Functions of One Complex Variable

Fundamental theory: Holomorphic functions and domains of holomorphy Implicit functions and analytic sets The Poincare, Cousin, and Runge problems Pseudoconvex domains and pseudoconcave sets Holomorphic mappings Theory of analytic spaces: Ramified domains Analytic sets and holomorphic functions Analytic spaces Normal pseudoconvex spaces Bibliography Index.

Function theory in several complex variables

With the development of a new generation of hydroxyethyl starches (HES), there has been renewed interest in their clinical potential. High doses of first- and second-generation HES were associated with adverse effects on renal function, coagulation, and tissue storage, thereby limiting their clinical applicability. Newer HES products have lower molar substitution and in vivo molecular weight, resulting in more rapid metabolism and clearance. In this review article, the differences between HES generations are highlighted, with particular emphasis on the improved safety profile of the third generation products. These improvements have been achieved with no loss of efficacy, and they contradict the assumption that efficacy of HES solutions is directly linked to plasma concentration. The impact of source material on structure and pharmacokinetics is highlighted, and the role of the carrier solution is critically assessed.

Hydroxyethyl starches: different products--different effects.

Itch is the most frequent symptom in dermatology and has been researched more extensively in recent years. Nevertheless, there are few true epidemiological studies on itch. The aim of this paper is to review the current state of research on the epidemiology of chronic itch in Western and non-Western populations. The electronic databases PubMed, Medline and the Cochrane Library were searched. Conference proceedings and national and international studies were included. It is difficult to compare existing studies due to differing methodology and lack of standardized measures. The symptom of itch is a challenge, not only to clinicians, but also within the structure of regional health systems, and with regards to accessibility to specialized medical doctors in non-Western countries. Published studies show that the symptom of itch is highly prevalent; it should therefore receive adequate attention from physicians and other healthcare providers, including healthcare planners.

Epidemiology of itch: adding to the burden of skin morbidity.

Hypothesis Safety differences exist among colloids widely used for fluid management in acutely ill patients, as judged according to the comparative incidence of adverse events. Data Sources Colloid safety data for human subjects were sought, without language or time period restrictions, by means of computer searches of bibliographic and clinical trial databases, hand searches of medical journals and Index Medicus, inquiries with investigators and colloid suppliers, and examination of reference lists. Search terms included "colloids", "morbidity", and "mortality". Study Selection Controlled trials, cohort studies, pharmacovigilance studies, and prior meta-analyses were independently selected by 2 unblinded investigators. Of 189 candidate studies, 113 were included, with safety data encompassing 1.54 × 10 6 patients and 1.09 × 10 8 colloid infusions. Data Extraction Two unblinded investigators independently extracted data. Study limitations and confounding factors were tabulated. Data Synthesis With albumin as the reference colloid, the incidence rate ratio for anaphylactoid reactions was 4.51 (95% confidence interval, 2.06-9.89) after hydroxyethyl starch administration, 2.32 (95% confidence interval, 1.21-4.45) after dextran, and 12.4 (95% confidence interval, 6.40-24.0) after gelatin. Pruritus occurrence was significantly increased by hydroxyethyl starch exposure (odds ratio, 1.78; 95% confidence interval, 1.23-2.58). Artificial colloid administration was consistently associated with coagulopathy and clinical bleeding, most frequently in cardiac surgery patients receiving hydroxyethyl starch. On the basis of large-scale pharmacovigilance study results, albumin infusion resulted in a low rate of both total adverse events (3.1 to 8.6 per 10 5 infusions) and serious adverse events (1.29 per 10 6 infusions). Conclusions Significant safety differences exist among colloids. Therefore, conclusions regarding the clinical usefulness of colloids as a fluid class should be formed with caution.

https://jamanetwork.com/journals/jamasurgery/articlepdf/396679/srv3001.pdf

A Systematic Review of the Comparative Safety of Colloids

We prove a Schwarz lemma for a domain
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in ℂ3 that arises in connection with a problem in H∞ control theory. We describe a class of automorphisms of
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and determine the distinguished boundary of
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We apply our Schwarz lemma to a special case of the μ-synthesis problem.

A Schwarz Lemma for a domain related to μ-synthesis

We prove a Schwarz lemma for a domain E in 3-dimensional complex space that arises in connection with a problem in H infinity control theory. We describe a class of automorphisms of E and determine the distinguished boundary of E. We obtain a type of Schwarz-Pick lemma for a two by two mu-synthesis problem.

A Schwarz lemma for a domain related to mu-synthesis

We study the structure of weakly compact homomorphisms between Banach algebras. In particular, it is shown that between many pairs of algebras, the only weakly compact homomorphisms are those of finite rank

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Weakly compact homomorphisms

with the convention that, in the definition of σ(x), eigenvalues are counted according to multiplicity. This paper is devoted to a study of holomorphic maps F : Ω→ Ω, where Ω = {x ∈Mn : ρ(x) < 1}. We are motivated by two considerations. One is the natural desire to extend results about bounded domains to unbounded ones; for Ω it turns out that some do carry over, though in a ‘spectral’ way. The other is to determine whether the automorphisms of Ω are transitive. For if this were the case, then Nevanlinna iteration could be used to solve the spectral Nevanlinna-Pick problem (see [2]), a special case of the problem of μ-synthesis, which is of much interest to control theorists. Unfortunately, as we show in Theorem 4, the automorphism group of Ω is very far from being transitive.

Holomorphic Self‐Maps of the Spectral unit Ball

In this paper we study classes of projective, injective and flat modules over Banach algebras and introduce a numerical invariant for these modules. In particular we consider when the inclusion from a uniform algebra to the algebra of continuous functions on its Shilov boundary is a flat homomorphism.

Michael C. White

Papers

A Schwarz Lemma for a domain related to μ-synthesis

A Schwarz lemma for a domain related to mu-synthesis

Weakly compact homomorphisms

Holomorphic Self‐Maps of the Spectral unit Ball

Injective Modules for Uniform Algebras