On the algebra of AkA^k-functions

summary:For a domain $\Omega \subset {\mathbb{C}}^n$ let $H(\Omega )$ be the holomorphic functions on $\Omega$ and for any $k\in \mathbb{N}$ let $A^k(\Omega )=H(\Omega )\cap C^k(\overline{\Omega })$. Denote by ${\mathcal{A}}_D^k(\Omega )$ the set of functions $f\: \Omega \rightarrow [0,\infty )$ with the property that there exists a sequence of functions $f_j\in A^k(\Omega )$ such that $\lbrace |f_j|\rbrace$ is a nonincreasing sequence and such that $f(z)=\lim _{j\rightarrow \infty }|f_j(z)|$. By ${\mathcal{A}}_I^k(\Omega )$ denote the set of functions $f\: \Omega \rightarrow (0,\infty )$ with the property that there exists a sequence of functions $f_j\in A^k(\Omega )$ such that $\lbrace |f_j|\rbrace$ is a nondecreasing sequence and such that $f(z)=\lim _{j\rightarrow \infty }|f_j(z)|$. Let $k\in \mathbb{N}$ and let $\Omega _1$ and $\Omega _2$ be bounded $A^k$-domains of holomorphy in $\mathbb{C}^{m_1}$ and $\mathbb{C}^{m_2}$ respectively. Let $g_1\in {\mathcal{A}}_D^k(\Omega _1)$, $g_2\in {\mathcal{A}}_I^k(\Omega _1)$ and $h\in {\mathcal{A}}_D^k(\Omega _2)\cap {\mathcal{A}}_I^k(\Omega _2)$. We prove that the domains $\Omega =\left\rbrace (z,w)\in \Omega _1\times \Omega _2\: g_1(z)<h(w)<g_2(z)\right\lbrace$ are $A^k$-domains of holomorphy if $\mathop {\mathrm int}\overline{\Omega }=\Omega$. We also prove that under certain assumptions they have a Stein neighbourhood basis and are convex with respect to the class of $A^k$-functions. If these domains in addition have $C^1$-boundary, then we prove that the $A^k$-corona problem can be solved. Furthermore we prove two general theorems concerning the projection on ${\mathbb{C}}^n$ of the spectrum of the algebra $A^k$

Spelar förtroendet någon roll? : Vid valet av K2 eller K3-reglerna

The Swedish Accounting Standards Board has developed rules of simplification to unlisted companies in Sweden. This project is called the K-project and is divided into four different categories, K1-K4, after the different companies’ size and legal form. The K-project was put together to develop how the ongoing reporting should be ended with an annual report. 2013 is the year to choose between K2 and K3-regulations in smaller, unlisted companies. Therefore, we wonder if the choice between those regulations will affect the trust in the relationship between the business management and the accounting consultant and/or the auditor. We used the trust theory because a lot of the companies outsourced both their ongoing accounting and/or their financial statement, the companies don’t always think that competence is within the company and some companies must use an auditor. Because of that we will find out how the companies trust is affected for the consultant or/and the auditor. To find out how the trust is in the company we did a qualitative study because we want to create a discussion about the trust, we need to describe it. We made a case study because we don’t want to compare K2 and K3-regulations with each other; we just like to use the regulations as our case. We decided to collect our data by interviewing ten persons in different companies and different branches. Our conclusion is that our companies don’t want to make any decisions about the regulation choice and they feel trust towards the consultant or auditor to make the decision. The trust is affected by the consultants or auditors honesty and wants them to tell both positive and negative things about the new accounting regulations.Bokföringsnämnden har utvecklat förenklingsregler för onoterade företag i Sverige, detta projekt kallas för K-projektet och är uppdelat i fyra olika kategorier, K1-K4, efter företagens storlek och associationsform. K-projektet utvecklades för att sammanställa reglerna för hur den löpande redovisningen ska avslutas med en årsredovisning. Mindre och onoterade aktiebolag ska under år 2013 välja om de ska tillämpa K2 eller K3-reglerna i sitt företag och vi har därmed valt att analysera företagsledningens förtroende för redovisningskonsulten och/eller revisorn i valet av dessa regler för att det är aktuellt under detta år. Vi valde att använda oss av förtroendeteorin därför att många företag outsourcar den löpande redovisningen och/eller bokslutet på grund av att den förmågan inte finns i företaget och för att en del aktiebolag är tvungna att använda sig av en revisor. Vi ville därför ta reda på hur förtroendet påverkas vid valet av K2 eller K3-reglerna. För att kunna få reda på vad som påverkar förtroendet valde vi att göra en kvalitativ undersökning eftersom vi ville skapa en diskussion kring förtroendet då det måste beskrivas. K-reglerna är relativt nya men vi ville inte jämföra dem med varandra utan vi valde K2 och K3-reglerna som vårt fall istället och därmed gjorde vi en fallstudie. Empirin samlade vi in genom att intervjua tio respondenter från mindre och onoterade aktiebolag inom olika branscher i närområdet. Vår slutsats visar att respondenterna vill att redovisningskonsulten eller revisorn ska fatta beslutet om företaget ska tillämpa K2 eller K3-reglerna därför att de känner förtroende för denna person sedan tidigare samarbeten. Förtroendet för konsulten eller revisorn påverkas av ärligheten hos personen eftersom företagsledningen är intresserad av det som är positivt och negativt inom redovisningen

Identification of the local stiffness reduction of a damaged composite plate using the virtual fields method

In the present study, a damage detection problem is formulated as the identification of the spatial stiffness distribution in a damaged composite plate. Full-field heterogeneous curvature fields obtained from an optical deflectometry technique are processed by using the virtual fields method adapted to retrieve the 2D stiffness distribution map of a damaged carbon-epoxy plate. The method not only picks up the location of the damage but also provides a fairly good estimate of the stiffness reduction in the damaged area. In this paper, the procedure is described, validated on simulated measurements and some initial experimental results are given. � 2007 Elsevier Ltd. All rights reserved

Comparative multifactorial analysis of the effects of idiopathic adolescent scoliosis and Scheuermann kyphosis on the self-perceived health status of adolescents treated with brace

Bracing is the most effective non-operative treatment for mild progressive spinal deformities in adolescence but it has shown a considerable impact on several aspects of adolescents’ functioning. This cross-sectional study investigated the self-perceived health status of adolescents with the two most common deformities, treated with body orthosis. Seventy-nine adolescents with spinal deformities (idiopathic adolescent scoliosis, thoracic Scheuermann kyphosis) and 62 adolescents without spinal deformities were asked to complete the Quality of Life profile for Spine Deformities Instrument. This study showed that adolescents with deformities are significantly less likely to have back pain in training than controls, but more likely to have difficulty in forward bending, and in the most common daily activities while in brace. These individuals claim they wake up because of back pain and feel quite nervous with the external appearance of their body. These patients face often problems with their relations with friends, while they reported difficulties in getting up from bed and sleep at night more often than their counterparts without deformities. As they grow older, patients feel increasing ashamed of their body, as they are more concerned about the future effect of the deformity on their body. As the bracing time increases, patients have much more probability than controls to get low back pain. Girls with deformity have a higher probability than boys to get low back pain while working in the house and while training. Individuals with larger spinal curvatures have more difficulties in bending and increased incidence of back pain than their counterparts with smaller curvatures. Psychological reasons associated mainly with relations at school and back pain are the main causes for low compliance in adolescents with spinal deformities treated with body orthosis. Careful instructions for all individuals who will undergo brace therapy, psychological support for all patients who develop psychological reactions and physical training particularly for older girls should be recommended to increase bracing compliance

Braces for idiopathic scoliosis in adolescents

STUDY DESIGN. Cochrane systematic review. OBJECTIVE. To evaluate the efficacy of bracing in adolescent patients with adolescent idiopathic scoliosis (AIS). SUMMARY OF BACKGROUND DATA. AIS is a 3-dimensional deformity of the spine. Although AIS can progress during growth and cause a surface deformity, it is usually not symptomatic. However, in adulthood, if the final spinal curvature surpasses a certain critical threshold, the risk of health problems and curve progression is increased. Braces are traditionally recommended to stop curvature progression in some countries and criticized in others. They generally need to be worn full time, with treatment extending over years. METHODS. The following databases (up to July 2008) were searched with no language limitations: the Cochrane Central Register of Controlled Trials, MEDLINE (from January 1966), EMBASE (from January 1980), and CINHAL (from January 1982), and reference lists of the articles. An extensive handsearch of the gray literature was also conducted. Randomized controlled trials (RCTs) and prospective cohort studies were searched for comparing braces with no treatment, other treatment, surgery, and different types of braces. Two review authors independently assessed trial quality and extracted data. RESULTS. We included 2 studies. There was very low quality evidence from 1 prospective cohort study with 286 girls that a brace curbed curve progression at the end of growth (success rate, 74 95% confidence interval {CI}: 52%-84%), better than observation (success rate, 34% 95% CI: 16%-49%) and electrical stimulation (success rate, 33% 95% CI: 12%-60%). There is low-quality evidence from 1 RCT with 43 girls that a rigid brace is more successful than an elastic one (SpineCor) at curbing curve progression when measured in Cobb degrees, but there were no significant differences between the 2 groups in the subjective perception of daily difficulties associated with wearing the brace. CONCLUSION. There is very low quality evidence in favor of using braces, making generalization very difficult. Further research could change the actual results and our confidence in them; in the meantime, patients' choices should be informed by multidisciplinary discussion. Future research should focus on short- and long-term patient-centered outcomes, in addition to measures such as Cobb angles. RCTs and prospective cohort studies should follow both the Scoliosis Research Society and Society on Scoliosis Orthopedic and Rehabilitation Treatment criteria for bracing studies. © 2010, Lippincott Williams & Wilkins