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We consider a quasilinear Neumann problem with exponent p is an element of]1, +infinity[, in a multidomain of R-N, N greater than or equal to 2, consisting of two vertical cylinders, one placed upon the other: the first one with given height and small cross section, the other one with small height and given cross section. Assuming that the volumes of the two cylinders tend to zero with same rate, we prove that the limit problem is well posed in the union of the limit domains, with respective dimension 1 and N - 1. Moreover, this limit problem is coupled if p > N - 1 and uncoupled if 1 < p less than or equal to N - 1., QC 20100525

The author, who was a student and colleague of Harold S. Shapiro, gives some personal memories from Shapiro's time as a professor at KTH, Stockholm, 1972-2021., QC 20220301

Starting from a Lagrangian action functional for two scalar fields we construct, by variational methods, the Laplacian Green function for a bounded domain and an appropriate stress tensor. By a further variation, imposed by a given vector field, we arrive at an interior version of the Hadamard variational formula, previously considered by P. Garabedian. It gives the variation of the Green function in terms of a pairing between the stress tensor and a strain tensor in the interior of the domain, this contrasting the classical Hadamard formula which is expressed as a pure boundary variation., QC 20220121

We give a new proof of Dennis Hejhal's theorem on the nondegeneracy of the matrix that appears in the identity relating the Bergman and Szego kernels of a smoothly bounded finitely connected domain in the plane. Mergelyan's theorem is at the heart of the argument. We explore connections of Hejhal's theorem to properties of the zeroes of the Szego kernel and propose some ideas to better understand Hejhal's original theorem., QC 20220110

We set up general equations of motion for point vortex systems on closed Riemannian surfaces, allowing for the case that the sum of vorticities is not zero and there hence must be counter-vorticity present. The dynamics of global circulations which is coupled to the dynamics of the vortices is carefully taken into account. Much emphasis is put to the study of vortex pairs, having the Kimura conjecture in focus. This says that vortex pairs move, in the dipole limit, along geodesic curves, and proofs for it have previously been given by S. Boatto and J. Koiller by using Gaussian geodesic coordinates. In the present paper, we reach the same conclusion by following a slightly different route, leading directly to the geodesic equation with a reparametrized time variable. In a final section, we explain how vortex motion in planar domains can be seen as a special case of vortex motion on closed surfaces., QC 20220715

QC 20220215

The basic definitions and properties related to the Polubarinova-Galin and the Lowner-Kufarev equations are set up. This includes discussing subordinations and liftings to Riemann surfaces., Part of book: 978-3-030-69863-8, 978-3-030-69862-1 (Print)QC 20210518

Laplacian growth and partial balayage are extended to Riemann surfaces. The Riemann surfaces considered are more precisely covering surfaces of the complex plane, and the somewhat abstract theory is illustrated by examples. It is also shown that the partial balayage, which represents time evolution, commutes with the covering projection in a natural sense., Part of book: 978-3-030-69863-8, 978-3-030-69862-1 (Print)QC 20210518

Weak solutions, of variational inequality type, are introduced. Their defining properties can be equivalently expressed in terms of quadrature identities for subharmonic functions, or in terms of partial balayage. Some versions of inverse balayage are also discussed, this needed as a preparatory step for constructing more general Laplacian evolutions. Finally, the exponential transform and the elimination function are introduced., Part of book: 978-3-030-69863-8, 978-3-030-69862-1 (Print)QC 20210518

The major assertion (Theorem 5.1) in this chapter is that starting Laplacian growth from any simply connected planar domain with smooth boundary, the solution, in a weak form, can be continued forever as an evolution of simply connected domains. The price for keeping the domains simply connected is that the solution must be allowed to go up on a branched Riemann surface above the complex plane, a Riemann surface which is not known in advance and has to be created along with the solution. The proof of Theorem 5.1 depends on several technical lemmas, one of which (Lemma/Conjecture 5.3) is stated as a conjecture. There is no real doubt concerning the validity of that lemma/conjecture, but at present a rigorous proof is missing., Part of book: 978-3-030-69863-8, 978-3-030-69862-1 (Print)QC 20210518

This chapter gives an overview of the main themes of the book., Part of book: 978-3-030-69863-8, 978-3-030-69862-1 (Print)QC 20210518

Part of book: 978-3-030-69863-8, 978-3-030-69862-1 (Print)QC 20210518

The Polubarinova-Galin is identified with what is called the string equation in contexts of integrable hierarchies. In the non-univalent case the string equation requires further specification. We discuss the arising difficulties in this respect and illustrate by some examples., ISBN: 978-3-030-69863-8; 978-3-030-69862-1, QC 20210503

Several examples of Laplacian evolutions of a cardioid are given. One is the standard univalent evolution of the conformal map, while the others represent nonunivalent evolutions. One of these actually represents, in a certain sense, the suction case. Finally, a general discussion of injection contra suction from a Riemann surface perspective is given., ISBN: 978-3-030-69863-8; 978-3-030-69862-1, QC 20210503

We discuss the string equation in some more depth in cases when all but finitely many moments vanish. This assumption amounts to the domain being a quadrature Riemann surface of a certain form, and it allows for a rigorous treatment of the problems involved. It applies in particular to the case of polynomial mapping functions, in which case the treatment becomes fully algebraic and involves an explicit formula for the Jacobi determinant for the map from coefficients to harmonic moments., Part of book: ISBN 978-3-030-69863-8; 978-3-030-69862-1Not duplicate with DiVA 1466789QC 20230202

We formulate the dependence of the conformal map on harmonic moments and other parameters within a Hamiltonian framwork and by systematically using differential forms and other concept from differential geometry. This gives alternative ways of expressing Poisson brackets and the string equation., 978-3-030-69863-8; 978-3-030-69862-1, QC 20210503

The behaviour of such Riemann surface weak solutions for which the derivative of the conformal map is a rational function is investigated. The solution stays on the same form locally, as long as the zeros of the mentioned derivative stay away from the unit circle. However, when such zeros do reach the unit circle and new branch points are created, the rational function changes its structure, acquiring new zeros and poles. Two approaches for handling these questions are used: one direct approach and one via quadrature Riemann surfaces., ISBN: 978-3-030-69863-8; 978-3-030-69862-1, QC 20210503

The exponential orthogonal polynomials encode via the theory of hyponormal operators a shade function g supported by a bounded planar shape. We prove under natural regularity assumptions that these complex polynomials satisfy a three term relation if and only if the underlying shape is an ellipse carrying uniform black on white. More generally, we show that a finite term relation among these orthogonal polynomials holds if and only if the first row in the associated Hessenberg matrix has finite support. This rigidity phenomenon is in sharp contrast with the theory of classical complex orthogonal polynomials. On function theory side, we offer an effective way based on the Cauchy transforms of to decide whether a (d + 2)-term relation among the exponential orthogonal polynomials exists; in that case we indicate how the shade function g can be reconstructed from a resulting polynomial of degree d and the Cauchy transform of g. A discussion of the relevance of the main concepts in Hele-Shaw dynamics completes the article., QC 20200310

For conformal maps defined in the unit disk one can define a certain Poisson bracket that involves the harmonic moments of the image domain. When this bracket is applied to the conformal map itself together with its conformally reflected map the result is identically one. This is called the string equation, and it is closely connected to the governing equation, the Polubarinova-Galin equation, for the evolution of a Hele-Shaw blob of a viscous fluid (or, by another name, Laplacian growth). For non-univalent analytic functions the Poisson bracket may become ambiguous, hence the string equation need not make sense. In the present paper we show that for a certain class of (non-univalent) rational functions related to quadrature Riemann surfaces, the string equation does make sense, and holds., QC 20200914

Introduction: Inflammation is an important risk-associated component of many diseases and can be diagnosed by molecular imaging of specific molecules. The aim of this study was to evaluate the possibility of targeting adhesion molecules on inflammation-activated endothelial cells and macrophages using an innovative multimodal polyvinyl alcohol-based microbubble (MB) contrast agent developed for diagnostic use in ultrasound, magnetic resonance, and nuclear imaging. Methods: We assessed the binding efficiency of antibody-conjugated multimodal contrast to inflamed murine or human endothelial cells (ECs), and to peritoneal macrophages isolated from rats with peritonitis, utilizing the fluorescence characteristics of the MBs. Single-photon emission tomography (SPECT) was used to illustrate 99m Tc-labeled MB targeting and distribution in an experimental in vivo model of inflammation. Results: Flow cytometry and confocal microscopy showed that binding of antibody-targeted MBs to the adhesion molecules ICAM-1, VCAM-1, or E-selectin, expressed on cytokine-stimulated ECs, was up to sixfold higher for human and 12-fold higher for mouse ECs, compared with that of non-targeted MBs. Under flow conditions, both VCAM-1- and E-selectin-targeted MBs adhered more firmly to stimulated human ECs than to untreated cells, while VCAM-1-targeted MBs adhered best to stimulated murine ECs. SPECT imaging showed an approximate doubling of signal intensity from the abdomen of rats with peritonitis, compared with healthy controls, after injection of anti-ICAM-1-MBs. Conclusions: This novel multilayer contrast agent can specifically target adhesion molecules expressed as a result of inflammatory stimuli in vitro, and has potential for use in disease-specific multimodal diagnostics in vivo using antibodies against targets of interest., QC 20190313

In resonance with a recent geometric framework proposed by Douglas and Yang, we develop a functional model for certain linear bounded operators with rank-one self-commutator acting on a Hilbert space. By taking advantage of the refined existing theory of the principal function of a hyponormal operator, we transfer the whole action outside the spectrum, on the resolvent of the underlying operator, localized at a distinguished vector. The whole construction turns out to rely on an elementary algebra body involving analytic multipliers and Cauchy transforms. We propose a natural field theory interpretation of the resulting resolvent functional model., QC 20190426

We formulate the equations for point vortex dynamics on a closed two-dimensional Riemannian manifold in the language of affine and other kinds of connections. This can be viewed as a relaxation of standard approaches, using the Riemannian metric directly, to an approach based more on local coordinates provided with a minimal amount of extra structure. The speed of a vortex is then expressed in terms of the difference between an affine connection derived from the coordinate Robin function and the Levi-Civita connection associated with the Riemannian metric. A Hamiltonian formulation of the same dynamics is also given. The relevant Hamiltonian function consists of two main terms. One of the terms is the well-known quadratic form based on a matrix whose entries are Green and Robin functions, while the other term describes the energy contribution from those circulating flows which are not implicit in the Green functions. One main issue of the paper is a detailed analysis of the somewhat intricate exchanges of energy between these two terms of the Hamiltonian. This analysis confirms the mentioned dynamical equations formulated in terms of connections. This article is part of the theme issue 'Topological and geometrical aspects ofmass and vortex dynamics'., QC 20191022

Stem cells are considered the origin of neoplasms in general, and malignant tumours in particular, and the stage at which the stem cells stop their differentiation determines the degree of malignancy. However, there is increasing evidence supporting an alternative paradigm. Tumours may develop by dedifferentiation from mature cells able to proliferate. Studies of gastric carcinogenesis demonstrate that mature neuroendocrine (NE) cells upon long-term overstimulation may develop through stages of hyperplasia, dysplasia, and rather benign tumours, into highly malignant carcinomas. Dedifferentiation of cells may change the histological appearance and impede the identification of the cellular origin, as seen with gastric carcinomas, which in many cases are dedifferentiated neuroendocrine tumours. Finding the cell of origin is important to identify risk factors for cancer, prevent tumour development, and tailor treatment. In the present review, we focus not only on gastric tumours, but also evaluate the role of neuroendocrine cells in tumourigenesis in two other foregut-derived organs, the lungs and the pancreas, as well as in the midgut-derived small intestine.

A general theory of partial balayage on Riemannian manifolds is developed, with emphasis on compact manifolds. Partial balayage is an operation of sweeping measures, or charge distributions, to a prescribed density, which then is attained on an a priori unknown set. It is closely related to (construction of) quadrature domains for subharmonic functions, to weighted equilibrium distributions and, as for methods used, to the obstacle problem. Several examples are given in the paper, as well as some specific results. For instance, it is proved that, in two dimensions, harmonic and geodesic balls are the same if and only if the Gaussian curvature of the manifold is constant. © 2017 Elsevier Masson SAS, QC 20201002

Cauchy and exponential transforms are characterized, and constructed, as canonical holomorphic sections of certain line bundles on the Riemann sphere defined in terms of the Schwarz function. A well known natural connection between Schwarz reflection and line bundles defined on the Schottky double of a planar domain is briefly discussed in the same context., QC 20180719

For conformal maps defined in the unit disk one can define a certain Poisson bracket that involves the harmonic moments of the image domain. When this bracket is applied to the conformal map itself together with its conformally reflected map the result is identically one. This is called the string equation, and it is closely connected to the governing equation, the Polubarinova–Galin equation, for the evolution of a Hele-Shaw blob of a viscous fluid (or, by another name, Laplacian growth). In the present paper we show that the string equation makes sense and holds for general polynomials., QC 20190404

Stem cells are considered the origin of neoplasms in general, and malignant tumours in particular, and the stage at which the stem cells stop their differentiation determines the degree of malignancy. However, there is increasing evidence supporting an alternative paradigm. Tumours may develop by dedifferentiation from mature cells able to proliferate. Studies of gastric carcinogenesis demonstrate that mature neuroendocrine (NE) cells upon long-term overstimulation may develop through stages of hyperplasia, dysplasia, and rather benign tumours, into highly malignant carcinomas. Dedifferentiation of cells may change the histological appearance and impede the identification of the cellular origin, as seen with gastric carcinomas, which in many cases are dedifferentiated neuroendocrine tumours. Finding the cell of origin is important to identify risk factors for cancer, prevent tumour development, and tailor treatment. In the present review, we focus not only on gastric tumours, but also evaluate the role of neuroendocrine cells in tumourigenesis in two other foregut-derived organs, the lungs and the pancreas, as well as in the midgut-derived small intestine.

Stem cells are considered the origin of neoplasms in general, and malignant tumours in particular, and the stage at which the stem cells stop their differentiation determines the degree of malignancy. However, there is increasing evidence supporting an alternative paradigm. Tumours may develop by dedifferentiation from mature cells able to proliferate. Studies of gastric carcinogenesis demonstrate that mature neuroendocrine (NE) cells upon long-term overstimulation may develop through stages of hyperplasia, dysplasia, and rather benign tumours, into highly malignant carcinomas. Dedifferentiation of cells may change the histological appearance and impede the identification of the cellular origin, as seen with gastric carcinomas, which in many cases are dedifferentiated neuroendocrine tumours. Finding the cell of origin is important to identify risk factors for cancer, prevent tumour development, and tailor treatment. In the present review, we focus not only on gastric tumours, but also evaluate the role of neuroendocrine cells in tumourigenesis in two other foregut-derived organs, the lungs and the pancreas, as well as in the midgut-derived small intestine.

Stem cells are considered the origin of neoplasms in general, and malignant tumours in particular, and the stage at which the stem cells stop their differentiation determines the degree of malignancy. However, there is increasing evidence supporting an alternative paradigm. Tumours may develop by dedifferentiation from mature cells able to proliferate. Studies of gastric carcinogenesis demonstrate that mature neuroendocrine (NE) cells upon long-term overstimulation may develop through stages of hyperplasia, dysplasia, and rather benign tumours, into highly malignant carcinomas. Dedifferentiation of cells may change the histological appearance and impede the identification of the cellular origin, as seen with gastric carcinomas, which in many cases are dedifferentiated neuroendocrine tumours. Finding the cell of origin is important to identify risk factors for cancer, prevent tumour development, and tailor treatment. In the present review, we focus not only on gastric tumours, but also evaluate the role of neuroendocrine cells in tumourigenesis in two other foregut-derived organs, the lungs and the pancreas, as well as in the midgut-derived small intestine.

Stem cells are considered the origin of neoplasms in general, and malignant tumours in particular, and the stage at which the stem cells stop their differentiation determines the degree of malignancy. However, there is increasing evidence supporting an alternative paradigm. Tumours may develop by dedifferentiation from mature cells able to proliferate. Studies of gastric carcinogenesis demonstrate that mature neuroendocrine (NE) cells upon long-term overstimulation may develop through stages of hyperplasia, dysplasia, and rather benign tumours, into highly malignant carcinomas. Dedifferentiation of cells may change the histological appearance and impede the identification of the cellular origin, as seen with gastric carcinomas, which in many cases are dedifferentiated neuroendocrine tumours. Finding the cell of origin is important to identify risk factors for cancer, prevent tumour development, and tailor treatment. In the present review, we focus not only on gastric tumours, but also evaluate the role of neuroendocrine cells in tumourigenesis in two other foregut-derived organs, the lungs and the pancreas, as well as in the midgut-derived small intestine.

The basic definitions of the exponential transform EΩ(z, w) of a planar domain Ω⊂ ℂ and various functions derived from it are recorded in this chapter. The exponential moments having the exponential transform as the generating function are introduced. In addition, several positivity properties of the exponential transform are established. Finally, it is shown that the exponential transform, as a function of z with w kept fixed, can be characterized as being (part of) the unique holomorphic section of a certain line bundle over the Riemann sphere taking a prescribed value at infinity, or alternatively as being the unique solution of a corresponding Riemann-Hilbert problem., QC 20171017

This chapter offers an overview of the main interlacing themes, with emphasis on historical development and identification of the original sources. When looking at a picture through a mathematical lens, several intrinsic inner skeletons pop up. They are sometimes called in a suggestive and colorful way the “mother body”, or “madonna body”, or “the ridge”, or “caustic” of the original picture. Geometric or analytic features characterize these skeletons, but in general they remain very shy, displaying their shapes and qualitative features only after challenging technical obstacles are resolved. For example, the natural skeleton of a disk is its center, the interval between the foci of an ellipse stands out as a canonical ridge. For reasons to be discussed in these notes, the internal bisector segments in a triangle form its “mother body”. Disagreement starts with a sector of a disk, where the “bodies” (maternal, madonna type, or the one proposed below) are different. In the scenario outlined in these notes, a disjoint union of disks has their centers as a natural skeleton., QC 20171101

By interpreting the exponential orthogonal polynomials as characteristic polynomials of finite central truncations of the underlying hyponormal operator one opens a vast toolbox of Hilbert space geometry methods. In particular we prove in this chapter that trace class modifications of the hyponormal operator attached to a domain will not alter the convex hull of the support of any cluster point of the count in measures of the roots of the orthogonal polynomials. As a sharp departure from the case of complex orthogonal polynomials associated to a Lebesgue space we prove that the convex hull of these supports is not affected by taking the union of an open set with a disjoint quadrature domain. However, similar to the case of Bergman orthogonal polynomials, we prove that the exponential orthogonal polynomials satisfy a three term relation only in the case of an ellipse. Some general perturbation theory arguments are collected in the last section., QC 20171017

The positivity properties of the exponential transform define in a canonical way a Hilbert space ℋ(Ω) and a (co)hyponormal operator acting on it, such that the exponential transform itself appears as a polarized compressed resolvent of this operator. There are many variants of this procedure, but they are all equivalent. Historically the process actually went in the opposite direction starting with an abstract Hilbert space and hyponormal operator with rank one self-commutator, the exponential transform arose as a natural characteristic function obtained as the determinant of the multiplicative commutator of the resolvent. If one considers ℋ(Ω) as a function space, the analytic functions in it are very weak, i.e., have a small norm, and for a special class of domains, the quadrature domains, the analytic subspace, ℋa(Ω), even collapses to a finite dimensional space. Some more general kinds of quadrature domains are discussed in terms of analytic functionals, and we also show that some integral operators based on the exponential transform can be interpreted in terms of Silva-Köthe-Grothendieck duality., QC 20171016

In this chapter we present the results of our numerical experiments concerning zeros of exponential polynomials, with pictures indicating asymptotic distributions (or, at least, the distribution of the first 50–100 zeros). We also make the corresponding theoretical construction of mother bodies, and compare the two. In many cases there are reasonable, but far from perfect, agreements between the sets where zeros seem to accumulate and the supports of the corresponding mother bodies. And here we reach terra incognito as there is no agreement between the densities: they seem rather to be complementary to each other. In one case we have complete results, with theoretical proofs, namely for the ellipse. Taking a standard ellipse with foci ± 1, the zeros go to the focal segment, with density proportional to (Forumala prsented).while the mother body for the ellipse with uniform mass distribution has density (Forumala prsented). on the same segment., QC 20171101

We outline the general theory for a certain kind of potential theoretic skeletons, or ‘mother bodies’, associated to a given domain. The hope is, generally speaking, that such skeletons can be identified as attractors for zeros of orthogonal polynomials, and in a few cases such expectations have indeed been met, theoretically and/or experimentally. For the exponential polynomials the success is rather limited so far, but by building in enough flexibility in the models one expects in some not so distant future to reach a reasonable matching. In the present chapter we set up desirable properties (formulated as ‘axioms’) to be satisfied by mother bodies. Since the search for potential theoretic skeletons is a highly ill-posed problem (related to the Cauchy problem for an elliptic operator) very few domains admit mother bodies, but for domains with piecewise algebraic boundaries there is a rather constructive and efficient theory, bearing in mind that the same class of domains is also amenable for studying zeros of orthogonal polynomials., QC 20171017

This chapter contains some initial results, obtained by direct or classical methods, on the zeros of the exponential orthogonal polynomials. For example, we estimate the decay of coefficients of orthogonal expansion by using a result of J.L. Walsh and we prove that the zeros always stay in the convex hull of the closure of the domain. In addition, we identify the zeros as also being eigenvalues of the appropriate Hessenberg matrices, and we elaborate this connection further in the case of quadrature domains., QC 20171017

Two classical quantizations of planar shapes, via Toeplitz operators acting on Bergman space, respectively Hardy-Smirnov space, are briefly compared to the new hyponormal quantization developed in these lecture notes., QC 20171027

Using longitudinal national register data, we investigated labor-market attachment during the years 1993-1995 in Sweden for persons aged 25-35 years who had been in out-of-home care before the age of 18 in Sweden during the 1960s, 1970s, and 1980s. We consider whether an immigrant background has an additional influence on labor-market attachment. Compared to majority population peers, young persons who had been in foster care had shorter educations. Fewer had a strong labor-market attachment and more were dependent on social assistance. Results from multinomial regression models indicated that having been in foster care during childhood reduced the probability of high attachment to the labor-market and increased the probability of social assistance dependency, even after making adjustments for education, marital status, parenthood, domicile, and birth country. Few signs of additive effects from being both an immigrant and a former foster child are found.

In high-income countries, not completing secondary school often entails a high risk of social exclusion. Using data on young adults born in 1985 who grew up in metropolitan Sweden, we study factors associated with not graduating from upper-secondary school at age 21. Our hypothesis is that if a young person sees examples of people who are not able to earn a living despite having a long education, such negative examples are influential. Results from estimated logistic models are consistent with the hypothesis.

In this paper, we investigate to what degree young adults live in neighbourhoods that are similar, in terms of relative average household income, to the neighbourhoods in which they grew up. We use regression analysis on register data for all individuals who were born in 1974 and lived in metropolitan Sweden in both 1990 and 2006. During this period, the distribution of income in Sweden became far more unequal, unemployment rose dramatically, earlier housing policies were dismantled, the share of ‘visible minorities’ increased dramatically, and residential segregation increased very considerably. We find a correlation between average neighbourhood incomes at these two points in the sample's life cycle of 0.44, which is more than three times as high as the household income correlation. We also find that half of the children of ‘visible minorities’ grew up in the poorer quartile of neighbourhoods, and of these, almost two-thirds remained in the poorest quartile of neighbourhoods as adults. Several measures indicate that intergenerational persistency in context is lower in metropolitan Sweden than was found in a similar study in the US. However, it appears that if visible minority individuals lived in a neighbourhood in the lowest part of the distribution in Sweden as a child, the probability that they will do so also as adults is as high as the corresponding probability for an African-American person in the US.

We give an overview of some recent developments concerning harmonic and other moments of plane domains, their relationship to the Cauchy and exponential transforms, and to the meromorphic resultant and elimination function. The paper also connects to certain topics in mathematical physics, for example domain deformations generated by harmonic gradients (Laplacian growth) and related integrable structures., QC 20140113

QC 20150414

We give an overview of some recent developments concerning harmonic and other moments of plane domains, their relationship to the Cauchy and exponential transforms, and to the meromorphic resultant and elimination function. The paper also connects to certain topics in mathematical physics, for example domain deformations generated by harmonic gradients (Laplacian growth) and related integrable structures., QC 20140113

Vi lever idag i ett samhälle där goda prestationer är viktiga eftersom de utgör hur andra individer uppmärksammar oss, vilket är avgörande för att känna sig accepterad. Samtidigt ställs det höga krav på att kunna föra sig inom olika sociala interaktioner och framstå som en social individ med en tillhörighet. Det är något som är särskilt påtagligt för barn och ungdomar eftersom de befinner sig i en utvecklingsperiod där relationen till sin omgivning spelar en betydande roll. Detta är något som inte alla individer klarar av vilket kan resultera i att dem utvecklar social fobi som är vanligt i dagens samhälle och som kan medföra olika svårigheter om man inte får behandling. Syftet med studien är att se på vilket sätt terapeuter inom kognitiv beteendeterapi samt lösningsfokuserad korttidsterapis syn på social fobi hos barn och ungdomar under 18 år påverkar deras behandlingsarbete med dessa individer. Studien baseras på empiri från verksamma terapeuter inom de olika områdena. Resultatet visar att de olika terapiformerna har olika sociala konstruktioner av problemen och studien innehåller en redogörelse för hur det påverkar behandlingen i den kognitiva beteendeterapin och den lösningsfokuserade korttidsterapin., We live today in a society were good results are important, because they are a part of how other individuals judge us, which is crucial if we want to feel accepted by our society. At the same time we must be able to behave correctly in different social interactions and stand out as a social individual who has an affiliation. This is particularly evident when it comes to small children and adolescents due to that they are in a crucial stage in their development were their relationship with their social environment is important. Not all individuals can handle the pressure and could therefore develop social phobia, a common illness in our society, which could result in a number of different difficulties for the affected if not treated. The aim of this study is to examine how therapists within cognitive behavioral therapy and solution focused brief therapy view on social phobia amongst children and adolescents under the age of 18 affect their treatment with these individuals. The study is based on the empiricism we received from active therapist within the different form of therapies. The result shows that cognitive behavioral therapy and solution focused brief therapy has different social constructions of the illness social phobia and it also includes a report about how this affect their treatment.

We give an overview of some recent developments concerning harmonic and other moments of plane domains, their relationship to the Cauchy and exponential transforms, and to the meromorphic resultant and elimination function. The paper also connects to certain topics in mathematical physics, for example domain deformations generated by harmonic gradients (Laplacian growth) and related integrable structures., QC 20140113

We give an overview of some recent developments concerning harmonic and other moments of plane domains, their relationship to the Cauchy and exponential transforms, and to the meromorphic resultant and elimination function. The paper also connects to certain topics in mathematical physics, for example domain deformations generated by harmonic gradients (Laplacian growth) and related integrable structures., QC 20140113

Vi lever idag i ett samhälle där goda prestationer är viktiga eftersom de utgör hur andra individer uppmärksammar oss, vilket är avgörande för att känna sig accepterad. Samtidigt ställs det höga krav på att kunna föra sig inom olika sociala interaktioner och framstå som en social individ med en tillhörighet. Det är något som är särskilt påtagligt för barn och ungdomar eftersom de befinner sig i en utvecklingsperiod där relationen till sin omgivning spelar en betydande roll. Detta är något som inte alla individer klarar av vilket kan resultera i att dem utvecklar social fobi som är vanligt i dagens samhälle och som kan medföra olika svårigheter om man inte får behandling. Syftet med studien är att se på vilket sätt terapeuter inom kognitiv beteendeterapi samt lösningsfokuserad korttidsterapis syn på social fobi hos barn och ungdomar under 18 år påverkar deras behandlingsarbete med dessa individer. Studien baseras på empiri från verksamma terapeuter inom de olika områdena. Resultatet visar att de olika terapiformerna har olika sociala konstruktioner av problemen och studien innehåller en redogörelse för hur det påverkar behandlingen i den kognitiva beteendeterapin och den lösningsfokuserade korttidsterapin., We live today in a society were good results are important, because they are a part of how other individuals judge us, which is crucial if we want to feel accepted by our society. At the same time we must be able to behave correctly in different social interactions and stand out as a social individual who has an affiliation. This is particularly evident when it comes to small children and adolescents due to that they are in a crucial stage in their development were their relationship with their social environment is important. Not all individuals can handle the pressure and could therefore develop social phobia, a common illness in our society, which could result in a number of different difficulties for the affected if not treated. The aim of this study is to examine how therapists within cognitive behavioral therapy and solution focused brief therapy view on social phobia amongst children and adolescents under the age of 18 affect their treatment with these individuals. The study is based on the empiricism we received from active therapist within the different form of therapies. The result shows that cognitive behavioral therapy and solution focused brief therapy has different social constructions of the illness social phobia and it also includes a report about how this affect their treatment.

We give an overview of some recent developments concerning harmonic and other moments of plane domains, their relationship to the Cauchy and exponential transforms, and to the meromorphic resultant and elimination function. The paper also connects to certain topics in mathematical physics, for example domain deformations generated by harmonic gradients (Laplacian growth) and related integrable structures., QC 20140113

We study the dynamics of roots of f'(zeta, t), where F(zeta, t) is a locally univalent polynomial solution of the Polubarinova-Galin equation for the evolution of the conformal map onto a Hele-Shaw blob subject to injection at one point. We give examples of the sometimes complicated motion of roots, but show also that the asymptotic behavior is simple. More generally we allow f'(zeta, t) to be a rational function and give sharp estimates for the motion of poles and for the decay of the Taylor coefficients. We also prove that any global in time locally univalent solution actually has to be univalent., QC 20130419