Carsten Lunde Petersen

Bio: Carsten Lunde Petersen is an academic researcher from Roskilde University. The author has contributed to research in topics: Julia set & Filled Julia set. The author has an hindex of 9, co-authored 43 publications receiving 416 citations. Previous affiliations of Carsten Lunde Petersen include Technical University of Denmark.

Local connectivity of some Julia sets containing a circle with an irrational rotation

Abstract: The Fatou set FR for a rational map R: C--*C is the set of points z c C possessing a neighbourhood on which the family of iterates {R n }n~>o is normal (in the sense of Montel). The Julia set JR=C--FR is the complement of the Fatou set. (The monographs [CG], [Be], [St] provide introductions to the theory of iteration of rational maps.) Let 0E ]0, 1 [ Q be an irrational number and write it as a continued fraction

On the Julia set of a typical quadratic polynomial with a Siegel disk

Abstract: Let 0 << 1 be an irrational number with continued fraction expan- sion =( a1 ;a 2 ;a 3 ;::: ), and consider the quadratic polynomial P : z 7! e 2i z +z 2 . By performing a trans-quasiconformal surgery on an associated Blaschke product model, we prove that if log an = O( p n )a sn !1 ; then the Julia set of P is locally-connected and has Lebesgue measure zero. In particular, it follows that for almost every 0 << 1, the quadratic P has a Siegel disk whose boundary is a Jordan curve passing through the critical point of P.B y standard renormalization theory, these results generalize to the quadratics which have Siegel disks of higher periods.

Identification of two Nereis virens (Annelida: Polychaeta) cytochromes P450 and induction by xenobiotics

Abstract: Cytochrome P450 (CYP) enzyme catalysed metabolism of xenobiotics such as polycyclic aromatic hydrocarbons (PAHs) are known to occur in polychaetes. Yet specific polychaete CYP enzymes have so far not been identified. Here, we report two partial CYP cDNA sequences, both of 453 bp, characterised from Nereis virens. These are the first CYP sequences reported in annelids. The deduced amino acid sequences both share highest identities to mammalian CYP4F enzymes (61% and 58%), indicating membership of the CYP4 family (accordingly, referred to as CYP41 and CYP42, respectively). The CYP42 gene expression was significantly higher in vehicle controls (corn oil) compared to untreated controls. Clofibrate increased the expression of the CYP42 genes. The induction by clofibrate and corn oil indicates regulatory similarities to vertebrate CYP4 enzymes, which are primarily involved in the metabolism of endogenous compounds such as fatty acids. Crude oil and benz(a)anthracene significantly induced CYP42 gene expression 2.6-fold, and because CYP enzymes often are induced by their own substrates, this induction may indicate involvement of N. virens CYP4 enzymes in the detoxification of environmental contaminants such as PAHs. The present study demonstrates that these N. virens CYP genes are transcriptionally inducible, and suggests that N. virens CYP4 enzymes may be involved in the metabolism of both exogenous and endogenous compounds.

On The Notions of Mating

Abstract: The different notions of matings of pairs of equal degree polynomials are introduced and are related to each other as well as known results on matings. The possible obstructions to matings are identified and related. Moreover the relations between the polynomials and their matings are discussed and proved. Finally holomorphic motion properties of slow-mating are proved.

Polycyclic aromatic hydrocarbon (PAH) ecotoxicology in marine ecosystems.

Abstract: Low levels of oil and hence polycyclic aromatic hydrocarbons (PAHs) are naturally present in the marine environment, although levels have increased significantly following human extraction and use of oil and gas. Other major anthropogenic sources of PAHs include smelters, the use of fossil fuels in general, and various methods of waste disposal, especially incineration. There are two major sources for PAHs to marine ecosystems in Norway: the inshore smelter industry, and offshore oil and gas production activities. A distinction is generally made between petrogenic (oil-derived) and pyrogenic (combustion-derived) PAHs. Although petrogenic PAHs appear to be bioavailable to a large extent, pyrogenic PAHs are often associated with soot particles and less available for uptake into organisms. There is extensive evidence linking sediment-associated PAHs to induction of phase-I enzymes, development of DNA adducts, and eventually neoplastic lesions in fish. Most studies have focused on high-molecular-weight, carci...

Real and Complex Analysis. By W. Rudin. Pp. 412. 84s. 1966. (McGraw-Hill, New York.)

Abstract: Preface Prologue: The Exponential Function Chapter 1: Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures Arithmetic in [0, ] Integration of positive functions Integration of complex functions The role played by sets of measure zero Exercises Chapter 2: Positive Borel Measures Vector spaces Topological preliminaries The Riesz representation theorem Regularity properties of Borel measures Lebesgue measure Continuity properties of measurable functions Exercises Chapter 3: Lp-Spaces Convex functions and inequalities The Lp-spaces Approximation by continuous functions Exercises Chapter 4: Elementary Hilbert Space Theory Inner products and linear functionals Orthonormal sets Trigonometric series Exercises Chapter 5: Examples of Banach Space Techniques Banach spaces Consequences of Baire's theorem Fourier series of continuous functions Fourier coefficients of L1-functions The Hahn-Banach theorem An abstract approach to the Poisson integral Exercises Chapter 6: Complex Measures Total variation Absolute continuity Consequences of the Radon-Nikodym theorem Bounded linear functionals on Lp The Riesz representation theorem Exercises Chapter 7: Differentiation Derivatives of measures The fundamental theorem of Calculus Differentiable transformations Exercises Chapter 8: Integration on Product Spaces Measurability on cartesian products Product measures The Fubini theorem Completion of product measures Convolutions Distribution functions Exercises Chapter 9: Fourier Transforms Formal properties The inversion theorem The Plancherel theorem The Banach algebra L1 Exercises Chapter 10: Elementary Properties of Holomorphic Functions Complex differentiation Integration over paths The local Cauchy theorem The power series representation The open mapping theorem The global Cauchy theorem The calculus of residues Exercises Chapter 11: Harmonic Functions The Cauchy-Riemann equations The Poisson integral The mean value property Boundary behavior of Poisson integrals Representation theorems Exercises Chapter 12: The Maximum Modulus Principle Introduction The Schwarz lemma The Phragmen-Lindelof method An interpolation theorem A converse of the maximum modulus theorem Exercises Chapter 13: Approximation by Rational Functions Preparation Runge's theorem The Mittag-Leffler theorem Simply connected regions Exercises Chapter 14: Conformal Mapping Preservation of angles Linear fractional transformations Normal families The Riemann mapping theorem The class L Continuity at the boundary Conformal mapping of an annulus Exercises Chapter 15: Zeros of Holomorphic Functions Infinite Products The Weierstrass factorization theorem An interpolation problem Jensen's formula Blaschke products The Muntz-Szas theorem Exercises Chapter 16: Analytic Continuation Regular points and singular points Continuation along curves The monodromy theorem Construction of a modular function The Picard theorem Exercises Chapter 17: Hp-Spaces Subharmonic functions The spaces Hp and N The theorem of F. and M. Riesz Factorization theorems The shift operator Conjugate functions Exercises Chapter 18: Elementary Theory of Banach Algebras Introduction The invertible elements Ideals and homomorphisms Applications Exercises Chapter 19: Holomorphic Fourier Transforms Introduction Two theorems of Paley and Wiener Quasi-analytic classes The Denjoy-Carleman theorem Exercises Chapter 20: Uniform Approximation by Polynomials Introduction Some lemmas Mergelyan's theorem Exercises Appendix: Hausdorff's Maximality Theorem Notes and Comments Bibliography List of Special Symbols Index

Marine invertebrate cytochrome P450: Emerging insights from vertebrate and insect analogies

Abstract: Cytochrome P450 enzymes (P450s) are responsible for the oxidative metabolism of a plethora of endogenous and exogenous substrates. P450s and associated activities have been demonstrated in numerous marine invertebrates belonging to the phyla Cnidaria, Annelida (Polychaeta), Mollusca, Arthropoda (Crustacea) and Echinodermata. P450s of marine invertebrates and vertebrates show considerable sequence divergence and the few orthologs reveal the selective constraint on physiologically significant enzymes. P450s are present in virtually all tissues of marine invertebrates, although high levels usually are found in hepatic-like organs and steroidogenic tissues. High-throughput technologies result in the rapid acquisition of new marine invertebrate P450 sequences; however, the understanding of their function is poor. Based on analogy to vertebrates and insects, it is likely that P450s play a pivotal role in the physiology of marine invertebrates by catalyzing the biosynthesis of signal molecules including steroids such as 20-hydroxyecdysone (the molting hormone of crustaceans). The metabolism of many exogenous compounds including benzo(a)pyrene (BaP), pyrene, ethoxyresorufin, ethoxycoumarin and aniline is mediated by P450 enzymes in tissues of marine invertebrates. P450 gene expression, protein levels and P450 mediated metabolism of xenobiotics are induced by PAHs in some marine invertebrate species. Thus, regulation of P450 enzyme activity may play a central role in the adaptation of animals to environmental pollutants. Emphasis should be put on the elucidation of the function and regulation of the ever-increasing number of marine invertebrate P450s.