-time dimensions. These are the cases for which ``classical'' superstring makes sense, and also the values of $d$ for which Hooke's force law is compatible with the simplest superparticle dynamics. The basic question we address is: When is it possible to replace such harmonic force laws with more general ones, including forces which vanish at large distances? This is an important question because forces between string-bits that do not fall off with distance will almost certainly destroy cluster decomposition. We show that the answer is affirmative for $d=1,2$, negative for $d=8$, and so far inconclusive for $d=4$.Comment: 17 pages, Late

Effects of the background radiation on radio pulsar and supernova remnant searches and the birth rates of these objects

In different directions of the Galaxy the Galactic background radio radiation and radiation of complex star formation regions which include large number of OB associations have different influences on radio pulsar (PSR) and supernova remnant (SNR) searches. In this work we analyse the effects of these background radiations on the observations of PSRs at 1400 MHz and SNRs at 1000 MHz. In the interval l=0$^o$$\pm60^o$ the PSRs with flux F$_{1400}$$>$0.2 mJy and the SNRs with surface brightness $\Sigma$$>10^{-21}$ Wm$^{-2}$Hz$^{-1}$sr$^{-1}$ are observable for all values of l and b. All the SNRs with $\Sigma$$>3\times10^{-22}$ Wm$^{-2}$Hz$^{-1}$sr$^{-1}$ can be observed in the interval 60$^o$$<$l$<300^o$. We have examined samples of PSRs and SNRs to estimate the birth rates of these objects in the region up to 3.2 kpc from the Sun and also in the Galaxy. The birth rate of PSRs is about one in 200 years and the birth rate of SNRs is about one in 65 years in our galaxy.Comment: revised versio

Complete solution of a constrained tropical optimization problem with application to location analysis

We present a multidimensional optimization problem that is formulated and solved in the tropical mathematics setting. The problem consists of minimizing a nonlinear objective function defined on vectors over an idempotent semifield by means of a conjugate transposition operator, subject to constraints in the form of linear vector inequalities. A complete direct solution to the problem under fairly general assumptions is given in a compact vector form suitable for both further analysis and practical implementation. We apply the result to solve a multidimensional minimax single facility location problem with Chebyshev distance and with inequality constraints imposed on the feasible location area.Comment: 20 pages, 3 figure