Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

인공고관절의 세라믹 볼 헤드의 기계적 안정성 평가를 위한 3 차원 유한요소 해석

The Geometry Of Fractal Sets

This paper presents an opportunity for the uncertainty that has plagued the novel's criticism to appear as absences in the body of historical knowledge, particularly regarding the notion of life after death. Taking appearance (eg. proof of existence), as opposed to disappearance, as a universally accepted value allows this analysis to interrogate the novel's logic in relation to a variety of conventional systems whose very existence depends on the reproduction of their systems. The ineffectuality of Foucauldian disciplinary institutions in the novel establishes the threat of nonexistence. A significant relationship to Dante's Inferno is rendered, lending the appearance of language an 'enchanted' value through allusions to Dante's intentional invocation of Augustinian corporeal vision. The novel's metalanguage appears enchanted by the body of historical knowledge, particularly as the product of capitalism, discipline and Judeo-Christianity, and programmed by literary precursors William S. Burroughs, Gertrude Stein and Ernest Hemingway. Foregrounded by this complex network, an analysis of the novel’s first chapter demonstrates how an attention to appearance brings the language to life and draws the narrator, equally invested in appearance, into its realm of representation.

Will To Appear

First published in 1202, Fibonacci's "Liber abaci" was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe.Its author, Leonardo Pisano, known today as Fibonacci, was a citizen of Pisa, an active maritime power, with trading outposts on the Barbary Coast and other points in the Muslim Empire. As a youth Fibonacci was instructed in mathematics in one of these outposts he continued his study of mathematics while traveling extensively on business and developed contacts with scientists throughout the Mediterranean world. A member of the academic court around the Emperor Frederick II, Leonardo saw clearly the advantages for both commerce and scholarship of the Hindu positional number system and the algebraic methods developed by al-Khwarizmi and other Muslim scientists.Though it is known as an introduction to the Hindu number system and the algorithms of arithmetic that children now learn in grade school, "Liber abaci" is much more: an encyclopaedia of thirteenth-century mathematics, both theoretical and practical. It develops the tools rigorously, establishing them with Euclidean geometric proofs, and then shows how to apply them to all kinds of situations in business and trade - conversion of measures and currency, allocations of profit, computation of interest, alloying of currencies, and so forth. It is rigorous mathematics, well applied, and vividly described. As the first translation into a modern language of the "Liber abaci", this book will be of interest not only to historians of science, but to all mathematicians and mathematics teachers interested in the origins of their methods.

https://jps.library.utoronto.ca/index.php/aestimatio/article/download/25709/18857

Fibonacci's Liber Abaci: A Translation into Modern English of Leonardo Pisano's Book of Calculation

Let f be a transcendental meromorphic function and denote by J(f) the Julia set and by I(f) the escaping set. We show that if f has a direct singularity over infinity, then I(f) has an unbounded component and I(f)∩J(f) contains continua. Moreover, under this hypothesis I(f)∩J(f) has an unbounded component if and only if f has no Baker wandering domain. If f has a logarithmic singularity over infinity, then the upper box dimension of I(f)∩J(f) is 2 and the Hausdorff dimension of J(f) is strictly greater than 1. The above theorems are deduced from more general results concerning functions which have ‘direct or logarithmic tracts’, but which need not be meromorphic in the plane. These results are obtained by using a generalization of Wiman–Valiron theory. This method is also applied to complex differential equations.

Dynamics of meromorphic functions with direct or logarithmic singularities

We show that if a meromorphic function has a direct singularity over infinity, then the escaping set has an unbounded component and the intersection of the escaping set with the Julia set contains continua. This intersection has an unbounded component if and only if the function has no Baker wandering domains. We also give estimates of the Hausdorff dimension and the upper box dimension of the Julia set of a meromorphic function with a logarithmic singularity over infinity. The above theorems are deduced from more general results concerning functions which have "direct or logarithmic tracts", but which need not be meromorphic in the plane. These results are obtained by using a generalization of Wiman-Valiron theory. The method is also applied to complex differential equations.

The dynamical behaviour of a transcendental entire function in any periodic component of the Fatou set is well understood. Here we study the dynamical behaviour of a transcendental entire function $f$ in any multiply connected wandering domain $U$ of $f$. By introducing a certain positive harmonic function $h$ in $U$, related to harmonic measure, we are able to give the first detailed description of this dynamical behaviour. Using this new technique, we show that, for sufficiently large $n$, the image domains $U_n=f^n(U)$ contain large annuli, $C_n$, and that the union of these annuli acts as an absorbing set for the iterates of $f$ in $U$. Moreover, $f$ behaves like a monomial within each of these annuli and the orbits of points in $U$ settle in the long term at particular `levels' within the annuli, determined by the function $h$. We also discuss the proximity of $\partial U_n$ and $\partial C_n$ for large $n$, and the connectivity properties of the components of $U_n \setminus \bar{C_n}$. These properties are deduced from new results about the behaviour of an entire function which omits certain values in an annulus.

Multiply connected wandering domains of entire functions

The dynamical behaviour of a transcendental entire function in any periodic component of the Fatou set is well understood. Here we study the dynamical behaviour of a transcendental entire function $f$ in any multiply connected wandering domain $U$ of $f$. By introducing a certain positive harmonic function $h$ in $U$, related to harmonic measure, we are able to give the first detailed description of this dynamical behaviour. Using this new technique, we show that, for sufficiently large $n$, the image domains $U_n=f^n(U)$ contain large annuli, $C_n$, and that the union of these annuli acts as an absorbing set for the iterates of $f$ in $U$. Moreover, $f$ behaves like a monomial within each of these annuli and the orbits of points in $U$ settle in the long term at particular `levels' within the annuli, determined by the function $h$. We also discuss the proximity of $\partial U_n$ and $\partial C_n$ for large $n$, and the connectivity properties of the components of $U_n \setminus \overline{C_n}$. These properties are deduced from new results about the behaviour of entire functions that omit certain values in an annulus.

We prove a form of the cos πρ theorem which gives strong estimates for the minimum modulus of a transcendental entire function of order zero. We also prove a generalisation of a result of Hinkkanen that gives a sufficient condition for a transcendental entire function to have no unbounded Fatou components. These two results enable us to show that there is a large class of entire functions of order zero which have no unbounded Fatou components. On the other hand, we give examples which show that there are in fact functions of order zero which not only fail to satisfy Hinkkanen’s condition but also fail to satisfy our more general condition. We also give a new regularity condition that is sufficient to ensure that a transcendental entire function of order less than 1/2 has no unbounded Fatou components. Finally, we observe that all the conditions given here which guarantee that a transcendental entire function has no unbounded Fatou components also guarantee that the escaping set is connected, thus answering a question of Eremenko for such functions.

Philip J. Rippon

Papers

Dynamics of meromorphic functions with direct or logarithmic singularities

Dynamics of meromorphic functions with direct or logarithmic singularities

Multiply connected wandering domains of entire functions

Multiply connected wandering domains of entire functions

Functions of small growth with no unbounded Fatou components